%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV570-1.043 : TPTP v9.0.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:35:41 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 714
% Syntax : Number of formulae : 1999 (1563 unt; 0 typ; 0 def)
% Number of atoms : 2451 (2442 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 597 ( 153 ~; 149 |; 0 &)
% ( 295 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 364 ( 364 usr; 354 con; 0-3 aty)
% Number of variables : 425 ( 410 !; 0 ?; 425 :)
% Comments :
%------------------------------------------------------------------------------
tff(elem_265_type,type,
elem_265: $i ).
tff(elem_262_type,type,
elem_262: $i ).
tff(select_type,type,
select: ( $i * $i ) > $i ).
tff(index_264_type,type,
index_264: $i ).
tff(earray_260_type,type,
earray_260: $i ).
tff(rselect_tail_type,type,
rselect_tail: $i > $i ).
tff(q42_type,type,
q42: $i ).
tff(store_type,type,
store: ( $i * $i * $i ) > $i ).
tff(e42_type,type,
e42: $i ).
tff(rselect_seq_type,type,
rselect_seq: $i > $i ).
tff(p_type,type,
p: $i > $i ).
tff(s_type,type,
s: $i > $i ).
tff(index_225_type,type,
index_225: $i ).
tff(rstore_tail_type,type,
rstore_tail: ( $i * $i ) > $i ).
tff(rstore_seq_type,type,
rstore_seq: ( $i * $i ) > $i ).
tff(earray_226_type,type,
earray_226: $i ).
tff(q43_type,type,
q43: $i ).
tff(index_228_type,type,
index_228: $i ).
tff(queue_227_type,type,
queue_227: $i ).
tff(queue_229_type,type,
queue_229: $i ).
tff(index_263_type,type,
index_263: $i ).
tff(earray_224_type,type,
earray_224: $i ).
tff(index_222_type,type,
index_222: $i ).
tff(queue_221_type,type,
queue_221: $i ).
tff(queue_223_type,type,
queue_223: $i ).
tff(index_261_type,type,
index_261: $i ).
tff(index_219_type,type,
index_219: $i ).
tff(earray_220_type,type,
earray_220: $i ).
tff(q41_type,type,
q41: $i ).
tff(q39_type,type,
q39: $i ).
tff(index_213_type,type,
index_213: $i ).
tff(q40_type,type,
q40: $i ).
tff(index_207_type,type,
index_207: $i ).
tff(earray_208_type,type,
earray_208: $i ).
tff(index_210_type,type,
index_210: $i ).
tff(queue_209_type,type,
queue_209: $i ).
tff(queue_211_type,type,
queue_211: $i ).
tff(earray_214_type,type,
earray_214: $i ).
tff(index_216_type,type,
index_216: $i ).
tff(queue_215_type,type,
queue_215: $i ).
tff(queue_217_type,type,
queue_217: $i ).
tff(index_195_type,type,
index_195: $i ).
tff(earray_196_type,type,
earray_196: $i ).
tff(q38_type,type,
q38: $i ).
tff(index_198_type,type,
index_198: $i ).
tff(queue_197_type,type,
queue_197: $i ).
tff(queue_199_type,type,
queue_199: $i ).
tff(q36_type,type,
q36: $i ).
tff(index_189_type,type,
index_189: $i ).
tff(q37_type,type,
q37: $i ).
tff(index_183_type,type,
index_183: $i ).
tff(earray_184_type,type,
earray_184: $i ).
tff(index_186_type,type,
index_186: $i ).
tff(queue_185_type,type,
queue_185: $i ).
tff(queue_187_type,type,
queue_187: $i ).
tff(earray_190_type,type,
earray_190: $i ).
tff(index_192_type,type,
index_192: $i ).
tff(queue_191_type,type,
queue_191: $i ).
tff(queue_193_type,type,
queue_193: $i ).
tff(index_177_type,type,
index_177: $i ).
tff(earray_178_type,type,
earray_178: $i ).
tff(q35_type,type,
q35: $i ).
tff(index_180_type,type,
index_180: $i ).
tff(queue_179_type,type,
queue_179: $i ).
tff(queue_181_type,type,
queue_181: $i ).
tff(q33_type,type,
q33: $i ).
tff(index_171_type,type,
index_171: $i ).
tff(q34_type,type,
q34: $i ).
tff(index_165_type,type,
index_165: $i ).
tff(earray_166_type,type,
earray_166: $i ).
tff(index_168_type,type,
index_168: $i ).
tff(queue_167_type,type,
queue_167: $i ).
tff(queue_169_type,type,
queue_169: $i ).
tff(earray_172_type,type,
earray_172: $i ).
tff(index_174_type,type,
index_174: $i ).
tff(queue_173_type,type,
queue_173: $i ).
tff(queue_175_type,type,
queue_175: $i ).
tff(index_159_type,type,
index_159: $i ).
tff(earray_160_type,type,
earray_160: $i ).
tff(q32_type,type,
q32: $i ).
tff(index_162_type,type,
index_162: $i ).
tff(queue_161_type,type,
queue_161: $i ).
tff(queue_163_type,type,
queue_163: $i ).
tff(q30_type,type,
q30: $i ).
tff(index_153_type,type,
index_153: $i ).
tff(q31_type,type,
q31: $i ).
tff(index_147_type,type,
index_147: $i ).
tff(earray_148_type,type,
earray_148: $i ).
tff(index_150_type,type,
index_150: $i ).
tff(queue_149_type,type,
queue_149: $i ).
tff(queue_151_type,type,
queue_151: $i ).
tff(earray_154_type,type,
earray_154: $i ).
tff(index_156_type,type,
index_156: $i ).
tff(queue_155_type,type,
queue_155: $i ).
tff(queue_157_type,type,
queue_157: $i ).
tff(index_141_type,type,
index_141: $i ).
tff(earray_142_type,type,
earray_142: $i ).
tff(q29_type,type,
q29: $i ).
tff(index_144_type,type,
index_144: $i ).
tff(queue_143_type,type,
queue_143: $i ).
tff(queue_145_type,type,
queue_145: $i ).
tff(q27_type,type,
q27: $i ).
tff(index_129_type,type,
index_129: $i ).
tff(q28_type,type,
q28: $i ).
tff(index_123_type,type,
index_123: $i ).
tff(earray_124_type,type,
earray_124: $i ).
tff(index_126_type,type,
index_126: $i ).
tff(queue_125_type,type,
queue_125: $i ).
tff(queue_127_type,type,
queue_127: $i ).
tff(earray_130_type,type,
earray_130: $i ).
tff(index_132_type,type,
index_132: $i ).
tff(queue_131_type,type,
queue_131: $i ).
tff(queue_133_type,type,
queue_133: $i ).
tff(index_117_type,type,
index_117: $i ).
tff(earray_118_type,type,
earray_118: $i ).
tff(q26_type,type,
q26: $i ).
tff(index_120_type,type,
index_120: $i ).
tff(queue_119_type,type,
queue_119: $i ).
tff(queue_121_type,type,
queue_121: $i ).
tff(q24_type,type,
q24: $i ).
tff(index_111_type,type,
index_111: $i ).
tff(q25_type,type,
q25: $i ).
tff(index_105_type,type,
index_105: $i ).
tff(earray_106_type,type,
earray_106: $i ).
tff(index_108_type,type,
index_108: $i ).
tff(queue_107_type,type,
queue_107: $i ).
tff(queue_109_type,type,
queue_109: $i ).
tff(earray_112_type,type,
earray_112: $i ).
tff(queue_115_type,type,
queue_115: $i ).
tff(index_114_type,type,
index_114: $i ).
tff(queue_113_type,type,
queue_113: $i ).
tff(index_99_type,type,
index_99: $i ).
tff(earray_100_type,type,
earray_100: $i ).
tff(q23_type,type,
q23: $i ).
tff(index_102_type,type,
index_102: $i ).
tff(queue_101_type,type,
queue_101: $i ).
tff(queue_103_type,type,
queue_103: $i ).
tff(q21_type,type,
q21: $i ).
tff(index_93_type,type,
index_93: $i ).
tff(q22_type,type,
q22: $i ).
tff(index_87_type,type,
index_87: $i ).
tff(earray_88_type,type,
earray_88: $i ).
tff(index_90_type,type,
index_90: $i ).
tff(queue_89_type,type,
queue_89: $i ).
tff(queue_91_type,type,
queue_91: $i ).
tff(earray_94_type,type,
earray_94: $i ).
tff(queue_97_type,type,
queue_97: $i ).
tff(index_96_type,type,
index_96: $i ).
tff(queue_95_type,type,
queue_95: $i ).
tff(index_81_type,type,
index_81: $i ).
tff(earray_82_type,type,
earray_82: $i ).
tff(q20_type,type,
q20: $i ).
tff(index_84_type,type,
index_84: $i ).
tff(queue_83_type,type,
queue_83: $i ).
tff(queue_85_type,type,
queue_85: $i ).
tff(q18_type,type,
q18: $i ).
tff(index_75_type,type,
index_75: $i ).
tff(q19_type,type,
q19: $i ).
tff(index_63_type,type,
index_63: $i ).
tff(earray_64_type,type,
earray_64: $i ).
tff(index_66_type,type,
index_66: $i ).
tff(queue_65_type,type,
queue_65: $i ).
tff(queue_67_type,type,
queue_67: $i ).
tff(earray_76_type,type,
earray_76: $i ).
tff(queue_79_type,type,
queue_79: $i ).
tff(index_78_type,type,
index_78: $i ).
tff(queue_77_type,type,
queue_77: $i ).
tff(index_57_type,type,
index_57: $i ).
tff(earray_58_type,type,
earray_58: $i ).
tff(q17_type,type,
q17: $i ).
tff(index_60_type,type,
index_60: $i ).
tff(queue_59_type,type,
queue_59: $i ).
tff(queue_61_type,type,
queue_61: $i ).
tff(q15_type,type,
q15: $i ).
tff(index_51_type,type,
index_51: $i ).
tff(q16_type,type,
q16: $i ).
tff(index_45_type,type,
index_45: $i ).
tff(earray_46_type,type,
earray_46: $i ).
tff(index_48_type,type,
index_48: $i ).
tff(queue_47_type,type,
queue_47: $i ).
tff(queue_49_type,type,
queue_49: $i ).
tff(earray_52_type,type,
earray_52: $i ).
tff(queue_55_type,type,
queue_55: $i ).
tff(index_54_type,type,
index_54: $i ).
tff(queue_53_type,type,
queue_53: $i ).
tff(index_39_type,type,
index_39: $i ).
tff(earray_40_type,type,
earray_40: $i ).
tff(q14_type,type,
q14: $i ).
tff(index_42_type,type,
index_42: $i ).
tff(queue_41_type,type,
queue_41: $i ).
tff(queue_43_type,type,
queue_43: $i ).
tff(q12_type,type,
q12: $i ).
tff(index_33_type,type,
index_33: $i ).
tff(q13_type,type,
q13: $i ).
tff(index_27_type,type,
index_27: $i ).
tff(earray_28_type,type,
earray_28: $i ).
tff(queue_31_type,type,
queue_31: $i ).
tff(index_30_type,type,
index_30: $i ).
tff(queue_29_type,type,
queue_29: $i ).
tff(earray_34_type,type,
earray_34: $i ).
tff(queue_37_type,type,
queue_37: $i ).
tff(index_36_type,type,
index_36: $i ).
tff(queue_35_type,type,
queue_35: $i ).
tff(index_21_type,type,
index_21: $i ).
tff(earray_22_type,type,
earray_22: $i ).
tff(q11_type,type,
q11: $i ).
tff(index_24_type,type,
index_24: $i ).
tff(queue_23_type,type,
queue_23: $i ).
tff(queue_25_type,type,
queue_25: $i ).
tff(q9_type,type,
q9: $i ).
tff(index_15_type,type,
index_15: $i ).
tff(q10_type,type,
q10: $i ).
tff(index_9_type,type,
index_9: $i ).
tff(earray_10_type,type,
earray_10: $i ).
tff(queue_13_type,type,
queue_13: $i ).
tff(index_12_type,type,
index_12: $i ).
tff(queue_11_type,type,
queue_11: $i ).
tff(earray_16_type,type,
earray_16: $i ).
tff(queue_19_type,type,
queue_19: $i ).
tff(index_18_type,type,
index_18: $i ).
tff(queue_17_type,type,
queue_17: $i ).
tff(index_255_type,type,
index_255: $i ).
tff(earray_256_type,type,
earray_256: $i ).
tff(q8_type,type,
q8: $i ).
tff(index_258_type,type,
index_258: $i ).
tff(queue_257_type,type,
queue_257: $i ).
tff(queue_259_type,type,
queue_259: $i ).
tff(q6_type,type,
q6: $i ).
tff(index_249_type,type,
index_249: $i ).
tff(q7_type,type,
q7: $i ).
tff(index_243_type,type,
index_243: $i ).
tff(earray_244_type,type,
earray_244: $i ).
tff(queue_247_type,type,
queue_247: $i ).
tff(index_246_type,type,
index_246: $i ).
tff(queue_245_type,type,
queue_245: $i ).
tff(earray_250_type,type,
earray_250: $i ).
tff(queue_253_type,type,
queue_253: $i ).
tff(index_252_type,type,
index_252: $i ).
tff(queue_251_type,type,
queue_251: $i ).
tff(index_237_type,type,
index_237: $i ).
tff(earray_238_type,type,
earray_238: $i ).
tff(q5_type,type,
q5: $i ).
tff(index_240_type,type,
index_240: $i ).
tff(queue_239_type,type,
queue_239: $i ).
tff(queue_241_type,type,
queue_241: $i ).
tff(q3_type,type,
q3: $i ).
tff(index_231_type,type,
index_231: $i ).
tff(q4_type,type,
q4: $i ).
tff(index_201_type,type,
index_201: $i ).
tff(earray_202_type,type,
earray_202: $i ).
tff(queue_205_type,type,
queue_205: $i ).
tff(index_204_type,type,
index_204: $i ).
tff(queue_203_type,type,
queue_203: $i ).
tff(earray_232_type,type,
earray_232: $i ).
tff(queue_235_type,type,
queue_235: $i ).
tff(index_234_type,type,
index_234: $i ).
tff(queue_233_type,type,
queue_233: $i ).
tff(index_135_type,type,
index_135: $i ).
tff(earray_136_type,type,
earray_136: $i ).
tff(q2_type,type,
q2: $i ).
tff(index_138_type,type,
index_138: $i ).
tff(queue_137_type,type,
queue_137: $i ).
tff(queue_139_type,type,
queue_139: $i ).
tff(q0_type,type,
q0: $i ).
tff(index_69_type,type,
index_69: $i ).
tff(q1_type,type,
q1: $i ).
tff(index_3_type,type,
index_3: $i ).
tff(earray_4_type,type,
earray_4: $i ).
tff(queue_7_type,type,
queue_7: $i ).
tff(index_6_type,type,
index_6: $i ).
tff(queue_5_type,type,
queue_5: $i ).
tff(earray_70_type,type,
earray_70: $i ).
tff(queue_73_type,type,
queue_73: $i ).
tff(index_72_type,type,
index_72: $i ).
tff(queue_71_type,type,
queue_71: $i ).
tff(rstore_head_type,type,
rstore_head: ( $i * $i ) > $i ).
tff(q_type,type,
q: $i ).
tff(index_0_type,type,
index_0: $i ).
tff(queue_1_type,type,
queue_1: $i ).
tff(rselect_head_type,type,
rselect_head: $i > $i ).
tff(e0_type,type,
e0: $i ).
tff(earray_2_type,type,
earray_2: $i ).
tff(e1_type,type,
e1: $i ).
tff(earray_68_type,type,
earray_68: $i ).
tff(e2_type,type,
e2: $i ).
tff(earray_134_type,type,
earray_134: $i ).
tff(e3_type,type,
e3: $i ).
tff(earray_200_type,type,
earray_200: $i ).
tff(e4_type,type,
e4: $i ).
tff(earray_230_type,type,
earray_230: $i ).
tff(e5_type,type,
e5: $i ).
tff(earray_236_type,type,
earray_236: $i ).
tff(e6_type,type,
e6: $i ).
tff(earray_242_type,type,
earray_242: $i ).
tff(e7_type,type,
e7: $i ).
tff(earray_248_type,type,
earray_248: $i ).
tff(e8_type,type,
e8: $i ).
tff(earray_254_type,type,
earray_254: $i ).
tff(e9_type,type,
e9: $i ).
tff(earray_8_type,type,
earray_8: $i ).
tff(e10_type,type,
e10: $i ).
tff(earray_14_type,type,
earray_14: $i ).
tff(e11_type,type,
e11: $i ).
tff(earray_20_type,type,
earray_20: $i ).
tff(e12_type,type,
e12: $i ).
tff(earray_26_type,type,
earray_26: $i ).
tff(e13_type,type,
e13: $i ).
tff(earray_32_type,type,
earray_32: $i ).
tff(e14_type,type,
e14: $i ).
tff(earray_38_type,type,
earray_38: $i ).
tff(e15_type,type,
e15: $i ).
tff(earray_44_type,type,
earray_44: $i ).
tff(e16_type,type,
e16: $i ).
tff(earray_50_type,type,
earray_50: $i ).
tff(e17_type,type,
e17: $i ).
tff(earray_56_type,type,
earray_56: $i ).
tff(e18_type,type,
e18: $i ).
tff(earray_62_type,type,
earray_62: $i ).
tff(e19_type,type,
e19: $i ).
tff(earray_74_type,type,
earray_74: $i ).
tff(e20_type,type,
e20: $i ).
tff(earray_80_type,type,
earray_80: $i ).
tff(e21_type,type,
e21: $i ).
tff(earray_86_type,type,
earray_86: $i ).
tff(e22_type,type,
e22: $i ).
tff(earray_92_type,type,
earray_92: $i ).
tff(e23_type,type,
e23: $i ).
tff(earray_98_type,type,
earray_98: $i ).
tff(e24_type,type,
e24: $i ).
tff(earray_104_type,type,
earray_104: $i ).
tff(e25_type,type,
e25: $i ).
tff(earray_110_type,type,
earray_110: $i ).
tff(e26_type,type,
e26: $i ).
tff(earray_116_type,type,
earray_116: $i ).
tff(e27_type,type,
e27: $i ).
tff(earray_122_type,type,
earray_122: $i ).
tff(e28_type,type,
e28: $i ).
tff(earray_128_type,type,
earray_128: $i ).
tff(e29_type,type,
e29: $i ).
tff(earray_140_type,type,
earray_140: $i ).
tff(e30_type,type,
e30: $i ).
tff(earray_146_type,type,
earray_146: $i ).
tff(e31_type,type,
e31: $i ).
tff(earray_152_type,type,
earray_152: $i ).
tff(e32_type,type,
e32: $i ).
tff(earray_158_type,type,
earray_158: $i ).
tff(e33_type,type,
e33: $i ).
tff(earray_164_type,type,
earray_164: $i ).
tff(e34_type,type,
e34: $i ).
tff(earray_170_type,type,
earray_170: $i ).
tff(e35_type,type,
e35: $i ).
tff(earray_176_type,type,
earray_176: $i ).
tff(e36_type,type,
e36: $i ).
tff(earray_182_type,type,
earray_182: $i ).
tff(e37_type,type,
e37: $i ).
tff(earray_188_type,type,
earray_188: $i ).
tff(e38_type,type,
e38: $i ).
tff(earray_194_type,type,
earray_194: $i ).
tff(e39_type,type,
e39: $i ).
tff(earray_206_type,type,
earray_206: $i ).
tff(e40_type,type,
e40: $i ).
tff(earray_212_type,type,
earray_212: $i ).
tff(e41_type,type,
e41: $i ).
tff(earray_218_type,type,
earray_218: $i ).
tff(1,plain,
( ( elem_265 = select(earray_260,index_264) )
<=> ( elem_265 = select(earray_260,index_264) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
elem_265 = select(earray_260,index_264),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp88) ).
tff(3,plain,
elem_265 = select(earray_260,index_264),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
select(earray_260,index_264) = elem_265,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] : ( p(s(X)) = X )
<=> ! [X: $i] : ( p(s(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
( ! [X: $i] : ( p(s(X)) = X )
<=> ! [X: $i] : ( p(s(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [X: $i] : ( p(s(X)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ps) ).
tff(8,plain,
! [X: $i] : ( p(s(X)) = X ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i] : ( p(s(X)) = X ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] : ( p(s(X)) = X ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [X: $i] : ( p(s(X)) = X )
| ( p(s(rselect_tail(q42))) = rselect_tail(q42) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
p(s(rselect_tail(q42))) = rselect_tail(q42),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( ( index_225 = rselect_tail(q42) )
<=> ( index_225 = rselect_tail(q42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
index_225 = rselect_tail(q42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp135) ).
tff(15,plain,
index_225 = rselect_tail(q42),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
rselect_tail(q42) = index_225,
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
s(rselect_tail(q42)) = s(index_225),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
s(index_225) = s(rselect_tail(q42)),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_tail(rstore_tail(A,E)) = E )
<=> ( rselect_tail(rstore_tail(A,E)) = E ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_tail) ).
tff(23,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q42,earray_226),s(index_225))) = s(index_225) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
rselect_tail(rstore_tail(rstore_seq(q42,earray_226),s(index_225))) = s(index_225),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
( ( index_228 = s(index_225) )
<=> ( index_228 = s(index_225) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
index_228 = s(index_225),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp136) ).
tff(30,plain,
index_228 = s(index_225),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
s(index_225) = index_228,
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ( queue_227 = rstore_seq(q42,earray_226) )
<=> ( queue_227 = rstore_seq(q42,earray_226) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
queue_227 = rstore_seq(q42,earray_226),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp226) ).
tff(34,plain,
queue_227 = rstore_seq(q42,earray_226),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
rstore_seq(q42,earray_226) = queue_227,
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
rstore_tail(rstore_seq(q42,earray_226),s(index_225)) = rstore_tail(queue_227,index_228),
inference(monotonicity,[status(thm)],[35,31]) ).
tff(37,plain,
rstore_tail(queue_227,index_228) = rstore_tail(rstore_seq(q42,earray_226),s(index_225)),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( ( queue_229 = rstore_tail(queue_227,index_228) )
<=> ( queue_229 = rstore_tail(queue_227,index_228) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
queue_229 = rstore_tail(queue_227,index_228),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp227) ).
tff(40,plain,
queue_229 = rstore_tail(queue_227,index_228),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ( q43 = queue_229 )
<=> ( q43 = queue_229 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
q43 = queue_229,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp304) ).
tff(43,plain,
q43 = queue_229,
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
q43 = rstore_tail(rstore_seq(q42,earray_226),s(index_225)),
inference(transitivity,[status(thm)],[43,40,37]) ).
tff(45,plain,
rselect_tail(q43) = rselect_tail(rstore_tail(rstore_seq(q42,earray_226),s(index_225))),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( index_263 = rselect_tail(q43) )
<=> ( index_263 = rselect_tail(q43) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
index_263 = rselect_tail(q43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp149) ).
tff(48,plain,
index_263 = rselect_tail(q43),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( ( s(index_264) = index_263 )
<=> ( s(index_264) = index_263 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
s(index_264) = index_263,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp150) ).
tff(51,plain,
s(index_264) = index_263,
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
s(index_264) = s(rselect_tail(q42)),
inference(transitivity,[status(thm)],[51,48,45,27,18]) ).
tff(53,plain,
p(s(index_264)) = p(s(rselect_tail(q42))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ~ ! [X: $i] : ( p(s(X)) = X )
| ( p(s(index_264)) = index_264 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
p(s(index_264)) = index_264,
inference(unit_resolution,[status(thm)],[54,10]) ).
tff(56,plain,
index_264 = p(s(index_264)),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
index_264 = rselect_tail(q42),
inference(transitivity,[status(thm)],[56,53,12]) ).
tff(58,plain,
( ( earray_224 = rselect_seq(q42) )
<=> ( earray_224 = rselect_seq(q42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
earray_224 = rselect_seq(q42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp47) ).
tff(60,plain,
earray_224 = rselect_seq(q42),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
rselect_seq(q42) = earray_224,
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
store(rselect_seq(q42),rselect_tail(q42),e42) = store(earray_224,index_225,e42),
inference(monotonicity,[status(thm)],[61,16]) ).
tff(63,plain,
store(earray_224,index_225,e42) = store(rselect_seq(q42),rselect_tail(q42),e42),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_seq(rstore_seq(A,E)) = E )
<=> ( rselect_seq(rstore_seq(A,E)) = E ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_seq) ).
tff(68,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e42))) = store(earray_224,index_225,e42) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
rselect_seq(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e42))) = store(earray_224,index_225,e42),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
( ( earray_226 = store(earray_224,index_225,e42) )
<=> ( earray_226 = store(earray_224,index_225,e42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
earray_226 = store(earray_224,index_225,e42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp48) ).
tff(75,plain,
earray_226 = store(earray_224,index_225,e42),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
store(earray_224,index_225,e42) = earray_226,
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ( q42 = queue_223 )
<=> ( q42 = queue_223 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
q42 = queue_223,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp303) ).
tff(79,plain,
q42 = queue_223,
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
queue_223 = q42,
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( ( queue_223 = rstore_tail(queue_221,index_222) )
<=> ( queue_223 = rstore_tail(queue_221,index_222) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,axiom,
queue_223 = rstore_tail(queue_221,index_222),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp225) ).
tff(83,plain,
queue_223 = rstore_tail(queue_221,index_222),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
rstore_tail(queue_221,index_222) = queue_223,
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
rstore_tail(queue_221,index_222) = q42,
inference(transitivity,[status(thm)],[84,80]) ).
tff(86,plain,
rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e42)) = rstore_seq(q42,earray_226),
inference(monotonicity,[status(thm)],[85,76]) ).
tff(87,plain,
rstore_seq(q42,earray_226) = rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e42)),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
rselect_seq(rstore_seq(q42,earray_226)) = rselect_seq(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e42))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
<=> ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_seq_tail) ).
tff(93,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q42,earray_226),s(index_225))) = rselect_seq(rstore_seq(q42,earray_226)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
rselect_seq(rstore_tail(rstore_seq(q42,earray_226),s(index_225))) = rselect_seq(rstore_seq(q42,earray_226)),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
rselect_seq(q43) = rselect_seq(rstore_tail(rstore_seq(q42,earray_226),s(index_225))),
inference(monotonicity,[status(thm)],[44]) ).
tff(99,plain,
( ( earray_260 = rselect_seq(q43) )
<=> ( earray_260 = rselect_seq(q43) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
earray_260 = rselect_seq(q43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp60) ).
tff(101,plain,
earray_260 = rselect_seq(q43),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
earray_260 = store(rselect_seq(q42),rselect_tail(q42),e42),
inference(transitivity,[status(thm)],[101,98,97,88,72,63]) ).
tff(103,plain,
select(earray_260,index_264) = select(store(rselect_seq(q42),rselect_tail(q42),e42),rselect_tail(q42)),
inference(monotonicity,[status(thm)],[102,57]) ).
tff(104,plain,
select(store(rselect_seq(q42),rselect_tail(q42),e42),rselect_tail(q42)) = select(earray_260,index_264),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ( index_222 = s(index_219) )
<=> ( index_222 = s(index_219) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,axiom,
index_222 = s(index_219),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp134) ).
tff(107,plain,
index_222 = s(index_219),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
s(index_219) = index_222,
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ( queue_221 = rstore_seq(q41,earray_220) )
<=> ( queue_221 = rstore_seq(q41,earray_220) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,axiom,
queue_221 = rstore_seq(q41,earray_220),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp224) ).
tff(111,plain,
queue_221 = rstore_seq(q41,earray_220),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
rstore_seq(q41,earray_220) = queue_221,
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
rstore_tail(rstore_seq(q41,earray_220),s(index_219)) = rstore_tail(queue_221,index_222),
inference(monotonicity,[status(thm)],[112,108]) ).
tff(114,plain,
rstore_tail(queue_221,index_222) = rstore_tail(rstore_seq(q41,earray_220),s(index_219)),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
q42 = rstore_tail(rstore_seq(q41,earray_220),s(index_219)),
inference(transitivity,[status(thm)],[79,83,114]) ).
tff(116,plain,
rselect_tail(q42) = rselect_tail(rstore_tail(rstore_seq(q41,earray_220),s(index_219))),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
rselect_tail(rstore_tail(rstore_seq(q41,earray_220),s(index_219))) = rselect_tail(q42),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q41,earray_220),s(index_219))) = s(index_219) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
rselect_tail(rstore_tail(rstore_seq(q41,earray_220),s(index_219))) = s(index_219),
inference(unit_resolution,[status(thm)],[118,25]) ).
tff(120,plain,
s(index_219) = rselect_tail(rstore_tail(rstore_seq(q41,earray_220),s(index_219))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ( index_213 = rselect_tail(q40) )
<=> ( index_213 = rselect_tail(q40) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,axiom,
index_213 = rselect_tail(q40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp131) ).
tff(123,plain,
index_213 = rselect_tail(q40),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
rselect_tail(q40) = index_213,
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
( ( index_210 = s(index_207) )
<=> ( index_210 = s(index_207) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,axiom,
index_210 = s(index_207),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp130) ).
tff(127,plain,
index_210 = s(index_207),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
s(index_207) = index_210,
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
( ( queue_209 = rstore_seq(q39,earray_208) )
<=> ( queue_209 = rstore_seq(q39,earray_208) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,axiom,
queue_209 = rstore_seq(q39,earray_208),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp220) ).
tff(131,plain,
queue_209 = rstore_seq(q39,earray_208),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
rstore_seq(q39,earray_208) = queue_209,
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
rstore_tail(rstore_seq(q39,earray_208),s(index_207)) = rstore_tail(queue_209,index_210),
inference(monotonicity,[status(thm)],[132,128]) ).
tff(134,plain,
rstore_tail(queue_209,index_210) = rstore_tail(rstore_seq(q39,earray_208),s(index_207)),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ( queue_211 = rstore_tail(queue_209,index_210) )
<=> ( queue_211 = rstore_tail(queue_209,index_210) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,axiom,
queue_211 = rstore_tail(queue_209,index_210),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp221) ).
tff(137,plain,
queue_211 = rstore_tail(queue_209,index_210),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ( q40 = queue_211 )
<=> ( q40 = queue_211 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,axiom,
q40 = queue_211,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp301) ).
tff(140,plain,
q40 = queue_211,
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
q40 = rstore_tail(rstore_seq(q39,earray_208),s(index_207)),
inference(transitivity,[status(thm)],[140,137,134]) ).
tff(142,plain,
rselect_tail(q40) = rselect_tail(rstore_tail(rstore_seq(q39,earray_208),s(index_207))),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
rselect_tail(rstore_tail(rstore_seq(q39,earray_208),s(index_207))) = rselect_tail(q40),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q39,earray_208),s(index_207))) = s(index_207) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
rselect_tail(rstore_tail(rstore_seq(q39,earray_208),s(index_207))) = s(index_207),
inference(unit_resolution,[status(thm)],[144,25]) ).
tff(146,plain,
s(index_207) = rselect_tail(rstore_tail(rstore_seq(q39,earray_208),s(index_207))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
( ( index_207 = rselect_tail(q39) )
<=> ( index_207 = rselect_tail(q39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,axiom,
index_207 = rselect_tail(q39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp128) ).
tff(149,plain,
index_207 = rselect_tail(q39),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
rselect_tail(q39) = index_207,
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
s(rselect_tail(q39)) = s(index_207),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
s(rselect_tail(q39)) = index_213,
inference(transitivity,[status(thm)],[151,146,143,124]) ).
tff(153,plain,
s(s(rselect_tail(q39))) = s(index_213),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
s(index_213) = s(s(rselect_tail(q39))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q40,earray_214),s(index_213))) = s(index_213) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
rselect_tail(rstore_tail(rstore_seq(q40,earray_214),s(index_213))) = s(index_213),
inference(unit_resolution,[status(thm)],[155,25]) ).
tff(157,plain,
( ( index_216 = s(index_213) )
<=> ( index_216 = s(index_213) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,axiom,
index_216 = s(index_213),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp132) ).
tff(159,plain,
index_216 = s(index_213),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
s(index_213) = index_216,
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ( queue_215 = rstore_seq(q40,earray_214) )
<=> ( queue_215 = rstore_seq(q40,earray_214) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,axiom,
queue_215 = rstore_seq(q40,earray_214),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp222) ).
tff(163,plain,
queue_215 = rstore_seq(q40,earray_214),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
rstore_seq(q40,earray_214) = queue_215,
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
rstore_tail(rstore_seq(q40,earray_214),s(index_213)) = rstore_tail(queue_215,index_216),
inference(monotonicity,[status(thm)],[164,160]) ).
tff(166,plain,
rstore_tail(queue_215,index_216) = rstore_tail(rstore_seq(q40,earray_214),s(index_213)),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
( ( queue_217 = rstore_tail(queue_215,index_216) )
<=> ( queue_217 = rstore_tail(queue_215,index_216) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(168,axiom,
queue_217 = rstore_tail(queue_215,index_216),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp223) ).
tff(169,plain,
queue_217 = rstore_tail(queue_215,index_216),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
( ( q41 = queue_217 )
<=> ( q41 = queue_217 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,axiom,
q41 = queue_217,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp302) ).
tff(172,plain,
q41 = queue_217,
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
q41 = rstore_tail(rstore_seq(q40,earray_214),s(index_213)),
inference(transitivity,[status(thm)],[172,169,166]) ).
tff(174,plain,
rselect_tail(q41) = rselect_tail(rstore_tail(rstore_seq(q40,earray_214),s(index_213))),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
( ( index_219 = rselect_tail(q41) )
<=> ( index_219 = rselect_tail(q41) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,axiom,
index_219 = rselect_tail(q41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp133) ).
tff(177,plain,
index_219 = rselect_tail(q41),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
index_219 = s(s(rselect_tail(q39))),
inference(transitivity,[status(thm)],[177,174,156,154]) ).
tff(179,plain,
s(index_219) = s(s(s(rselect_tail(q39)))),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
s(s(s(rselect_tail(q39)))) = s(index_219),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
^ [X: $i] :
refl(( ( s(s(s(X))) = X )
<=> ( s(s(s(X))) = X ) )),
inference(bind,[status(th)],[]) ).
tff(182,plain,
( ! [X: $i] : ( s(s(s(X))) = X )
<=> ! [X: $i] : ( s(s(s(X))) = X ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,plain,
( ! [X: $i] : ( s(s(s(X))) = X )
<=> ! [X: $i] : ( s(s(s(X))) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,axiom,
! [X: $i] : ( s(s(s(X))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',circular) ).
tff(185,plain,
! [X: $i] : ( s(s(s(X))) = X ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
! [X: $i] : ( s(s(s(X))) = X ),
inference(skolemize,[status(sab)],[185]) ).
tff(187,plain,
! [X: $i] : ( s(s(s(X))) = X ),
inference(modus_ponens,[status(thm)],[186,182]) ).
tff(188,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q39)))) = rselect_tail(q39) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
s(s(s(rselect_tail(q39)))) = rselect_tail(q39),
inference(unit_resolution,[status(thm)],[188,187]) ).
tff(190,plain,
rselect_tail(q39) = s(s(s(rselect_tail(q39)))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ( index_198 = s(index_195) )
<=> ( index_198 = s(index_195) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(192,axiom,
index_198 = s(index_195),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp125) ).
tff(193,plain,
index_198 = s(index_195),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
s(index_195) = index_198,
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
( ( queue_197 = rstore_seq(q38,earray_196) )
<=> ( queue_197 = rstore_seq(q38,earray_196) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(196,axiom,
queue_197 = rstore_seq(q38,earray_196),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp216) ).
tff(197,plain,
queue_197 = rstore_seq(q38,earray_196),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
rstore_seq(q38,earray_196) = queue_197,
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
rstore_tail(rstore_seq(q38,earray_196),s(index_195)) = rstore_tail(queue_197,index_198),
inference(monotonicity,[status(thm)],[198,194]) ).
tff(200,plain,
rstore_tail(queue_197,index_198) = rstore_tail(rstore_seq(q38,earray_196),s(index_195)),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
( ( queue_199 = rstore_tail(queue_197,index_198) )
<=> ( queue_199 = rstore_tail(queue_197,index_198) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(202,axiom,
queue_199 = rstore_tail(queue_197,index_198),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp217) ).
tff(203,plain,
queue_199 = rstore_tail(queue_197,index_198),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
( ( q39 = queue_199 )
<=> ( q39 = queue_199 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,axiom,
q39 = queue_199,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp299) ).
tff(206,plain,
q39 = queue_199,
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
q39 = rstore_tail(rstore_seq(q38,earray_196),s(index_195)),
inference(transitivity,[status(thm)],[206,203,200]) ).
tff(208,plain,
rselect_tail(q39) = rselect_tail(rstore_tail(rstore_seq(q38,earray_196),s(index_195))),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
rselect_tail(rstore_tail(rstore_seq(q38,earray_196),s(index_195))) = rselect_tail(q39),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q38,earray_196),s(index_195))) = s(index_195) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(211,plain,
rselect_tail(rstore_tail(rstore_seq(q38,earray_196),s(index_195))) = s(index_195),
inference(unit_resolution,[status(thm)],[210,25]) ).
tff(212,plain,
s(index_195) = rselect_tail(rstore_tail(rstore_seq(q38,earray_196),s(index_195))),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
( ( index_189 = rselect_tail(q37) )
<=> ( index_189 = rselect_tail(q37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,axiom,
index_189 = rselect_tail(q37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp122) ).
tff(215,plain,
index_189 = rselect_tail(q37),
inference(modus_ponens,[status(thm)],[214,213]) ).
tff(216,plain,
rselect_tail(q37) = index_189,
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
( ( index_186 = s(index_183) )
<=> ( index_186 = s(index_183) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(218,axiom,
index_186 = s(index_183),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp121) ).
tff(219,plain,
index_186 = s(index_183),
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
s(index_183) = index_186,
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
( ( queue_185 = rstore_seq(q36,earray_184) )
<=> ( queue_185 = rstore_seq(q36,earray_184) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(222,axiom,
queue_185 = rstore_seq(q36,earray_184),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp211) ).
tff(223,plain,
queue_185 = rstore_seq(q36,earray_184),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
rstore_seq(q36,earray_184) = queue_185,
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
rstore_tail(rstore_seq(q36,earray_184),s(index_183)) = rstore_tail(queue_185,index_186),
inference(monotonicity,[status(thm)],[224,220]) ).
tff(226,plain,
rstore_tail(queue_185,index_186) = rstore_tail(rstore_seq(q36,earray_184),s(index_183)),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
( ( queue_187 = rstore_tail(queue_185,index_186) )
<=> ( queue_187 = rstore_tail(queue_185,index_186) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,axiom,
queue_187 = rstore_tail(queue_185,index_186),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp212) ).
tff(229,plain,
queue_187 = rstore_tail(queue_185,index_186),
inference(modus_ponens,[status(thm)],[228,227]) ).
tff(230,plain,
( ( q37 = queue_187 )
<=> ( q37 = queue_187 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(231,axiom,
q37 = queue_187,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp297) ).
tff(232,plain,
q37 = queue_187,
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
q37 = rstore_tail(rstore_seq(q36,earray_184),s(index_183)),
inference(transitivity,[status(thm)],[232,229,226]) ).
tff(234,plain,
rselect_tail(q37) = rselect_tail(rstore_tail(rstore_seq(q36,earray_184),s(index_183))),
inference(monotonicity,[status(thm)],[233]) ).
tff(235,plain,
rselect_tail(rstore_tail(rstore_seq(q36,earray_184),s(index_183))) = rselect_tail(q37),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q36,earray_184),s(index_183))) = s(index_183) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(237,plain,
rselect_tail(rstore_tail(rstore_seq(q36,earray_184),s(index_183))) = s(index_183),
inference(unit_resolution,[status(thm)],[236,25]) ).
tff(238,plain,
s(index_183) = rselect_tail(rstore_tail(rstore_seq(q36,earray_184),s(index_183))),
inference(symmetry,[status(thm)],[237]) ).
tff(239,plain,
( ( index_183 = rselect_tail(q36) )
<=> ( index_183 = rselect_tail(q36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(240,axiom,
index_183 = rselect_tail(q36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp120) ).
tff(241,plain,
index_183 = rselect_tail(q36),
inference(modus_ponens,[status(thm)],[240,239]) ).
tff(242,plain,
rselect_tail(q36) = index_183,
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
s(rselect_tail(q36)) = s(index_183),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
s(rselect_tail(q36)) = index_189,
inference(transitivity,[status(thm)],[243,238,235,216]) ).
tff(245,plain,
s(s(rselect_tail(q36))) = s(index_189),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
s(index_189) = s(s(rselect_tail(q36))),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q37,earray_190),s(index_189))) = s(index_189) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
rselect_tail(rstore_tail(rstore_seq(q37,earray_190),s(index_189))) = s(index_189),
inference(unit_resolution,[status(thm)],[247,25]) ).
tff(249,plain,
( ( index_192 = s(index_189) )
<=> ( index_192 = s(index_189) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(250,axiom,
index_192 = s(index_189),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp123) ).
tff(251,plain,
index_192 = s(index_189),
inference(modus_ponens,[status(thm)],[250,249]) ).
tff(252,plain,
s(index_189) = index_192,
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
( ( queue_191 = rstore_seq(q37,earray_190) )
<=> ( queue_191 = rstore_seq(q37,earray_190) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(254,axiom,
queue_191 = rstore_seq(q37,earray_190),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp214) ).
tff(255,plain,
queue_191 = rstore_seq(q37,earray_190),
inference(modus_ponens,[status(thm)],[254,253]) ).
tff(256,plain,
rstore_seq(q37,earray_190) = queue_191,
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
rstore_tail(rstore_seq(q37,earray_190),s(index_189)) = rstore_tail(queue_191,index_192),
inference(monotonicity,[status(thm)],[256,252]) ).
tff(258,plain,
rstore_tail(queue_191,index_192) = rstore_tail(rstore_seq(q37,earray_190),s(index_189)),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
( ( queue_193 = rstore_tail(queue_191,index_192) )
<=> ( queue_193 = rstore_tail(queue_191,index_192) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(260,axiom,
queue_193 = rstore_tail(queue_191,index_192),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp215) ).
tff(261,plain,
queue_193 = rstore_tail(queue_191,index_192),
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
( ( q38 = queue_193 )
<=> ( q38 = queue_193 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(263,axiom,
q38 = queue_193,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp298) ).
tff(264,plain,
q38 = queue_193,
inference(modus_ponens,[status(thm)],[263,262]) ).
tff(265,plain,
q38 = rstore_tail(rstore_seq(q37,earray_190),s(index_189)),
inference(transitivity,[status(thm)],[264,261,258]) ).
tff(266,plain,
rselect_tail(q38) = rselect_tail(rstore_tail(rstore_seq(q37,earray_190),s(index_189))),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
( ( index_195 = rselect_tail(q38) )
<=> ( index_195 = rselect_tail(q38) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(268,axiom,
index_195 = rselect_tail(q38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp124) ).
tff(269,plain,
index_195 = rselect_tail(q38),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
index_195 = s(s(rselect_tail(q36))),
inference(transitivity,[status(thm)],[269,266,248,246]) ).
tff(271,plain,
s(index_195) = s(s(s(rselect_tail(q36)))),
inference(monotonicity,[status(thm)],[270]) ).
tff(272,plain,
s(s(s(rselect_tail(q36)))) = s(index_195),
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q36)))) = rselect_tail(q36) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(274,plain,
s(s(s(rselect_tail(q36)))) = rselect_tail(q36),
inference(unit_resolution,[status(thm)],[273,187]) ).
tff(275,plain,
rselect_tail(q36) = s(s(s(rselect_tail(q36)))),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
( ( index_180 = s(index_177) )
<=> ( index_180 = s(index_177) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(277,axiom,
index_180 = s(index_177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp119) ).
tff(278,plain,
index_180 = s(index_177),
inference(modus_ponens,[status(thm)],[277,276]) ).
tff(279,plain,
s(index_177) = index_180,
inference(symmetry,[status(thm)],[278]) ).
tff(280,plain,
( ( queue_179 = rstore_seq(q35,earray_178) )
<=> ( queue_179 = rstore_seq(q35,earray_178) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(281,axiom,
queue_179 = rstore_seq(q35,earray_178),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp209) ).
tff(282,plain,
queue_179 = rstore_seq(q35,earray_178),
inference(modus_ponens,[status(thm)],[281,280]) ).
tff(283,plain,
rstore_seq(q35,earray_178) = queue_179,
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
rstore_tail(rstore_seq(q35,earray_178),s(index_177)) = rstore_tail(queue_179,index_180),
inference(monotonicity,[status(thm)],[283,279]) ).
tff(285,plain,
rstore_tail(queue_179,index_180) = rstore_tail(rstore_seq(q35,earray_178),s(index_177)),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
( ( queue_181 = rstore_tail(queue_179,index_180) )
<=> ( queue_181 = rstore_tail(queue_179,index_180) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(287,axiom,
queue_181 = rstore_tail(queue_179,index_180),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp210) ).
tff(288,plain,
queue_181 = rstore_tail(queue_179,index_180),
inference(modus_ponens,[status(thm)],[287,286]) ).
tff(289,plain,
( ( q36 = queue_181 )
<=> ( q36 = queue_181 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(290,axiom,
q36 = queue_181,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp296) ).
tff(291,plain,
q36 = queue_181,
inference(modus_ponens,[status(thm)],[290,289]) ).
tff(292,plain,
q36 = rstore_tail(rstore_seq(q35,earray_178),s(index_177)),
inference(transitivity,[status(thm)],[291,288,285]) ).
tff(293,plain,
rselect_tail(q36) = rselect_tail(rstore_tail(rstore_seq(q35,earray_178),s(index_177))),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
rselect_tail(rstore_tail(rstore_seq(q35,earray_178),s(index_177))) = rselect_tail(q36),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q35,earray_178),s(index_177))) = s(index_177) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(296,plain,
rselect_tail(rstore_tail(rstore_seq(q35,earray_178),s(index_177))) = s(index_177),
inference(unit_resolution,[status(thm)],[295,25]) ).
tff(297,plain,
s(index_177) = rselect_tail(rstore_tail(rstore_seq(q35,earray_178),s(index_177))),
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
( ( index_171 = rselect_tail(q34) )
<=> ( index_171 = rselect_tail(q34) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(299,axiom,
index_171 = rselect_tail(q34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp115) ).
tff(300,plain,
index_171 = rselect_tail(q34),
inference(modus_ponens,[status(thm)],[299,298]) ).
tff(301,plain,
rselect_tail(q34) = index_171,
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
( ( index_168 = s(index_165) )
<=> ( index_168 = s(index_165) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(303,axiom,
index_168 = s(index_165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp114) ).
tff(304,plain,
index_168 = s(index_165),
inference(modus_ponens,[status(thm)],[303,302]) ).
tff(305,plain,
s(index_165) = index_168,
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
( ( queue_167 = rstore_seq(q33,earray_166) )
<=> ( queue_167 = rstore_seq(q33,earray_166) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(307,axiom,
queue_167 = rstore_seq(q33,earray_166),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp204) ).
tff(308,plain,
queue_167 = rstore_seq(q33,earray_166),
inference(modus_ponens,[status(thm)],[307,306]) ).
tff(309,plain,
rstore_seq(q33,earray_166) = queue_167,
inference(symmetry,[status(thm)],[308]) ).
tff(310,plain,
rstore_tail(rstore_seq(q33,earray_166),s(index_165)) = rstore_tail(queue_167,index_168),
inference(monotonicity,[status(thm)],[309,305]) ).
tff(311,plain,
rstore_tail(queue_167,index_168) = rstore_tail(rstore_seq(q33,earray_166),s(index_165)),
inference(symmetry,[status(thm)],[310]) ).
tff(312,plain,
( ( queue_169 = rstore_tail(queue_167,index_168) )
<=> ( queue_169 = rstore_tail(queue_167,index_168) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(313,axiom,
queue_169 = rstore_tail(queue_167,index_168),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp205) ).
tff(314,plain,
queue_169 = rstore_tail(queue_167,index_168),
inference(modus_ponens,[status(thm)],[313,312]) ).
tff(315,plain,
( ( q34 = queue_169 )
<=> ( q34 = queue_169 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(316,axiom,
q34 = queue_169,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp294) ).
tff(317,plain,
q34 = queue_169,
inference(modus_ponens,[status(thm)],[316,315]) ).
tff(318,plain,
q34 = rstore_tail(rstore_seq(q33,earray_166),s(index_165)),
inference(transitivity,[status(thm)],[317,314,311]) ).
tff(319,plain,
rselect_tail(q34) = rselect_tail(rstore_tail(rstore_seq(q33,earray_166),s(index_165))),
inference(monotonicity,[status(thm)],[318]) ).
tff(320,plain,
rselect_tail(rstore_tail(rstore_seq(q33,earray_166),s(index_165))) = rselect_tail(q34),
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q33,earray_166),s(index_165))) = s(index_165) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
rselect_tail(rstore_tail(rstore_seq(q33,earray_166),s(index_165))) = s(index_165),
inference(unit_resolution,[status(thm)],[321,25]) ).
tff(323,plain,
s(index_165) = rselect_tail(rstore_tail(rstore_seq(q33,earray_166),s(index_165))),
inference(symmetry,[status(thm)],[322]) ).
tff(324,plain,
( ( index_165 = rselect_tail(q33) )
<=> ( index_165 = rselect_tail(q33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(325,axiom,
index_165 = rselect_tail(q33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp113) ).
tff(326,plain,
index_165 = rselect_tail(q33),
inference(modus_ponens,[status(thm)],[325,324]) ).
tff(327,plain,
rselect_tail(q33) = index_165,
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
s(rselect_tail(q33)) = s(index_165),
inference(monotonicity,[status(thm)],[327]) ).
tff(329,plain,
s(rselect_tail(q33)) = index_171,
inference(transitivity,[status(thm)],[328,323,320,301]) ).
tff(330,plain,
s(s(rselect_tail(q33))) = s(index_171),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
s(index_171) = s(s(rselect_tail(q33))),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q34,earray_172),s(index_171))) = s(index_171) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
rselect_tail(rstore_tail(rstore_seq(q34,earray_172),s(index_171))) = s(index_171),
inference(unit_resolution,[status(thm)],[332,25]) ).
tff(334,plain,
( ( index_174 = s(index_171) )
<=> ( index_174 = s(index_171) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(335,axiom,
index_174 = s(index_171),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp116) ).
tff(336,plain,
index_174 = s(index_171),
inference(modus_ponens,[status(thm)],[335,334]) ).
tff(337,plain,
s(index_171) = index_174,
inference(symmetry,[status(thm)],[336]) ).
tff(338,plain,
( ( queue_173 = rstore_seq(q34,earray_172) )
<=> ( queue_173 = rstore_seq(q34,earray_172) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(339,axiom,
queue_173 = rstore_seq(q34,earray_172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp207) ).
tff(340,plain,
queue_173 = rstore_seq(q34,earray_172),
inference(modus_ponens,[status(thm)],[339,338]) ).
tff(341,plain,
rstore_seq(q34,earray_172) = queue_173,
inference(symmetry,[status(thm)],[340]) ).
tff(342,plain,
rstore_tail(rstore_seq(q34,earray_172),s(index_171)) = rstore_tail(queue_173,index_174),
inference(monotonicity,[status(thm)],[341,337]) ).
tff(343,plain,
rstore_tail(queue_173,index_174) = rstore_tail(rstore_seq(q34,earray_172),s(index_171)),
inference(symmetry,[status(thm)],[342]) ).
tff(344,plain,
( ( queue_175 = rstore_tail(queue_173,index_174) )
<=> ( queue_175 = rstore_tail(queue_173,index_174) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(345,axiom,
queue_175 = rstore_tail(queue_173,index_174),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp208) ).
tff(346,plain,
queue_175 = rstore_tail(queue_173,index_174),
inference(modus_ponens,[status(thm)],[345,344]) ).
tff(347,plain,
( ( q35 = queue_175 )
<=> ( q35 = queue_175 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(348,axiom,
q35 = queue_175,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp295) ).
tff(349,plain,
q35 = queue_175,
inference(modus_ponens,[status(thm)],[348,347]) ).
tff(350,plain,
q35 = rstore_tail(rstore_seq(q34,earray_172),s(index_171)),
inference(transitivity,[status(thm)],[349,346,343]) ).
tff(351,plain,
rselect_tail(q35) = rselect_tail(rstore_tail(rstore_seq(q34,earray_172),s(index_171))),
inference(monotonicity,[status(thm)],[350]) ).
tff(352,plain,
( ( index_177 = rselect_tail(q35) )
<=> ( index_177 = rselect_tail(q35) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(353,axiom,
index_177 = rselect_tail(q35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp117) ).
tff(354,plain,
index_177 = rselect_tail(q35),
inference(modus_ponens,[status(thm)],[353,352]) ).
tff(355,plain,
index_177 = s(s(rselect_tail(q33))),
inference(transitivity,[status(thm)],[354,351,333,331]) ).
tff(356,plain,
s(index_177) = s(s(s(rselect_tail(q33)))),
inference(monotonicity,[status(thm)],[355]) ).
tff(357,plain,
s(s(s(rselect_tail(q33)))) = s(index_177),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q33)))) = rselect_tail(q33) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(359,plain,
s(s(s(rselect_tail(q33)))) = rselect_tail(q33),
inference(unit_resolution,[status(thm)],[358,187]) ).
tff(360,plain,
rselect_tail(q33) = s(s(s(rselect_tail(q33)))),
inference(symmetry,[status(thm)],[359]) ).
tff(361,plain,
( ( index_162 = s(index_159) )
<=> ( index_162 = s(index_159) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(362,axiom,
index_162 = s(index_159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp112) ).
tff(363,plain,
index_162 = s(index_159),
inference(modus_ponens,[status(thm)],[362,361]) ).
tff(364,plain,
s(index_159) = index_162,
inference(symmetry,[status(thm)],[363]) ).
tff(365,plain,
( ( queue_161 = rstore_seq(q32,earray_160) )
<=> ( queue_161 = rstore_seq(q32,earray_160) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(366,axiom,
queue_161 = rstore_seq(q32,earray_160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp202) ).
tff(367,plain,
queue_161 = rstore_seq(q32,earray_160),
inference(modus_ponens,[status(thm)],[366,365]) ).
tff(368,plain,
rstore_seq(q32,earray_160) = queue_161,
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
rstore_tail(rstore_seq(q32,earray_160),s(index_159)) = rstore_tail(queue_161,index_162),
inference(monotonicity,[status(thm)],[368,364]) ).
tff(370,plain,
rstore_tail(queue_161,index_162) = rstore_tail(rstore_seq(q32,earray_160),s(index_159)),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
( ( queue_163 = rstore_tail(queue_161,index_162) )
<=> ( queue_163 = rstore_tail(queue_161,index_162) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(372,axiom,
queue_163 = rstore_tail(queue_161,index_162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp203) ).
tff(373,plain,
queue_163 = rstore_tail(queue_161,index_162),
inference(modus_ponens,[status(thm)],[372,371]) ).
tff(374,plain,
( ( q33 = queue_163 )
<=> ( q33 = queue_163 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(375,axiom,
q33 = queue_163,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp293) ).
tff(376,plain,
q33 = queue_163,
inference(modus_ponens,[status(thm)],[375,374]) ).
tff(377,plain,
q33 = rstore_tail(rstore_seq(q32,earray_160),s(index_159)),
inference(transitivity,[status(thm)],[376,373,370]) ).
tff(378,plain,
rselect_tail(q33) = rselect_tail(rstore_tail(rstore_seq(q32,earray_160),s(index_159))),
inference(monotonicity,[status(thm)],[377]) ).
tff(379,plain,
rselect_tail(rstore_tail(rstore_seq(q32,earray_160),s(index_159))) = rselect_tail(q33),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q32,earray_160),s(index_159))) = s(index_159) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(381,plain,
rselect_tail(rstore_tail(rstore_seq(q32,earray_160),s(index_159))) = s(index_159),
inference(unit_resolution,[status(thm)],[380,25]) ).
tff(382,plain,
s(index_159) = rselect_tail(rstore_tail(rstore_seq(q32,earray_160),s(index_159))),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
( ( index_153 = rselect_tail(q31) )
<=> ( index_153 = rselect_tail(q31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(384,axiom,
index_153 = rselect_tail(q31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp109) ).
tff(385,plain,
index_153 = rselect_tail(q31),
inference(modus_ponens,[status(thm)],[384,383]) ).
tff(386,plain,
rselect_tail(q31) = index_153,
inference(symmetry,[status(thm)],[385]) ).
tff(387,plain,
( ( index_150 = s(index_147) )
<=> ( index_150 = s(index_147) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(388,axiom,
index_150 = s(index_147),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp108) ).
tff(389,plain,
index_150 = s(index_147),
inference(modus_ponens,[status(thm)],[388,387]) ).
tff(390,plain,
s(index_147) = index_150,
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
( ( queue_149 = rstore_seq(q30,earray_148) )
<=> ( queue_149 = rstore_seq(q30,earray_148) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(392,axiom,
queue_149 = rstore_seq(q30,earray_148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp198) ).
tff(393,plain,
queue_149 = rstore_seq(q30,earray_148),
inference(modus_ponens,[status(thm)],[392,391]) ).
tff(394,plain,
rstore_seq(q30,earray_148) = queue_149,
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
rstore_tail(rstore_seq(q30,earray_148),s(index_147)) = rstore_tail(queue_149,index_150),
inference(monotonicity,[status(thm)],[394,390]) ).
tff(396,plain,
rstore_tail(queue_149,index_150) = rstore_tail(rstore_seq(q30,earray_148),s(index_147)),
inference(symmetry,[status(thm)],[395]) ).
tff(397,plain,
( ( queue_151 = rstore_tail(queue_149,index_150) )
<=> ( queue_151 = rstore_tail(queue_149,index_150) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(398,axiom,
queue_151 = rstore_tail(queue_149,index_150),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp199) ).
tff(399,plain,
queue_151 = rstore_tail(queue_149,index_150),
inference(modus_ponens,[status(thm)],[398,397]) ).
tff(400,plain,
( ( q31 = queue_151 )
<=> ( q31 = queue_151 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(401,axiom,
q31 = queue_151,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp291) ).
tff(402,plain,
q31 = queue_151,
inference(modus_ponens,[status(thm)],[401,400]) ).
tff(403,plain,
q31 = rstore_tail(rstore_seq(q30,earray_148),s(index_147)),
inference(transitivity,[status(thm)],[402,399,396]) ).
tff(404,plain,
rselect_tail(q31) = rselect_tail(rstore_tail(rstore_seq(q30,earray_148),s(index_147))),
inference(monotonicity,[status(thm)],[403]) ).
tff(405,plain,
rselect_tail(rstore_tail(rstore_seq(q30,earray_148),s(index_147))) = rselect_tail(q31),
inference(symmetry,[status(thm)],[404]) ).
tff(406,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q30,earray_148),s(index_147))) = s(index_147) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(407,plain,
rselect_tail(rstore_tail(rstore_seq(q30,earray_148),s(index_147))) = s(index_147),
inference(unit_resolution,[status(thm)],[406,25]) ).
tff(408,plain,
s(index_147) = rselect_tail(rstore_tail(rstore_seq(q30,earray_148),s(index_147))),
inference(symmetry,[status(thm)],[407]) ).
tff(409,plain,
( ( index_147 = rselect_tail(q30) )
<=> ( index_147 = rselect_tail(q30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(410,axiom,
index_147 = rselect_tail(q30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp106) ).
tff(411,plain,
index_147 = rselect_tail(q30),
inference(modus_ponens,[status(thm)],[410,409]) ).
tff(412,plain,
rselect_tail(q30) = index_147,
inference(symmetry,[status(thm)],[411]) ).
tff(413,plain,
s(rselect_tail(q30)) = s(index_147),
inference(monotonicity,[status(thm)],[412]) ).
tff(414,plain,
s(rselect_tail(q30)) = index_153,
inference(transitivity,[status(thm)],[413,408,405,386]) ).
tff(415,plain,
s(s(rselect_tail(q30))) = s(index_153),
inference(monotonicity,[status(thm)],[414]) ).
tff(416,plain,
s(index_153) = s(s(rselect_tail(q30))),
inference(symmetry,[status(thm)],[415]) ).
tff(417,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q31,earray_154),s(index_153))) = s(index_153) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(418,plain,
rselect_tail(rstore_tail(rstore_seq(q31,earray_154),s(index_153))) = s(index_153),
inference(unit_resolution,[status(thm)],[417,25]) ).
tff(419,plain,
( ( index_156 = s(index_153) )
<=> ( index_156 = s(index_153) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(420,axiom,
index_156 = s(index_153),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp110) ).
tff(421,plain,
index_156 = s(index_153),
inference(modus_ponens,[status(thm)],[420,419]) ).
tff(422,plain,
s(index_153) = index_156,
inference(symmetry,[status(thm)],[421]) ).
tff(423,plain,
( ( queue_155 = rstore_seq(q31,earray_154) )
<=> ( queue_155 = rstore_seq(q31,earray_154) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(424,axiom,
queue_155 = rstore_seq(q31,earray_154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp200) ).
tff(425,plain,
queue_155 = rstore_seq(q31,earray_154),
inference(modus_ponens,[status(thm)],[424,423]) ).
tff(426,plain,
rstore_seq(q31,earray_154) = queue_155,
inference(symmetry,[status(thm)],[425]) ).
tff(427,plain,
rstore_tail(rstore_seq(q31,earray_154),s(index_153)) = rstore_tail(queue_155,index_156),
inference(monotonicity,[status(thm)],[426,422]) ).
tff(428,plain,
rstore_tail(queue_155,index_156) = rstore_tail(rstore_seq(q31,earray_154),s(index_153)),
inference(symmetry,[status(thm)],[427]) ).
tff(429,plain,
( ( queue_157 = rstore_tail(queue_155,index_156) )
<=> ( queue_157 = rstore_tail(queue_155,index_156) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(430,axiom,
queue_157 = rstore_tail(queue_155,index_156),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp201) ).
tff(431,plain,
queue_157 = rstore_tail(queue_155,index_156),
inference(modus_ponens,[status(thm)],[430,429]) ).
tff(432,plain,
( ( q32 = queue_157 )
<=> ( q32 = queue_157 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(433,axiom,
q32 = queue_157,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp292) ).
tff(434,plain,
q32 = queue_157,
inference(modus_ponens,[status(thm)],[433,432]) ).
tff(435,plain,
q32 = rstore_tail(rstore_seq(q31,earray_154),s(index_153)),
inference(transitivity,[status(thm)],[434,431,428]) ).
tff(436,plain,
rselect_tail(q32) = rselect_tail(rstore_tail(rstore_seq(q31,earray_154),s(index_153))),
inference(monotonicity,[status(thm)],[435]) ).
tff(437,plain,
( ( index_159 = rselect_tail(q32) )
<=> ( index_159 = rselect_tail(q32) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(438,axiom,
index_159 = rselect_tail(q32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp111) ).
tff(439,plain,
index_159 = rselect_tail(q32),
inference(modus_ponens,[status(thm)],[438,437]) ).
tff(440,plain,
index_159 = s(s(rselect_tail(q30))),
inference(transitivity,[status(thm)],[439,436,418,416]) ).
tff(441,plain,
s(index_159) = s(s(s(rselect_tail(q30)))),
inference(monotonicity,[status(thm)],[440]) ).
tff(442,plain,
s(s(s(rselect_tail(q30)))) = s(index_159),
inference(symmetry,[status(thm)],[441]) ).
tff(443,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q30)))) = rselect_tail(q30) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(444,plain,
s(s(s(rselect_tail(q30)))) = rselect_tail(q30),
inference(unit_resolution,[status(thm)],[443,187]) ).
tff(445,plain,
rselect_tail(q30) = s(s(s(rselect_tail(q30)))),
inference(symmetry,[status(thm)],[444]) ).
tff(446,plain,
( ( index_144 = s(index_141) )
<=> ( index_144 = s(index_141) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(447,axiom,
index_144 = s(index_141),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp105) ).
tff(448,plain,
index_144 = s(index_141),
inference(modus_ponens,[status(thm)],[447,446]) ).
tff(449,plain,
s(index_141) = index_144,
inference(symmetry,[status(thm)],[448]) ).
tff(450,plain,
( ( queue_143 = rstore_seq(q29,earray_142) )
<=> ( queue_143 = rstore_seq(q29,earray_142) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(451,axiom,
queue_143 = rstore_seq(q29,earray_142),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp196) ).
tff(452,plain,
queue_143 = rstore_seq(q29,earray_142),
inference(modus_ponens,[status(thm)],[451,450]) ).
tff(453,plain,
rstore_seq(q29,earray_142) = queue_143,
inference(symmetry,[status(thm)],[452]) ).
tff(454,plain,
rstore_tail(rstore_seq(q29,earray_142),s(index_141)) = rstore_tail(queue_143,index_144),
inference(monotonicity,[status(thm)],[453,449]) ).
tff(455,plain,
rstore_tail(queue_143,index_144) = rstore_tail(rstore_seq(q29,earray_142),s(index_141)),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
( ( queue_145 = rstore_tail(queue_143,index_144) )
<=> ( queue_145 = rstore_tail(queue_143,index_144) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(457,axiom,
queue_145 = rstore_tail(queue_143,index_144),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp197) ).
tff(458,plain,
queue_145 = rstore_tail(queue_143,index_144),
inference(modus_ponens,[status(thm)],[457,456]) ).
tff(459,plain,
( ( q30 = queue_145 )
<=> ( q30 = queue_145 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(460,axiom,
q30 = queue_145,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp290) ).
tff(461,plain,
q30 = queue_145,
inference(modus_ponens,[status(thm)],[460,459]) ).
tff(462,plain,
q30 = rstore_tail(rstore_seq(q29,earray_142),s(index_141)),
inference(transitivity,[status(thm)],[461,458,455]) ).
tff(463,plain,
rselect_tail(q30) = rselect_tail(rstore_tail(rstore_seq(q29,earray_142),s(index_141))),
inference(monotonicity,[status(thm)],[462]) ).
tff(464,plain,
rselect_tail(rstore_tail(rstore_seq(q29,earray_142),s(index_141))) = rselect_tail(q30),
inference(symmetry,[status(thm)],[463]) ).
tff(465,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q29,earray_142),s(index_141))) = s(index_141) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(466,plain,
rselect_tail(rstore_tail(rstore_seq(q29,earray_142),s(index_141))) = s(index_141),
inference(unit_resolution,[status(thm)],[465,25]) ).
tff(467,plain,
s(index_141) = rselect_tail(rstore_tail(rstore_seq(q29,earray_142),s(index_141))),
inference(symmetry,[status(thm)],[466]) ).
tff(468,plain,
( ( index_129 = rselect_tail(q28) )
<=> ( index_129 = rselect_tail(q28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(469,axiom,
index_129 = rselect_tail(q28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp100) ).
tff(470,plain,
index_129 = rselect_tail(q28),
inference(modus_ponens,[status(thm)],[469,468]) ).
tff(471,plain,
rselect_tail(q28) = index_129,
inference(symmetry,[status(thm)],[470]) ).
tff(472,plain,
( ( index_126 = s(index_123) )
<=> ( index_126 = s(index_123) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(473,axiom,
index_126 = s(index_123),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp99) ).
tff(474,plain,
index_126 = s(index_123),
inference(modus_ponens,[status(thm)],[473,472]) ).
tff(475,plain,
s(index_123) = index_126,
inference(symmetry,[status(thm)],[474]) ).
tff(476,plain,
( ( queue_125 = rstore_seq(q27,earray_124) )
<=> ( queue_125 = rstore_seq(q27,earray_124) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(477,axiom,
queue_125 = rstore_seq(q27,earray_124),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp189) ).
tff(478,plain,
queue_125 = rstore_seq(q27,earray_124),
inference(modus_ponens,[status(thm)],[477,476]) ).
tff(479,plain,
rstore_seq(q27,earray_124) = queue_125,
inference(symmetry,[status(thm)],[478]) ).
tff(480,plain,
rstore_tail(rstore_seq(q27,earray_124),s(index_123)) = rstore_tail(queue_125,index_126),
inference(monotonicity,[status(thm)],[479,475]) ).
tff(481,plain,
rstore_tail(queue_125,index_126) = rstore_tail(rstore_seq(q27,earray_124),s(index_123)),
inference(symmetry,[status(thm)],[480]) ).
tff(482,plain,
( ( queue_127 = rstore_tail(queue_125,index_126) )
<=> ( queue_127 = rstore_tail(queue_125,index_126) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(483,axiom,
queue_127 = rstore_tail(queue_125,index_126),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp190) ).
tff(484,plain,
queue_127 = rstore_tail(queue_125,index_126),
inference(modus_ponens,[status(thm)],[483,482]) ).
tff(485,plain,
( ( q28 = queue_127 )
<=> ( q28 = queue_127 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(486,axiom,
q28 = queue_127,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp287) ).
tff(487,plain,
q28 = queue_127,
inference(modus_ponens,[status(thm)],[486,485]) ).
tff(488,plain,
q28 = rstore_tail(rstore_seq(q27,earray_124),s(index_123)),
inference(transitivity,[status(thm)],[487,484,481]) ).
tff(489,plain,
rselect_tail(q28) = rselect_tail(rstore_tail(rstore_seq(q27,earray_124),s(index_123))),
inference(monotonicity,[status(thm)],[488]) ).
tff(490,plain,
rselect_tail(rstore_tail(rstore_seq(q27,earray_124),s(index_123))) = rselect_tail(q28),
inference(symmetry,[status(thm)],[489]) ).
tff(491,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q27,earray_124),s(index_123))) = s(index_123) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(492,plain,
rselect_tail(rstore_tail(rstore_seq(q27,earray_124),s(index_123))) = s(index_123),
inference(unit_resolution,[status(thm)],[491,25]) ).
tff(493,plain,
s(index_123) = rselect_tail(rstore_tail(rstore_seq(q27,earray_124),s(index_123))),
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
( ( index_123 = rselect_tail(q27) )
<=> ( index_123 = rselect_tail(q27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(495,axiom,
index_123 = rselect_tail(q27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp98) ).
tff(496,plain,
index_123 = rselect_tail(q27),
inference(modus_ponens,[status(thm)],[495,494]) ).
tff(497,plain,
rselect_tail(q27) = index_123,
inference(symmetry,[status(thm)],[496]) ).
tff(498,plain,
s(rselect_tail(q27)) = s(index_123),
inference(monotonicity,[status(thm)],[497]) ).
tff(499,plain,
s(rselect_tail(q27)) = index_129,
inference(transitivity,[status(thm)],[498,493,490,471]) ).
tff(500,plain,
s(s(rselect_tail(q27))) = s(index_129),
inference(monotonicity,[status(thm)],[499]) ).
tff(501,plain,
s(index_129) = s(s(rselect_tail(q27))),
inference(symmetry,[status(thm)],[500]) ).
tff(502,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q28,earray_130),s(index_129))) = s(index_129) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(503,plain,
rselect_tail(rstore_tail(rstore_seq(q28,earray_130),s(index_129))) = s(index_129),
inference(unit_resolution,[status(thm)],[502,25]) ).
tff(504,plain,
( ( index_132 = s(index_129) )
<=> ( index_132 = s(index_129) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(505,axiom,
index_132 = s(index_129),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp101) ).
tff(506,plain,
index_132 = s(index_129),
inference(modus_ponens,[status(thm)],[505,504]) ).
tff(507,plain,
s(index_129) = index_132,
inference(symmetry,[status(thm)],[506]) ).
tff(508,plain,
( ( queue_131 = rstore_seq(q28,earray_130) )
<=> ( queue_131 = rstore_seq(q28,earray_130) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(509,axiom,
queue_131 = rstore_seq(q28,earray_130),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp192) ).
tff(510,plain,
queue_131 = rstore_seq(q28,earray_130),
inference(modus_ponens,[status(thm)],[509,508]) ).
tff(511,plain,
rstore_seq(q28,earray_130) = queue_131,
inference(symmetry,[status(thm)],[510]) ).
tff(512,plain,
rstore_tail(rstore_seq(q28,earray_130),s(index_129)) = rstore_tail(queue_131,index_132),
inference(monotonicity,[status(thm)],[511,507]) ).
tff(513,plain,
rstore_tail(queue_131,index_132) = rstore_tail(rstore_seq(q28,earray_130),s(index_129)),
inference(symmetry,[status(thm)],[512]) ).
tff(514,plain,
( ( queue_133 = rstore_tail(queue_131,index_132) )
<=> ( queue_133 = rstore_tail(queue_131,index_132) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(515,axiom,
queue_133 = rstore_tail(queue_131,index_132),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp193) ).
tff(516,plain,
queue_133 = rstore_tail(queue_131,index_132),
inference(modus_ponens,[status(thm)],[515,514]) ).
tff(517,plain,
( ( q29 = queue_133 )
<=> ( q29 = queue_133 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(518,axiom,
q29 = queue_133,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp288) ).
tff(519,plain,
q29 = queue_133,
inference(modus_ponens,[status(thm)],[518,517]) ).
tff(520,plain,
q29 = rstore_tail(rstore_seq(q28,earray_130),s(index_129)),
inference(transitivity,[status(thm)],[519,516,513]) ).
tff(521,plain,
rselect_tail(q29) = rselect_tail(rstore_tail(rstore_seq(q28,earray_130),s(index_129))),
inference(monotonicity,[status(thm)],[520]) ).
tff(522,plain,
( ( index_141 = rselect_tail(q29) )
<=> ( index_141 = rselect_tail(q29) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(523,axiom,
index_141 = rselect_tail(q29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp104) ).
tff(524,plain,
index_141 = rselect_tail(q29),
inference(modus_ponens,[status(thm)],[523,522]) ).
tff(525,plain,
index_141 = s(s(rselect_tail(q27))),
inference(transitivity,[status(thm)],[524,521,503,501]) ).
tff(526,plain,
s(index_141) = s(s(s(rselect_tail(q27)))),
inference(monotonicity,[status(thm)],[525]) ).
tff(527,plain,
s(s(s(rselect_tail(q27)))) = s(index_141),
inference(symmetry,[status(thm)],[526]) ).
tff(528,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q27)))) = rselect_tail(q27) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(529,plain,
s(s(s(rselect_tail(q27)))) = rselect_tail(q27),
inference(unit_resolution,[status(thm)],[528,187]) ).
tff(530,plain,
rselect_tail(q27) = s(s(s(rselect_tail(q27)))),
inference(symmetry,[status(thm)],[529]) ).
tff(531,plain,
( ( index_120 = s(index_117) )
<=> ( index_120 = s(index_117) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(532,axiom,
index_120 = s(index_117),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp97) ).
tff(533,plain,
index_120 = s(index_117),
inference(modus_ponens,[status(thm)],[532,531]) ).
tff(534,plain,
s(index_117) = index_120,
inference(symmetry,[status(thm)],[533]) ).
tff(535,plain,
( ( queue_119 = rstore_seq(q26,earray_118) )
<=> ( queue_119 = rstore_seq(q26,earray_118) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(536,axiom,
queue_119 = rstore_seq(q26,earray_118),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp187) ).
tff(537,plain,
queue_119 = rstore_seq(q26,earray_118),
inference(modus_ponens,[status(thm)],[536,535]) ).
tff(538,plain,
rstore_seq(q26,earray_118) = queue_119,
inference(symmetry,[status(thm)],[537]) ).
tff(539,plain,
rstore_tail(rstore_seq(q26,earray_118),s(index_117)) = rstore_tail(queue_119,index_120),
inference(monotonicity,[status(thm)],[538,534]) ).
tff(540,plain,
rstore_tail(queue_119,index_120) = rstore_tail(rstore_seq(q26,earray_118),s(index_117)),
inference(symmetry,[status(thm)],[539]) ).
tff(541,plain,
( ( queue_121 = rstore_tail(queue_119,index_120) )
<=> ( queue_121 = rstore_tail(queue_119,index_120) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(542,axiom,
queue_121 = rstore_tail(queue_119,index_120),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp188) ).
tff(543,plain,
queue_121 = rstore_tail(queue_119,index_120),
inference(modus_ponens,[status(thm)],[542,541]) ).
tff(544,plain,
( ( q27 = queue_121 )
<=> ( q27 = queue_121 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(545,axiom,
q27 = queue_121,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp286) ).
tff(546,plain,
q27 = queue_121,
inference(modus_ponens,[status(thm)],[545,544]) ).
tff(547,plain,
q27 = rstore_tail(rstore_seq(q26,earray_118),s(index_117)),
inference(transitivity,[status(thm)],[546,543,540]) ).
tff(548,plain,
rselect_tail(q27) = rselect_tail(rstore_tail(rstore_seq(q26,earray_118),s(index_117))),
inference(monotonicity,[status(thm)],[547]) ).
tff(549,plain,
rselect_tail(rstore_tail(rstore_seq(q26,earray_118),s(index_117))) = rselect_tail(q27),
inference(symmetry,[status(thm)],[548]) ).
tff(550,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q26,earray_118),s(index_117))) = s(index_117) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(551,plain,
rselect_tail(rstore_tail(rstore_seq(q26,earray_118),s(index_117))) = s(index_117),
inference(unit_resolution,[status(thm)],[550,25]) ).
tff(552,plain,
s(index_117) = rselect_tail(rstore_tail(rstore_seq(q26,earray_118),s(index_117))),
inference(symmetry,[status(thm)],[551]) ).
tff(553,plain,
( ( index_111 = rselect_tail(q25) )
<=> ( index_111 = rselect_tail(q25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(554,axiom,
index_111 = rselect_tail(q25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp93) ).
tff(555,plain,
index_111 = rselect_tail(q25),
inference(modus_ponens,[status(thm)],[554,553]) ).
tff(556,plain,
rselect_tail(q25) = index_111,
inference(symmetry,[status(thm)],[555]) ).
tff(557,plain,
( ( index_108 = s(index_105) )
<=> ( index_108 = s(index_105) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(558,axiom,
index_108 = s(index_105),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp92) ).
tff(559,plain,
index_108 = s(index_105),
inference(modus_ponens,[status(thm)],[558,557]) ).
tff(560,plain,
s(index_105) = index_108,
inference(symmetry,[status(thm)],[559]) ).
tff(561,plain,
( ( queue_107 = rstore_seq(q24,earray_106) )
<=> ( queue_107 = rstore_seq(q24,earray_106) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(562,axiom,
queue_107 = rstore_seq(q24,earray_106),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp182) ).
tff(563,plain,
queue_107 = rstore_seq(q24,earray_106),
inference(modus_ponens,[status(thm)],[562,561]) ).
tff(564,plain,
rstore_seq(q24,earray_106) = queue_107,
inference(symmetry,[status(thm)],[563]) ).
tff(565,plain,
rstore_tail(rstore_seq(q24,earray_106),s(index_105)) = rstore_tail(queue_107,index_108),
inference(monotonicity,[status(thm)],[564,560]) ).
tff(566,plain,
rstore_tail(queue_107,index_108) = rstore_tail(rstore_seq(q24,earray_106),s(index_105)),
inference(symmetry,[status(thm)],[565]) ).
tff(567,plain,
( ( queue_109 = rstore_tail(queue_107,index_108) )
<=> ( queue_109 = rstore_tail(queue_107,index_108) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(568,axiom,
queue_109 = rstore_tail(queue_107,index_108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp183) ).
tff(569,plain,
queue_109 = rstore_tail(queue_107,index_108),
inference(modus_ponens,[status(thm)],[568,567]) ).
tff(570,plain,
( ( q25 = queue_109 )
<=> ( q25 = queue_109 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(571,axiom,
q25 = queue_109,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp284) ).
tff(572,plain,
q25 = queue_109,
inference(modus_ponens,[status(thm)],[571,570]) ).
tff(573,plain,
q25 = rstore_tail(rstore_seq(q24,earray_106),s(index_105)),
inference(transitivity,[status(thm)],[572,569,566]) ).
tff(574,plain,
rselect_tail(q25) = rselect_tail(rstore_tail(rstore_seq(q24,earray_106),s(index_105))),
inference(monotonicity,[status(thm)],[573]) ).
tff(575,plain,
rselect_tail(rstore_tail(rstore_seq(q24,earray_106),s(index_105))) = rselect_tail(q25),
inference(symmetry,[status(thm)],[574]) ).
tff(576,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q24,earray_106),s(index_105))) = s(index_105) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(577,plain,
rselect_tail(rstore_tail(rstore_seq(q24,earray_106),s(index_105))) = s(index_105),
inference(unit_resolution,[status(thm)],[576,25]) ).
tff(578,plain,
s(index_105) = rselect_tail(rstore_tail(rstore_seq(q24,earray_106),s(index_105))),
inference(symmetry,[status(thm)],[577]) ).
tff(579,plain,
( ( index_105 = rselect_tail(q24) )
<=> ( index_105 = rselect_tail(q24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(580,axiom,
index_105 = rselect_tail(q24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp91) ).
tff(581,plain,
index_105 = rselect_tail(q24),
inference(modus_ponens,[status(thm)],[580,579]) ).
tff(582,plain,
rselect_tail(q24) = index_105,
inference(symmetry,[status(thm)],[581]) ).
tff(583,plain,
s(rselect_tail(q24)) = s(index_105),
inference(monotonicity,[status(thm)],[582]) ).
tff(584,plain,
s(rselect_tail(q24)) = index_111,
inference(transitivity,[status(thm)],[583,578,575,556]) ).
tff(585,plain,
s(s(rselect_tail(q24))) = s(index_111),
inference(monotonicity,[status(thm)],[584]) ).
tff(586,plain,
s(index_111) = s(s(rselect_tail(q24))),
inference(symmetry,[status(thm)],[585]) ).
tff(587,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q25,earray_112),s(index_111))) = s(index_111) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(588,plain,
rselect_tail(rstore_tail(rstore_seq(q25,earray_112),s(index_111))) = s(index_111),
inference(unit_resolution,[status(thm)],[587,25]) ).
tff(589,plain,
( ( q26 = queue_115 )
<=> ( q26 = queue_115 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(590,axiom,
q26 = queue_115,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp285) ).
tff(591,plain,
q26 = queue_115,
inference(modus_ponens,[status(thm)],[590,589]) ).
tff(592,plain,
queue_115 = q26,
inference(symmetry,[status(thm)],[591]) ).
tff(593,plain,
( ( queue_115 = rstore_tail(queue_113,index_114) )
<=> ( queue_115 = rstore_tail(queue_113,index_114) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(594,axiom,
queue_115 = rstore_tail(queue_113,index_114),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp186) ).
tff(595,plain,
queue_115 = rstore_tail(queue_113,index_114),
inference(modus_ponens,[status(thm)],[594,593]) ).
tff(596,plain,
rstore_tail(queue_113,index_114) = queue_115,
inference(symmetry,[status(thm)],[595]) ).
tff(597,plain,
( ( index_114 = s(index_111) )
<=> ( index_114 = s(index_111) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(598,axiom,
index_114 = s(index_111),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp94) ).
tff(599,plain,
index_114 = s(index_111),
inference(modus_ponens,[status(thm)],[598,597]) ).
tff(600,plain,
s(index_111) = index_114,
inference(symmetry,[status(thm)],[599]) ).
tff(601,plain,
( ( queue_113 = rstore_seq(q25,earray_112) )
<=> ( queue_113 = rstore_seq(q25,earray_112) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(602,axiom,
queue_113 = rstore_seq(q25,earray_112),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp185) ).
tff(603,plain,
queue_113 = rstore_seq(q25,earray_112),
inference(modus_ponens,[status(thm)],[602,601]) ).
tff(604,plain,
rstore_seq(q25,earray_112) = queue_113,
inference(symmetry,[status(thm)],[603]) ).
tff(605,plain,
rstore_tail(rstore_seq(q25,earray_112),s(index_111)) = rstore_tail(queue_113,index_114),
inference(monotonicity,[status(thm)],[604,600]) ).
tff(606,plain,
rstore_tail(rstore_seq(q25,earray_112),s(index_111)) = q26,
inference(transitivity,[status(thm)],[605,596,592]) ).
tff(607,plain,
rselect_tail(rstore_tail(rstore_seq(q25,earray_112),s(index_111))) = rselect_tail(q26),
inference(monotonicity,[status(thm)],[606]) ).
tff(608,plain,
rselect_tail(q26) = rselect_tail(rstore_tail(rstore_seq(q25,earray_112),s(index_111))),
inference(symmetry,[status(thm)],[607]) ).
tff(609,plain,
( ( index_117 = rselect_tail(q26) )
<=> ( index_117 = rselect_tail(q26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(610,axiom,
index_117 = rselect_tail(q26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp95) ).
tff(611,plain,
index_117 = rselect_tail(q26),
inference(modus_ponens,[status(thm)],[610,609]) ).
tff(612,plain,
index_117 = s(s(rselect_tail(q24))),
inference(transitivity,[status(thm)],[611,608,588,586]) ).
tff(613,plain,
s(index_117) = s(s(s(rselect_tail(q24)))),
inference(monotonicity,[status(thm)],[612]) ).
tff(614,plain,
s(s(s(rselect_tail(q24)))) = s(index_117),
inference(symmetry,[status(thm)],[613]) ).
tff(615,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q24)))) = rselect_tail(q24) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(616,plain,
s(s(s(rselect_tail(q24)))) = rselect_tail(q24),
inference(unit_resolution,[status(thm)],[615,187]) ).
tff(617,plain,
rselect_tail(q24) = s(s(s(rselect_tail(q24)))),
inference(symmetry,[status(thm)],[616]) ).
tff(618,plain,
( ( index_102 = s(index_99) )
<=> ( index_102 = s(index_99) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(619,axiom,
index_102 = s(index_99),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp90) ).
tff(620,plain,
index_102 = s(index_99),
inference(modus_ponens,[status(thm)],[619,618]) ).
tff(621,plain,
s(index_99) = index_102,
inference(symmetry,[status(thm)],[620]) ).
tff(622,plain,
( ( queue_101 = rstore_seq(q23,earray_100) )
<=> ( queue_101 = rstore_seq(q23,earray_100) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(623,axiom,
queue_101 = rstore_seq(q23,earray_100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp180) ).
tff(624,plain,
queue_101 = rstore_seq(q23,earray_100),
inference(modus_ponens,[status(thm)],[623,622]) ).
tff(625,plain,
rstore_seq(q23,earray_100) = queue_101,
inference(symmetry,[status(thm)],[624]) ).
tff(626,plain,
rstore_tail(rstore_seq(q23,earray_100),s(index_99)) = rstore_tail(queue_101,index_102),
inference(monotonicity,[status(thm)],[625,621]) ).
tff(627,plain,
rstore_tail(queue_101,index_102) = rstore_tail(rstore_seq(q23,earray_100),s(index_99)),
inference(symmetry,[status(thm)],[626]) ).
tff(628,plain,
( ( queue_103 = rstore_tail(queue_101,index_102) )
<=> ( queue_103 = rstore_tail(queue_101,index_102) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(629,axiom,
queue_103 = rstore_tail(queue_101,index_102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp181) ).
tff(630,plain,
queue_103 = rstore_tail(queue_101,index_102),
inference(modus_ponens,[status(thm)],[629,628]) ).
tff(631,plain,
( ( q24 = queue_103 )
<=> ( q24 = queue_103 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(632,axiom,
q24 = queue_103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp283) ).
tff(633,plain,
q24 = queue_103,
inference(modus_ponens,[status(thm)],[632,631]) ).
tff(634,plain,
q24 = rstore_tail(rstore_seq(q23,earray_100),s(index_99)),
inference(transitivity,[status(thm)],[633,630,627]) ).
tff(635,plain,
rselect_tail(q24) = rselect_tail(rstore_tail(rstore_seq(q23,earray_100),s(index_99))),
inference(monotonicity,[status(thm)],[634]) ).
tff(636,plain,
rselect_tail(rstore_tail(rstore_seq(q23,earray_100),s(index_99))) = rselect_tail(q24),
inference(symmetry,[status(thm)],[635]) ).
tff(637,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q23,earray_100),s(index_99))) = s(index_99) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(638,plain,
rselect_tail(rstore_tail(rstore_seq(q23,earray_100),s(index_99))) = s(index_99),
inference(unit_resolution,[status(thm)],[637,25]) ).
tff(639,plain,
s(index_99) = rselect_tail(rstore_tail(rstore_seq(q23,earray_100),s(index_99))),
inference(symmetry,[status(thm)],[638]) ).
tff(640,plain,
( ( index_93 = rselect_tail(q22) )
<=> ( index_93 = rselect_tail(q22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(641,axiom,
index_93 = rselect_tail(q22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp176) ).
tff(642,plain,
index_93 = rselect_tail(q22),
inference(modus_ponens,[status(thm)],[641,640]) ).
tff(643,plain,
rselect_tail(q22) = index_93,
inference(symmetry,[status(thm)],[642]) ).
tff(644,plain,
( ( index_90 = s(index_87) )
<=> ( index_90 = s(index_87) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(645,axiom,
index_90 = s(index_87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp175) ).
tff(646,plain,
index_90 = s(index_87),
inference(modus_ponens,[status(thm)],[645,644]) ).
tff(647,plain,
s(index_87) = index_90,
inference(symmetry,[status(thm)],[646]) ).
tff(648,plain,
( ( queue_89 = rstore_seq(q21,earray_88) )
<=> ( queue_89 = rstore_seq(q21,earray_88) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(649,axiom,
queue_89 = rstore_seq(q21,earray_88),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp262) ).
tff(650,plain,
queue_89 = rstore_seq(q21,earray_88),
inference(modus_ponens,[status(thm)],[649,648]) ).
tff(651,plain,
rstore_seq(q21,earray_88) = queue_89,
inference(symmetry,[status(thm)],[650]) ).
tff(652,plain,
rstore_tail(rstore_seq(q21,earray_88),s(index_87)) = rstore_tail(queue_89,index_90),
inference(monotonicity,[status(thm)],[651,647]) ).
tff(653,plain,
rstore_tail(queue_89,index_90) = rstore_tail(rstore_seq(q21,earray_88),s(index_87)),
inference(symmetry,[status(thm)],[652]) ).
tff(654,plain,
( ( queue_91 = rstore_tail(queue_89,index_90) )
<=> ( queue_91 = rstore_tail(queue_89,index_90) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(655,axiom,
queue_91 = rstore_tail(queue_89,index_90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp263) ).
tff(656,plain,
queue_91 = rstore_tail(queue_89,index_90),
inference(modus_ponens,[status(thm)],[655,654]) ).
tff(657,plain,
( ( q22 = queue_91 )
<=> ( q22 = queue_91 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(658,axiom,
q22 = queue_91,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp281) ).
tff(659,plain,
q22 = queue_91,
inference(modus_ponens,[status(thm)],[658,657]) ).
tff(660,plain,
q22 = rstore_tail(rstore_seq(q21,earray_88),s(index_87)),
inference(transitivity,[status(thm)],[659,656,653]) ).
tff(661,plain,
rselect_tail(q22) = rselect_tail(rstore_tail(rstore_seq(q21,earray_88),s(index_87))),
inference(monotonicity,[status(thm)],[660]) ).
tff(662,plain,
rselect_tail(rstore_tail(rstore_seq(q21,earray_88),s(index_87))) = rselect_tail(q22),
inference(symmetry,[status(thm)],[661]) ).
tff(663,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q21,earray_88),s(index_87))) = s(index_87) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(664,plain,
rselect_tail(rstore_tail(rstore_seq(q21,earray_88),s(index_87))) = s(index_87),
inference(unit_resolution,[status(thm)],[663,25]) ).
tff(665,plain,
s(index_87) = rselect_tail(rstore_tail(rstore_seq(q21,earray_88),s(index_87))),
inference(symmetry,[status(thm)],[664]) ).
tff(666,plain,
( ( index_87 = rselect_tail(q21) )
<=> ( index_87 = rselect_tail(q21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(667,axiom,
index_87 = rselect_tail(q21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp173) ).
tff(668,plain,
index_87 = rselect_tail(q21),
inference(modus_ponens,[status(thm)],[667,666]) ).
tff(669,plain,
rselect_tail(q21) = index_87,
inference(symmetry,[status(thm)],[668]) ).
tff(670,plain,
s(rselect_tail(q21)) = s(index_87),
inference(monotonicity,[status(thm)],[669]) ).
tff(671,plain,
s(rselect_tail(q21)) = index_93,
inference(transitivity,[status(thm)],[670,665,662,643]) ).
tff(672,plain,
s(s(rselect_tail(q21))) = s(index_93),
inference(monotonicity,[status(thm)],[671]) ).
tff(673,plain,
s(index_93) = s(s(rselect_tail(q21))),
inference(symmetry,[status(thm)],[672]) ).
tff(674,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q22,earray_94),s(index_93))) = s(index_93) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(675,plain,
rselect_tail(rstore_tail(rstore_seq(q22,earray_94),s(index_93))) = s(index_93),
inference(unit_resolution,[status(thm)],[674,25]) ).
tff(676,plain,
( ( q23 = queue_97 )
<=> ( q23 = queue_97 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(677,axiom,
q23 = queue_97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp282) ).
tff(678,plain,
q23 = queue_97,
inference(modus_ponens,[status(thm)],[677,676]) ).
tff(679,plain,
queue_97 = q23,
inference(symmetry,[status(thm)],[678]) ).
tff(680,plain,
( ( queue_97 = rstore_tail(queue_95,index_96) )
<=> ( queue_97 = rstore_tail(queue_95,index_96) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(681,axiom,
queue_97 = rstore_tail(queue_95,index_96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp265) ).
tff(682,plain,
queue_97 = rstore_tail(queue_95,index_96),
inference(modus_ponens,[status(thm)],[681,680]) ).
tff(683,plain,
rstore_tail(queue_95,index_96) = queue_97,
inference(symmetry,[status(thm)],[682]) ).
tff(684,plain,
( ( index_96 = s(index_93) )
<=> ( index_96 = s(index_93) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(685,axiom,
index_96 = s(index_93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp177) ).
tff(686,plain,
index_96 = s(index_93),
inference(modus_ponens,[status(thm)],[685,684]) ).
tff(687,plain,
s(index_93) = index_96,
inference(symmetry,[status(thm)],[686]) ).
tff(688,plain,
( ( queue_95 = rstore_seq(q22,earray_94) )
<=> ( queue_95 = rstore_seq(q22,earray_94) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(689,axiom,
queue_95 = rstore_seq(q22,earray_94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp264) ).
tff(690,plain,
queue_95 = rstore_seq(q22,earray_94),
inference(modus_ponens,[status(thm)],[689,688]) ).
tff(691,plain,
rstore_seq(q22,earray_94) = queue_95,
inference(symmetry,[status(thm)],[690]) ).
tff(692,plain,
rstore_tail(rstore_seq(q22,earray_94),s(index_93)) = rstore_tail(queue_95,index_96),
inference(monotonicity,[status(thm)],[691,687]) ).
tff(693,plain,
rstore_tail(rstore_seq(q22,earray_94),s(index_93)) = q23,
inference(transitivity,[status(thm)],[692,683,679]) ).
tff(694,plain,
rselect_tail(rstore_tail(rstore_seq(q22,earray_94),s(index_93))) = rselect_tail(q23),
inference(monotonicity,[status(thm)],[693]) ).
tff(695,plain,
rselect_tail(q23) = rselect_tail(rstore_tail(rstore_seq(q22,earray_94),s(index_93))),
inference(symmetry,[status(thm)],[694]) ).
tff(696,plain,
( ( index_99 = rselect_tail(q23) )
<=> ( index_99 = rselect_tail(q23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(697,axiom,
index_99 = rselect_tail(q23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp178) ).
tff(698,plain,
index_99 = rselect_tail(q23),
inference(modus_ponens,[status(thm)],[697,696]) ).
tff(699,plain,
index_99 = s(s(rselect_tail(q21))),
inference(transitivity,[status(thm)],[698,695,675,673]) ).
tff(700,plain,
s(index_99) = s(s(s(rselect_tail(q21)))),
inference(monotonicity,[status(thm)],[699]) ).
tff(701,plain,
s(s(s(rselect_tail(q21)))) = s(index_99),
inference(symmetry,[status(thm)],[700]) ).
tff(702,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q21)))) = rselect_tail(q21) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(703,plain,
s(s(s(rselect_tail(q21)))) = rselect_tail(q21),
inference(unit_resolution,[status(thm)],[702,187]) ).
tff(704,plain,
rselect_tail(q21) = s(s(s(rselect_tail(q21)))),
inference(symmetry,[status(thm)],[703]) ).
tff(705,plain,
( ( index_84 = s(index_81) )
<=> ( index_84 = s(index_81) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(706,axiom,
index_84 = s(index_81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp172) ).
tff(707,plain,
index_84 = s(index_81),
inference(modus_ponens,[status(thm)],[706,705]) ).
tff(708,plain,
s(index_81) = index_84,
inference(symmetry,[status(thm)],[707]) ).
tff(709,plain,
( ( queue_83 = rstore_seq(q20,earray_82) )
<=> ( queue_83 = rstore_seq(q20,earray_82) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(710,axiom,
queue_83 = rstore_seq(q20,earray_82),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp260) ).
tff(711,plain,
queue_83 = rstore_seq(q20,earray_82),
inference(modus_ponens,[status(thm)],[710,709]) ).
tff(712,plain,
rstore_seq(q20,earray_82) = queue_83,
inference(symmetry,[status(thm)],[711]) ).
tff(713,plain,
rstore_tail(rstore_seq(q20,earray_82),s(index_81)) = rstore_tail(queue_83,index_84),
inference(monotonicity,[status(thm)],[712,708]) ).
tff(714,plain,
rstore_tail(queue_83,index_84) = rstore_tail(rstore_seq(q20,earray_82),s(index_81)),
inference(symmetry,[status(thm)],[713]) ).
tff(715,plain,
( ( queue_85 = rstore_tail(queue_83,index_84) )
<=> ( queue_85 = rstore_tail(queue_83,index_84) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(716,axiom,
queue_85 = rstore_tail(queue_83,index_84),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp261) ).
tff(717,plain,
queue_85 = rstore_tail(queue_83,index_84),
inference(modus_ponens,[status(thm)],[716,715]) ).
tff(718,plain,
( ( q21 = queue_85 )
<=> ( q21 = queue_85 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(719,axiom,
q21 = queue_85,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp280) ).
tff(720,plain,
q21 = queue_85,
inference(modus_ponens,[status(thm)],[719,718]) ).
tff(721,plain,
q21 = rstore_tail(rstore_seq(q20,earray_82),s(index_81)),
inference(transitivity,[status(thm)],[720,717,714]) ).
tff(722,plain,
rselect_tail(q21) = rselect_tail(rstore_tail(rstore_seq(q20,earray_82),s(index_81))),
inference(monotonicity,[status(thm)],[721]) ).
tff(723,plain,
rselect_tail(rstore_tail(rstore_seq(q20,earray_82),s(index_81))) = rselect_tail(q21),
inference(symmetry,[status(thm)],[722]) ).
tff(724,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q20,earray_82),s(index_81))) = s(index_81) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(725,plain,
rselect_tail(rstore_tail(rstore_seq(q20,earray_82),s(index_81))) = s(index_81),
inference(unit_resolution,[status(thm)],[724,25]) ).
tff(726,plain,
s(index_81) = rselect_tail(rstore_tail(rstore_seq(q20,earray_82),s(index_81))),
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
( ( index_75 = rselect_tail(q19) )
<=> ( index_75 = rselect_tail(q19) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(728,axiom,
index_75 = rselect_tail(q19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp169) ).
tff(729,plain,
index_75 = rselect_tail(q19),
inference(modus_ponens,[status(thm)],[728,727]) ).
tff(730,plain,
rselect_tail(q19) = index_75,
inference(symmetry,[status(thm)],[729]) ).
tff(731,plain,
( ( index_66 = s(index_63) )
<=> ( index_66 = s(index_63) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(732,axiom,
index_66 = s(index_63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp166) ).
tff(733,plain,
index_66 = s(index_63),
inference(modus_ponens,[status(thm)],[732,731]) ).
tff(734,plain,
s(index_63) = index_66,
inference(symmetry,[status(thm)],[733]) ).
tff(735,plain,
( ( queue_65 = rstore_seq(q18,earray_64) )
<=> ( queue_65 = rstore_seq(q18,earray_64) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(736,axiom,
queue_65 = rstore_seq(q18,earray_64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp253) ).
tff(737,plain,
queue_65 = rstore_seq(q18,earray_64),
inference(modus_ponens,[status(thm)],[736,735]) ).
tff(738,plain,
rstore_seq(q18,earray_64) = queue_65,
inference(symmetry,[status(thm)],[737]) ).
tff(739,plain,
rstore_tail(rstore_seq(q18,earray_64),s(index_63)) = rstore_tail(queue_65,index_66),
inference(monotonicity,[status(thm)],[738,734]) ).
tff(740,plain,
rstore_tail(queue_65,index_66) = rstore_tail(rstore_seq(q18,earray_64),s(index_63)),
inference(symmetry,[status(thm)],[739]) ).
tff(741,plain,
( ( queue_67 = rstore_tail(queue_65,index_66) )
<=> ( queue_67 = rstore_tail(queue_65,index_66) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(742,axiom,
queue_67 = rstore_tail(queue_65,index_66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp254) ).
tff(743,plain,
queue_67 = rstore_tail(queue_65,index_66),
inference(modus_ponens,[status(thm)],[742,741]) ).
tff(744,plain,
( ( q19 = queue_67 )
<=> ( q19 = queue_67 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(745,axiom,
q19 = queue_67,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp277) ).
tff(746,plain,
q19 = queue_67,
inference(modus_ponens,[status(thm)],[745,744]) ).
tff(747,plain,
q19 = rstore_tail(rstore_seq(q18,earray_64),s(index_63)),
inference(transitivity,[status(thm)],[746,743,740]) ).
tff(748,plain,
rselect_tail(q19) = rselect_tail(rstore_tail(rstore_seq(q18,earray_64),s(index_63))),
inference(monotonicity,[status(thm)],[747]) ).
tff(749,plain,
rselect_tail(rstore_tail(rstore_seq(q18,earray_64),s(index_63))) = rselect_tail(q19),
inference(symmetry,[status(thm)],[748]) ).
tff(750,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q18,earray_64),s(index_63))) = s(index_63) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(751,plain,
rselect_tail(rstore_tail(rstore_seq(q18,earray_64),s(index_63))) = s(index_63),
inference(unit_resolution,[status(thm)],[750,25]) ).
tff(752,plain,
s(index_63) = rselect_tail(rstore_tail(rstore_seq(q18,earray_64),s(index_63))),
inference(symmetry,[status(thm)],[751]) ).
tff(753,plain,
( ( index_63 = rselect_tail(q18) )
<=> ( index_63 = rselect_tail(q18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(754,axiom,
index_63 = rselect_tail(q18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp165) ).
tff(755,plain,
index_63 = rselect_tail(q18),
inference(modus_ponens,[status(thm)],[754,753]) ).
tff(756,plain,
rselect_tail(q18) = index_63,
inference(symmetry,[status(thm)],[755]) ).
tff(757,plain,
s(rselect_tail(q18)) = s(index_63),
inference(monotonicity,[status(thm)],[756]) ).
tff(758,plain,
s(rselect_tail(q18)) = index_75,
inference(transitivity,[status(thm)],[757,752,749,730]) ).
tff(759,plain,
s(s(rselect_tail(q18))) = s(index_75),
inference(monotonicity,[status(thm)],[758]) ).
tff(760,plain,
s(index_75) = s(s(rselect_tail(q18))),
inference(symmetry,[status(thm)],[759]) ).
tff(761,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q19,earray_76),s(index_75))) = s(index_75) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(762,plain,
rselect_tail(rstore_tail(rstore_seq(q19,earray_76),s(index_75))) = s(index_75),
inference(unit_resolution,[status(thm)],[761,25]) ).
tff(763,plain,
( ( q20 = queue_79 )
<=> ( q20 = queue_79 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(764,axiom,
q20 = queue_79,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp279) ).
tff(765,plain,
q20 = queue_79,
inference(modus_ponens,[status(thm)],[764,763]) ).
tff(766,plain,
queue_79 = q20,
inference(symmetry,[status(thm)],[765]) ).
tff(767,plain,
( ( queue_79 = rstore_tail(queue_77,index_78) )
<=> ( queue_79 = rstore_tail(queue_77,index_78) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(768,axiom,
queue_79 = rstore_tail(queue_77,index_78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp259) ).
tff(769,plain,
queue_79 = rstore_tail(queue_77,index_78),
inference(modus_ponens,[status(thm)],[768,767]) ).
tff(770,plain,
rstore_tail(queue_77,index_78) = queue_79,
inference(symmetry,[status(thm)],[769]) ).
tff(771,plain,
( ( index_78 = s(index_75) )
<=> ( index_78 = s(index_75) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(772,axiom,
index_78 = s(index_75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp170) ).
tff(773,plain,
index_78 = s(index_75),
inference(modus_ponens,[status(thm)],[772,771]) ).
tff(774,plain,
s(index_75) = index_78,
inference(symmetry,[status(thm)],[773]) ).
tff(775,plain,
( ( queue_77 = rstore_seq(q19,earray_76) )
<=> ( queue_77 = rstore_seq(q19,earray_76) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(776,axiom,
queue_77 = rstore_seq(q19,earray_76),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp258) ).
tff(777,plain,
queue_77 = rstore_seq(q19,earray_76),
inference(modus_ponens,[status(thm)],[776,775]) ).
tff(778,plain,
rstore_seq(q19,earray_76) = queue_77,
inference(symmetry,[status(thm)],[777]) ).
tff(779,plain,
rstore_tail(rstore_seq(q19,earray_76),s(index_75)) = rstore_tail(queue_77,index_78),
inference(monotonicity,[status(thm)],[778,774]) ).
tff(780,plain,
rstore_tail(rstore_seq(q19,earray_76),s(index_75)) = q20,
inference(transitivity,[status(thm)],[779,770,766]) ).
tff(781,plain,
rselect_tail(rstore_tail(rstore_seq(q19,earray_76),s(index_75))) = rselect_tail(q20),
inference(monotonicity,[status(thm)],[780]) ).
tff(782,plain,
rselect_tail(q20) = rselect_tail(rstore_tail(rstore_seq(q19,earray_76),s(index_75))),
inference(symmetry,[status(thm)],[781]) ).
tff(783,plain,
( ( index_81 = rselect_tail(q20) )
<=> ( index_81 = rselect_tail(q20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(784,axiom,
index_81 = rselect_tail(q20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp171) ).
tff(785,plain,
index_81 = rselect_tail(q20),
inference(modus_ponens,[status(thm)],[784,783]) ).
tff(786,plain,
index_81 = s(s(rselect_tail(q18))),
inference(transitivity,[status(thm)],[785,782,762,760]) ).
tff(787,plain,
s(index_81) = s(s(s(rselect_tail(q18)))),
inference(monotonicity,[status(thm)],[786]) ).
tff(788,plain,
s(s(s(rselect_tail(q18)))) = s(index_81),
inference(symmetry,[status(thm)],[787]) ).
tff(789,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q18)))) = rselect_tail(q18) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(790,plain,
s(s(s(rselect_tail(q18)))) = rselect_tail(q18),
inference(unit_resolution,[status(thm)],[789,187]) ).
tff(791,plain,
rselect_tail(q18) = s(s(s(rselect_tail(q18)))),
inference(symmetry,[status(thm)],[790]) ).
tff(792,plain,
( ( index_60 = s(index_57) )
<=> ( index_60 = s(index_57) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(793,axiom,
index_60 = s(index_57),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp164) ).
tff(794,plain,
index_60 = s(index_57),
inference(modus_ponens,[status(thm)],[793,792]) ).
tff(795,plain,
s(index_57) = index_60,
inference(symmetry,[status(thm)],[794]) ).
tff(796,plain,
( ( queue_59 = rstore_seq(q17,earray_58) )
<=> ( queue_59 = rstore_seq(q17,earray_58) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(797,axiom,
queue_59 = rstore_seq(q17,earray_58),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp251) ).
tff(798,plain,
queue_59 = rstore_seq(q17,earray_58),
inference(modus_ponens,[status(thm)],[797,796]) ).
tff(799,plain,
rstore_seq(q17,earray_58) = queue_59,
inference(symmetry,[status(thm)],[798]) ).
tff(800,plain,
rstore_tail(rstore_seq(q17,earray_58),s(index_57)) = rstore_tail(queue_59,index_60),
inference(monotonicity,[status(thm)],[799,795]) ).
tff(801,plain,
rstore_tail(queue_59,index_60) = rstore_tail(rstore_seq(q17,earray_58),s(index_57)),
inference(symmetry,[status(thm)],[800]) ).
tff(802,plain,
( ( queue_61 = rstore_tail(queue_59,index_60) )
<=> ( queue_61 = rstore_tail(queue_59,index_60) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(803,axiom,
queue_61 = rstore_tail(queue_59,index_60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp252) ).
tff(804,plain,
queue_61 = rstore_tail(queue_59,index_60),
inference(modus_ponens,[status(thm)],[803,802]) ).
tff(805,plain,
( ( q18 = queue_61 )
<=> ( q18 = queue_61 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(806,axiom,
q18 = queue_61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp276) ).
tff(807,plain,
q18 = queue_61,
inference(modus_ponens,[status(thm)],[806,805]) ).
tff(808,plain,
q18 = rstore_tail(rstore_seq(q17,earray_58),s(index_57)),
inference(transitivity,[status(thm)],[807,804,801]) ).
tff(809,plain,
rselect_tail(q18) = rselect_tail(rstore_tail(rstore_seq(q17,earray_58),s(index_57))),
inference(monotonicity,[status(thm)],[808]) ).
tff(810,plain,
rselect_tail(rstore_tail(rstore_seq(q17,earray_58),s(index_57))) = rselect_tail(q18),
inference(symmetry,[status(thm)],[809]) ).
tff(811,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q17,earray_58),s(index_57))) = s(index_57) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(812,plain,
rselect_tail(rstore_tail(rstore_seq(q17,earray_58),s(index_57))) = s(index_57),
inference(unit_resolution,[status(thm)],[811,25]) ).
tff(813,plain,
s(index_57) = rselect_tail(rstore_tail(rstore_seq(q17,earray_58),s(index_57))),
inference(symmetry,[status(thm)],[812]) ).
tff(814,plain,
( ( index_51 = rselect_tail(q16) )
<=> ( index_51 = rselect_tail(q16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(815,axiom,
index_51 = rselect_tail(q16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp160) ).
tff(816,plain,
index_51 = rselect_tail(q16),
inference(modus_ponens,[status(thm)],[815,814]) ).
tff(817,plain,
rselect_tail(q16) = index_51,
inference(symmetry,[status(thm)],[816]) ).
tff(818,plain,
( ( index_48 = s(index_45) )
<=> ( index_48 = s(index_45) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(819,axiom,
index_48 = s(index_45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp159) ).
tff(820,plain,
index_48 = s(index_45),
inference(modus_ponens,[status(thm)],[819,818]) ).
tff(821,plain,
s(index_45) = index_48,
inference(symmetry,[status(thm)],[820]) ).
tff(822,plain,
( ( queue_47 = rstore_seq(q15,earray_46) )
<=> ( queue_47 = rstore_seq(q15,earray_46) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(823,axiom,
queue_47 = rstore_seq(q15,earray_46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp246) ).
tff(824,plain,
queue_47 = rstore_seq(q15,earray_46),
inference(modus_ponens,[status(thm)],[823,822]) ).
tff(825,plain,
rstore_seq(q15,earray_46) = queue_47,
inference(symmetry,[status(thm)],[824]) ).
tff(826,plain,
rstore_tail(rstore_seq(q15,earray_46),s(index_45)) = rstore_tail(queue_47,index_48),
inference(monotonicity,[status(thm)],[825,821]) ).
tff(827,plain,
rstore_tail(queue_47,index_48) = rstore_tail(rstore_seq(q15,earray_46),s(index_45)),
inference(symmetry,[status(thm)],[826]) ).
tff(828,plain,
( ( queue_49 = rstore_tail(queue_47,index_48) )
<=> ( queue_49 = rstore_tail(queue_47,index_48) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(829,axiom,
queue_49 = rstore_tail(queue_47,index_48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp247) ).
tff(830,plain,
queue_49 = rstore_tail(queue_47,index_48),
inference(modus_ponens,[status(thm)],[829,828]) ).
tff(831,plain,
( ( q16 = queue_49 )
<=> ( q16 = queue_49 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(832,axiom,
q16 = queue_49,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp274) ).
tff(833,plain,
q16 = queue_49,
inference(modus_ponens,[status(thm)],[832,831]) ).
tff(834,plain,
q16 = rstore_tail(rstore_seq(q15,earray_46),s(index_45)),
inference(transitivity,[status(thm)],[833,830,827]) ).
tff(835,plain,
rselect_tail(q16) = rselect_tail(rstore_tail(rstore_seq(q15,earray_46),s(index_45))),
inference(monotonicity,[status(thm)],[834]) ).
tff(836,plain,
rselect_tail(rstore_tail(rstore_seq(q15,earray_46),s(index_45))) = rselect_tail(q16),
inference(symmetry,[status(thm)],[835]) ).
tff(837,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q15,earray_46),s(index_45))) = s(index_45) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(838,plain,
rselect_tail(rstore_tail(rstore_seq(q15,earray_46),s(index_45))) = s(index_45),
inference(unit_resolution,[status(thm)],[837,25]) ).
tff(839,plain,
s(index_45) = rselect_tail(rstore_tail(rstore_seq(q15,earray_46),s(index_45))),
inference(symmetry,[status(thm)],[838]) ).
tff(840,plain,
( ( index_45 = rselect_tail(q15) )
<=> ( index_45 = rselect_tail(q15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(841,axiom,
index_45 = rselect_tail(q15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp158) ).
tff(842,plain,
index_45 = rselect_tail(q15),
inference(modus_ponens,[status(thm)],[841,840]) ).
tff(843,plain,
rselect_tail(q15) = index_45,
inference(symmetry,[status(thm)],[842]) ).
tff(844,plain,
s(rselect_tail(q15)) = s(index_45),
inference(monotonicity,[status(thm)],[843]) ).
tff(845,plain,
s(rselect_tail(q15)) = index_51,
inference(transitivity,[status(thm)],[844,839,836,817]) ).
tff(846,plain,
s(s(rselect_tail(q15))) = s(index_51),
inference(monotonicity,[status(thm)],[845]) ).
tff(847,plain,
s(index_51) = s(s(rselect_tail(q15))),
inference(symmetry,[status(thm)],[846]) ).
tff(848,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q16,earray_52),s(index_51))) = s(index_51) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(849,plain,
rselect_tail(rstore_tail(rstore_seq(q16,earray_52),s(index_51))) = s(index_51),
inference(unit_resolution,[status(thm)],[848,25]) ).
tff(850,plain,
( ( q17 = queue_55 )
<=> ( q17 = queue_55 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(851,axiom,
q17 = queue_55,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp275) ).
tff(852,plain,
q17 = queue_55,
inference(modus_ponens,[status(thm)],[851,850]) ).
tff(853,plain,
queue_55 = q17,
inference(symmetry,[status(thm)],[852]) ).
tff(854,plain,
( ( queue_55 = rstore_tail(queue_53,index_54) )
<=> ( queue_55 = rstore_tail(queue_53,index_54) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(855,axiom,
queue_55 = rstore_tail(queue_53,index_54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp250) ).
tff(856,plain,
queue_55 = rstore_tail(queue_53,index_54),
inference(modus_ponens,[status(thm)],[855,854]) ).
tff(857,plain,
rstore_tail(queue_53,index_54) = queue_55,
inference(symmetry,[status(thm)],[856]) ).
tff(858,plain,
( ( index_54 = s(index_51) )
<=> ( index_54 = s(index_51) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(859,axiom,
index_54 = s(index_51),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp161) ).
tff(860,plain,
index_54 = s(index_51),
inference(modus_ponens,[status(thm)],[859,858]) ).
tff(861,plain,
s(index_51) = index_54,
inference(symmetry,[status(thm)],[860]) ).
tff(862,plain,
( ( queue_53 = rstore_seq(q16,earray_52) )
<=> ( queue_53 = rstore_seq(q16,earray_52) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(863,axiom,
queue_53 = rstore_seq(q16,earray_52),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp249) ).
tff(864,plain,
queue_53 = rstore_seq(q16,earray_52),
inference(modus_ponens,[status(thm)],[863,862]) ).
tff(865,plain,
rstore_seq(q16,earray_52) = queue_53,
inference(symmetry,[status(thm)],[864]) ).
tff(866,plain,
rstore_tail(rstore_seq(q16,earray_52),s(index_51)) = rstore_tail(queue_53,index_54),
inference(monotonicity,[status(thm)],[865,861]) ).
tff(867,plain,
rstore_tail(rstore_seq(q16,earray_52),s(index_51)) = q17,
inference(transitivity,[status(thm)],[866,857,853]) ).
tff(868,plain,
rselect_tail(rstore_tail(rstore_seq(q16,earray_52),s(index_51))) = rselect_tail(q17),
inference(monotonicity,[status(thm)],[867]) ).
tff(869,plain,
rselect_tail(q17) = rselect_tail(rstore_tail(rstore_seq(q16,earray_52),s(index_51))),
inference(symmetry,[status(thm)],[868]) ).
tff(870,plain,
( ( index_57 = rselect_tail(q17) )
<=> ( index_57 = rselect_tail(q17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(871,axiom,
index_57 = rselect_tail(q17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp162) ).
tff(872,plain,
index_57 = rselect_tail(q17),
inference(modus_ponens,[status(thm)],[871,870]) ).
tff(873,plain,
index_57 = s(s(rselect_tail(q15))),
inference(transitivity,[status(thm)],[872,869,849,847]) ).
tff(874,plain,
s(index_57) = s(s(s(rselect_tail(q15)))),
inference(monotonicity,[status(thm)],[873]) ).
tff(875,plain,
s(s(s(rselect_tail(q15)))) = s(index_57),
inference(symmetry,[status(thm)],[874]) ).
tff(876,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q15)))) = rselect_tail(q15) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(877,plain,
s(s(s(rselect_tail(q15)))) = rselect_tail(q15),
inference(unit_resolution,[status(thm)],[876,187]) ).
tff(878,plain,
rselect_tail(q15) = s(s(s(rselect_tail(q15)))),
inference(symmetry,[status(thm)],[877]) ).
tff(879,plain,
( ( index_42 = s(index_39) )
<=> ( index_42 = s(index_39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(880,axiom,
index_42 = s(index_39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp157) ).
tff(881,plain,
index_42 = s(index_39),
inference(modus_ponens,[status(thm)],[880,879]) ).
tff(882,plain,
s(index_39) = index_42,
inference(symmetry,[status(thm)],[881]) ).
tff(883,plain,
( ( queue_41 = rstore_seq(q14,earray_40) )
<=> ( queue_41 = rstore_seq(q14,earray_40) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(884,axiom,
queue_41 = rstore_seq(q14,earray_40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp244) ).
tff(885,plain,
queue_41 = rstore_seq(q14,earray_40),
inference(modus_ponens,[status(thm)],[884,883]) ).
tff(886,plain,
rstore_seq(q14,earray_40) = queue_41,
inference(symmetry,[status(thm)],[885]) ).
tff(887,plain,
rstore_tail(rstore_seq(q14,earray_40),s(index_39)) = rstore_tail(queue_41,index_42),
inference(monotonicity,[status(thm)],[886,882]) ).
tff(888,plain,
rstore_tail(queue_41,index_42) = rstore_tail(rstore_seq(q14,earray_40),s(index_39)),
inference(symmetry,[status(thm)],[887]) ).
tff(889,plain,
( ( queue_43 = rstore_tail(queue_41,index_42) )
<=> ( queue_43 = rstore_tail(queue_41,index_42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(890,axiom,
queue_43 = rstore_tail(queue_41,index_42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp245) ).
tff(891,plain,
queue_43 = rstore_tail(queue_41,index_42),
inference(modus_ponens,[status(thm)],[890,889]) ).
tff(892,plain,
( ( q15 = queue_43 )
<=> ( q15 = queue_43 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(893,axiom,
q15 = queue_43,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp273) ).
tff(894,plain,
q15 = queue_43,
inference(modus_ponens,[status(thm)],[893,892]) ).
tff(895,plain,
q15 = rstore_tail(rstore_seq(q14,earray_40),s(index_39)),
inference(transitivity,[status(thm)],[894,891,888]) ).
tff(896,plain,
rselect_tail(q15) = rselect_tail(rstore_tail(rstore_seq(q14,earray_40),s(index_39))),
inference(monotonicity,[status(thm)],[895]) ).
tff(897,plain,
rselect_tail(rstore_tail(rstore_seq(q14,earray_40),s(index_39))) = rselect_tail(q15),
inference(symmetry,[status(thm)],[896]) ).
tff(898,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q14,earray_40),s(index_39))) = s(index_39) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(899,plain,
rselect_tail(rstore_tail(rstore_seq(q14,earray_40),s(index_39))) = s(index_39),
inference(unit_resolution,[status(thm)],[898,25]) ).
tff(900,plain,
s(index_39) = rselect_tail(rstore_tail(rstore_seq(q14,earray_40),s(index_39))),
inference(symmetry,[status(thm)],[899]) ).
tff(901,plain,
( ( index_33 = rselect_tail(q13) )
<=> ( index_33 = rselect_tail(q13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(902,axiom,
index_33 = rselect_tail(q13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp154) ).
tff(903,plain,
index_33 = rselect_tail(q13),
inference(modus_ponens,[status(thm)],[902,901]) ).
tff(904,plain,
rselect_tail(q13) = index_33,
inference(symmetry,[status(thm)],[903]) ).
tff(905,plain,
( ( q13 = queue_31 )
<=> ( q13 = queue_31 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(906,axiom,
q13 = queue_31,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp271) ).
tff(907,plain,
q13 = queue_31,
inference(modus_ponens,[status(thm)],[906,905]) ).
tff(908,plain,
queue_31 = q13,
inference(symmetry,[status(thm)],[907]) ).
tff(909,plain,
( ( queue_31 = rstore_tail(queue_29,index_30) )
<=> ( queue_31 = rstore_tail(queue_29,index_30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(910,axiom,
queue_31 = rstore_tail(queue_29,index_30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp241) ).
tff(911,plain,
queue_31 = rstore_tail(queue_29,index_30),
inference(modus_ponens,[status(thm)],[910,909]) ).
tff(912,plain,
rstore_tail(queue_29,index_30) = queue_31,
inference(symmetry,[status(thm)],[911]) ).
tff(913,plain,
( ( index_30 = s(index_27) )
<=> ( index_30 = s(index_27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(914,axiom,
index_30 = s(index_27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp153) ).
tff(915,plain,
index_30 = s(index_27),
inference(modus_ponens,[status(thm)],[914,913]) ).
tff(916,plain,
s(index_27) = index_30,
inference(symmetry,[status(thm)],[915]) ).
tff(917,plain,
( ( queue_29 = rstore_seq(q12,earray_28) )
<=> ( queue_29 = rstore_seq(q12,earray_28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(918,axiom,
queue_29 = rstore_seq(q12,earray_28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp240) ).
tff(919,plain,
queue_29 = rstore_seq(q12,earray_28),
inference(modus_ponens,[status(thm)],[918,917]) ).
tff(920,plain,
rstore_seq(q12,earray_28) = queue_29,
inference(symmetry,[status(thm)],[919]) ).
tff(921,plain,
rstore_tail(rstore_seq(q12,earray_28),s(index_27)) = rstore_tail(queue_29,index_30),
inference(monotonicity,[status(thm)],[920,916]) ).
tff(922,plain,
rstore_tail(rstore_seq(q12,earray_28),s(index_27)) = q13,
inference(transitivity,[status(thm)],[921,912,908]) ).
tff(923,plain,
rselect_tail(rstore_tail(rstore_seq(q12,earray_28),s(index_27))) = rselect_tail(q13),
inference(monotonicity,[status(thm)],[922]) ).
tff(924,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q12,earray_28),s(index_27))) = s(index_27) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(925,plain,
rselect_tail(rstore_tail(rstore_seq(q12,earray_28),s(index_27))) = s(index_27),
inference(unit_resolution,[status(thm)],[924,25]) ).
tff(926,plain,
s(index_27) = rselect_tail(rstore_tail(rstore_seq(q12,earray_28),s(index_27))),
inference(symmetry,[status(thm)],[925]) ).
tff(927,plain,
( ( index_27 = rselect_tail(q12) )
<=> ( index_27 = rselect_tail(q12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(928,axiom,
index_27 = rselect_tail(q12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp151) ).
tff(929,plain,
index_27 = rselect_tail(q12),
inference(modus_ponens,[status(thm)],[928,927]) ).
tff(930,plain,
rselect_tail(q12) = index_27,
inference(symmetry,[status(thm)],[929]) ).
tff(931,plain,
s(rselect_tail(q12)) = s(index_27),
inference(monotonicity,[status(thm)],[930]) ).
tff(932,plain,
s(rselect_tail(q12)) = index_33,
inference(transitivity,[status(thm)],[931,926,923,904]) ).
tff(933,plain,
s(s(rselect_tail(q12))) = s(index_33),
inference(monotonicity,[status(thm)],[932]) ).
tff(934,plain,
s(index_33) = s(s(rselect_tail(q12))),
inference(symmetry,[status(thm)],[933]) ).
tff(935,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q13,earray_34),s(index_33))) = s(index_33) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(936,plain,
rselect_tail(rstore_tail(rstore_seq(q13,earray_34),s(index_33))) = s(index_33),
inference(unit_resolution,[status(thm)],[935,25]) ).
tff(937,plain,
( ( q14 = queue_37 )
<=> ( q14 = queue_37 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(938,axiom,
q14 = queue_37,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp272) ).
tff(939,plain,
q14 = queue_37,
inference(modus_ponens,[status(thm)],[938,937]) ).
tff(940,plain,
queue_37 = q14,
inference(symmetry,[status(thm)],[939]) ).
tff(941,plain,
( ( queue_37 = rstore_tail(queue_35,index_36) )
<=> ( queue_37 = rstore_tail(queue_35,index_36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(942,axiom,
queue_37 = rstore_tail(queue_35,index_36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp243) ).
tff(943,plain,
queue_37 = rstore_tail(queue_35,index_36),
inference(modus_ponens,[status(thm)],[942,941]) ).
tff(944,plain,
rstore_tail(queue_35,index_36) = queue_37,
inference(symmetry,[status(thm)],[943]) ).
tff(945,plain,
( ( index_36 = s(index_33) )
<=> ( index_36 = s(index_33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(946,axiom,
index_36 = s(index_33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp155) ).
tff(947,plain,
index_36 = s(index_33),
inference(modus_ponens,[status(thm)],[946,945]) ).
tff(948,plain,
s(index_33) = index_36,
inference(symmetry,[status(thm)],[947]) ).
tff(949,plain,
( ( queue_35 = rstore_seq(q13,earray_34) )
<=> ( queue_35 = rstore_seq(q13,earray_34) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(950,axiom,
queue_35 = rstore_seq(q13,earray_34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp242) ).
tff(951,plain,
queue_35 = rstore_seq(q13,earray_34),
inference(modus_ponens,[status(thm)],[950,949]) ).
tff(952,plain,
rstore_seq(q13,earray_34) = queue_35,
inference(symmetry,[status(thm)],[951]) ).
tff(953,plain,
rstore_tail(rstore_seq(q13,earray_34),s(index_33)) = rstore_tail(queue_35,index_36),
inference(monotonicity,[status(thm)],[952,948]) ).
tff(954,plain,
rstore_tail(rstore_seq(q13,earray_34),s(index_33)) = q14,
inference(transitivity,[status(thm)],[953,944,940]) ).
tff(955,plain,
rselect_tail(rstore_tail(rstore_seq(q13,earray_34),s(index_33))) = rselect_tail(q14),
inference(monotonicity,[status(thm)],[954]) ).
tff(956,plain,
rselect_tail(q14) = rselect_tail(rstore_tail(rstore_seq(q13,earray_34),s(index_33))),
inference(symmetry,[status(thm)],[955]) ).
tff(957,plain,
( ( index_39 = rselect_tail(q14) )
<=> ( index_39 = rselect_tail(q14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(958,axiom,
index_39 = rselect_tail(q14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp156) ).
tff(959,plain,
index_39 = rselect_tail(q14),
inference(modus_ponens,[status(thm)],[958,957]) ).
tff(960,plain,
index_39 = s(s(rselect_tail(q12))),
inference(transitivity,[status(thm)],[959,956,936,934]) ).
tff(961,plain,
s(index_39) = s(s(s(rselect_tail(q12)))),
inference(monotonicity,[status(thm)],[960]) ).
tff(962,plain,
s(s(s(rselect_tail(q12)))) = s(index_39),
inference(symmetry,[status(thm)],[961]) ).
tff(963,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q12)))) = rselect_tail(q12) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(964,plain,
s(s(s(rselect_tail(q12)))) = rselect_tail(q12),
inference(unit_resolution,[status(thm)],[963,187]) ).
tff(965,plain,
rselect_tail(q12) = s(s(s(rselect_tail(q12)))),
inference(symmetry,[status(thm)],[964]) ).
tff(966,plain,
( ( index_24 = s(index_21) )
<=> ( index_24 = s(index_21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(967,axiom,
index_24 = s(index_21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp140) ).
tff(968,plain,
index_24 = s(index_21),
inference(modus_ponens,[status(thm)],[967,966]) ).
tff(969,plain,
s(index_21) = index_24,
inference(symmetry,[status(thm)],[968]) ).
tff(970,plain,
( ( queue_23 = rstore_seq(q11,earray_22) )
<=> ( queue_23 = rstore_seq(q11,earray_22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(971,axiom,
queue_23 = rstore_seq(q11,earray_22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp228) ).
tff(972,plain,
queue_23 = rstore_seq(q11,earray_22),
inference(modus_ponens,[status(thm)],[971,970]) ).
tff(973,plain,
rstore_seq(q11,earray_22) = queue_23,
inference(symmetry,[status(thm)],[972]) ).
tff(974,plain,
rstore_tail(rstore_seq(q11,earray_22),s(index_21)) = rstore_tail(queue_23,index_24),
inference(monotonicity,[status(thm)],[973,969]) ).
tff(975,plain,
rstore_tail(queue_23,index_24) = rstore_tail(rstore_seq(q11,earray_22),s(index_21)),
inference(symmetry,[status(thm)],[974]) ).
tff(976,plain,
( ( queue_25 = rstore_tail(queue_23,index_24) )
<=> ( queue_25 = rstore_tail(queue_23,index_24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(977,axiom,
queue_25 = rstore_tail(queue_23,index_24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp235) ).
tff(978,plain,
queue_25 = rstore_tail(queue_23,index_24),
inference(modus_ponens,[status(thm)],[977,976]) ).
tff(979,plain,
( ( q12 = queue_25 )
<=> ( q12 = queue_25 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(980,axiom,
q12 = queue_25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp270) ).
tff(981,plain,
q12 = queue_25,
inference(modus_ponens,[status(thm)],[980,979]) ).
tff(982,plain,
q12 = rstore_tail(rstore_seq(q11,earray_22),s(index_21)),
inference(transitivity,[status(thm)],[981,978,975]) ).
tff(983,plain,
rselect_tail(q12) = rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(monotonicity,[status(thm)],[982]) ).
tff(984,plain,
rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_tail(q12),
inference(symmetry,[status(thm)],[983]) ).
tff(985,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = s(index_21) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(986,plain,
rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = s(index_21),
inference(unit_resolution,[status(thm)],[985,25]) ).
tff(987,plain,
s(index_21) = rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(symmetry,[status(thm)],[986]) ).
tff(988,plain,
( ( index_15 = rselect_tail(q10) )
<=> ( index_15 = rselect_tail(q10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(989,axiom,
index_15 = rselect_tail(q10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp107) ).
tff(990,plain,
index_15 = rselect_tail(q10),
inference(modus_ponens,[status(thm)],[989,988]) ).
tff(991,plain,
rselect_tail(q10) = index_15,
inference(symmetry,[status(thm)],[990]) ).
tff(992,plain,
( ( q10 = queue_13 )
<=> ( q10 = queue_13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(993,axiom,
q10 = queue_13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp268) ).
tff(994,plain,
q10 = queue_13,
inference(modus_ponens,[status(thm)],[993,992]) ).
tff(995,plain,
queue_13 = q10,
inference(symmetry,[status(thm)],[994]) ).
tff(996,plain,
( ( queue_13 = rstore_tail(queue_11,index_12) )
<=> ( queue_13 = rstore_tail(queue_11,index_12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(997,axiom,
queue_13 = rstore_tail(queue_11,index_12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp191) ).
tff(998,plain,
queue_13 = rstore_tail(queue_11,index_12),
inference(modus_ponens,[status(thm)],[997,996]) ).
tff(999,plain,
rstore_tail(queue_11,index_12) = queue_13,
inference(symmetry,[status(thm)],[998]) ).
tff(1000,plain,
( ( index_12 = s(index_9) )
<=> ( index_12 = s(index_9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1001,axiom,
index_12 = s(index_9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp96) ).
tff(1002,plain,
index_12 = s(index_9),
inference(modus_ponens,[status(thm)],[1001,1000]) ).
tff(1003,plain,
s(index_9) = index_12,
inference(symmetry,[status(thm)],[1002]) ).
tff(1004,plain,
( ( queue_11 = rstore_seq(q9,earray_10) )
<=> ( queue_11 = rstore_seq(q9,earray_10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1005,axiom,
queue_11 = rstore_seq(q9,earray_10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp184) ).
tff(1006,plain,
queue_11 = rstore_seq(q9,earray_10),
inference(modus_ponens,[status(thm)],[1005,1004]) ).
tff(1007,plain,
rstore_seq(q9,earray_10) = queue_11,
inference(symmetry,[status(thm)],[1006]) ).
tff(1008,plain,
rstore_tail(rstore_seq(q9,earray_10),s(index_9)) = rstore_tail(queue_11,index_12),
inference(monotonicity,[status(thm)],[1007,1003]) ).
tff(1009,plain,
rstore_tail(rstore_seq(q9,earray_10),s(index_9)) = q10,
inference(transitivity,[status(thm)],[1008,999,995]) ).
tff(1010,plain,
rselect_tail(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = rselect_tail(q10),
inference(monotonicity,[status(thm)],[1009]) ).
tff(1011,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = s(index_9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1012,plain,
rselect_tail(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = s(index_9),
inference(unit_resolution,[status(thm)],[1011,25]) ).
tff(1013,plain,
s(index_9) = rselect_tail(rstore_tail(rstore_seq(q9,earray_10),s(index_9))),
inference(symmetry,[status(thm)],[1012]) ).
tff(1014,plain,
( ( index_9 = rselect_tail(q9) )
<=> ( index_9 = rselect_tail(q9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1015,axiom,
index_9 = rselect_tail(q9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp174) ).
tff(1016,plain,
index_9 = rselect_tail(q9),
inference(modus_ponens,[status(thm)],[1015,1014]) ).
tff(1017,plain,
rselect_tail(q9) = index_9,
inference(symmetry,[status(thm)],[1016]) ).
tff(1018,plain,
s(rselect_tail(q9)) = s(index_9),
inference(monotonicity,[status(thm)],[1017]) ).
tff(1019,plain,
s(rselect_tail(q9)) = index_15,
inference(transitivity,[status(thm)],[1018,1013,1010,991]) ).
tff(1020,plain,
s(s(rselect_tail(q9))) = s(index_15),
inference(monotonicity,[status(thm)],[1019]) ).
tff(1021,plain,
s(index_15) = s(s(rselect_tail(q9))),
inference(symmetry,[status(thm)],[1020]) ).
tff(1022,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = s(index_15) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1023,plain,
rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = s(index_15),
inference(unit_resolution,[status(thm)],[1022,25]) ).
tff(1024,plain,
( ( q11 = queue_19 )
<=> ( q11 = queue_19 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1025,axiom,
q11 = queue_19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp269) ).
tff(1026,plain,
q11 = queue_19,
inference(modus_ponens,[status(thm)],[1025,1024]) ).
tff(1027,plain,
queue_19 = q11,
inference(symmetry,[status(thm)],[1026]) ).
tff(1028,plain,
( ( queue_19 = rstore_tail(queue_17,index_18) )
<=> ( queue_19 = rstore_tail(queue_17,index_18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1029,axiom,
queue_19 = rstore_tail(queue_17,index_18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp213) ).
tff(1030,plain,
queue_19 = rstore_tail(queue_17,index_18),
inference(modus_ponens,[status(thm)],[1029,1028]) ).
tff(1031,plain,
rstore_tail(queue_17,index_18) = queue_19,
inference(symmetry,[status(thm)],[1030]) ).
tff(1032,plain,
( ( index_18 = s(index_15) )
<=> ( index_18 = s(index_15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1033,axiom,
index_18 = s(index_15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp118) ).
tff(1034,plain,
index_18 = s(index_15),
inference(modus_ponens,[status(thm)],[1033,1032]) ).
tff(1035,plain,
s(index_15) = index_18,
inference(symmetry,[status(thm)],[1034]) ).
tff(1036,plain,
( ( queue_17 = rstore_seq(q10,earray_16) )
<=> ( queue_17 = rstore_seq(q10,earray_16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1037,axiom,
queue_17 = rstore_seq(q10,earray_16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp206) ).
tff(1038,plain,
queue_17 = rstore_seq(q10,earray_16),
inference(modus_ponens,[status(thm)],[1037,1036]) ).
tff(1039,plain,
rstore_seq(q10,earray_16) = queue_17,
inference(symmetry,[status(thm)],[1038]) ).
tff(1040,plain,
rstore_tail(rstore_seq(q10,earray_16),s(index_15)) = rstore_tail(queue_17,index_18),
inference(monotonicity,[status(thm)],[1039,1035]) ).
tff(1041,plain,
rstore_tail(rstore_seq(q10,earray_16),s(index_15)) = q11,
inference(transitivity,[status(thm)],[1040,1031,1027]) ).
tff(1042,plain,
rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_tail(q11),
inference(monotonicity,[status(thm)],[1041]) ).
tff(1043,plain,
rselect_tail(q11) = rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))),
inference(symmetry,[status(thm)],[1042]) ).
tff(1044,plain,
( ( index_21 = rselect_tail(q11) )
<=> ( index_21 = rselect_tail(q11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1045,axiom,
index_21 = rselect_tail(q11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp129) ).
tff(1046,plain,
index_21 = rselect_tail(q11),
inference(modus_ponens,[status(thm)],[1045,1044]) ).
tff(1047,plain,
index_21 = s(s(rselect_tail(q9))),
inference(transitivity,[status(thm)],[1046,1043,1023,1021]) ).
tff(1048,plain,
s(index_21) = s(s(s(rselect_tail(q9)))),
inference(monotonicity,[status(thm)],[1047]) ).
tff(1049,plain,
s(s(s(rselect_tail(q9)))) = s(index_21),
inference(symmetry,[status(thm)],[1048]) ).
tff(1050,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q9)))) = rselect_tail(q9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1051,plain,
s(s(s(rselect_tail(q9)))) = rselect_tail(q9),
inference(unit_resolution,[status(thm)],[1050,187]) ).
tff(1052,plain,
rselect_tail(q9) = s(s(s(rselect_tail(q9)))),
inference(symmetry,[status(thm)],[1051]) ).
tff(1053,plain,
( ( index_258 = s(index_255) )
<=> ( index_258 = s(index_255) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1054,axiom,
index_258 = s(index_255),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp147) ).
tff(1055,plain,
index_258 = s(index_255),
inference(modus_ponens,[status(thm)],[1054,1053]) ).
tff(1056,plain,
s(index_255) = index_258,
inference(symmetry,[status(thm)],[1055]) ).
tff(1057,plain,
( ( queue_257 = rstore_seq(q8,earray_256) )
<=> ( queue_257 = rstore_seq(q8,earray_256) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1058,axiom,
queue_257 = rstore_seq(q8,earray_256),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp238) ).
tff(1059,plain,
queue_257 = rstore_seq(q8,earray_256),
inference(modus_ponens,[status(thm)],[1058,1057]) ).
tff(1060,plain,
rstore_seq(q8,earray_256) = queue_257,
inference(symmetry,[status(thm)],[1059]) ).
tff(1061,plain,
rstore_tail(rstore_seq(q8,earray_256),s(index_255)) = rstore_tail(queue_257,index_258),
inference(monotonicity,[status(thm)],[1060,1056]) ).
tff(1062,plain,
rstore_tail(queue_257,index_258) = rstore_tail(rstore_seq(q8,earray_256),s(index_255)),
inference(symmetry,[status(thm)],[1061]) ).
tff(1063,plain,
( ( queue_259 = rstore_tail(queue_257,index_258) )
<=> ( queue_259 = rstore_tail(queue_257,index_258) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1064,axiom,
queue_259 = rstore_tail(queue_257,index_258),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp239) ).
tff(1065,plain,
queue_259 = rstore_tail(queue_257,index_258),
inference(modus_ponens,[status(thm)],[1064,1063]) ).
tff(1066,plain,
( ( q9 = queue_259 )
<=> ( q9 = queue_259 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1067,axiom,
q9 = queue_259,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp309) ).
tff(1068,plain,
q9 = queue_259,
inference(modus_ponens,[status(thm)],[1067,1066]) ).
tff(1069,plain,
q9 = rstore_tail(rstore_seq(q8,earray_256),s(index_255)),
inference(transitivity,[status(thm)],[1068,1065,1062]) ).
tff(1070,plain,
rselect_tail(q9) = rselect_tail(rstore_tail(rstore_seq(q8,earray_256),s(index_255))),
inference(monotonicity,[status(thm)],[1069]) ).
tff(1071,plain,
rselect_tail(rstore_tail(rstore_seq(q8,earray_256),s(index_255))) = rselect_tail(q9),
inference(symmetry,[status(thm)],[1070]) ).
tff(1072,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q8,earray_256),s(index_255))) = s(index_255) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1073,plain,
rselect_tail(rstore_tail(rstore_seq(q8,earray_256),s(index_255))) = s(index_255),
inference(unit_resolution,[status(thm)],[1072,25]) ).
tff(1074,plain,
s(index_255) = rselect_tail(rstore_tail(rstore_seq(q8,earray_256),s(index_255))),
inference(symmetry,[status(thm)],[1073]) ).
tff(1075,plain,
( ( index_249 = rselect_tail(q7) )
<=> ( index_249 = rselect_tail(q7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1076,axiom,
index_249 = rselect_tail(q7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp144) ).
tff(1077,plain,
index_249 = rselect_tail(q7),
inference(modus_ponens,[status(thm)],[1076,1075]) ).
tff(1078,plain,
rselect_tail(q7) = index_249,
inference(symmetry,[status(thm)],[1077]) ).
tff(1079,plain,
( ( q7 = queue_247 )
<=> ( q7 = queue_247 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1080,axiom,
q7 = queue_247,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp307) ).
tff(1081,plain,
q7 = queue_247,
inference(modus_ponens,[status(thm)],[1080,1079]) ).
tff(1082,plain,
queue_247 = q7,
inference(symmetry,[status(thm)],[1081]) ).
tff(1083,plain,
( ( queue_247 = rstore_tail(queue_245,index_246) )
<=> ( queue_247 = rstore_tail(queue_245,index_246) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1084,axiom,
queue_247 = rstore_tail(queue_245,index_246),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp234) ).
tff(1085,plain,
queue_247 = rstore_tail(queue_245,index_246),
inference(modus_ponens,[status(thm)],[1084,1083]) ).
tff(1086,plain,
rstore_tail(queue_245,index_246) = queue_247,
inference(symmetry,[status(thm)],[1085]) ).
tff(1087,plain,
( ( index_246 = s(index_243) )
<=> ( index_246 = s(index_243) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1088,axiom,
index_246 = s(index_243),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp143) ).
tff(1089,plain,
index_246 = s(index_243),
inference(modus_ponens,[status(thm)],[1088,1087]) ).
tff(1090,plain,
s(index_243) = index_246,
inference(symmetry,[status(thm)],[1089]) ).
tff(1091,plain,
( ( queue_245 = rstore_seq(q6,earray_244) )
<=> ( queue_245 = rstore_seq(q6,earray_244) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1092,axiom,
queue_245 = rstore_seq(q6,earray_244),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp233) ).
tff(1093,plain,
queue_245 = rstore_seq(q6,earray_244),
inference(modus_ponens,[status(thm)],[1092,1091]) ).
tff(1094,plain,
rstore_seq(q6,earray_244) = queue_245,
inference(symmetry,[status(thm)],[1093]) ).
tff(1095,plain,
rstore_tail(rstore_seq(q6,earray_244),s(index_243)) = rstore_tail(queue_245,index_246),
inference(monotonicity,[status(thm)],[1094,1090]) ).
tff(1096,plain,
rstore_tail(rstore_seq(q6,earray_244),s(index_243)) = q7,
inference(transitivity,[status(thm)],[1095,1086,1082]) ).
tff(1097,plain,
rselect_tail(rstore_tail(rstore_seq(q6,earray_244),s(index_243))) = rselect_tail(q7),
inference(monotonicity,[status(thm)],[1096]) ).
tff(1098,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q6,earray_244),s(index_243))) = s(index_243) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1099,plain,
rselect_tail(rstore_tail(rstore_seq(q6,earray_244),s(index_243))) = s(index_243),
inference(unit_resolution,[status(thm)],[1098,25]) ).
tff(1100,plain,
s(index_243) = rselect_tail(rstore_tail(rstore_seq(q6,earray_244),s(index_243))),
inference(symmetry,[status(thm)],[1099]) ).
tff(1101,plain,
( ( index_243 = rselect_tail(q6) )
<=> ( index_243 = rselect_tail(q6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1102,axiom,
index_243 = rselect_tail(q6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp142) ).
tff(1103,plain,
index_243 = rselect_tail(q6),
inference(modus_ponens,[status(thm)],[1102,1101]) ).
tff(1104,plain,
rselect_tail(q6) = index_243,
inference(symmetry,[status(thm)],[1103]) ).
tff(1105,plain,
s(rselect_tail(q6)) = s(index_243),
inference(monotonicity,[status(thm)],[1104]) ).
tff(1106,plain,
s(rselect_tail(q6)) = index_249,
inference(transitivity,[status(thm)],[1105,1100,1097,1078]) ).
tff(1107,plain,
s(s(rselect_tail(q6))) = s(index_249),
inference(monotonicity,[status(thm)],[1106]) ).
tff(1108,plain,
s(index_249) = s(s(rselect_tail(q6))),
inference(symmetry,[status(thm)],[1107]) ).
tff(1109,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q7,earray_250),s(index_249))) = s(index_249) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1110,plain,
rselect_tail(rstore_tail(rstore_seq(q7,earray_250),s(index_249))) = s(index_249),
inference(unit_resolution,[status(thm)],[1109,25]) ).
tff(1111,plain,
( ( q8 = queue_253 )
<=> ( q8 = queue_253 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1112,axiom,
q8 = queue_253,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp308) ).
tff(1113,plain,
q8 = queue_253,
inference(modus_ponens,[status(thm)],[1112,1111]) ).
tff(1114,plain,
queue_253 = q8,
inference(symmetry,[status(thm)],[1113]) ).
tff(1115,plain,
( ( queue_253 = rstore_tail(queue_251,index_252) )
<=> ( queue_253 = rstore_tail(queue_251,index_252) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1116,axiom,
queue_253 = rstore_tail(queue_251,index_252),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp237) ).
tff(1117,plain,
queue_253 = rstore_tail(queue_251,index_252),
inference(modus_ponens,[status(thm)],[1116,1115]) ).
tff(1118,plain,
rstore_tail(queue_251,index_252) = queue_253,
inference(symmetry,[status(thm)],[1117]) ).
tff(1119,plain,
( ( index_252 = s(index_249) )
<=> ( index_252 = s(index_249) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1120,axiom,
index_252 = s(index_249),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp145) ).
tff(1121,plain,
index_252 = s(index_249),
inference(modus_ponens,[status(thm)],[1120,1119]) ).
tff(1122,plain,
s(index_249) = index_252,
inference(symmetry,[status(thm)],[1121]) ).
tff(1123,plain,
( ( queue_251 = rstore_seq(q7,earray_250) )
<=> ( queue_251 = rstore_seq(q7,earray_250) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1124,axiom,
queue_251 = rstore_seq(q7,earray_250),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp236) ).
tff(1125,plain,
queue_251 = rstore_seq(q7,earray_250),
inference(modus_ponens,[status(thm)],[1124,1123]) ).
tff(1126,plain,
rstore_seq(q7,earray_250) = queue_251,
inference(symmetry,[status(thm)],[1125]) ).
tff(1127,plain,
rstore_tail(rstore_seq(q7,earray_250),s(index_249)) = rstore_tail(queue_251,index_252),
inference(monotonicity,[status(thm)],[1126,1122]) ).
tff(1128,plain,
rstore_tail(rstore_seq(q7,earray_250),s(index_249)) = q8,
inference(transitivity,[status(thm)],[1127,1118,1114]) ).
tff(1129,plain,
rselect_tail(rstore_tail(rstore_seq(q7,earray_250),s(index_249))) = rselect_tail(q8),
inference(monotonicity,[status(thm)],[1128]) ).
tff(1130,plain,
rselect_tail(q8) = rselect_tail(rstore_tail(rstore_seq(q7,earray_250),s(index_249))),
inference(symmetry,[status(thm)],[1129]) ).
tff(1131,plain,
( ( index_255 = rselect_tail(q8) )
<=> ( index_255 = rselect_tail(q8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1132,axiom,
index_255 = rselect_tail(q8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp146) ).
tff(1133,plain,
index_255 = rselect_tail(q8),
inference(modus_ponens,[status(thm)],[1132,1131]) ).
tff(1134,plain,
index_255 = s(s(rselect_tail(q6))),
inference(transitivity,[status(thm)],[1133,1130,1110,1108]) ).
tff(1135,plain,
s(index_255) = s(s(s(rselect_tail(q6)))),
inference(monotonicity,[status(thm)],[1134]) ).
tff(1136,plain,
s(s(s(rselect_tail(q6)))) = s(index_255),
inference(symmetry,[status(thm)],[1135]) ).
tff(1137,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q6)))) = rselect_tail(q6) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1138,plain,
s(s(s(rselect_tail(q6)))) = rselect_tail(q6),
inference(unit_resolution,[status(thm)],[1137,187]) ).
tff(1139,plain,
rselect_tail(q6) = s(s(s(rselect_tail(q6)))),
inference(symmetry,[status(thm)],[1138]) ).
tff(1140,plain,
( ( index_240 = s(index_237) )
<=> ( index_240 = s(index_237) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1141,axiom,
index_240 = s(index_237),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp141) ).
tff(1142,plain,
index_240 = s(index_237),
inference(modus_ponens,[status(thm)],[1141,1140]) ).
tff(1143,plain,
s(index_237) = index_240,
inference(symmetry,[status(thm)],[1142]) ).
tff(1144,plain,
( ( queue_239 = rstore_seq(q5,earray_238) )
<=> ( queue_239 = rstore_seq(q5,earray_238) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1145,axiom,
queue_239 = rstore_seq(q5,earray_238),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp231) ).
tff(1146,plain,
queue_239 = rstore_seq(q5,earray_238),
inference(modus_ponens,[status(thm)],[1145,1144]) ).
tff(1147,plain,
rstore_seq(q5,earray_238) = queue_239,
inference(symmetry,[status(thm)],[1146]) ).
tff(1148,plain,
rstore_tail(rstore_seq(q5,earray_238),s(index_237)) = rstore_tail(queue_239,index_240),
inference(monotonicity,[status(thm)],[1147,1143]) ).
tff(1149,plain,
rstore_tail(queue_239,index_240) = rstore_tail(rstore_seq(q5,earray_238),s(index_237)),
inference(symmetry,[status(thm)],[1148]) ).
tff(1150,plain,
( ( queue_241 = rstore_tail(queue_239,index_240) )
<=> ( queue_241 = rstore_tail(queue_239,index_240) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1151,axiom,
queue_241 = rstore_tail(queue_239,index_240),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp232) ).
tff(1152,plain,
queue_241 = rstore_tail(queue_239,index_240),
inference(modus_ponens,[status(thm)],[1151,1150]) ).
tff(1153,plain,
( ( q6 = queue_241 )
<=> ( q6 = queue_241 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1154,axiom,
q6 = queue_241,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp306) ).
tff(1155,plain,
q6 = queue_241,
inference(modus_ponens,[status(thm)],[1154,1153]) ).
tff(1156,plain,
q6 = rstore_tail(rstore_seq(q5,earray_238),s(index_237)),
inference(transitivity,[status(thm)],[1155,1152,1149]) ).
tff(1157,plain,
rselect_tail(q6) = rselect_tail(rstore_tail(rstore_seq(q5,earray_238),s(index_237))),
inference(monotonicity,[status(thm)],[1156]) ).
tff(1158,plain,
rselect_tail(rstore_tail(rstore_seq(q5,earray_238),s(index_237))) = rselect_tail(q6),
inference(symmetry,[status(thm)],[1157]) ).
tff(1159,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q5,earray_238),s(index_237))) = s(index_237) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1160,plain,
rselect_tail(rstore_tail(rstore_seq(q5,earray_238),s(index_237))) = s(index_237),
inference(unit_resolution,[status(thm)],[1159,25]) ).
tff(1161,plain,
s(index_237) = rselect_tail(rstore_tail(rstore_seq(q5,earray_238),s(index_237))),
inference(symmetry,[status(thm)],[1160]) ).
tff(1162,plain,
( ( index_231 = rselect_tail(q4) )
<=> ( index_231 = rselect_tail(q4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1163,axiom,
index_231 = rselect_tail(q4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp137) ).
tff(1164,plain,
index_231 = rselect_tail(q4),
inference(modus_ponens,[status(thm)],[1163,1162]) ).
tff(1165,plain,
rselect_tail(q4) = index_231,
inference(symmetry,[status(thm)],[1164]) ).
tff(1166,plain,
( ( q4 = queue_205 )
<=> ( q4 = queue_205 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1167,axiom,
q4 = queue_205,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp300) ).
tff(1168,plain,
q4 = queue_205,
inference(modus_ponens,[status(thm)],[1167,1166]) ).
tff(1169,plain,
queue_205 = q4,
inference(symmetry,[status(thm)],[1168]) ).
tff(1170,plain,
( ( queue_205 = rstore_tail(queue_203,index_204) )
<=> ( queue_205 = rstore_tail(queue_203,index_204) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1171,axiom,
queue_205 = rstore_tail(queue_203,index_204),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp219) ).
tff(1172,plain,
queue_205 = rstore_tail(queue_203,index_204),
inference(modus_ponens,[status(thm)],[1171,1170]) ).
tff(1173,plain,
rstore_tail(queue_203,index_204) = queue_205,
inference(symmetry,[status(thm)],[1172]) ).
tff(1174,plain,
( ( index_204 = s(index_201) )
<=> ( index_204 = s(index_201) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1175,axiom,
index_204 = s(index_201),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp127) ).
tff(1176,plain,
index_204 = s(index_201),
inference(modus_ponens,[status(thm)],[1175,1174]) ).
tff(1177,plain,
s(index_201) = index_204,
inference(symmetry,[status(thm)],[1176]) ).
tff(1178,plain,
( ( queue_203 = rstore_seq(q3,earray_202) )
<=> ( queue_203 = rstore_seq(q3,earray_202) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1179,axiom,
queue_203 = rstore_seq(q3,earray_202),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp218) ).
tff(1180,plain,
queue_203 = rstore_seq(q3,earray_202),
inference(modus_ponens,[status(thm)],[1179,1178]) ).
tff(1181,plain,
rstore_seq(q3,earray_202) = queue_203,
inference(symmetry,[status(thm)],[1180]) ).
tff(1182,plain,
rstore_tail(rstore_seq(q3,earray_202),s(index_201)) = rstore_tail(queue_203,index_204),
inference(monotonicity,[status(thm)],[1181,1177]) ).
tff(1183,plain,
rstore_tail(rstore_seq(q3,earray_202),s(index_201)) = q4,
inference(transitivity,[status(thm)],[1182,1173,1169]) ).
tff(1184,plain,
rselect_tail(rstore_tail(rstore_seq(q3,earray_202),s(index_201))) = rselect_tail(q4),
inference(monotonicity,[status(thm)],[1183]) ).
tff(1185,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q3,earray_202),s(index_201))) = s(index_201) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1186,plain,
rselect_tail(rstore_tail(rstore_seq(q3,earray_202),s(index_201))) = s(index_201),
inference(unit_resolution,[status(thm)],[1185,25]) ).
tff(1187,plain,
s(index_201) = rselect_tail(rstore_tail(rstore_seq(q3,earray_202),s(index_201))),
inference(symmetry,[status(thm)],[1186]) ).
tff(1188,plain,
( ( index_201 = rselect_tail(q3) )
<=> ( index_201 = rselect_tail(q3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1189,axiom,
index_201 = rselect_tail(q3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp126) ).
tff(1190,plain,
index_201 = rselect_tail(q3),
inference(modus_ponens,[status(thm)],[1189,1188]) ).
tff(1191,plain,
rselect_tail(q3) = index_201,
inference(symmetry,[status(thm)],[1190]) ).
tff(1192,plain,
s(rselect_tail(q3)) = s(index_201),
inference(monotonicity,[status(thm)],[1191]) ).
tff(1193,plain,
s(rselect_tail(q3)) = index_231,
inference(transitivity,[status(thm)],[1192,1187,1184,1165]) ).
tff(1194,plain,
s(s(rselect_tail(q3))) = s(index_231),
inference(monotonicity,[status(thm)],[1193]) ).
tff(1195,plain,
s(index_231) = s(s(rselect_tail(q3))),
inference(symmetry,[status(thm)],[1194]) ).
tff(1196,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q4,earray_232),s(index_231))) = s(index_231) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1197,plain,
rselect_tail(rstore_tail(rstore_seq(q4,earray_232),s(index_231))) = s(index_231),
inference(unit_resolution,[status(thm)],[1196,25]) ).
tff(1198,plain,
( ( q5 = queue_235 )
<=> ( q5 = queue_235 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1199,axiom,
q5 = queue_235,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp305) ).
tff(1200,plain,
q5 = queue_235,
inference(modus_ponens,[status(thm)],[1199,1198]) ).
tff(1201,plain,
queue_235 = q5,
inference(symmetry,[status(thm)],[1200]) ).
tff(1202,plain,
( ( queue_235 = rstore_tail(queue_233,index_234) )
<=> ( queue_235 = rstore_tail(queue_233,index_234) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1203,axiom,
queue_235 = rstore_tail(queue_233,index_234),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp230) ).
tff(1204,plain,
queue_235 = rstore_tail(queue_233,index_234),
inference(modus_ponens,[status(thm)],[1203,1202]) ).
tff(1205,plain,
rstore_tail(queue_233,index_234) = queue_235,
inference(symmetry,[status(thm)],[1204]) ).
tff(1206,plain,
( ( index_234 = s(index_231) )
<=> ( index_234 = s(index_231) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1207,axiom,
index_234 = s(index_231),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp138) ).
tff(1208,plain,
index_234 = s(index_231),
inference(modus_ponens,[status(thm)],[1207,1206]) ).
tff(1209,plain,
s(index_231) = index_234,
inference(symmetry,[status(thm)],[1208]) ).
tff(1210,plain,
( ( queue_233 = rstore_seq(q4,earray_232) )
<=> ( queue_233 = rstore_seq(q4,earray_232) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1211,axiom,
queue_233 = rstore_seq(q4,earray_232),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp229) ).
tff(1212,plain,
queue_233 = rstore_seq(q4,earray_232),
inference(modus_ponens,[status(thm)],[1211,1210]) ).
tff(1213,plain,
rstore_seq(q4,earray_232) = queue_233,
inference(symmetry,[status(thm)],[1212]) ).
tff(1214,plain,
rstore_tail(rstore_seq(q4,earray_232),s(index_231)) = rstore_tail(queue_233,index_234),
inference(monotonicity,[status(thm)],[1213,1209]) ).
tff(1215,plain,
rstore_tail(rstore_seq(q4,earray_232),s(index_231)) = q5,
inference(transitivity,[status(thm)],[1214,1205,1201]) ).
tff(1216,plain,
rselect_tail(rstore_tail(rstore_seq(q4,earray_232),s(index_231))) = rselect_tail(q5),
inference(monotonicity,[status(thm)],[1215]) ).
tff(1217,plain,
rselect_tail(q5) = rselect_tail(rstore_tail(rstore_seq(q4,earray_232),s(index_231))),
inference(symmetry,[status(thm)],[1216]) ).
tff(1218,plain,
( ( index_237 = rselect_tail(q5) )
<=> ( index_237 = rselect_tail(q5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1219,axiom,
index_237 = rselect_tail(q5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp139) ).
tff(1220,plain,
index_237 = rselect_tail(q5),
inference(modus_ponens,[status(thm)],[1219,1218]) ).
tff(1221,plain,
index_237 = s(s(rselect_tail(q3))),
inference(transitivity,[status(thm)],[1220,1217,1197,1195]) ).
tff(1222,plain,
s(index_237) = s(s(s(rselect_tail(q3)))),
inference(monotonicity,[status(thm)],[1221]) ).
tff(1223,plain,
s(s(s(rselect_tail(q3)))) = s(index_237),
inference(symmetry,[status(thm)],[1222]) ).
tff(1224,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q3)))) = rselect_tail(q3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1225,plain,
s(s(s(rselect_tail(q3)))) = rselect_tail(q3),
inference(unit_resolution,[status(thm)],[1224,187]) ).
tff(1226,plain,
rselect_tail(q3) = s(s(s(rselect_tail(q3)))),
inference(symmetry,[status(thm)],[1225]) ).
tff(1227,plain,
( ( index_138 = s(index_135) )
<=> ( index_138 = s(index_135) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1228,axiom,
index_138 = s(index_135),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp103) ).
tff(1229,plain,
index_138 = s(index_135),
inference(modus_ponens,[status(thm)],[1228,1227]) ).
tff(1230,plain,
s(index_135) = index_138,
inference(symmetry,[status(thm)],[1229]) ).
tff(1231,plain,
( ( queue_137 = rstore_seq(q2,earray_136) )
<=> ( queue_137 = rstore_seq(q2,earray_136) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1232,axiom,
queue_137 = rstore_seq(q2,earray_136),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp194) ).
tff(1233,plain,
queue_137 = rstore_seq(q2,earray_136),
inference(modus_ponens,[status(thm)],[1232,1231]) ).
tff(1234,plain,
rstore_seq(q2,earray_136) = queue_137,
inference(symmetry,[status(thm)],[1233]) ).
tff(1235,plain,
rstore_tail(rstore_seq(q2,earray_136),s(index_135)) = rstore_tail(queue_137,index_138),
inference(monotonicity,[status(thm)],[1234,1230]) ).
tff(1236,plain,
rstore_tail(queue_137,index_138) = rstore_tail(rstore_seq(q2,earray_136),s(index_135)),
inference(symmetry,[status(thm)],[1235]) ).
tff(1237,plain,
( ( queue_139 = rstore_tail(queue_137,index_138) )
<=> ( queue_139 = rstore_tail(queue_137,index_138) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1238,axiom,
queue_139 = rstore_tail(queue_137,index_138),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp195) ).
tff(1239,plain,
queue_139 = rstore_tail(queue_137,index_138),
inference(modus_ponens,[status(thm)],[1238,1237]) ).
tff(1240,plain,
( ( q3 = queue_139 )
<=> ( q3 = queue_139 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1241,axiom,
q3 = queue_139,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp289) ).
tff(1242,plain,
q3 = queue_139,
inference(modus_ponens,[status(thm)],[1241,1240]) ).
tff(1243,plain,
q3 = rstore_tail(rstore_seq(q2,earray_136),s(index_135)),
inference(transitivity,[status(thm)],[1242,1239,1236]) ).
tff(1244,plain,
rselect_tail(q3) = rselect_tail(rstore_tail(rstore_seq(q2,earray_136),s(index_135))),
inference(monotonicity,[status(thm)],[1243]) ).
tff(1245,plain,
rselect_tail(rstore_tail(rstore_seq(q2,earray_136),s(index_135))) = rselect_tail(q3),
inference(symmetry,[status(thm)],[1244]) ).
tff(1246,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q2,earray_136),s(index_135))) = s(index_135) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1247,plain,
rselect_tail(rstore_tail(rstore_seq(q2,earray_136),s(index_135))) = s(index_135),
inference(unit_resolution,[status(thm)],[1246,25]) ).
tff(1248,plain,
s(index_135) = rselect_tail(rstore_tail(rstore_seq(q2,earray_136),s(index_135))),
inference(symmetry,[status(thm)],[1247]) ).
tff(1249,plain,
( ( index_69 = rselect_tail(q1) )
<=> ( index_69 = rselect_tail(q1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1250,axiom,
index_69 = rselect_tail(q1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp167) ).
tff(1251,plain,
index_69 = rselect_tail(q1),
inference(modus_ponens,[status(thm)],[1250,1249]) ).
tff(1252,plain,
rselect_tail(q1) = index_69,
inference(symmetry,[status(thm)],[1251]) ).
tff(1253,plain,
( ( q1 = queue_7 )
<=> ( q1 = queue_7 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1254,axiom,
q1 = queue_7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp267) ).
tff(1255,plain,
q1 = queue_7,
inference(modus_ponens,[status(thm)],[1254,1253]) ).
tff(1256,plain,
queue_7 = q1,
inference(symmetry,[status(thm)],[1255]) ).
tff(1257,plain,
( ( queue_7 = rstore_tail(queue_5,index_6) )
<=> ( queue_7 = rstore_tail(queue_5,index_6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1258,axiom,
queue_7 = rstore_tail(queue_5,index_6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp255) ).
tff(1259,plain,
queue_7 = rstore_tail(queue_5,index_6),
inference(modus_ponens,[status(thm)],[1258,1257]) ).
tff(1260,plain,
rstore_tail(queue_5,index_6) = queue_7,
inference(symmetry,[status(thm)],[1259]) ).
tff(1261,plain,
( ( index_6 = s(index_3) )
<=> ( index_6 = s(index_3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1262,axiom,
index_6 = s(index_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp163) ).
tff(1263,plain,
index_6 = s(index_3),
inference(modus_ponens,[status(thm)],[1262,1261]) ).
tff(1264,plain,
s(index_3) = index_6,
inference(symmetry,[status(thm)],[1263]) ).
tff(1265,plain,
( ( queue_5 = rstore_seq(q0,earray_4) )
<=> ( queue_5 = rstore_seq(q0,earray_4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1266,axiom,
queue_5 = rstore_seq(q0,earray_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp248) ).
tff(1267,plain,
queue_5 = rstore_seq(q0,earray_4),
inference(modus_ponens,[status(thm)],[1266,1265]) ).
tff(1268,plain,
rstore_seq(q0,earray_4) = queue_5,
inference(symmetry,[status(thm)],[1267]) ).
tff(1269,plain,
rstore_tail(rstore_seq(q0,earray_4),s(index_3)) = rstore_tail(queue_5,index_6),
inference(monotonicity,[status(thm)],[1268,1264]) ).
tff(1270,plain,
rstore_tail(rstore_seq(q0,earray_4),s(index_3)) = q1,
inference(transitivity,[status(thm)],[1269,1260,1256]) ).
tff(1271,plain,
rselect_tail(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = rselect_tail(q1),
inference(monotonicity,[status(thm)],[1270]) ).
tff(1272,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = s(index_3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1273,plain,
rselect_tail(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = s(index_3),
inference(unit_resolution,[status(thm)],[1272,25]) ).
tff(1274,plain,
s(index_3) = rselect_tail(rstore_tail(rstore_seq(q0,earray_4),s(index_3))),
inference(symmetry,[status(thm)],[1273]) ).
tff(1275,plain,
( ( index_3 = rselect_tail(q0) )
<=> ( index_3 = rselect_tail(q0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1276,axiom,
index_3 = rselect_tail(q0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp152) ).
tff(1277,plain,
index_3 = rselect_tail(q0),
inference(modus_ponens,[status(thm)],[1276,1275]) ).
tff(1278,plain,
rselect_tail(q0) = index_3,
inference(symmetry,[status(thm)],[1277]) ).
tff(1279,plain,
s(rselect_tail(q0)) = s(index_3),
inference(monotonicity,[status(thm)],[1278]) ).
tff(1280,plain,
s(rselect_tail(q0)) = index_69,
inference(transitivity,[status(thm)],[1279,1274,1271,1252]) ).
tff(1281,plain,
s(s(rselect_tail(q0))) = s(index_69),
inference(monotonicity,[status(thm)],[1280]) ).
tff(1282,plain,
s(index_69) = s(s(rselect_tail(q0))),
inference(symmetry,[status(thm)],[1281]) ).
tff(1283,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q1,earray_70),s(index_69))) = s(index_69) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1284,plain,
rselect_tail(rstore_tail(rstore_seq(q1,earray_70),s(index_69))) = s(index_69),
inference(unit_resolution,[status(thm)],[1283,25]) ).
tff(1285,plain,
( ( q2 = queue_73 )
<=> ( q2 = queue_73 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1286,axiom,
q2 = queue_73,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp278) ).
tff(1287,plain,
q2 = queue_73,
inference(modus_ponens,[status(thm)],[1286,1285]) ).
tff(1288,plain,
queue_73 = q2,
inference(symmetry,[status(thm)],[1287]) ).
tff(1289,plain,
( ( queue_73 = rstore_tail(queue_71,index_72) )
<=> ( queue_73 = rstore_tail(queue_71,index_72) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1290,axiom,
queue_73 = rstore_tail(queue_71,index_72),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp257) ).
tff(1291,plain,
queue_73 = rstore_tail(queue_71,index_72),
inference(modus_ponens,[status(thm)],[1290,1289]) ).
tff(1292,plain,
rstore_tail(queue_71,index_72) = queue_73,
inference(symmetry,[status(thm)],[1291]) ).
tff(1293,plain,
( ( index_72 = s(index_69) )
<=> ( index_72 = s(index_69) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1294,axiom,
index_72 = s(index_69),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp168) ).
tff(1295,plain,
index_72 = s(index_69),
inference(modus_ponens,[status(thm)],[1294,1293]) ).
tff(1296,plain,
s(index_69) = index_72,
inference(symmetry,[status(thm)],[1295]) ).
tff(1297,plain,
( ( queue_71 = rstore_seq(q1,earray_70) )
<=> ( queue_71 = rstore_seq(q1,earray_70) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1298,axiom,
queue_71 = rstore_seq(q1,earray_70),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp256) ).
tff(1299,plain,
queue_71 = rstore_seq(q1,earray_70),
inference(modus_ponens,[status(thm)],[1298,1297]) ).
tff(1300,plain,
rstore_seq(q1,earray_70) = queue_71,
inference(symmetry,[status(thm)],[1299]) ).
tff(1301,plain,
rstore_tail(rstore_seq(q1,earray_70),s(index_69)) = rstore_tail(queue_71,index_72),
inference(monotonicity,[status(thm)],[1300,1296]) ).
tff(1302,plain,
rstore_tail(rstore_seq(q1,earray_70),s(index_69)) = q2,
inference(transitivity,[status(thm)],[1301,1292,1288]) ).
tff(1303,plain,
rselect_tail(rstore_tail(rstore_seq(q1,earray_70),s(index_69))) = rselect_tail(q2),
inference(monotonicity,[status(thm)],[1302]) ).
tff(1304,plain,
rselect_tail(q2) = rselect_tail(rstore_tail(rstore_seq(q1,earray_70),s(index_69))),
inference(symmetry,[status(thm)],[1303]) ).
tff(1305,plain,
( ( index_135 = rselect_tail(q2) )
<=> ( index_135 = rselect_tail(q2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1306,axiom,
index_135 = rselect_tail(q2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp102) ).
tff(1307,plain,
index_135 = rselect_tail(q2),
inference(modus_ponens,[status(thm)],[1306,1305]) ).
tff(1308,plain,
index_135 = s(s(rselect_tail(q0))),
inference(transitivity,[status(thm)],[1307,1304,1284,1282]) ).
tff(1309,plain,
s(index_135) = s(s(s(rselect_tail(q0)))),
inference(monotonicity,[status(thm)],[1308]) ).
tff(1310,plain,
s(s(s(rselect_tail(q0)))) = s(index_135),
inference(symmetry,[status(thm)],[1309]) ).
tff(1311,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(rselect_tail(q0)))) = rselect_tail(q0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1312,plain,
s(s(s(rselect_tail(q0)))) = rselect_tail(q0),
inference(unit_resolution,[status(thm)],[1311,187]) ).
tff(1313,plain,
rselect_tail(q0) = s(s(s(rselect_tail(q0)))),
inference(symmetry,[status(thm)],[1312]) ).
tff(1314,plain,
( ( index_0 = rselect_tail(q) )
<=> ( index_0 = rselect_tail(q) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1315,axiom,
index_0 = rselect_tail(q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp89) ).
tff(1316,plain,
index_0 = rselect_tail(q),
inference(modus_ponens,[status(thm)],[1315,1314]) ).
tff(1317,plain,
rselect_tail(q) = index_0,
inference(symmetry,[status(thm)],[1316]) ).
tff(1318,plain,
rstore_head(q,rselect_tail(q)) = rstore_head(q,index_0),
inference(monotonicity,[status(thm)],[1317]) ).
tff(1319,plain,
rstore_head(q,index_0) = rstore_head(q,rselect_tail(q)),
inference(symmetry,[status(thm)],[1318]) ).
tff(1320,plain,
( ( queue_1 = rstore_head(q,index_0) )
<=> ( queue_1 = rstore_head(q,index_0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1321,axiom,
queue_1 = rstore_head(q,index_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp179) ).
tff(1322,plain,
queue_1 = rstore_head(q,index_0),
inference(modus_ponens,[status(thm)],[1321,1320]) ).
tff(1323,plain,
( ( q0 = queue_1 )
<=> ( q0 = queue_1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1324,axiom,
q0 = queue_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp266) ).
tff(1325,plain,
q0 = queue_1,
inference(modus_ponens,[status(thm)],[1324,1323]) ).
tff(1326,plain,
q0 = rstore_head(q,rselect_tail(q)),
inference(transitivity,[status(thm)],[1325,1322,1319]) ).
tff(1327,plain,
rselect_tail(q0) = rselect_tail(rstore_head(q,rselect_tail(q))),
inference(monotonicity,[status(thm)],[1326]) ).
tff(1328,plain,
rselect_tail(rstore_head(q,rselect_tail(q))) = rselect_tail(q0),
inference(symmetry,[status(thm)],[1327]) ).
tff(1329,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
<=> ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ) )),
inference(bind,[status(th)],[]) ).
tff(1330,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ) ),
inference(quant_intro,[status(thm)],[1329]) ).
tff(1331,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1332,axiom,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_tail_head) ).
tff(1333,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
inference(modus_ponens,[status(thm)],[1332,1331]) ).
tff(1334,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
inference(skolemize,[status(sab)],[1333]) ).
tff(1335,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
inference(modus_ponens,[status(thm)],[1334,1330]) ).
tff(1336,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(q,rselect_tail(q))) = rselect_tail(q) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1337,plain,
rselect_tail(rstore_head(q,rselect_tail(q))) = rselect_tail(q),
inference(unit_resolution,[status(thm)],[1336,1335]) ).
tff(1338,plain,
rselect_tail(q) = rselect_tail(rstore_head(q,rselect_tail(q))),
inference(symmetry,[status(thm)],[1337]) ).
tff(1339,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_head(rstore_head(A,E)) = E )
<=> ( rselect_head(rstore_head(A,E)) = E ) )),
inference(bind,[status(th)],[]) ).
tff(1340,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ) ),
inference(quant_intro,[status(thm)],[1339]) ).
tff(1341,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1342,axiom,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_head) ).
tff(1343,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
inference(modus_ponens,[status(thm)],[1342,1341]) ).
tff(1344,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
inference(skolemize,[status(sab)],[1343]) ).
tff(1345,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
inference(modus_ponens,[status(thm)],[1344,1340]) ).
tff(1346,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(q,rselect_tail(q))) = rselect_tail(q) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1347,plain,
rselect_head(rstore_head(q,rselect_tail(q))) = rselect_tail(q),
inference(unit_resolution,[status(thm)],[1346,1345]) ).
tff(1348,plain,
rselect_head(rstore_head(q,rselect_tail(q))) = rselect_head(rstore_head(q,index_0)),
inference(monotonicity,[status(thm)],[1318]) ).
tff(1349,plain,
rselect_head(rstore_head(q,index_0)) = rselect_head(rstore_head(q,rselect_tail(q))),
inference(symmetry,[status(thm)],[1348]) ).
tff(1350,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
<=> ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ) )),
inference(bind,[status(th)],[]) ).
tff(1351,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ) ),
inference(quant_intro,[status(thm)],[1350]) ).
tff(1352,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1353,axiom,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_head_seq) ).
tff(1354,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[1353,1352]) ).
tff(1355,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
inference(skolemize,[status(sab)],[1354]) ).
tff(1356,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[1355,1351]) ).
tff(1357,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))) = rselect_head(rstore_head(q,index_0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1358,plain,
rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))) = rselect_head(rstore_head(q,index_0)),
inference(unit_resolution,[status(thm)],[1357,1356]) ).
tff(1359,plain,
( ( earray_4 = store(earray_2,index_3,e0) )
<=> ( earray_4 = store(earray_2,index_3,e0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1360,axiom,
earray_4 = store(earray_2,index_3,e0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp65) ).
tff(1361,plain,
earray_4 = store(earray_2,index_3,e0),
inference(modus_ponens,[status(thm)],[1360,1359]) ).
tff(1362,plain,
store(earray_2,index_3,e0) = earray_4,
inference(symmetry,[status(thm)],[1361]) ).
tff(1363,plain,
queue_1 = q0,
inference(symmetry,[status(thm)],[1325]) ).
tff(1364,plain,
rstore_head(q,index_0) = queue_1,
inference(symmetry,[status(thm)],[1322]) ).
tff(1365,plain,
rstore_head(q,index_0) = q0,
inference(transitivity,[status(thm)],[1364,1363]) ).
tff(1366,plain,
rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0)) = rstore_seq(q0,earray_4),
inference(monotonicity,[status(thm)],[1365,1362]) ).
tff(1367,plain,
rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))) = rselect_head(rstore_seq(q0,earray_4)),
inference(monotonicity,[status(thm)],[1366]) ).
tff(1368,plain,
rselect_head(rstore_seq(q0,earray_4)) = rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))),
inference(symmetry,[status(thm)],[1367]) ).
tff(1369,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
<=> ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ) )),
inference(bind,[status(th)],[]) ).
tff(1370,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ) ),
inference(quant_intro,[status(thm)],[1369]) ).
tff(1371,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1372,axiom,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_head_tail) ).
tff(1373,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[1372,1371]) ).
tff(1374,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
inference(skolemize,[status(sab)],[1373]) ).
tff(1375,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[1374,1370]) ).
tff(1376,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = rselect_head(rstore_seq(q0,earray_4)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1377,plain,
rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = rselect_head(rstore_seq(q0,earray_4)),
inference(unit_resolution,[status(thm)],[1376,1375]) ).
tff(1378,plain,
rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = rselect_head(rstore_tail(queue_5,index_6)),
inference(monotonicity,[status(thm)],[1269]) ).
tff(1379,plain,
rselect_head(rstore_tail(queue_5,index_6)) = rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))),
inference(symmetry,[status(thm)],[1378]) ).
tff(1380,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_68,index_69,e1))) = rselect_head(rstore_tail(queue_5,index_6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1381,plain,
rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_68,index_69,e1))) = rselect_head(rstore_tail(queue_5,index_6)),
inference(unit_resolution,[status(thm)],[1380,1356]) ).
tff(1382,plain,
( ( earray_70 = store(earray_68,index_69,e1) )
<=> ( earray_70 = store(earray_68,index_69,e1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1383,axiom,
earray_70 = store(earray_68,index_69,e1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp76) ).
tff(1384,plain,
earray_70 = store(earray_68,index_69,e1),
inference(modus_ponens,[status(thm)],[1383,1382]) ).
tff(1385,plain,
store(earray_68,index_69,e1) = earray_70,
inference(symmetry,[status(thm)],[1384]) ).
tff(1386,plain,
rstore_tail(queue_5,index_6) = q1,
inference(transitivity,[status(thm)],[1260,1256]) ).
tff(1387,plain,
rstore_seq(rstore_tail(queue_5,index_6),store(earray_68,index_69,e1)) = rstore_seq(q1,earray_70),
inference(monotonicity,[status(thm)],[1386,1385]) ).
tff(1388,plain,
rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_68,index_69,e1))) = rselect_head(rstore_seq(q1,earray_70)),
inference(monotonicity,[status(thm)],[1387]) ).
tff(1389,plain,
rselect_head(rstore_seq(q1,earray_70)) = rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_68,index_69,e1))),
inference(symmetry,[status(thm)],[1388]) ).
tff(1390,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q1,earray_70),s(index_69))) = rselect_head(rstore_seq(q1,earray_70)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1391,plain,
rselect_head(rstore_tail(rstore_seq(q1,earray_70),s(index_69))) = rselect_head(rstore_seq(q1,earray_70)),
inference(unit_resolution,[status(thm)],[1390,1375]) ).
tff(1392,plain,
rselect_head(rstore_tail(rstore_seq(q1,earray_70),s(index_69))) = rselect_head(rstore_tail(queue_71,index_72)),
inference(monotonicity,[status(thm)],[1301]) ).
tff(1393,plain,
rselect_head(rstore_tail(queue_71,index_72)) = rselect_head(rstore_tail(rstore_seq(q1,earray_70),s(index_69))),
inference(symmetry,[status(thm)],[1392]) ).
tff(1394,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_71,index_72),store(earray_134,index_135,e2))) = rselect_head(rstore_tail(queue_71,index_72)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1395,plain,
rselect_head(rstore_seq(rstore_tail(queue_71,index_72),store(earray_134,index_135,e2))) = rselect_head(rstore_tail(queue_71,index_72)),
inference(unit_resolution,[status(thm)],[1394,1356]) ).
tff(1396,plain,
( ( earray_136 = store(earray_134,index_135,e2) )
<=> ( earray_136 = store(earray_134,index_135,e2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1397,axiom,
earray_136 = store(earray_134,index_135,e2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp13) ).
tff(1398,plain,
earray_136 = store(earray_134,index_135,e2),
inference(modus_ponens,[status(thm)],[1397,1396]) ).
tff(1399,plain,
store(earray_134,index_135,e2) = earray_136,
inference(symmetry,[status(thm)],[1398]) ).
tff(1400,plain,
rstore_tail(queue_71,index_72) = q2,
inference(transitivity,[status(thm)],[1292,1288]) ).
tff(1401,plain,
rstore_seq(rstore_tail(queue_71,index_72),store(earray_134,index_135,e2)) = rstore_seq(q2,earray_136),
inference(monotonicity,[status(thm)],[1400,1399]) ).
tff(1402,plain,
rselect_head(rstore_seq(rstore_tail(queue_71,index_72),store(earray_134,index_135,e2))) = rselect_head(rstore_seq(q2,earray_136)),
inference(monotonicity,[status(thm)],[1401]) ).
tff(1403,plain,
rselect_head(rstore_seq(q2,earray_136)) = rselect_head(rstore_seq(rstore_tail(queue_71,index_72),store(earray_134,index_135,e2))),
inference(symmetry,[status(thm)],[1402]) ).
tff(1404,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q2,earray_136),s(index_135))) = rselect_head(rstore_seq(q2,earray_136)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1405,plain,
rselect_head(rstore_tail(rstore_seq(q2,earray_136),s(index_135))) = rselect_head(rstore_seq(q2,earray_136)),
inference(unit_resolution,[status(thm)],[1404,1375]) ).
tff(1406,plain,
rselect_head(rstore_tail(rstore_seq(q2,earray_136),s(index_135))) = rselect_head(rstore_tail(queue_137,index_138)),
inference(monotonicity,[status(thm)],[1235]) ).
tff(1407,plain,
rselect_head(rstore_tail(queue_137,index_138)) = rselect_head(rstore_tail(rstore_seq(q2,earray_136),s(index_135))),
inference(symmetry,[status(thm)],[1406]) ).
tff(1408,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_137,index_138),store(earray_200,index_201,e3))) = rselect_head(rstore_tail(queue_137,index_138)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1409,plain,
rselect_head(rstore_seq(rstore_tail(queue_137,index_138),store(earray_200,index_201,e3))) = rselect_head(rstore_tail(queue_137,index_138)),
inference(unit_resolution,[status(thm)],[1408,1356]) ).
tff(1410,plain,
( ( earray_202 = store(earray_200,index_201,e3) )
<=> ( earray_202 = store(earray_200,index_201,e3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1411,axiom,
earray_202 = store(earray_200,index_201,e3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp39) ).
tff(1412,plain,
earray_202 = store(earray_200,index_201,e3),
inference(modus_ponens,[status(thm)],[1411,1410]) ).
tff(1413,plain,
store(earray_200,index_201,e3) = earray_202,
inference(symmetry,[status(thm)],[1412]) ).
tff(1414,plain,
queue_139 = q3,
inference(symmetry,[status(thm)],[1242]) ).
tff(1415,plain,
rstore_tail(queue_137,index_138) = queue_139,
inference(symmetry,[status(thm)],[1239]) ).
tff(1416,plain,
rstore_tail(queue_137,index_138) = q3,
inference(transitivity,[status(thm)],[1415,1414]) ).
tff(1417,plain,
rstore_seq(rstore_tail(queue_137,index_138),store(earray_200,index_201,e3)) = rstore_seq(q3,earray_202),
inference(monotonicity,[status(thm)],[1416,1413]) ).
tff(1418,plain,
rselect_head(rstore_seq(rstore_tail(queue_137,index_138),store(earray_200,index_201,e3))) = rselect_head(rstore_seq(q3,earray_202)),
inference(monotonicity,[status(thm)],[1417]) ).
tff(1419,plain,
rselect_head(rstore_seq(q3,earray_202)) = rselect_head(rstore_seq(rstore_tail(queue_137,index_138),store(earray_200,index_201,e3))),
inference(symmetry,[status(thm)],[1418]) ).
tff(1420,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q3,earray_202),s(index_201))) = rselect_head(rstore_seq(q3,earray_202)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1421,plain,
rselect_head(rstore_tail(rstore_seq(q3,earray_202),s(index_201))) = rselect_head(rstore_seq(q3,earray_202)),
inference(unit_resolution,[status(thm)],[1420,1375]) ).
tff(1422,plain,
rstore_tail(queue_203,index_204) = rstore_tail(rstore_seq(q3,earray_202),s(index_201)),
inference(symmetry,[status(thm)],[1182]) ).
tff(1423,plain,
rselect_head(rstore_tail(queue_203,index_204)) = rselect_head(rstore_tail(rstore_seq(q3,earray_202),s(index_201))),
inference(monotonicity,[status(thm)],[1422]) ).
tff(1424,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_203,index_204),store(earray_230,index_231,e4))) = rselect_head(rstore_tail(queue_203,index_204)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1425,plain,
rselect_head(rstore_seq(rstore_tail(queue_203,index_204),store(earray_230,index_231,e4))) = rselect_head(rstore_tail(queue_203,index_204)),
inference(unit_resolution,[status(thm)],[1424,1356]) ).
tff(1426,plain,
( ( earray_232 = store(earray_230,index_231,e4) )
<=> ( earray_232 = store(earray_230,index_231,e4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1427,axiom,
earray_232 = store(earray_230,index_231,e4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp50) ).
tff(1428,plain,
earray_232 = store(earray_230,index_231,e4),
inference(modus_ponens,[status(thm)],[1427,1426]) ).
tff(1429,plain,
store(earray_230,index_231,e4) = earray_232,
inference(symmetry,[status(thm)],[1428]) ).
tff(1430,plain,
rstore_tail(queue_203,index_204) = q4,
inference(transitivity,[status(thm)],[1173,1169]) ).
tff(1431,plain,
rstore_seq(rstore_tail(queue_203,index_204),store(earray_230,index_231,e4)) = rstore_seq(q4,earray_232),
inference(monotonicity,[status(thm)],[1430,1429]) ).
tff(1432,plain,
rstore_seq(q4,earray_232) = rstore_seq(rstore_tail(queue_203,index_204),store(earray_230,index_231,e4)),
inference(symmetry,[status(thm)],[1431]) ).
tff(1433,plain,
rselect_head(rstore_seq(q4,earray_232)) = rselect_head(rstore_seq(rstore_tail(queue_203,index_204),store(earray_230,index_231,e4))),
inference(monotonicity,[status(thm)],[1432]) ).
tff(1434,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q4,earray_232),s(index_231))) = rselect_head(rstore_seq(q4,earray_232)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1435,plain,
rselect_head(rstore_tail(rstore_seq(q4,earray_232),s(index_231))) = rselect_head(rstore_seq(q4,earray_232)),
inference(unit_resolution,[status(thm)],[1434,1375]) ).
tff(1436,plain,
rstore_tail(queue_233,index_234) = rstore_tail(rstore_seq(q4,earray_232),s(index_231)),
inference(symmetry,[status(thm)],[1214]) ).
tff(1437,plain,
rselect_head(rstore_tail(queue_233,index_234)) = rselect_head(rstore_tail(rstore_seq(q4,earray_232),s(index_231))),
inference(monotonicity,[status(thm)],[1436]) ).
tff(1438,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_233,index_234),store(earray_236,index_237,e5))) = rselect_head(rstore_tail(queue_233,index_234)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1439,plain,
rselect_head(rstore_seq(rstore_tail(queue_233,index_234),store(earray_236,index_237,e5))) = rselect_head(rstore_tail(queue_233,index_234)),
inference(unit_resolution,[status(thm)],[1438,1356]) ).
tff(1440,plain,
( ( earray_238 = store(earray_236,index_237,e5) )
<=> ( earray_238 = store(earray_236,index_237,e5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1441,axiom,
earray_238 = store(earray_236,index_237,e5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp52) ).
tff(1442,plain,
earray_238 = store(earray_236,index_237,e5),
inference(modus_ponens,[status(thm)],[1441,1440]) ).
tff(1443,plain,
store(earray_236,index_237,e5) = earray_238,
inference(symmetry,[status(thm)],[1442]) ).
tff(1444,plain,
rstore_tail(queue_233,index_234) = q5,
inference(transitivity,[status(thm)],[1205,1201]) ).
tff(1445,plain,
rstore_seq(rstore_tail(queue_233,index_234),store(earray_236,index_237,e5)) = rstore_seq(q5,earray_238),
inference(monotonicity,[status(thm)],[1444,1443]) ).
tff(1446,plain,
rstore_seq(q5,earray_238) = rstore_seq(rstore_tail(queue_233,index_234),store(earray_236,index_237,e5)),
inference(symmetry,[status(thm)],[1445]) ).
tff(1447,plain,
rselect_head(rstore_seq(q5,earray_238)) = rselect_head(rstore_seq(rstore_tail(queue_233,index_234),store(earray_236,index_237,e5))),
inference(monotonicity,[status(thm)],[1446]) ).
tff(1448,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q5,earray_238),s(index_237))) = rselect_head(rstore_seq(q5,earray_238)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1449,plain,
rselect_head(rstore_tail(rstore_seq(q5,earray_238),s(index_237))) = rselect_head(rstore_seq(q5,earray_238)),
inference(unit_resolution,[status(thm)],[1448,1375]) ).
tff(1450,plain,
rselect_head(rstore_tail(queue_239,index_240)) = rselect_head(rstore_tail(rstore_seq(q5,earray_238),s(index_237))),
inference(monotonicity,[status(thm)],[1149]) ).
tff(1451,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_239,index_240),store(earray_242,index_243,e6))) = rselect_head(rstore_tail(queue_239,index_240)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1452,plain,
rselect_head(rstore_seq(rstore_tail(queue_239,index_240),store(earray_242,index_243,e6))) = rselect_head(rstore_tail(queue_239,index_240)),
inference(unit_resolution,[status(thm)],[1451,1356]) ).
tff(1453,plain,
( ( earray_244 = store(earray_242,index_243,e6) )
<=> ( earray_244 = store(earray_242,index_243,e6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1454,axiom,
earray_244 = store(earray_242,index_243,e6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp54) ).
tff(1455,plain,
earray_244 = store(earray_242,index_243,e6),
inference(modus_ponens,[status(thm)],[1454,1453]) ).
tff(1456,plain,
store(earray_242,index_243,e6) = earray_244,
inference(symmetry,[status(thm)],[1455]) ).
tff(1457,plain,
queue_241 = q6,
inference(symmetry,[status(thm)],[1155]) ).
tff(1458,plain,
rstore_tail(queue_239,index_240) = queue_241,
inference(symmetry,[status(thm)],[1152]) ).
tff(1459,plain,
rstore_tail(queue_239,index_240) = q6,
inference(transitivity,[status(thm)],[1458,1457]) ).
tff(1460,plain,
rstore_seq(rstore_tail(queue_239,index_240),store(earray_242,index_243,e6)) = rstore_seq(q6,earray_244),
inference(monotonicity,[status(thm)],[1459,1456]) ).
tff(1461,plain,
rstore_seq(q6,earray_244) = rstore_seq(rstore_tail(queue_239,index_240),store(earray_242,index_243,e6)),
inference(symmetry,[status(thm)],[1460]) ).
tff(1462,plain,
rselect_head(rstore_seq(q6,earray_244)) = rselect_head(rstore_seq(rstore_tail(queue_239,index_240),store(earray_242,index_243,e6))),
inference(monotonicity,[status(thm)],[1461]) ).
tff(1463,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q6,earray_244),s(index_243))) = rselect_head(rstore_seq(q6,earray_244)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1464,plain,
rselect_head(rstore_tail(rstore_seq(q6,earray_244),s(index_243))) = rselect_head(rstore_seq(q6,earray_244)),
inference(unit_resolution,[status(thm)],[1463,1375]) ).
tff(1465,plain,
rstore_tail(queue_245,index_246) = rstore_tail(rstore_seq(q6,earray_244),s(index_243)),
inference(symmetry,[status(thm)],[1095]) ).
tff(1466,plain,
rselect_head(rstore_tail(queue_245,index_246)) = rselect_head(rstore_tail(rstore_seq(q6,earray_244),s(index_243))),
inference(monotonicity,[status(thm)],[1465]) ).
tff(1467,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_245,index_246),store(earray_248,index_249,e7))) = rselect_head(rstore_tail(queue_245,index_246)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1468,plain,
rselect_head(rstore_seq(rstore_tail(queue_245,index_246),store(earray_248,index_249,e7))) = rselect_head(rstore_tail(queue_245,index_246)),
inference(unit_resolution,[status(thm)],[1467,1356]) ).
tff(1469,plain,
( ( earray_250 = store(earray_248,index_249,e7) )
<=> ( earray_250 = store(earray_248,index_249,e7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1470,axiom,
earray_250 = store(earray_248,index_249,e7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp56) ).
tff(1471,plain,
earray_250 = store(earray_248,index_249,e7),
inference(modus_ponens,[status(thm)],[1470,1469]) ).
tff(1472,plain,
store(earray_248,index_249,e7) = earray_250,
inference(symmetry,[status(thm)],[1471]) ).
tff(1473,plain,
rstore_tail(queue_245,index_246) = q7,
inference(transitivity,[status(thm)],[1086,1082]) ).
tff(1474,plain,
rstore_seq(rstore_tail(queue_245,index_246),store(earray_248,index_249,e7)) = rstore_seq(q7,earray_250),
inference(monotonicity,[status(thm)],[1473,1472]) ).
tff(1475,plain,
rstore_seq(q7,earray_250) = rstore_seq(rstore_tail(queue_245,index_246),store(earray_248,index_249,e7)),
inference(symmetry,[status(thm)],[1474]) ).
tff(1476,plain,
rselect_head(rstore_seq(q7,earray_250)) = rselect_head(rstore_seq(rstore_tail(queue_245,index_246),store(earray_248,index_249,e7))),
inference(monotonicity,[status(thm)],[1475]) ).
tff(1477,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q7,earray_250),s(index_249))) = rselect_head(rstore_seq(q7,earray_250)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1478,plain,
rselect_head(rstore_tail(rstore_seq(q7,earray_250),s(index_249))) = rselect_head(rstore_seq(q7,earray_250)),
inference(unit_resolution,[status(thm)],[1477,1375]) ).
tff(1479,plain,
rstore_tail(queue_251,index_252) = rstore_tail(rstore_seq(q7,earray_250),s(index_249)),
inference(symmetry,[status(thm)],[1127]) ).
tff(1480,plain,
rselect_head(rstore_tail(queue_251,index_252)) = rselect_head(rstore_tail(rstore_seq(q7,earray_250),s(index_249))),
inference(monotonicity,[status(thm)],[1479]) ).
tff(1481,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_251,index_252),store(earray_254,index_255,e8))) = rselect_head(rstore_tail(queue_251,index_252)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1482,plain,
rselect_head(rstore_seq(rstore_tail(queue_251,index_252),store(earray_254,index_255,e8))) = rselect_head(rstore_tail(queue_251,index_252)),
inference(unit_resolution,[status(thm)],[1481,1356]) ).
tff(1483,plain,
( ( earray_256 = store(earray_254,index_255,e8) )
<=> ( earray_256 = store(earray_254,index_255,e8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1484,axiom,
earray_256 = store(earray_254,index_255,e8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp58) ).
tff(1485,plain,
earray_256 = store(earray_254,index_255,e8),
inference(modus_ponens,[status(thm)],[1484,1483]) ).
tff(1486,plain,
store(earray_254,index_255,e8) = earray_256,
inference(symmetry,[status(thm)],[1485]) ).
tff(1487,plain,
rstore_tail(queue_251,index_252) = q8,
inference(transitivity,[status(thm)],[1118,1114]) ).
tff(1488,plain,
rstore_seq(rstore_tail(queue_251,index_252),store(earray_254,index_255,e8)) = rstore_seq(q8,earray_256),
inference(monotonicity,[status(thm)],[1487,1486]) ).
tff(1489,plain,
rstore_seq(q8,earray_256) = rstore_seq(rstore_tail(queue_251,index_252),store(earray_254,index_255,e8)),
inference(symmetry,[status(thm)],[1488]) ).
tff(1490,plain,
rselect_head(rstore_seq(q8,earray_256)) = rselect_head(rstore_seq(rstore_tail(queue_251,index_252),store(earray_254,index_255,e8))),
inference(monotonicity,[status(thm)],[1489]) ).
tff(1491,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q8,earray_256),s(index_255))) = rselect_head(rstore_seq(q8,earray_256)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1492,plain,
rselect_head(rstore_tail(rstore_seq(q8,earray_256),s(index_255))) = rselect_head(rstore_seq(q8,earray_256)),
inference(unit_resolution,[status(thm)],[1491,1375]) ).
tff(1493,plain,
rselect_head(rstore_tail(queue_257,index_258)) = rselect_head(rstore_tail(rstore_seq(q8,earray_256),s(index_255))),
inference(monotonicity,[status(thm)],[1062]) ).
tff(1494,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_257,index_258),store(earray_8,index_9,e9))) = rselect_head(rstore_tail(queue_257,index_258)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1495,plain,
rselect_head(rstore_seq(rstore_tail(queue_257,index_258),store(earray_8,index_9,e9))) = rselect_head(rstore_tail(queue_257,index_258)),
inference(unit_resolution,[status(thm)],[1494,1356]) ).
tff(1496,plain,
( ( earray_10 = store(earray_8,index_9,e9) )
<=> ( earray_10 = store(earray_8,index_9,e9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1497,axiom,
earray_10 = store(earray_8,index_9,e9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp0) ).
tff(1498,plain,
earray_10 = store(earray_8,index_9,e9),
inference(modus_ponens,[status(thm)],[1497,1496]) ).
tff(1499,plain,
store(earray_8,index_9,e9) = earray_10,
inference(symmetry,[status(thm)],[1498]) ).
tff(1500,plain,
queue_259 = q9,
inference(symmetry,[status(thm)],[1068]) ).
tff(1501,plain,
rstore_tail(queue_257,index_258) = queue_259,
inference(symmetry,[status(thm)],[1065]) ).
tff(1502,plain,
rstore_tail(queue_257,index_258) = q9,
inference(transitivity,[status(thm)],[1501,1500]) ).
tff(1503,plain,
rstore_seq(rstore_tail(queue_257,index_258),store(earray_8,index_9,e9)) = rstore_seq(q9,earray_10),
inference(monotonicity,[status(thm)],[1502,1499]) ).
tff(1504,plain,
rstore_seq(q9,earray_10) = rstore_seq(rstore_tail(queue_257,index_258),store(earray_8,index_9,e9)),
inference(symmetry,[status(thm)],[1503]) ).
tff(1505,plain,
rselect_head(rstore_seq(q9,earray_10)) = rselect_head(rstore_seq(rstore_tail(queue_257,index_258),store(earray_8,index_9,e9))),
inference(monotonicity,[status(thm)],[1504]) ).
tff(1506,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = rselect_head(rstore_seq(q9,earray_10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1507,plain,
rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = rselect_head(rstore_seq(q9,earray_10)),
inference(unit_resolution,[status(thm)],[1506,1375]) ).
tff(1508,plain,
rstore_tail(queue_11,index_12) = rstore_tail(rstore_seq(q9,earray_10),s(index_9)),
inference(symmetry,[status(thm)],[1008]) ).
tff(1509,plain,
rselect_head(rstore_tail(queue_11,index_12)) = rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))),
inference(monotonicity,[status(thm)],[1508]) ).
tff(1510,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))) = rselect_head(rstore_tail(queue_11,index_12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1511,plain,
rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))) = rselect_head(rstore_tail(queue_11,index_12)),
inference(unit_resolution,[status(thm)],[1510,1356]) ).
tff(1512,plain,
( ( earray_16 = store(earray_14,index_15,e10) )
<=> ( earray_16 = store(earray_14,index_15,e10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1513,axiom,
earray_16 = store(earray_14,index_15,e10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp22) ).
tff(1514,plain,
earray_16 = store(earray_14,index_15,e10),
inference(modus_ponens,[status(thm)],[1513,1512]) ).
tff(1515,plain,
store(earray_14,index_15,e10) = earray_16,
inference(symmetry,[status(thm)],[1514]) ).
tff(1516,plain,
rstore_tail(queue_11,index_12) = q10,
inference(transitivity,[status(thm)],[999,995]) ).
tff(1517,plain,
rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10)) = rstore_seq(q10,earray_16),
inference(monotonicity,[status(thm)],[1516,1515]) ).
tff(1518,plain,
rstore_seq(q10,earray_16) = rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10)),
inference(symmetry,[status(thm)],[1517]) ).
tff(1519,plain,
rselect_head(rstore_seq(q10,earray_16)) = rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))),
inference(monotonicity,[status(thm)],[1518]) ).
tff(1520,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_head(rstore_seq(q10,earray_16)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1521,plain,
rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_head(rstore_seq(q10,earray_16)),
inference(unit_resolution,[status(thm)],[1520,1375]) ).
tff(1522,plain,
rstore_tail(queue_17,index_18) = rstore_tail(rstore_seq(q10,earray_16),s(index_15)),
inference(symmetry,[status(thm)],[1040]) ).
tff(1523,plain,
rselect_head(rstore_tail(queue_17,index_18)) = rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))),
inference(monotonicity,[status(thm)],[1522]) ).
tff(1524,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))) = rselect_head(rstore_tail(queue_17,index_18)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1525,plain,
rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))) = rselect_head(rstore_tail(queue_17,index_18)),
inference(unit_resolution,[status(thm)],[1524,1356]) ).
tff(1526,plain,
( ( earray_22 = store(earray_20,index_21,e11) )
<=> ( earray_22 = store(earray_20,index_21,e11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1527,axiom,
earray_22 = store(earray_20,index_21,e11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp45) ).
tff(1528,plain,
earray_22 = store(earray_20,index_21,e11),
inference(modus_ponens,[status(thm)],[1527,1526]) ).
tff(1529,plain,
store(earray_20,index_21,e11) = earray_22,
inference(symmetry,[status(thm)],[1528]) ).
tff(1530,plain,
rstore_tail(queue_17,index_18) = q11,
inference(transitivity,[status(thm)],[1031,1027]) ).
tff(1531,plain,
rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11)) = rstore_seq(q11,earray_22),
inference(monotonicity,[status(thm)],[1530,1529]) ).
tff(1532,plain,
rstore_seq(q11,earray_22) = rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11)),
inference(symmetry,[status(thm)],[1531]) ).
tff(1533,plain,
rselect_head(rstore_seq(q11,earray_22)) = rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))),
inference(monotonicity,[status(thm)],[1532]) ).
tff(1534,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_head(rstore_seq(q11,earray_22)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1535,plain,
rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_head(rstore_seq(q11,earray_22)),
inference(unit_resolution,[status(thm)],[1534,1375]) ).
tff(1536,plain,
rselect_head(rstore_tail(queue_23,index_24)) = rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(monotonicity,[status(thm)],[975]) ).
tff(1537,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_23,index_24),store(earray_26,index_27,e12))) = rselect_head(rstore_tail(queue_23,index_24)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1538,plain,
rselect_head(rstore_seq(rstore_tail(queue_23,index_24),store(earray_26,index_27,e12))) = rselect_head(rstore_tail(queue_23,index_24)),
inference(unit_resolution,[status(thm)],[1537,1356]) ).
tff(1539,plain,
( ( earray_28 = store(earray_26,index_27,e12) )
<=> ( earray_28 = store(earray_26,index_27,e12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1540,axiom,
earray_28 = store(earray_26,index_27,e12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp61) ).
tff(1541,plain,
earray_28 = store(earray_26,index_27,e12),
inference(modus_ponens,[status(thm)],[1540,1539]) ).
tff(1542,plain,
store(earray_26,index_27,e12) = earray_28,
inference(symmetry,[status(thm)],[1541]) ).
tff(1543,plain,
queue_25 = q12,
inference(symmetry,[status(thm)],[981]) ).
tff(1544,plain,
rstore_tail(queue_23,index_24) = queue_25,
inference(symmetry,[status(thm)],[978]) ).
tff(1545,plain,
rstore_tail(queue_23,index_24) = q12,
inference(transitivity,[status(thm)],[1544,1543]) ).
tff(1546,plain,
rstore_seq(rstore_tail(queue_23,index_24),store(earray_26,index_27,e12)) = rstore_seq(q12,earray_28),
inference(monotonicity,[status(thm)],[1545,1542]) ).
tff(1547,plain,
rstore_seq(q12,earray_28) = rstore_seq(rstore_tail(queue_23,index_24),store(earray_26,index_27,e12)),
inference(symmetry,[status(thm)],[1546]) ).
tff(1548,plain,
rselect_head(rstore_seq(q12,earray_28)) = rselect_head(rstore_seq(rstore_tail(queue_23,index_24),store(earray_26,index_27,e12))),
inference(monotonicity,[status(thm)],[1547]) ).
tff(1549,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q12,earray_28),s(index_27))) = rselect_head(rstore_seq(q12,earray_28)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1550,plain,
rselect_head(rstore_tail(rstore_seq(q12,earray_28),s(index_27))) = rselect_head(rstore_seq(q12,earray_28)),
inference(unit_resolution,[status(thm)],[1549,1375]) ).
tff(1551,plain,
rstore_tail(queue_29,index_30) = rstore_tail(rstore_seq(q12,earray_28),s(index_27)),
inference(symmetry,[status(thm)],[921]) ).
tff(1552,plain,
rselect_head(rstore_tail(queue_29,index_30)) = rselect_head(rstore_tail(rstore_seq(q12,earray_28),s(index_27))),
inference(monotonicity,[status(thm)],[1551]) ).
tff(1553,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_29,index_30),store(earray_32,index_33,e13))) = rselect_head(rstore_tail(queue_29,index_30)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1554,plain,
rselect_head(rstore_seq(rstore_tail(queue_29,index_30),store(earray_32,index_33,e13))) = rselect_head(rstore_tail(queue_29,index_30)),
inference(unit_resolution,[status(thm)],[1553,1356]) ).
tff(1555,plain,
( ( earray_34 = store(earray_32,index_33,e13) )
<=> ( earray_34 = store(earray_32,index_33,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1556,axiom,
earray_34 = store(earray_32,index_33,e13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp63) ).
tff(1557,plain,
earray_34 = store(earray_32,index_33,e13),
inference(modus_ponens,[status(thm)],[1556,1555]) ).
tff(1558,plain,
store(earray_32,index_33,e13) = earray_34,
inference(symmetry,[status(thm)],[1557]) ).
tff(1559,plain,
rstore_tail(queue_29,index_30) = q13,
inference(transitivity,[status(thm)],[912,908]) ).
tff(1560,plain,
rstore_seq(rstore_tail(queue_29,index_30),store(earray_32,index_33,e13)) = rstore_seq(q13,earray_34),
inference(monotonicity,[status(thm)],[1559,1558]) ).
tff(1561,plain,
rstore_seq(q13,earray_34) = rstore_seq(rstore_tail(queue_29,index_30),store(earray_32,index_33,e13)),
inference(symmetry,[status(thm)],[1560]) ).
tff(1562,plain,
rselect_head(rstore_seq(q13,earray_34)) = rselect_head(rstore_seq(rstore_tail(queue_29,index_30),store(earray_32,index_33,e13))),
inference(monotonicity,[status(thm)],[1561]) ).
tff(1563,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q13,earray_34),s(index_33))) = rselect_head(rstore_seq(q13,earray_34)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1564,plain,
rselect_head(rstore_tail(rstore_seq(q13,earray_34),s(index_33))) = rselect_head(rstore_seq(q13,earray_34)),
inference(unit_resolution,[status(thm)],[1563,1375]) ).
tff(1565,plain,
rstore_tail(queue_35,index_36) = rstore_tail(rstore_seq(q13,earray_34),s(index_33)),
inference(symmetry,[status(thm)],[953]) ).
tff(1566,plain,
rselect_head(rstore_tail(queue_35,index_36)) = rselect_head(rstore_tail(rstore_seq(q13,earray_34),s(index_33))),
inference(monotonicity,[status(thm)],[1565]) ).
tff(1567,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_35,index_36),store(earray_38,index_39,e14))) = rselect_head(rstore_tail(queue_35,index_36)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1568,plain,
rselect_head(rstore_seq(rstore_tail(queue_35,index_36),store(earray_38,index_39,e14))) = rselect_head(rstore_tail(queue_35,index_36)),
inference(unit_resolution,[status(thm)],[1567,1356]) ).
tff(1569,plain,
( ( earray_40 = store(earray_38,index_39,e14) )
<=> ( earray_40 = store(earray_38,index_39,e14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1570,axiom,
earray_40 = store(earray_38,index_39,e14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp66) ).
tff(1571,plain,
earray_40 = store(earray_38,index_39,e14),
inference(modus_ponens,[status(thm)],[1570,1569]) ).
tff(1572,plain,
store(earray_38,index_39,e14) = earray_40,
inference(symmetry,[status(thm)],[1571]) ).
tff(1573,plain,
rstore_tail(queue_35,index_36) = q14,
inference(transitivity,[status(thm)],[944,940]) ).
tff(1574,plain,
rstore_seq(rstore_tail(queue_35,index_36),store(earray_38,index_39,e14)) = rstore_seq(q14,earray_40),
inference(monotonicity,[status(thm)],[1573,1572]) ).
tff(1575,plain,
rstore_seq(q14,earray_40) = rstore_seq(rstore_tail(queue_35,index_36),store(earray_38,index_39,e14)),
inference(symmetry,[status(thm)],[1574]) ).
tff(1576,plain,
rselect_head(rstore_seq(q14,earray_40)) = rselect_head(rstore_seq(rstore_tail(queue_35,index_36),store(earray_38,index_39,e14))),
inference(monotonicity,[status(thm)],[1575]) ).
tff(1577,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q14,earray_40),s(index_39))) = rselect_head(rstore_seq(q14,earray_40)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1578,plain,
rselect_head(rstore_tail(rstore_seq(q14,earray_40),s(index_39))) = rselect_head(rstore_seq(q14,earray_40)),
inference(unit_resolution,[status(thm)],[1577,1375]) ).
tff(1579,plain,
rselect_head(rstore_tail(queue_41,index_42)) = rselect_head(rstore_tail(rstore_seq(q14,earray_40),s(index_39))),
inference(monotonicity,[status(thm)],[888]) ).
tff(1580,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_41,index_42),store(earray_44,index_45,e15))) = rselect_head(rstore_tail(queue_41,index_42)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1581,plain,
rselect_head(rstore_seq(rstore_tail(queue_41,index_42),store(earray_44,index_45,e15))) = rselect_head(rstore_tail(queue_41,index_42)),
inference(unit_resolution,[status(thm)],[1580,1356]) ).
tff(1582,plain,
( ( earray_46 = store(earray_44,index_45,e15) )
<=> ( earray_46 = store(earray_44,index_45,e15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1583,axiom,
earray_46 = store(earray_44,index_45,e15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp68) ).
tff(1584,plain,
earray_46 = store(earray_44,index_45,e15),
inference(modus_ponens,[status(thm)],[1583,1582]) ).
tff(1585,plain,
store(earray_44,index_45,e15) = earray_46,
inference(symmetry,[status(thm)],[1584]) ).
tff(1586,plain,
queue_43 = q15,
inference(symmetry,[status(thm)],[894]) ).
tff(1587,plain,
rstore_tail(queue_41,index_42) = queue_43,
inference(symmetry,[status(thm)],[891]) ).
tff(1588,plain,
rstore_tail(queue_41,index_42) = q15,
inference(transitivity,[status(thm)],[1587,1586]) ).
tff(1589,plain,
rstore_seq(rstore_tail(queue_41,index_42),store(earray_44,index_45,e15)) = rstore_seq(q15,earray_46),
inference(monotonicity,[status(thm)],[1588,1585]) ).
tff(1590,plain,
rstore_seq(q15,earray_46) = rstore_seq(rstore_tail(queue_41,index_42),store(earray_44,index_45,e15)),
inference(symmetry,[status(thm)],[1589]) ).
tff(1591,plain,
rselect_head(rstore_seq(q15,earray_46)) = rselect_head(rstore_seq(rstore_tail(queue_41,index_42),store(earray_44,index_45,e15))),
inference(monotonicity,[status(thm)],[1590]) ).
tff(1592,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q15,earray_46),s(index_45))) = rselect_head(rstore_seq(q15,earray_46)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1593,plain,
rselect_head(rstore_tail(rstore_seq(q15,earray_46),s(index_45))) = rselect_head(rstore_seq(q15,earray_46)),
inference(unit_resolution,[status(thm)],[1592,1375]) ).
tff(1594,plain,
rselect_head(rstore_tail(queue_47,index_48)) = rselect_head(rstore_tail(rstore_seq(q15,earray_46),s(index_45))),
inference(monotonicity,[status(thm)],[827]) ).
tff(1595,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_47,index_48),store(earray_50,index_51,e16))) = rselect_head(rstore_tail(queue_47,index_48)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1596,plain,
rselect_head(rstore_seq(rstore_tail(queue_47,index_48),store(earray_50,index_51,e16))) = rselect_head(rstore_tail(queue_47,index_48)),
inference(unit_resolution,[status(thm)],[1595,1356]) ).
tff(1597,plain,
( ( earray_52 = store(earray_50,index_51,e16) )
<=> ( earray_52 = store(earray_50,index_51,e16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1598,axiom,
earray_52 = store(earray_50,index_51,e16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp70) ).
tff(1599,plain,
earray_52 = store(earray_50,index_51,e16),
inference(modus_ponens,[status(thm)],[1598,1597]) ).
tff(1600,plain,
store(earray_50,index_51,e16) = earray_52,
inference(symmetry,[status(thm)],[1599]) ).
tff(1601,plain,
queue_49 = q16,
inference(symmetry,[status(thm)],[833]) ).
tff(1602,plain,
rstore_tail(queue_47,index_48) = queue_49,
inference(symmetry,[status(thm)],[830]) ).
tff(1603,plain,
rstore_tail(queue_47,index_48) = q16,
inference(transitivity,[status(thm)],[1602,1601]) ).
tff(1604,plain,
rstore_seq(rstore_tail(queue_47,index_48),store(earray_50,index_51,e16)) = rstore_seq(q16,earray_52),
inference(monotonicity,[status(thm)],[1603,1600]) ).
tff(1605,plain,
rstore_seq(q16,earray_52) = rstore_seq(rstore_tail(queue_47,index_48),store(earray_50,index_51,e16)),
inference(symmetry,[status(thm)],[1604]) ).
tff(1606,plain,
rselect_head(rstore_seq(q16,earray_52)) = rselect_head(rstore_seq(rstore_tail(queue_47,index_48),store(earray_50,index_51,e16))),
inference(monotonicity,[status(thm)],[1605]) ).
tff(1607,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q16,earray_52),s(index_51))) = rselect_head(rstore_seq(q16,earray_52)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1608,plain,
rselect_head(rstore_tail(rstore_seq(q16,earray_52),s(index_51))) = rselect_head(rstore_seq(q16,earray_52)),
inference(unit_resolution,[status(thm)],[1607,1375]) ).
tff(1609,plain,
rstore_tail(queue_53,index_54) = rstore_tail(rstore_seq(q16,earray_52),s(index_51)),
inference(symmetry,[status(thm)],[866]) ).
tff(1610,plain,
rselect_head(rstore_tail(queue_53,index_54)) = rselect_head(rstore_tail(rstore_seq(q16,earray_52),s(index_51))),
inference(monotonicity,[status(thm)],[1609]) ).
tff(1611,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e17))) = rselect_head(rstore_tail(queue_53,index_54)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1612,plain,
rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e17))) = rselect_head(rstore_tail(queue_53,index_54)),
inference(unit_resolution,[status(thm)],[1611,1356]) ).
tff(1613,plain,
( ( earray_58 = store(earray_56,index_57,e17) )
<=> ( earray_58 = store(earray_56,index_57,e17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1614,axiom,
earray_58 = store(earray_56,index_57,e17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp72) ).
tff(1615,plain,
earray_58 = store(earray_56,index_57,e17),
inference(modus_ponens,[status(thm)],[1614,1613]) ).
tff(1616,plain,
store(earray_56,index_57,e17) = earray_58,
inference(symmetry,[status(thm)],[1615]) ).
tff(1617,plain,
rstore_tail(queue_53,index_54) = q17,
inference(transitivity,[status(thm)],[857,853]) ).
tff(1618,plain,
rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e17)) = rstore_seq(q17,earray_58),
inference(monotonicity,[status(thm)],[1617,1616]) ).
tff(1619,plain,
rstore_seq(q17,earray_58) = rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e17)),
inference(symmetry,[status(thm)],[1618]) ).
tff(1620,plain,
rselect_head(rstore_seq(q17,earray_58)) = rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e17))),
inference(monotonicity,[status(thm)],[1619]) ).
tff(1621,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q17,earray_58),s(index_57))) = rselect_head(rstore_seq(q17,earray_58)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1622,plain,
rselect_head(rstore_tail(rstore_seq(q17,earray_58),s(index_57))) = rselect_head(rstore_seq(q17,earray_58)),
inference(unit_resolution,[status(thm)],[1621,1375]) ).
tff(1623,plain,
rselect_head(rstore_tail(queue_59,index_60)) = rselect_head(rstore_tail(rstore_seq(q17,earray_58),s(index_57))),
inference(monotonicity,[status(thm)],[801]) ).
tff(1624,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e18))) = rselect_head(rstore_tail(queue_59,index_60)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1625,plain,
rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e18))) = rselect_head(rstore_tail(queue_59,index_60)),
inference(unit_resolution,[status(thm)],[1624,1356]) ).
tff(1626,plain,
( ( earray_64 = store(earray_62,index_63,e18) )
<=> ( earray_64 = store(earray_62,index_63,e18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1627,axiom,
earray_64 = store(earray_62,index_63,e18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp74) ).
tff(1628,plain,
earray_64 = store(earray_62,index_63,e18),
inference(modus_ponens,[status(thm)],[1627,1626]) ).
tff(1629,plain,
store(earray_62,index_63,e18) = earray_64,
inference(symmetry,[status(thm)],[1628]) ).
tff(1630,plain,
queue_61 = q18,
inference(symmetry,[status(thm)],[807]) ).
tff(1631,plain,
rstore_tail(queue_59,index_60) = queue_61,
inference(symmetry,[status(thm)],[804]) ).
tff(1632,plain,
rstore_tail(queue_59,index_60) = q18,
inference(transitivity,[status(thm)],[1631,1630]) ).
tff(1633,plain,
rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e18)) = rstore_seq(q18,earray_64),
inference(monotonicity,[status(thm)],[1632,1629]) ).
tff(1634,plain,
rstore_seq(q18,earray_64) = rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e18)),
inference(symmetry,[status(thm)],[1633]) ).
tff(1635,plain,
rselect_head(rstore_seq(q18,earray_64)) = rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e18))),
inference(monotonicity,[status(thm)],[1634]) ).
tff(1636,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q18,earray_64),s(index_63))) = rselect_head(rstore_seq(q18,earray_64)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1637,plain,
rselect_head(rstore_tail(rstore_seq(q18,earray_64),s(index_63))) = rselect_head(rstore_seq(q18,earray_64)),
inference(unit_resolution,[status(thm)],[1636,1375]) ).
tff(1638,plain,
rselect_head(rstore_tail(queue_65,index_66)) = rselect_head(rstore_tail(rstore_seq(q18,earray_64),s(index_63))),
inference(monotonicity,[status(thm)],[740]) ).
tff(1639,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_65,index_66),store(earray_74,index_75,e19))) = rselect_head(rstore_tail(queue_65,index_66)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1640,plain,
rselect_head(rstore_seq(rstore_tail(queue_65,index_66),store(earray_74,index_75,e19))) = rselect_head(rstore_tail(queue_65,index_66)),
inference(unit_resolution,[status(thm)],[1639,1356]) ).
tff(1641,plain,
( ( earray_76 = store(earray_74,index_75,e19) )
<=> ( earray_76 = store(earray_74,index_75,e19) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1642,axiom,
earray_76 = store(earray_74,index_75,e19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp78) ).
tff(1643,plain,
earray_76 = store(earray_74,index_75,e19),
inference(modus_ponens,[status(thm)],[1642,1641]) ).
tff(1644,plain,
store(earray_74,index_75,e19) = earray_76,
inference(symmetry,[status(thm)],[1643]) ).
tff(1645,plain,
queue_67 = q19,
inference(symmetry,[status(thm)],[746]) ).
tff(1646,plain,
rstore_tail(queue_65,index_66) = queue_67,
inference(symmetry,[status(thm)],[743]) ).
tff(1647,plain,
rstore_tail(queue_65,index_66) = q19,
inference(transitivity,[status(thm)],[1646,1645]) ).
tff(1648,plain,
rstore_seq(rstore_tail(queue_65,index_66),store(earray_74,index_75,e19)) = rstore_seq(q19,earray_76),
inference(monotonicity,[status(thm)],[1647,1644]) ).
tff(1649,plain,
rstore_seq(q19,earray_76) = rstore_seq(rstore_tail(queue_65,index_66),store(earray_74,index_75,e19)),
inference(symmetry,[status(thm)],[1648]) ).
tff(1650,plain,
rselect_head(rstore_seq(q19,earray_76)) = rselect_head(rstore_seq(rstore_tail(queue_65,index_66),store(earray_74,index_75,e19))),
inference(monotonicity,[status(thm)],[1649]) ).
tff(1651,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q19,earray_76),s(index_75))) = rselect_head(rstore_seq(q19,earray_76)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1652,plain,
rselect_head(rstore_tail(rstore_seq(q19,earray_76),s(index_75))) = rselect_head(rstore_seq(q19,earray_76)),
inference(unit_resolution,[status(thm)],[1651,1375]) ).
tff(1653,plain,
rstore_tail(queue_77,index_78) = rstore_tail(rstore_seq(q19,earray_76),s(index_75)),
inference(symmetry,[status(thm)],[779]) ).
tff(1654,plain,
rselect_head(rstore_tail(queue_77,index_78)) = rselect_head(rstore_tail(rstore_seq(q19,earray_76),s(index_75))),
inference(monotonicity,[status(thm)],[1653]) ).
tff(1655,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_77,index_78),store(earray_80,index_81,e20))) = rselect_head(rstore_tail(queue_77,index_78)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1656,plain,
rselect_head(rstore_seq(rstore_tail(queue_77,index_78),store(earray_80,index_81,e20))) = rselect_head(rstore_tail(queue_77,index_78)),
inference(unit_resolution,[status(thm)],[1655,1356]) ).
tff(1657,plain,
( ( earray_82 = store(earray_80,index_81,e20) )
<=> ( earray_82 = store(earray_80,index_81,e20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1658,axiom,
earray_82 = store(earray_80,index_81,e20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp81) ).
tff(1659,plain,
earray_82 = store(earray_80,index_81,e20),
inference(modus_ponens,[status(thm)],[1658,1657]) ).
tff(1660,plain,
store(earray_80,index_81,e20) = earray_82,
inference(symmetry,[status(thm)],[1659]) ).
tff(1661,plain,
rstore_tail(queue_77,index_78) = q20,
inference(transitivity,[status(thm)],[770,766]) ).
tff(1662,plain,
rstore_seq(rstore_tail(queue_77,index_78),store(earray_80,index_81,e20)) = rstore_seq(q20,earray_82),
inference(monotonicity,[status(thm)],[1661,1660]) ).
tff(1663,plain,
rstore_seq(q20,earray_82) = rstore_seq(rstore_tail(queue_77,index_78),store(earray_80,index_81,e20)),
inference(symmetry,[status(thm)],[1662]) ).
tff(1664,plain,
rselect_head(rstore_seq(q20,earray_82)) = rselect_head(rstore_seq(rstore_tail(queue_77,index_78),store(earray_80,index_81,e20))),
inference(monotonicity,[status(thm)],[1663]) ).
tff(1665,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q20,earray_82),s(index_81))) = rselect_head(rstore_seq(q20,earray_82)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1666,plain,
rselect_head(rstore_tail(rstore_seq(q20,earray_82),s(index_81))) = rselect_head(rstore_seq(q20,earray_82)),
inference(unit_resolution,[status(thm)],[1665,1375]) ).
tff(1667,plain,
rselect_head(rstore_tail(queue_83,index_84)) = rselect_head(rstore_tail(rstore_seq(q20,earray_82),s(index_81))),
inference(monotonicity,[status(thm)],[714]) ).
tff(1668,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_83,index_84),store(earray_86,index_87,e21))) = rselect_head(rstore_tail(queue_83,index_84)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1669,plain,
rselect_head(rstore_seq(rstore_tail(queue_83,index_84),store(earray_86,index_87,e21))) = rselect_head(rstore_tail(queue_83,index_84)),
inference(unit_resolution,[status(thm)],[1668,1356]) ).
tff(1670,plain,
( ( earray_88 = store(earray_86,index_87,e21) )
<=> ( earray_88 = store(earray_86,index_87,e21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1671,axiom,
earray_88 = store(earray_86,index_87,e21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp83) ).
tff(1672,plain,
earray_88 = store(earray_86,index_87,e21),
inference(modus_ponens,[status(thm)],[1671,1670]) ).
tff(1673,plain,
store(earray_86,index_87,e21) = earray_88,
inference(symmetry,[status(thm)],[1672]) ).
tff(1674,plain,
queue_85 = q21,
inference(symmetry,[status(thm)],[720]) ).
tff(1675,plain,
rstore_tail(queue_83,index_84) = queue_85,
inference(symmetry,[status(thm)],[717]) ).
tff(1676,plain,
rstore_tail(queue_83,index_84) = q21,
inference(transitivity,[status(thm)],[1675,1674]) ).
tff(1677,plain,
rstore_seq(rstore_tail(queue_83,index_84),store(earray_86,index_87,e21)) = rstore_seq(q21,earray_88),
inference(monotonicity,[status(thm)],[1676,1673]) ).
tff(1678,plain,
rstore_seq(q21,earray_88) = rstore_seq(rstore_tail(queue_83,index_84),store(earray_86,index_87,e21)),
inference(symmetry,[status(thm)],[1677]) ).
tff(1679,plain,
rselect_head(rstore_seq(q21,earray_88)) = rselect_head(rstore_seq(rstore_tail(queue_83,index_84),store(earray_86,index_87,e21))),
inference(monotonicity,[status(thm)],[1678]) ).
tff(1680,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q21,earray_88),s(index_87))) = rselect_head(rstore_seq(q21,earray_88)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1681,plain,
rselect_head(rstore_tail(rstore_seq(q21,earray_88),s(index_87))) = rselect_head(rstore_seq(q21,earray_88)),
inference(unit_resolution,[status(thm)],[1680,1375]) ).
tff(1682,plain,
rselect_head(rstore_tail(queue_89,index_90)) = rselect_head(rstore_tail(rstore_seq(q21,earray_88),s(index_87))),
inference(monotonicity,[status(thm)],[653]) ).
tff(1683,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_89,index_90),store(earray_92,index_93,e22))) = rselect_head(rstore_tail(queue_89,index_90)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1684,plain,
rselect_head(rstore_seq(rstore_tail(queue_89,index_90),store(earray_92,index_93,e22))) = rselect_head(rstore_tail(queue_89,index_90)),
inference(unit_resolution,[status(thm)],[1683,1356]) ).
tff(1685,plain,
( ( earray_94 = store(earray_92,index_93,e22) )
<=> ( earray_94 = store(earray_92,index_93,e22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1686,axiom,
earray_94 = store(earray_92,index_93,e22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp85) ).
tff(1687,plain,
earray_94 = store(earray_92,index_93,e22),
inference(modus_ponens,[status(thm)],[1686,1685]) ).
tff(1688,plain,
store(earray_92,index_93,e22) = earray_94,
inference(symmetry,[status(thm)],[1687]) ).
tff(1689,plain,
queue_91 = q22,
inference(symmetry,[status(thm)],[659]) ).
tff(1690,plain,
rstore_tail(queue_89,index_90) = queue_91,
inference(symmetry,[status(thm)],[656]) ).
tff(1691,plain,
rstore_tail(queue_89,index_90) = q22,
inference(transitivity,[status(thm)],[1690,1689]) ).
tff(1692,plain,
rstore_seq(rstore_tail(queue_89,index_90),store(earray_92,index_93,e22)) = rstore_seq(q22,earray_94),
inference(monotonicity,[status(thm)],[1691,1688]) ).
tff(1693,plain,
rstore_seq(q22,earray_94) = rstore_seq(rstore_tail(queue_89,index_90),store(earray_92,index_93,e22)),
inference(symmetry,[status(thm)],[1692]) ).
tff(1694,plain,
rselect_head(rstore_seq(q22,earray_94)) = rselect_head(rstore_seq(rstore_tail(queue_89,index_90),store(earray_92,index_93,e22))),
inference(monotonicity,[status(thm)],[1693]) ).
tff(1695,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q22,earray_94),s(index_93))) = rselect_head(rstore_seq(q22,earray_94)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1696,plain,
rselect_head(rstore_tail(rstore_seq(q22,earray_94),s(index_93))) = rselect_head(rstore_seq(q22,earray_94)),
inference(unit_resolution,[status(thm)],[1695,1375]) ).
tff(1697,plain,
rstore_tail(queue_95,index_96) = rstore_tail(rstore_seq(q22,earray_94),s(index_93)),
inference(symmetry,[status(thm)],[692]) ).
tff(1698,plain,
rselect_head(rstore_tail(queue_95,index_96)) = rselect_head(rstore_tail(rstore_seq(q22,earray_94),s(index_93))),
inference(monotonicity,[status(thm)],[1697]) ).
tff(1699,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_95,index_96),store(earray_98,index_99,e23))) = rselect_head(rstore_tail(queue_95,index_96)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1700,plain,
rselect_head(rstore_seq(rstore_tail(queue_95,index_96),store(earray_98,index_99,e23))) = rselect_head(rstore_tail(queue_95,index_96)),
inference(unit_resolution,[status(thm)],[1699,1356]) ).
tff(1701,plain,
( ( earray_100 = store(earray_98,index_99,e23) )
<=> ( earray_100 = store(earray_98,index_99,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1702,axiom,
earray_100 = store(earray_98,index_99,e23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp1) ).
tff(1703,plain,
earray_100 = store(earray_98,index_99,e23),
inference(modus_ponens,[status(thm)],[1702,1701]) ).
tff(1704,plain,
store(earray_98,index_99,e23) = earray_100,
inference(symmetry,[status(thm)],[1703]) ).
tff(1705,plain,
rstore_tail(queue_95,index_96) = q23,
inference(transitivity,[status(thm)],[683,679]) ).
tff(1706,plain,
rstore_seq(rstore_tail(queue_95,index_96),store(earray_98,index_99,e23)) = rstore_seq(q23,earray_100),
inference(monotonicity,[status(thm)],[1705,1704]) ).
tff(1707,plain,
rstore_seq(q23,earray_100) = rstore_seq(rstore_tail(queue_95,index_96),store(earray_98,index_99,e23)),
inference(symmetry,[status(thm)],[1706]) ).
tff(1708,plain,
rselect_head(rstore_seq(q23,earray_100)) = rselect_head(rstore_seq(rstore_tail(queue_95,index_96),store(earray_98,index_99,e23))),
inference(monotonicity,[status(thm)],[1707]) ).
tff(1709,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q23,earray_100),s(index_99))) = rselect_head(rstore_seq(q23,earray_100)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1710,plain,
rselect_head(rstore_tail(rstore_seq(q23,earray_100),s(index_99))) = rselect_head(rstore_seq(q23,earray_100)),
inference(unit_resolution,[status(thm)],[1709,1375]) ).
tff(1711,plain,
rselect_head(rstore_tail(queue_101,index_102)) = rselect_head(rstore_tail(rstore_seq(q23,earray_100),s(index_99))),
inference(monotonicity,[status(thm)],[627]) ).
tff(1712,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e24))) = rselect_head(rstore_tail(queue_101,index_102)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1713,plain,
rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e24))) = rselect_head(rstore_tail(queue_101,index_102)),
inference(unit_resolution,[status(thm)],[1712,1356]) ).
tff(1714,plain,
( ( earray_106 = store(earray_104,index_105,e24) )
<=> ( earray_106 = store(earray_104,index_105,e24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1715,axiom,
earray_106 = store(earray_104,index_105,e24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp3) ).
tff(1716,plain,
earray_106 = store(earray_104,index_105,e24),
inference(modus_ponens,[status(thm)],[1715,1714]) ).
tff(1717,plain,
store(earray_104,index_105,e24) = earray_106,
inference(symmetry,[status(thm)],[1716]) ).
tff(1718,plain,
queue_103 = q24,
inference(symmetry,[status(thm)],[633]) ).
tff(1719,plain,
rstore_tail(queue_101,index_102) = queue_103,
inference(symmetry,[status(thm)],[630]) ).
tff(1720,plain,
rstore_tail(queue_101,index_102) = q24,
inference(transitivity,[status(thm)],[1719,1718]) ).
tff(1721,plain,
rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e24)) = rstore_seq(q24,earray_106),
inference(monotonicity,[status(thm)],[1720,1717]) ).
tff(1722,plain,
rstore_seq(q24,earray_106) = rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e24)),
inference(symmetry,[status(thm)],[1721]) ).
tff(1723,plain,
rselect_head(rstore_seq(q24,earray_106)) = rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e24))),
inference(monotonicity,[status(thm)],[1722]) ).
tff(1724,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q24,earray_106),s(index_105))) = rselect_head(rstore_seq(q24,earray_106)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1725,plain,
rselect_head(rstore_tail(rstore_seq(q24,earray_106),s(index_105))) = rselect_head(rstore_seq(q24,earray_106)),
inference(unit_resolution,[status(thm)],[1724,1375]) ).
tff(1726,plain,
rselect_head(rstore_tail(queue_107,index_108)) = rselect_head(rstore_tail(rstore_seq(q24,earray_106),s(index_105))),
inference(monotonicity,[status(thm)],[566]) ).
tff(1727,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e25))) = rselect_head(rstore_tail(queue_107,index_108)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1728,plain,
rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e25))) = rselect_head(rstore_tail(queue_107,index_108)),
inference(unit_resolution,[status(thm)],[1727,1356]) ).
tff(1729,plain,
( ( earray_112 = store(earray_110,index_111,e25) )
<=> ( earray_112 = store(earray_110,index_111,e25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1730,axiom,
earray_112 = store(earray_110,index_111,e25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp5) ).
tff(1731,plain,
earray_112 = store(earray_110,index_111,e25),
inference(modus_ponens,[status(thm)],[1730,1729]) ).
tff(1732,plain,
store(earray_110,index_111,e25) = earray_112,
inference(symmetry,[status(thm)],[1731]) ).
tff(1733,plain,
queue_109 = q25,
inference(symmetry,[status(thm)],[572]) ).
tff(1734,plain,
rstore_tail(queue_107,index_108) = queue_109,
inference(symmetry,[status(thm)],[569]) ).
tff(1735,plain,
rstore_tail(queue_107,index_108) = q25,
inference(transitivity,[status(thm)],[1734,1733]) ).
tff(1736,plain,
rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e25)) = rstore_seq(q25,earray_112),
inference(monotonicity,[status(thm)],[1735,1732]) ).
tff(1737,plain,
rstore_seq(q25,earray_112) = rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e25)),
inference(symmetry,[status(thm)],[1736]) ).
tff(1738,plain,
rselect_head(rstore_seq(q25,earray_112)) = rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e25))),
inference(monotonicity,[status(thm)],[1737]) ).
tff(1739,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q25,earray_112),s(index_111))) = rselect_head(rstore_seq(q25,earray_112)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1740,plain,
rselect_head(rstore_tail(rstore_seq(q25,earray_112),s(index_111))) = rselect_head(rstore_seq(q25,earray_112)),
inference(unit_resolution,[status(thm)],[1739,1375]) ).
tff(1741,plain,
rstore_tail(queue_113,index_114) = rstore_tail(rstore_seq(q25,earray_112),s(index_111)),
inference(symmetry,[status(thm)],[605]) ).
tff(1742,plain,
rselect_head(rstore_tail(queue_113,index_114)) = rselect_head(rstore_tail(rstore_seq(q25,earray_112),s(index_111))),
inference(monotonicity,[status(thm)],[1741]) ).
tff(1743,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_113,index_114),store(earray_116,index_117,e26))) = rselect_head(rstore_tail(queue_113,index_114)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1744,plain,
rselect_head(rstore_seq(rstore_tail(queue_113,index_114),store(earray_116,index_117,e26))) = rselect_head(rstore_tail(queue_113,index_114)),
inference(unit_resolution,[status(thm)],[1743,1356]) ).
tff(1745,plain,
( ( earray_118 = store(earray_116,index_117,e26) )
<=> ( earray_118 = store(earray_116,index_117,e26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1746,axiom,
earray_118 = store(earray_116,index_117,e26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp7) ).
tff(1747,plain,
earray_118 = store(earray_116,index_117,e26),
inference(modus_ponens,[status(thm)],[1746,1745]) ).
tff(1748,plain,
store(earray_116,index_117,e26) = earray_118,
inference(symmetry,[status(thm)],[1747]) ).
tff(1749,plain,
rstore_tail(queue_113,index_114) = q26,
inference(transitivity,[status(thm)],[596,592]) ).
tff(1750,plain,
rstore_seq(rstore_tail(queue_113,index_114),store(earray_116,index_117,e26)) = rstore_seq(q26,earray_118),
inference(monotonicity,[status(thm)],[1749,1748]) ).
tff(1751,plain,
rstore_seq(q26,earray_118) = rstore_seq(rstore_tail(queue_113,index_114),store(earray_116,index_117,e26)),
inference(symmetry,[status(thm)],[1750]) ).
tff(1752,plain,
rselect_head(rstore_seq(q26,earray_118)) = rselect_head(rstore_seq(rstore_tail(queue_113,index_114),store(earray_116,index_117,e26))),
inference(monotonicity,[status(thm)],[1751]) ).
tff(1753,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q26,earray_118),s(index_117))) = rselect_head(rstore_seq(q26,earray_118)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1754,plain,
rselect_head(rstore_tail(rstore_seq(q26,earray_118),s(index_117))) = rselect_head(rstore_seq(q26,earray_118)),
inference(unit_resolution,[status(thm)],[1753,1375]) ).
tff(1755,plain,
rselect_head(rstore_tail(queue_119,index_120)) = rselect_head(rstore_tail(rstore_seq(q26,earray_118),s(index_117))),
inference(monotonicity,[status(thm)],[540]) ).
tff(1756,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_119,index_120),store(earray_122,index_123,e27))) = rselect_head(rstore_tail(queue_119,index_120)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1757,plain,
rselect_head(rstore_seq(rstore_tail(queue_119,index_120),store(earray_122,index_123,e27))) = rselect_head(rstore_tail(queue_119,index_120)),
inference(unit_resolution,[status(thm)],[1756,1356]) ).
tff(1758,plain,
( ( earray_124 = store(earray_122,index_123,e27) )
<=> ( earray_124 = store(earray_122,index_123,e27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1759,axiom,
earray_124 = store(earray_122,index_123,e27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp9) ).
tff(1760,plain,
earray_124 = store(earray_122,index_123,e27),
inference(modus_ponens,[status(thm)],[1759,1758]) ).
tff(1761,plain,
store(earray_122,index_123,e27) = earray_124,
inference(symmetry,[status(thm)],[1760]) ).
tff(1762,plain,
queue_121 = q27,
inference(symmetry,[status(thm)],[546]) ).
tff(1763,plain,
rstore_tail(queue_119,index_120) = queue_121,
inference(symmetry,[status(thm)],[543]) ).
tff(1764,plain,
rstore_tail(queue_119,index_120) = q27,
inference(transitivity,[status(thm)],[1763,1762]) ).
tff(1765,plain,
rstore_seq(rstore_tail(queue_119,index_120),store(earray_122,index_123,e27)) = rstore_seq(q27,earray_124),
inference(monotonicity,[status(thm)],[1764,1761]) ).
tff(1766,plain,
rstore_seq(q27,earray_124) = rstore_seq(rstore_tail(queue_119,index_120),store(earray_122,index_123,e27)),
inference(symmetry,[status(thm)],[1765]) ).
tff(1767,plain,
rselect_head(rstore_seq(q27,earray_124)) = rselect_head(rstore_seq(rstore_tail(queue_119,index_120),store(earray_122,index_123,e27))),
inference(monotonicity,[status(thm)],[1766]) ).
tff(1768,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q27,earray_124),s(index_123))) = rselect_head(rstore_seq(q27,earray_124)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1769,plain,
rselect_head(rstore_tail(rstore_seq(q27,earray_124),s(index_123))) = rselect_head(rstore_seq(q27,earray_124)),
inference(unit_resolution,[status(thm)],[1768,1375]) ).
tff(1770,plain,
rselect_head(rstore_tail(queue_125,index_126)) = rselect_head(rstore_tail(rstore_seq(q27,earray_124),s(index_123))),
inference(monotonicity,[status(thm)],[481]) ).
tff(1771,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_125,index_126),store(earray_128,index_129,e28))) = rselect_head(rstore_tail(queue_125,index_126)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1772,plain,
rselect_head(rstore_seq(rstore_tail(queue_125,index_126),store(earray_128,index_129,e28))) = rselect_head(rstore_tail(queue_125,index_126)),
inference(unit_resolution,[status(thm)],[1771,1356]) ).
tff(1773,plain,
( ( earray_130 = store(earray_128,index_129,e28) )
<=> ( earray_130 = store(earray_128,index_129,e28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1774,axiom,
earray_130 = store(earray_128,index_129,e28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp11) ).
tff(1775,plain,
earray_130 = store(earray_128,index_129,e28),
inference(modus_ponens,[status(thm)],[1774,1773]) ).
tff(1776,plain,
store(earray_128,index_129,e28) = earray_130,
inference(symmetry,[status(thm)],[1775]) ).
tff(1777,plain,
queue_127 = q28,
inference(symmetry,[status(thm)],[487]) ).
tff(1778,plain,
rstore_tail(queue_125,index_126) = queue_127,
inference(symmetry,[status(thm)],[484]) ).
tff(1779,plain,
rstore_tail(queue_125,index_126) = q28,
inference(transitivity,[status(thm)],[1778,1777]) ).
tff(1780,plain,
rstore_seq(rstore_tail(queue_125,index_126),store(earray_128,index_129,e28)) = rstore_seq(q28,earray_130),
inference(monotonicity,[status(thm)],[1779,1776]) ).
tff(1781,plain,
rstore_seq(q28,earray_130) = rstore_seq(rstore_tail(queue_125,index_126),store(earray_128,index_129,e28)),
inference(symmetry,[status(thm)],[1780]) ).
tff(1782,plain,
rselect_head(rstore_seq(q28,earray_130)) = rselect_head(rstore_seq(rstore_tail(queue_125,index_126),store(earray_128,index_129,e28))),
inference(monotonicity,[status(thm)],[1781]) ).
tff(1783,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q28,earray_130),s(index_129))) = rselect_head(rstore_seq(q28,earray_130)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1784,plain,
rselect_head(rstore_tail(rstore_seq(q28,earray_130),s(index_129))) = rselect_head(rstore_seq(q28,earray_130)),
inference(unit_resolution,[status(thm)],[1783,1375]) ).
tff(1785,plain,
rselect_head(rstore_tail(queue_131,index_132)) = rselect_head(rstore_tail(rstore_seq(q28,earray_130),s(index_129))),
inference(monotonicity,[status(thm)],[513]) ).
tff(1786,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_131,index_132),store(earray_140,index_141,e29))) = rselect_head(rstore_tail(queue_131,index_132)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1787,plain,
rselect_head(rstore_seq(rstore_tail(queue_131,index_132),store(earray_140,index_141,e29))) = rselect_head(rstore_tail(queue_131,index_132)),
inference(unit_resolution,[status(thm)],[1786,1356]) ).
tff(1788,plain,
( ( earray_142 = store(earray_140,index_141,e29) )
<=> ( earray_142 = store(earray_140,index_141,e29) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1789,axiom,
earray_142 = store(earray_140,index_141,e29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp16) ).
tff(1790,plain,
earray_142 = store(earray_140,index_141,e29),
inference(modus_ponens,[status(thm)],[1789,1788]) ).
tff(1791,plain,
store(earray_140,index_141,e29) = earray_142,
inference(symmetry,[status(thm)],[1790]) ).
tff(1792,plain,
queue_133 = q29,
inference(symmetry,[status(thm)],[519]) ).
tff(1793,plain,
rstore_tail(queue_131,index_132) = queue_133,
inference(symmetry,[status(thm)],[516]) ).
tff(1794,plain,
rstore_tail(queue_131,index_132) = q29,
inference(transitivity,[status(thm)],[1793,1792]) ).
tff(1795,plain,
rstore_seq(rstore_tail(queue_131,index_132),store(earray_140,index_141,e29)) = rstore_seq(q29,earray_142),
inference(monotonicity,[status(thm)],[1794,1791]) ).
tff(1796,plain,
rstore_seq(q29,earray_142) = rstore_seq(rstore_tail(queue_131,index_132),store(earray_140,index_141,e29)),
inference(symmetry,[status(thm)],[1795]) ).
tff(1797,plain,
rselect_head(rstore_seq(q29,earray_142)) = rselect_head(rstore_seq(rstore_tail(queue_131,index_132),store(earray_140,index_141,e29))),
inference(monotonicity,[status(thm)],[1796]) ).
tff(1798,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q29,earray_142),s(index_141))) = rselect_head(rstore_seq(q29,earray_142)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1799,plain,
rselect_head(rstore_tail(rstore_seq(q29,earray_142),s(index_141))) = rselect_head(rstore_seq(q29,earray_142)),
inference(unit_resolution,[status(thm)],[1798,1375]) ).
tff(1800,plain,
rselect_head(rstore_tail(queue_143,index_144)) = rselect_head(rstore_tail(rstore_seq(q29,earray_142),s(index_141))),
inference(monotonicity,[status(thm)],[455]) ).
tff(1801,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e30))) = rselect_head(rstore_tail(queue_143,index_144)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1802,plain,
rselect_head(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e30))) = rselect_head(rstore_tail(queue_143,index_144)),
inference(unit_resolution,[status(thm)],[1801,1356]) ).
tff(1803,plain,
( ( earray_148 = store(earray_146,index_147,e30) )
<=> ( earray_148 = store(earray_146,index_147,e30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1804,axiom,
earray_148 = store(earray_146,index_147,e30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp18) ).
tff(1805,plain,
earray_148 = store(earray_146,index_147,e30),
inference(modus_ponens,[status(thm)],[1804,1803]) ).
tff(1806,plain,
store(earray_146,index_147,e30) = earray_148,
inference(symmetry,[status(thm)],[1805]) ).
tff(1807,plain,
queue_145 = q30,
inference(symmetry,[status(thm)],[461]) ).
tff(1808,plain,
rstore_tail(queue_143,index_144) = queue_145,
inference(symmetry,[status(thm)],[458]) ).
tff(1809,plain,
rstore_tail(queue_143,index_144) = q30,
inference(transitivity,[status(thm)],[1808,1807]) ).
tff(1810,plain,
rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e30)) = rstore_seq(q30,earray_148),
inference(monotonicity,[status(thm)],[1809,1806]) ).
tff(1811,plain,
rstore_seq(q30,earray_148) = rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e30)),
inference(symmetry,[status(thm)],[1810]) ).
tff(1812,plain,
rselect_head(rstore_seq(q30,earray_148)) = rselect_head(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e30))),
inference(monotonicity,[status(thm)],[1811]) ).
tff(1813,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q30,earray_148),s(index_147))) = rselect_head(rstore_seq(q30,earray_148)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1814,plain,
rselect_head(rstore_tail(rstore_seq(q30,earray_148),s(index_147))) = rselect_head(rstore_seq(q30,earray_148)),
inference(unit_resolution,[status(thm)],[1813,1375]) ).
tff(1815,plain,
rselect_head(rstore_tail(queue_149,index_150)) = rselect_head(rstore_tail(rstore_seq(q30,earray_148),s(index_147))),
inference(monotonicity,[status(thm)],[396]) ).
tff(1816,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_149,index_150),store(earray_152,index_153,e31))) = rselect_head(rstore_tail(queue_149,index_150)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1817,plain,
rselect_head(rstore_seq(rstore_tail(queue_149,index_150),store(earray_152,index_153,e31))) = rselect_head(rstore_tail(queue_149,index_150)),
inference(unit_resolution,[status(thm)],[1816,1356]) ).
tff(1818,plain,
( ( earray_154 = store(earray_152,index_153,e31) )
<=> ( earray_154 = store(earray_152,index_153,e31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1819,axiom,
earray_154 = store(earray_152,index_153,e31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp20) ).
tff(1820,plain,
earray_154 = store(earray_152,index_153,e31),
inference(modus_ponens,[status(thm)],[1819,1818]) ).
tff(1821,plain,
store(earray_152,index_153,e31) = earray_154,
inference(symmetry,[status(thm)],[1820]) ).
tff(1822,plain,
queue_151 = q31,
inference(symmetry,[status(thm)],[402]) ).
tff(1823,plain,
rstore_tail(queue_149,index_150) = queue_151,
inference(symmetry,[status(thm)],[399]) ).
tff(1824,plain,
rstore_tail(queue_149,index_150) = q31,
inference(transitivity,[status(thm)],[1823,1822]) ).
tff(1825,plain,
rstore_seq(rstore_tail(queue_149,index_150),store(earray_152,index_153,e31)) = rstore_seq(q31,earray_154),
inference(monotonicity,[status(thm)],[1824,1821]) ).
tff(1826,plain,
rstore_seq(q31,earray_154) = rstore_seq(rstore_tail(queue_149,index_150),store(earray_152,index_153,e31)),
inference(symmetry,[status(thm)],[1825]) ).
tff(1827,plain,
rselect_head(rstore_seq(q31,earray_154)) = rselect_head(rstore_seq(rstore_tail(queue_149,index_150),store(earray_152,index_153,e31))),
inference(monotonicity,[status(thm)],[1826]) ).
tff(1828,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q31,earray_154),s(index_153))) = rselect_head(rstore_seq(q31,earray_154)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1829,plain,
rselect_head(rstore_tail(rstore_seq(q31,earray_154),s(index_153))) = rselect_head(rstore_seq(q31,earray_154)),
inference(unit_resolution,[status(thm)],[1828,1375]) ).
tff(1830,plain,
rselect_head(rstore_tail(queue_155,index_156)) = rselect_head(rstore_tail(rstore_seq(q31,earray_154),s(index_153))),
inference(monotonicity,[status(thm)],[428]) ).
tff(1831,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_155,index_156),store(earray_158,index_159,e32))) = rselect_head(rstore_tail(queue_155,index_156)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1832,plain,
rselect_head(rstore_seq(rstore_tail(queue_155,index_156),store(earray_158,index_159,e32))) = rselect_head(rstore_tail(queue_155,index_156)),
inference(unit_resolution,[status(thm)],[1831,1356]) ).
tff(1833,plain,
( ( earray_160 = store(earray_158,index_159,e32) )
<=> ( earray_160 = store(earray_158,index_159,e32) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1834,axiom,
earray_160 = store(earray_158,index_159,e32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp23) ).
tff(1835,plain,
earray_160 = store(earray_158,index_159,e32),
inference(modus_ponens,[status(thm)],[1834,1833]) ).
tff(1836,plain,
store(earray_158,index_159,e32) = earray_160,
inference(symmetry,[status(thm)],[1835]) ).
tff(1837,plain,
queue_157 = q32,
inference(symmetry,[status(thm)],[434]) ).
tff(1838,plain,
rstore_tail(queue_155,index_156) = queue_157,
inference(symmetry,[status(thm)],[431]) ).
tff(1839,plain,
rstore_tail(queue_155,index_156) = q32,
inference(transitivity,[status(thm)],[1838,1837]) ).
tff(1840,plain,
rstore_seq(rstore_tail(queue_155,index_156),store(earray_158,index_159,e32)) = rstore_seq(q32,earray_160),
inference(monotonicity,[status(thm)],[1839,1836]) ).
tff(1841,plain,
rstore_seq(q32,earray_160) = rstore_seq(rstore_tail(queue_155,index_156),store(earray_158,index_159,e32)),
inference(symmetry,[status(thm)],[1840]) ).
tff(1842,plain,
rselect_head(rstore_seq(q32,earray_160)) = rselect_head(rstore_seq(rstore_tail(queue_155,index_156),store(earray_158,index_159,e32))),
inference(monotonicity,[status(thm)],[1841]) ).
tff(1843,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q32,earray_160),s(index_159))) = rselect_head(rstore_seq(q32,earray_160)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1844,plain,
rselect_head(rstore_tail(rstore_seq(q32,earray_160),s(index_159))) = rselect_head(rstore_seq(q32,earray_160)),
inference(unit_resolution,[status(thm)],[1843,1375]) ).
tff(1845,plain,
rselect_head(rstore_tail(queue_161,index_162)) = rselect_head(rstore_tail(rstore_seq(q32,earray_160),s(index_159))),
inference(monotonicity,[status(thm)],[370]) ).
tff(1846,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_161,index_162),store(earray_164,index_165,e33))) = rselect_head(rstore_tail(queue_161,index_162)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1847,plain,
rselect_head(rstore_seq(rstore_tail(queue_161,index_162),store(earray_164,index_165,e33))) = rselect_head(rstore_tail(queue_161,index_162)),
inference(unit_resolution,[status(thm)],[1846,1356]) ).
tff(1848,plain,
( ( earray_166 = store(earray_164,index_165,e33) )
<=> ( earray_166 = store(earray_164,index_165,e33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1849,axiom,
earray_166 = store(earray_164,index_165,e33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp25) ).
tff(1850,plain,
earray_166 = store(earray_164,index_165,e33),
inference(modus_ponens,[status(thm)],[1849,1848]) ).
tff(1851,plain,
store(earray_164,index_165,e33) = earray_166,
inference(symmetry,[status(thm)],[1850]) ).
tff(1852,plain,
queue_163 = q33,
inference(symmetry,[status(thm)],[376]) ).
tff(1853,plain,
rstore_tail(queue_161,index_162) = queue_163,
inference(symmetry,[status(thm)],[373]) ).
tff(1854,plain,
rstore_tail(queue_161,index_162) = q33,
inference(transitivity,[status(thm)],[1853,1852]) ).
tff(1855,plain,
rstore_seq(rstore_tail(queue_161,index_162),store(earray_164,index_165,e33)) = rstore_seq(q33,earray_166),
inference(monotonicity,[status(thm)],[1854,1851]) ).
tff(1856,plain,
rstore_seq(q33,earray_166) = rstore_seq(rstore_tail(queue_161,index_162),store(earray_164,index_165,e33)),
inference(symmetry,[status(thm)],[1855]) ).
tff(1857,plain,
rselect_head(rstore_seq(q33,earray_166)) = rselect_head(rstore_seq(rstore_tail(queue_161,index_162),store(earray_164,index_165,e33))),
inference(monotonicity,[status(thm)],[1856]) ).
tff(1858,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q33,earray_166),s(index_165))) = rselect_head(rstore_seq(q33,earray_166)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1859,plain,
rselect_head(rstore_tail(rstore_seq(q33,earray_166),s(index_165))) = rselect_head(rstore_seq(q33,earray_166)),
inference(unit_resolution,[status(thm)],[1858,1375]) ).
tff(1860,plain,
rselect_head(rstore_tail(queue_167,index_168)) = rselect_head(rstore_tail(rstore_seq(q33,earray_166),s(index_165))),
inference(monotonicity,[status(thm)],[311]) ).
tff(1861,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_167,index_168),store(earray_170,index_171,e34))) = rselect_head(rstore_tail(queue_167,index_168)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1862,plain,
rselect_head(rstore_seq(rstore_tail(queue_167,index_168),store(earray_170,index_171,e34))) = rselect_head(rstore_tail(queue_167,index_168)),
inference(unit_resolution,[status(thm)],[1861,1356]) ).
tff(1863,plain,
( ( earray_172 = store(earray_170,index_171,e34) )
<=> ( earray_172 = store(earray_170,index_171,e34) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1864,axiom,
earray_172 = store(earray_170,index_171,e34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp27) ).
tff(1865,plain,
earray_172 = store(earray_170,index_171,e34),
inference(modus_ponens,[status(thm)],[1864,1863]) ).
tff(1866,plain,
store(earray_170,index_171,e34) = earray_172,
inference(symmetry,[status(thm)],[1865]) ).
tff(1867,plain,
queue_169 = q34,
inference(symmetry,[status(thm)],[317]) ).
tff(1868,plain,
rstore_tail(queue_167,index_168) = queue_169,
inference(symmetry,[status(thm)],[314]) ).
tff(1869,plain,
rstore_tail(queue_167,index_168) = q34,
inference(transitivity,[status(thm)],[1868,1867]) ).
tff(1870,plain,
rstore_seq(rstore_tail(queue_167,index_168),store(earray_170,index_171,e34)) = rstore_seq(q34,earray_172),
inference(monotonicity,[status(thm)],[1869,1866]) ).
tff(1871,plain,
rstore_seq(q34,earray_172) = rstore_seq(rstore_tail(queue_167,index_168),store(earray_170,index_171,e34)),
inference(symmetry,[status(thm)],[1870]) ).
tff(1872,plain,
rselect_head(rstore_seq(q34,earray_172)) = rselect_head(rstore_seq(rstore_tail(queue_167,index_168),store(earray_170,index_171,e34))),
inference(monotonicity,[status(thm)],[1871]) ).
tff(1873,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q34,earray_172),s(index_171))) = rselect_head(rstore_seq(q34,earray_172)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1874,plain,
rselect_head(rstore_tail(rstore_seq(q34,earray_172),s(index_171))) = rselect_head(rstore_seq(q34,earray_172)),
inference(unit_resolution,[status(thm)],[1873,1375]) ).
tff(1875,plain,
rselect_head(rstore_tail(queue_173,index_174)) = rselect_head(rstore_tail(rstore_seq(q34,earray_172),s(index_171))),
inference(monotonicity,[status(thm)],[343]) ).
tff(1876,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e35))) = rselect_head(rstore_tail(queue_173,index_174)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1877,plain,
rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e35))) = rselect_head(rstore_tail(queue_173,index_174)),
inference(unit_resolution,[status(thm)],[1876,1356]) ).
tff(1878,plain,
( ( earray_178 = store(earray_176,index_177,e35) )
<=> ( earray_178 = store(earray_176,index_177,e35) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1879,axiom,
earray_178 = store(earray_176,index_177,e35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp29) ).
tff(1880,plain,
earray_178 = store(earray_176,index_177,e35),
inference(modus_ponens,[status(thm)],[1879,1878]) ).
tff(1881,plain,
store(earray_176,index_177,e35) = earray_178,
inference(symmetry,[status(thm)],[1880]) ).
tff(1882,plain,
queue_175 = q35,
inference(symmetry,[status(thm)],[349]) ).
tff(1883,plain,
rstore_tail(queue_173,index_174) = queue_175,
inference(symmetry,[status(thm)],[346]) ).
tff(1884,plain,
rstore_tail(queue_173,index_174) = q35,
inference(transitivity,[status(thm)],[1883,1882]) ).
tff(1885,plain,
rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e35)) = rstore_seq(q35,earray_178),
inference(monotonicity,[status(thm)],[1884,1881]) ).
tff(1886,plain,
rstore_seq(q35,earray_178) = rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e35)),
inference(symmetry,[status(thm)],[1885]) ).
tff(1887,plain,
rselect_head(rstore_seq(q35,earray_178)) = rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e35))),
inference(monotonicity,[status(thm)],[1886]) ).
tff(1888,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q35,earray_178),s(index_177))) = rselect_head(rstore_seq(q35,earray_178)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1889,plain,
rselect_head(rstore_tail(rstore_seq(q35,earray_178),s(index_177))) = rselect_head(rstore_seq(q35,earray_178)),
inference(unit_resolution,[status(thm)],[1888,1375]) ).
tff(1890,plain,
rselect_head(rstore_tail(queue_179,index_180)) = rselect_head(rstore_tail(rstore_seq(q35,earray_178),s(index_177))),
inference(monotonicity,[status(thm)],[285]) ).
tff(1891,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e36))) = rselect_head(rstore_tail(queue_179,index_180)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1892,plain,
rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e36))) = rselect_head(rstore_tail(queue_179,index_180)),
inference(unit_resolution,[status(thm)],[1891,1356]) ).
tff(1893,plain,
( ( earray_184 = store(earray_182,index_183,e36) )
<=> ( earray_184 = store(earray_182,index_183,e36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1894,axiom,
earray_184 = store(earray_182,index_183,e36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp31) ).
tff(1895,plain,
earray_184 = store(earray_182,index_183,e36),
inference(modus_ponens,[status(thm)],[1894,1893]) ).
tff(1896,plain,
store(earray_182,index_183,e36) = earray_184,
inference(symmetry,[status(thm)],[1895]) ).
tff(1897,plain,
queue_181 = q36,
inference(symmetry,[status(thm)],[291]) ).
tff(1898,plain,
rstore_tail(queue_179,index_180) = queue_181,
inference(symmetry,[status(thm)],[288]) ).
tff(1899,plain,
rstore_tail(queue_179,index_180) = q36,
inference(transitivity,[status(thm)],[1898,1897]) ).
tff(1900,plain,
rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e36)) = rstore_seq(q36,earray_184),
inference(monotonicity,[status(thm)],[1899,1896]) ).
tff(1901,plain,
rstore_seq(q36,earray_184) = rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e36)),
inference(symmetry,[status(thm)],[1900]) ).
tff(1902,plain,
rselect_head(rstore_seq(q36,earray_184)) = rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e36))),
inference(monotonicity,[status(thm)],[1901]) ).
tff(1903,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q36,earray_184),s(index_183))) = rselect_head(rstore_seq(q36,earray_184)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1904,plain,
rselect_head(rstore_tail(rstore_seq(q36,earray_184),s(index_183))) = rselect_head(rstore_seq(q36,earray_184)),
inference(unit_resolution,[status(thm)],[1903,1375]) ).
tff(1905,plain,
rselect_head(rstore_tail(queue_185,index_186)) = rselect_head(rstore_tail(rstore_seq(q36,earray_184),s(index_183))),
inference(monotonicity,[status(thm)],[226]) ).
tff(1906,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_185,index_186),store(earray_188,index_189,e37))) = rselect_head(rstore_tail(queue_185,index_186)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1907,plain,
rselect_head(rstore_seq(rstore_tail(queue_185,index_186),store(earray_188,index_189,e37))) = rselect_head(rstore_tail(queue_185,index_186)),
inference(unit_resolution,[status(thm)],[1906,1356]) ).
tff(1908,plain,
( ( earray_190 = store(earray_188,index_189,e37) )
<=> ( earray_190 = store(earray_188,index_189,e37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1909,axiom,
earray_190 = store(earray_188,index_189,e37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp33) ).
tff(1910,plain,
earray_190 = store(earray_188,index_189,e37),
inference(modus_ponens,[status(thm)],[1909,1908]) ).
tff(1911,plain,
store(earray_188,index_189,e37) = earray_190,
inference(symmetry,[status(thm)],[1910]) ).
tff(1912,plain,
queue_187 = q37,
inference(symmetry,[status(thm)],[232]) ).
tff(1913,plain,
rstore_tail(queue_185,index_186) = queue_187,
inference(symmetry,[status(thm)],[229]) ).
tff(1914,plain,
rstore_tail(queue_185,index_186) = q37,
inference(transitivity,[status(thm)],[1913,1912]) ).
tff(1915,plain,
rstore_seq(rstore_tail(queue_185,index_186),store(earray_188,index_189,e37)) = rstore_seq(q37,earray_190),
inference(monotonicity,[status(thm)],[1914,1911]) ).
tff(1916,plain,
rstore_seq(q37,earray_190) = rstore_seq(rstore_tail(queue_185,index_186),store(earray_188,index_189,e37)),
inference(symmetry,[status(thm)],[1915]) ).
tff(1917,plain,
rselect_head(rstore_seq(q37,earray_190)) = rselect_head(rstore_seq(rstore_tail(queue_185,index_186),store(earray_188,index_189,e37))),
inference(monotonicity,[status(thm)],[1916]) ).
tff(1918,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q37,earray_190),s(index_189))) = rselect_head(rstore_seq(q37,earray_190)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1919,plain,
rselect_head(rstore_tail(rstore_seq(q37,earray_190),s(index_189))) = rselect_head(rstore_seq(q37,earray_190)),
inference(unit_resolution,[status(thm)],[1918,1375]) ).
tff(1920,plain,
rselect_head(rstore_tail(queue_191,index_192)) = rselect_head(rstore_tail(rstore_seq(q37,earray_190),s(index_189))),
inference(monotonicity,[status(thm)],[258]) ).
tff(1921,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_191,index_192),store(earray_194,index_195,e38))) = rselect_head(rstore_tail(queue_191,index_192)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1922,plain,
rselect_head(rstore_seq(rstore_tail(queue_191,index_192),store(earray_194,index_195,e38))) = rselect_head(rstore_tail(queue_191,index_192)),
inference(unit_resolution,[status(thm)],[1921,1356]) ).
tff(1923,plain,
( ( earray_196 = store(earray_194,index_195,e38) )
<=> ( earray_196 = store(earray_194,index_195,e38) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1924,axiom,
earray_196 = store(earray_194,index_195,e38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp35) ).
tff(1925,plain,
earray_196 = store(earray_194,index_195,e38),
inference(modus_ponens,[status(thm)],[1924,1923]) ).
tff(1926,plain,
store(earray_194,index_195,e38) = earray_196,
inference(symmetry,[status(thm)],[1925]) ).
tff(1927,plain,
queue_193 = q38,
inference(symmetry,[status(thm)],[264]) ).
tff(1928,plain,
rstore_tail(queue_191,index_192) = queue_193,
inference(symmetry,[status(thm)],[261]) ).
tff(1929,plain,
rstore_tail(queue_191,index_192) = q38,
inference(transitivity,[status(thm)],[1928,1927]) ).
tff(1930,plain,
rstore_seq(rstore_tail(queue_191,index_192),store(earray_194,index_195,e38)) = rstore_seq(q38,earray_196),
inference(monotonicity,[status(thm)],[1929,1926]) ).
tff(1931,plain,
rstore_seq(q38,earray_196) = rstore_seq(rstore_tail(queue_191,index_192),store(earray_194,index_195,e38)),
inference(symmetry,[status(thm)],[1930]) ).
tff(1932,plain,
rselect_head(rstore_seq(q38,earray_196)) = rselect_head(rstore_seq(rstore_tail(queue_191,index_192),store(earray_194,index_195,e38))),
inference(monotonicity,[status(thm)],[1931]) ).
tff(1933,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q38,earray_196),s(index_195))) = rselect_head(rstore_seq(q38,earray_196)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1934,plain,
rselect_head(rstore_tail(rstore_seq(q38,earray_196),s(index_195))) = rselect_head(rstore_seq(q38,earray_196)),
inference(unit_resolution,[status(thm)],[1933,1375]) ).
tff(1935,plain,
rselect_head(rstore_tail(queue_197,index_198)) = rselect_head(rstore_tail(rstore_seq(q38,earray_196),s(index_195))),
inference(monotonicity,[status(thm)],[200]) ).
tff(1936,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_197,index_198),store(earray_206,index_207,e39))) = rselect_head(rstore_tail(queue_197,index_198)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1937,plain,
rselect_head(rstore_seq(rstore_tail(queue_197,index_198),store(earray_206,index_207,e39))) = rselect_head(rstore_tail(queue_197,index_198)),
inference(unit_resolution,[status(thm)],[1936,1356]) ).
tff(1938,plain,
( ( earray_208 = store(earray_206,index_207,e39) )
<=> ( earray_208 = store(earray_206,index_207,e39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1939,axiom,
earray_208 = store(earray_206,index_207,e39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp41) ).
tff(1940,plain,
earray_208 = store(earray_206,index_207,e39),
inference(modus_ponens,[status(thm)],[1939,1938]) ).
tff(1941,plain,
store(earray_206,index_207,e39) = earray_208,
inference(symmetry,[status(thm)],[1940]) ).
tff(1942,plain,
queue_199 = q39,
inference(symmetry,[status(thm)],[206]) ).
tff(1943,plain,
rstore_tail(queue_197,index_198) = queue_199,
inference(symmetry,[status(thm)],[203]) ).
tff(1944,plain,
rstore_tail(queue_197,index_198) = q39,
inference(transitivity,[status(thm)],[1943,1942]) ).
tff(1945,plain,
rstore_seq(rstore_tail(queue_197,index_198),store(earray_206,index_207,e39)) = rstore_seq(q39,earray_208),
inference(monotonicity,[status(thm)],[1944,1941]) ).
tff(1946,plain,
rstore_seq(q39,earray_208) = rstore_seq(rstore_tail(queue_197,index_198),store(earray_206,index_207,e39)),
inference(symmetry,[status(thm)],[1945]) ).
tff(1947,plain,
rselect_head(rstore_seq(q39,earray_208)) = rselect_head(rstore_seq(rstore_tail(queue_197,index_198),store(earray_206,index_207,e39))),
inference(monotonicity,[status(thm)],[1946]) ).
tff(1948,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q39,earray_208),s(index_207))) = rselect_head(rstore_seq(q39,earray_208)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1949,plain,
rselect_head(rstore_tail(rstore_seq(q39,earray_208),s(index_207))) = rselect_head(rstore_seq(q39,earray_208)),
inference(unit_resolution,[status(thm)],[1948,1375]) ).
tff(1950,plain,
rselect_head(rstore_tail(queue_209,index_210)) = rselect_head(rstore_tail(rstore_seq(q39,earray_208),s(index_207))),
inference(monotonicity,[status(thm)],[134]) ).
tff(1951,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_209,index_210),store(earray_212,index_213,e40))) = rselect_head(rstore_tail(queue_209,index_210)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1952,plain,
rselect_head(rstore_seq(rstore_tail(queue_209,index_210),store(earray_212,index_213,e40))) = rselect_head(rstore_tail(queue_209,index_210)),
inference(unit_resolution,[status(thm)],[1951,1356]) ).
tff(1953,plain,
( ( earray_214 = store(earray_212,index_213,e40) )
<=> ( earray_214 = store(earray_212,index_213,e40) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1954,axiom,
earray_214 = store(earray_212,index_213,e40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp43) ).
tff(1955,plain,
earray_214 = store(earray_212,index_213,e40),
inference(modus_ponens,[status(thm)],[1954,1953]) ).
tff(1956,plain,
store(earray_212,index_213,e40) = earray_214,
inference(symmetry,[status(thm)],[1955]) ).
tff(1957,plain,
queue_211 = q40,
inference(symmetry,[status(thm)],[140]) ).
tff(1958,plain,
rstore_tail(queue_209,index_210) = queue_211,
inference(symmetry,[status(thm)],[137]) ).
tff(1959,plain,
rstore_tail(queue_209,index_210) = q40,
inference(transitivity,[status(thm)],[1958,1957]) ).
tff(1960,plain,
rstore_seq(rstore_tail(queue_209,index_210),store(earray_212,index_213,e40)) = rstore_seq(q40,earray_214),
inference(monotonicity,[status(thm)],[1959,1956]) ).
tff(1961,plain,
rstore_seq(q40,earray_214) = rstore_seq(rstore_tail(queue_209,index_210),store(earray_212,index_213,e40)),
inference(symmetry,[status(thm)],[1960]) ).
tff(1962,plain,
rselect_head(rstore_seq(q40,earray_214)) = rselect_head(rstore_seq(rstore_tail(queue_209,index_210),store(earray_212,index_213,e40))),
inference(monotonicity,[status(thm)],[1961]) ).
tff(1963,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q40,earray_214),s(index_213))) = rselect_head(rstore_seq(q40,earray_214)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1964,plain,
rselect_head(rstore_tail(rstore_seq(q40,earray_214),s(index_213))) = rselect_head(rstore_seq(q40,earray_214)),
inference(unit_resolution,[status(thm)],[1963,1375]) ).
tff(1965,plain,
rselect_head(rstore_tail(queue_215,index_216)) = rselect_head(rstore_tail(rstore_seq(q40,earray_214),s(index_213))),
inference(monotonicity,[status(thm)],[166]) ).
tff(1966,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e41))) = rselect_head(rstore_tail(queue_215,index_216)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1967,plain,
rselect_head(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e41))) = rselect_head(rstore_tail(queue_215,index_216)),
inference(unit_resolution,[status(thm)],[1966,1356]) ).
tff(1968,plain,
( ( earray_220 = store(earray_218,index_219,e41) )
<=> ( earray_220 = store(earray_218,index_219,e41) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1969,axiom,
earray_220 = store(earray_218,index_219,e41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp46) ).
tff(1970,plain,
earray_220 = store(earray_218,index_219,e41),
inference(modus_ponens,[status(thm)],[1969,1968]) ).
tff(1971,plain,
store(earray_218,index_219,e41) = earray_220,
inference(symmetry,[status(thm)],[1970]) ).
tff(1972,plain,
queue_217 = q41,
inference(symmetry,[status(thm)],[172]) ).
tff(1973,plain,
rstore_tail(queue_215,index_216) = queue_217,
inference(symmetry,[status(thm)],[169]) ).
tff(1974,plain,
rstore_tail(queue_215,index_216) = q41,
inference(transitivity,[status(thm)],[1973,1972]) ).
tff(1975,plain,
rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e41)) = rstore_seq(q41,earray_220),
inference(monotonicity,[status(thm)],[1974,1971]) ).
tff(1976,plain,
rstore_seq(q41,earray_220) = rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e41)),
inference(symmetry,[status(thm)],[1975]) ).
tff(1977,plain,
rselect_head(rstore_seq(q41,earray_220)) = rselect_head(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e41))),
inference(monotonicity,[status(thm)],[1976]) ).
tff(1978,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q41,earray_220),s(index_219))) = rselect_head(rstore_seq(q41,earray_220)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1979,plain,
rselect_head(rstore_tail(rstore_seq(q41,earray_220),s(index_219))) = rselect_head(rstore_seq(q41,earray_220)),
inference(unit_resolution,[status(thm)],[1978,1375]) ).
tff(1980,plain,
rselect_head(rstore_tail(queue_221,index_222)) = rselect_head(rstore_tail(rstore_seq(q41,earray_220),s(index_219))),
inference(monotonicity,[status(thm)],[114]) ).
tff(1981,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e42))) = rselect_head(rstore_tail(queue_221,index_222)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1982,plain,
rselect_head(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e42))) = rselect_head(rstore_tail(queue_221,index_222)),
inference(unit_resolution,[status(thm)],[1981,1356]) ).
tff(1983,plain,
rselect_head(rstore_seq(q42,earray_226)) = rselect_head(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e42))),
inference(monotonicity,[status(thm)],[87]) ).
tff(1984,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q42,earray_226),s(index_225))) = rselect_head(rstore_seq(q42,earray_226)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1985,plain,
rselect_head(rstore_tail(rstore_seq(q42,earray_226),s(index_225))) = rselect_head(rstore_seq(q42,earray_226)),
inference(unit_resolution,[status(thm)],[1984,1375]) ).
tff(1986,plain,
rselect_head(q43) = rselect_head(rstore_tail(rstore_seq(q42,earray_226),s(index_225))),
inference(monotonicity,[status(thm)],[44]) ).
tff(1987,plain,
( ( index_261 = rselect_head(q43) )
<=> ( index_261 = rselect_head(q43) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1988,axiom,
index_261 = rselect_head(q43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp148) ).
tff(1989,plain,
index_261 = rselect_head(q43),
inference(modus_ponens,[status(thm)],[1988,1987]) ).
tff(1990,plain,
index_261 = rselect_tail(q42),
inference(transitivity,[status(thm)],[1989,1986,1985,1983,1982,1980,1979,1977,1967,1965,1964,1962,1952,1950,1949,1947,1937,1935,1934,1932,1922,1920,1919,1917,1907,1905,1904,1902,1892,1890,1889,1887,1877,1875,1874,1872,1862,1860,1859,1857,1847,1845,1844,1842,1832,1830,1829,1827,1817,1815,1814,1812,1802,1800,1799,1797,1787,1785,1784,1782,1772,1770,1769,1767,1757,1755,1754,1752,1744,1742,1740,1738,1728,1726,1725,1723,1713,1711,1710,1708,1700,1698,1696,1694,1684,1682,1681,1679,1669,1667,1666,1664,1656,1654,1652,1650,1640,1638,1637,1635,1625,1623,1622,1620,1612,1610,1608,1606,1596,1594,1593,1591,1581,1579,1578,1576,1568,1566,1564,1562,1554,1552,1550,1548,1538,1536,1535,1533,1525,1523,1521,1519,1511,1509,1507,1505,1495,1493,1492,1490,1482,1480,1478,1476,1468,1466,1464,1462,1452,1450,1449,1447,1439,1437,1435,1433,1425,1423,1421,1419,1409,1407,1405,1403,1395,1393,1391,1389,1381,1379,1377,1368,1358,1349,1347,1338,1328,1313,1310,1248,1245,1226,1223,1161,1158,1139,1136,1074,1071,1052,1049,987,984,965,962,900,897,878,875,813,810,791,788,726,723,704,701,639,636,617,614,552,549,530,527,467,464,445,442,382,379,360,357,297,294,275,272,212,209,190,180,120,117]) ).
tff(1991,plain,
select(earray_260,index_261) = select(store(rselect_seq(q42),rselect_tail(q42),e42),rselect_tail(q42)),
inference(monotonicity,[status(thm)],[102,1990]) ).
tff(1992,plain,
( ( elem_262 = select(earray_260,index_261) )
<=> ( elem_262 = select(earray_260,index_261) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1993,axiom,
elem_262 = select(earray_260,index_261),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp87) ).
tff(1994,plain,
elem_262 = select(earray_260,index_261),
inference(modus_ponens,[status(thm)],[1993,1992]) ).
tff(1995,plain,
elem_262 = elem_265,
inference(transitivity,[status(thm)],[1994,1991,104,4]) ).
tff(1996,plain,
( ( elem_262 != elem_265 )
<=> ( elem_262 != elem_265 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1997,axiom,
elem_262 != elem_265,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(1998,plain,
elem_262 != elem_265,
inference(modus_ponens,[status(thm)],[1997,1996]) ).
tff(1999,plain,
$false,
inference(unit_resolution,[status(thm)],[1998,1995]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV570-1.043 : TPTP v9.0.0. Bugfixed v5.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 10:25:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% See solution above
% 0.39/0.55 % E exiting
%------------------------------------------------------------------------------