%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG180+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n028.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 : Wed Apr 9 05:24:42 PM UTC 2025
% Result : Theorem 9.64s 3.30s
% Output : CNFRefutation 9.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 166 ( 152 unt; 0 typ; 0 def)
% Number of atoms : 371 ( 360 equ)
% Maximal formula atoms : 110 ( 2 avg)
% Number of connectives : 237 ( 32 ~; 70 |; 134 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 63 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ op2 > op1 > #nlpp > j > h > e24 > e23 > e22 > e21 > e20 > e14 > e13 > e12 > e11 > e10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(e21,type,
e21: $i ).
tff(e24,type,
e24: $i ).
tff(e20,type,
e20: $i ).
tff(e13,type,
e13: $i ).
tff(e22,type,
e22: $i ).
tff(op2,type,
op2: ( $i * $i ) > $i ).
tff(op1,type,
op1: ( $i * $i ) > $i ).
tff(e10,type,
e10: $i ).
tff(h,type,
h: $i > $i ).
tff(e23,type,
e23: $i ).
tff(e14,type,
e14: $i ).
tff(e12,type,
e12: $i ).
tff(j,type,
j: $i > $i ).
tff(e11,type,
e11: $i ).
tff(f_83,axiom,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e20 != e24 )
& ( e21 != e22 )
& ( e21 != e23 )
& ( e21 != e24 )
& ( e22 != e23 )
& ( e22 != e24 )
& ( e23 != e24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(f_54,axiom,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e10 != e14 )
& ( e11 != e12 )
& ( e11 != e13 )
& ( e11 != e14 )
& ( e12 != e13 )
& ( e12 != e14 )
& ( e13 != e14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(f_206,axiom,
( ( op1(e10,e10) = e13 )
& ( op1(e10,e11) = e12 )
& ( op1(e10,e12) = e10 )
& ( op1(e10,e13) = e11 )
& ( op1(e10,e14) = e14 )
& ( op1(e11,e10) = e10 )
& ( op1(e11,e11) = e14 )
& ( op1(e11,e12) = e11 )
& ( op1(e11,e13) = e12 )
& ( op1(e11,e14) = e13 )
& ( op1(e12,e10) = e11 )
& ( op1(e12,e11) = e13 )
& ( op1(e12,e12) = e12 )
& ( op1(e12,e13) = e14 )
& ( op1(e12,e14) = e10 )
& ( op1(e13,e10) = e14 )
& ( op1(e13,e11) = e11 )
& ( op1(e13,e12) = e13 )
& ( op1(e13,e13) = e10 )
& ( op1(e13,e14) = e12 )
& ( op1(e14,e10) = e12 )
& ( op1(e14,e11) = e10 )
& ( op1(e14,e12) = e14 )
& ( op1(e14,e13) = e13 )
& ( op1(e14,e14) = e11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(f_476,negated_conjecture,
~ ( ( ( ( h(e10) = e20 )
| ( h(e10) = e21 )
| ( h(e10) = e22 )
| ( h(e10) = e23 )
| ( h(e10) = e24 ) )
& ( ( h(e11) = e20 )
| ( h(e11) = e21 )
| ( h(e11) = e22 )
| ( h(e11) = e23 )
| ( h(e11) = e24 ) )
& ( ( h(e12) = e20 )
| ( h(e12) = e21 )
| ( h(e12) = e22 )
| ( h(e12) = e23 )
| ( h(e12) = e24 ) )
& ( ( h(e13) = e20 )
| ( h(e13) = e21 )
| ( h(e13) = e22 )
| ( h(e13) = e23 )
| ( h(e13) = e24 ) )
& ( ( h(e14) = e20 )
| ( h(e14) = e21 )
| ( h(e14) = e22 )
| ( h(e14) = e23 )
| ( h(e14) = e24 ) )
& ( ( j(e20) = e10 )
| ( j(e20) = e11 )
| ( j(e20) = e12 )
| ( j(e20) = e13 )
| ( j(e20) = e14 ) )
& ( ( j(e21) = e10 )
| ( j(e21) = e11 )
| ( j(e21) = e12 )
| ( j(e21) = e13 )
| ( j(e21) = e14 ) )
& ( ( j(e22) = e10 )
| ( j(e22) = e11 )
| ( j(e22) = e12 )
| ( j(e22) = e13 )
| ( j(e22) = e14 ) )
& ( ( j(e23) = e10 )
| ( j(e23) = e11 )
| ( j(e23) = e12 )
| ( j(e23) = e13 )
| ( j(e23) = e14 ) )
& ( ( j(e24) = e10 )
| ( j(e24) = e11 )
| ( j(e24) = e12 )
| ( j(e24) = e13 )
| ( j(e24) = e14 ) ) )
=> ~ ( ( h(op1(e10,e10)) = op2(h(e10),h(e10)) )
& ( h(op1(e10,e11)) = op2(h(e10),h(e11)) )
& ( h(op1(e10,e12)) = op2(h(e10),h(e12)) )
& ( h(op1(e10,e13)) = op2(h(e10),h(e13)) )
& ( h(op1(e10,e14)) = op2(h(e10),h(e14)) )
& ( h(op1(e11,e10)) = op2(h(e11),h(e10)) )
& ( h(op1(e11,e11)) = op2(h(e11),h(e11)) )
& ( h(op1(e11,e12)) = op2(h(e11),h(e12)) )
& ( h(op1(e11,e13)) = op2(h(e11),h(e13)) )
& ( h(op1(e11,e14)) = op2(h(e11),h(e14)) )
& ( h(op1(e12,e10)) = op2(h(e12),h(e10)) )
& ( h(op1(e12,e11)) = op2(h(e12),h(e11)) )
& ( h(op1(e12,e12)) = op2(h(e12),h(e12)) )
& ( h(op1(e12,e13)) = op2(h(e12),h(e13)) )
& ( h(op1(e12,e14)) = op2(h(e12),h(e14)) )
& ( h(op1(e13,e10)) = op2(h(e13),h(e10)) )
& ( h(op1(e13,e11)) = op2(h(e13),h(e11)) )
& ( h(op1(e13,e12)) = op2(h(e13),h(e12)) )
& ( h(op1(e13,e13)) = op2(h(e13),h(e13)) )
& ( h(op1(e13,e14)) = op2(h(e13),h(e14)) )
& ( h(op1(e14,e10)) = op2(h(e14),h(e10)) )
& ( h(op1(e14,e11)) = op2(h(e14),h(e11)) )
& ( h(op1(e14,e12)) = op2(h(e14),h(e12)) )
& ( h(op1(e14,e13)) = op2(h(e14),h(e13)) )
& ( h(op1(e14,e14)) = op2(h(e14),h(e14)) )
& ( j(op2(e20,e20)) = op1(j(e20),j(e20)) )
& ( j(op2(e20,e21)) = op1(j(e20),j(e21)) )
& ( j(op2(e20,e22)) = op1(j(e20),j(e22)) )
& ( j(op2(e20,e23)) = op1(j(e20),j(e23)) )
& ( j(op2(e20,e24)) = op1(j(e20),j(e24)) )
& ( j(op2(e21,e20)) = op1(j(e21),j(e20)) )
& ( j(op2(e21,e21)) = op1(j(e21),j(e21)) )
& ( j(op2(e21,e22)) = op1(j(e21),j(e22)) )
& ( j(op2(e21,e23)) = op1(j(e21),j(e23)) )
& ( j(op2(e21,e24)) = op1(j(e21),j(e24)) )
& ( j(op2(e22,e20)) = op1(j(e22),j(e20)) )
& ( j(op2(e22,e21)) = op1(j(e22),j(e21)) )
& ( j(op2(e22,e22)) = op1(j(e22),j(e22)) )
& ( j(op2(e22,e23)) = op1(j(e22),j(e23)) )
& ( j(op2(e22,e24)) = op1(j(e22),j(e24)) )
& ( j(op2(e23,e20)) = op1(j(e23),j(e20)) )
& ( j(op2(e23,e21)) = op1(j(e23),j(e21)) )
& ( j(op2(e23,e22)) = op1(j(e23),j(e22)) )
& ( j(op2(e23,e23)) = op1(j(e23),j(e23)) )
& ( j(op2(e23,e24)) = op1(j(e23),j(e24)) )
& ( j(op2(e24,e20)) = op1(j(e24),j(e20)) )
& ( j(op2(e24,e21)) = op1(j(e24),j(e21)) )
& ( j(op2(e24,e22)) = op1(j(e24),j(e22)) )
& ( j(op2(e24,e23)) = op1(j(e24),j(e23)) )
& ( j(op2(e24,e24)) = op1(j(e24),j(e24)) )
& ( h(j(e20)) = e20 )
& ( h(j(e21)) = e21 )
& ( h(j(e22)) = e22 )
& ( h(j(e23)) = e23 )
& ( h(j(e24)) = e24 )
& ( j(h(e10)) = e10 )
& ( j(h(e11)) = e11 )
& ( j(h(e12)) = e12 )
& ( j(h(e13)) = e13 )
& ( j(h(e14)) = e14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_255,axiom,
( ( op2(e20,e20) = e24 )
& ( op2(e20,e21) = e22 )
& ( op2(e20,e22) = e20 )
& ( op2(e20,e23) = e21 )
& ( op2(e20,e24) = e23 )
& ( op2(e21,e20) = e20 )
& ( op2(e21,e21) = e21 )
& ( op2(e21,e22) = e22 )
& ( op2(e21,e23) = e23 )
& ( op2(e21,e24) = e24 )
& ( op2(e22,e20) = e21 )
& ( op2(e22,e21) = e24 )
& ( op2(e22,e22) = e23 )
& ( op2(e22,e23) = e20 )
& ( op2(e22,e24) = e22 )
& ( op2(e23,e20) = e23 )
& ( op2(e23,e21) = e20 )
& ( op2(e23,e22) = e24 )
& ( op2(e23,e23) = e22 )
& ( op2(e23,e24) = e21 )
& ( op2(e24,e20) = e22 )
& ( op2(e24,e21) = e23 )
& ( op2(e24,e22) = e21 )
& ( op2(e24,e23) = e24 )
& ( op2(e24,e24) = e20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
tff(c_26,plain,
e23 != e22,
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_2,plain,
e14 != e13,
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_94,plain,
op1(e14,e13) = e13,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_140,plain,
op1(e10,e10) = e13,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_314,plain,
( ( j(e23) = e14 )
| ( j(e23) = e13 )
| ( j(e23) = e12 )
| ( j(e23) = e11 )
| ( j(e23) = e10 ) ),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_1159,plain,
j(e23) = e10,
inference(splitLeft,[status(thm)],[c_314]) ).
tff(c_154,plain,
op2(e23,e23) = e22,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_224,plain,
op1(j(e23),j(e23)) = j(op2(e23,e23)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_349,plain,
op1(j(e23),j(e23)) = j(e22),
inference(demodulation,[status(thm),theory(equality)],[c_154,c_224]) ).
tff(c_1169,plain,
op1(e10,e10) = j(e22),
inference(demodulation,[status(thm),theory(equality)],[c_1159,c_1159,c_349]) ).
tff(c_1172,plain,
j(e22) = e13,
inference(demodulation,[status(thm),theory(equality)],[c_140,c_1169]) ).
tff(c_322,plain,
( ( h(e14) = e24 )
| ( h(e14) = e23 )
| ( h(e14) = e22 )
| ( h(e14) = e21 )
| ( h(e14) = e20 ) ),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_873,plain,
h(e14) = e20,
inference(splitLeft,[status(thm)],[c_322]) ).
tff(c_192,plain,
j(h(e14)) = e14,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_874,plain,
j(e20) = e14,
inference(demodulation,[status(thm),theory(equality)],[c_873,c_192]) ).
tff(c_186,plain,
op2(e20,e22) = e20,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_256,plain,
op1(j(e20),j(e22)) = j(op2(e20,e22)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_333,plain,
op1(j(e20),j(e22)) = j(e20),
inference(demodulation,[status(thm),theory(equality)],[c_186,c_256]) ).
tff(c_987,plain,
op1(e14,j(e22)) = e14,
inference(demodulation,[status(thm),theory(equality)],[c_874,c_874,c_333]) ).
tff(c_1182,plain,
op1(e14,e13) = e14,
inference(demodulation,[status(thm),theory(equality)],[c_1172,c_987]) ).
tff(c_1187,plain,
e14 = e13,
inference(demodulation,[status(thm),theory(equality)],[c_94,c_1182]) ).
tff(c_1189,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2,c_1187]) ).
tff(c_1191,plain,
j(e23) != e10,
inference(splitRight,[status(thm)],[c_314]) ).
tff(c_98,plain,
op1(e14,e11) = e10,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_92,plain,
op1(e14,e14) = e11,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_190,plain,
op2(e20,e20) = e24,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_260,plain,
op1(j(e20),j(e20)) = j(op2(e20,e20)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_331,plain,
op1(j(e20),j(e20)) = j(e24),
inference(demodulation,[status(thm),theory(equality)],[c_190,c_260]) ).
tff(c_1200,plain,
j(e24) = e11,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_874,c_874,c_331]) ).
tff(c_182,plain,
op2(e20,e24) = e23,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_252,plain,
op1(j(e20),j(e24)) = j(op2(e20,e24)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_335,plain,
op1(j(e20),j(e24)) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_252]) ).
tff(c_939,plain,
op1(e14,j(e24)) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_874,c_335]) ).
tff(c_1211,plain,
op1(e14,e11) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_1200,c_939]) ).
tff(c_1215,plain,
j(e23) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_1211]) ).
tff(c_1217,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1191,c_1215]) ).
tff(c_1219,plain,
h(e14) != e20,
inference(splitRight,[status(thm)],[c_322]) ).
tff(c_110,plain,
op1(e13,e10) = e14,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_1990,plain,
j(e23) = e10,
inference(splitLeft,[status(thm)],[c_314]) ).
tff(c_2078,plain,
j(e22) = e13,
inference(demodulation,[status(thm),theory(equality)],[c_140,c_1990,c_1990,c_349]) ).
tff(c_164,plain,
op2(e22,e23) = e20,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_234,plain,
op1(j(e22),j(e23)) = j(op2(e22,e23)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_344,plain,
op1(j(e22),j(e23)) = j(e20),
inference(demodulation,[status(thm),theory(equality)],[c_164,c_234]) ).
tff(c_1996,plain,
op1(j(e22),e10) = j(e20),
inference(demodulation,[status(thm),theory(equality)],[c_1990,c_344]) ).
tff(c_2081,plain,
op1(e13,e10) = j(e20),
inference(demodulation,[status(thm),theory(equality)],[c_2078,c_1996]) ).
tff(c_2087,plain,
j(e20) = e14,
inference(demodulation,[status(thm),theory(equality)],[c_110,c_2081]) ).
tff(c_210,plain,
h(j(e20)) = e20,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_2099,plain,
h(e14) = e20,
inference(demodulation,[status(thm),theory(equality)],[c_2087,c_210]) ).
tff(c_2102,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1219,c_2099]) ).
tff(c_2104,plain,
j(e23) != e10,
inference(splitRight,[status(thm)],[c_314]) ).
tff(c_104,plain,
op1(e13,e13) = e10,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_10,plain,
e13 != e11,
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_108,plain,
op1(e13,e11) = e11,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_150,plain,
op2(e24,e20) = e22,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_312,plain,
( ( j(e24) = e14 )
| ( j(e24) = e13 )
| ( j(e24) = e12 )
| ( j(e24) = e11 )
| ( j(e24) = e10 ) ),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_2133,plain,
j(e24) = e10,
inference(splitLeft,[status(thm)],[c_312]) ).
tff(c_142,plain,
op2(e24,e24) = e20,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_212,plain,
op1(j(e24),j(e24)) = j(op2(e24,e24)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_355,plain,
op1(j(e24),j(e24)) = j(e20),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_212]) ).
tff(c_2135,plain,
op1(e10,e10) = j(e20),
inference(demodulation,[status(thm),theory(equality)],[c_2133,c_2133,c_355]) ).
tff(c_2141,plain,
j(e20) = e13,
inference(demodulation,[status(thm),theory(equality)],[c_140,c_2135]) ).
tff(c_2151,plain,
h(e13) = e20,
inference(demodulation,[status(thm),theory(equality)],[c_2141,c_210]) ).
tff(c_202,plain,
h(j(e24)) = e24,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_2140,plain,
h(e10) = e24,
inference(demodulation,[status(thm),theory(equality)],[c_2133,c_202]) ).
tff(c_134,plain,
op1(e10,e13) = e11,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_304,plain,
op2(h(e10),h(e13)) = h(op1(e10,e13)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_359,plain,
op2(h(e10),h(e13)) = h(e11),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_304]) ).
tff(c_2158,plain,
op2(e24,h(e13)) = h(e11),
inference(demodulation,[status(thm),theory(equality)],[c_2140,c_359]) ).
tff(c_2189,plain,
h(e11) = e22,
inference(demodulation,[status(thm),theory(equality)],[c_150,c_2151,c_2158]) ).
tff(c_198,plain,
j(h(e11)) = e11,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_2194,plain,
j(e22) = e11,
inference(demodulation,[status(thm),theory(equality)],[c_2189,c_198]) ).
tff(c_2146,plain,
op1(e13,j(e22)) = e13,
inference(demodulation,[status(thm),theory(equality)],[c_2141,c_2141,c_333]) ).
tff(c_2203,plain,
op1(e13,e11) = e13,
inference(demodulation,[status(thm),theory(equality)],[c_2194,c_2146]) ).
tff(c_2207,plain,
e13 = e11,
inference(demodulation,[status(thm),theory(equality)],[c_108,c_2203]) ).
tff(c_2209,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_2207]) ).
tff(c_2211,plain,
j(e24) != e10,
inference(splitRight,[status(thm)],[c_312]) ).
tff(c_324,plain,
( ( h(e13) = e24 )
| ( h(e13) = e23 )
| ( h(e13) = e22 )
| ( h(e13) = e21 )
| ( h(e13) = e20 ) ),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_2306,plain,
h(e13) = e20,
inference(splitLeft,[status(thm)],[c_324]) ).
tff(c_274,plain,
op2(h(e13),h(e13)) = h(op1(e13,e13)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_374,plain,
op2(h(e13),h(e13)) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_104,c_274]) ).
tff(c_2309,plain,
op2(e20,e20) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_2306,c_2306,c_374]) ).
tff(c_2313,plain,
h(e10) = e24,
inference(demodulation,[status(thm),theory(equality)],[c_190,c_2309]) ).
tff(c_200,plain,
j(h(e10)) = e10,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_2322,plain,
j(e24) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_2313,c_200]) ).
tff(c_2324,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2211,c_2322]) ).
tff(c_2326,plain,
h(e13) != e20,
inference(splitRight,[status(thm)],[c_324]) ).
tff(c_128,plain,
op1(e11,e11) = e14,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_122,plain,
op1(e11,e14) = e13,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_38,plain,
e22 != e20,
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_328,plain,
( ( h(e11) = e24 )
| ( h(e11) = e23 )
| ( h(e11) = e22 )
| ( h(e11) = e21 )
| ( h(e11) = e20 ) ),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_597,plain,
h(e11) = e20,
inference(splitLeft,[status(thm)],[c_328]) ).
tff(c_598,plain,
j(e20) = e11,
inference(demodulation,[status(thm),theory(equality)],[c_597,c_198]) ).
tff(c_790,plain,
j(e24) = e14,
inference(demodulation,[status(thm),theory(equality)],[c_128,c_598,c_598,c_331]) ).
tff(c_220,plain,
op1(j(e24),j(e20)) = j(op2(e24,e20)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_351,plain,
op1(j(e24),j(e20)) = j(e22),
inference(demodulation,[status(thm),theory(equality)],[c_150,c_220]) ).
tff(c_744,plain,
op1(j(e24),e11) = j(e22),
inference(demodulation,[status(thm),theory(equality)],[c_598,c_351]) ).
tff(c_794,plain,
op1(e14,e11) = j(e22),
inference(demodulation,[status(thm),theory(equality)],[c_790,c_744]) ).
tff(c_799,plain,
j(e22) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_794]) ).
tff(c_206,plain,
h(j(e22)) = e22,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_809,plain,
h(e10) = e22,
inference(demodulation,[status(thm),theory(equality)],[c_799,c_206]) ).
tff(c_130,plain,
op1(e11,e10) = e10,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_300,plain,
op2(h(e11),h(e10)) = h(op1(e11,e10)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_361,plain,
op2(h(e11),h(e10)) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_300]) ).
tff(c_633,plain,
op2(e20,h(e10)) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_597,c_361]) ).
tff(c_842,plain,
op2(e20,e22) = e22,
inference(demodulation,[status(thm),theory(equality)],[c_809,c_809,c_633]) ).
tff(c_844,plain,
e22 = e20,
inference(demodulation,[status(thm),theory(equality)],[c_186,c_842]) ).
tff(c_846,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_844]) ).
tff(c_848,plain,
h(e11) != e20,
inference(splitRight,[status(thm)],[c_328]) ).
tff(c_316,plain,
( ( j(e22) = e14 )
| ( j(e22) = e13 )
| ( j(e22) = e12 )
| ( j(e22) = e11 )
| ( j(e22) = e10 ) ),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_2240,plain,
j(e22) = e10,
inference(splitLeft,[status(thm)],[c_316]) ).
tff(c_166,plain,
op2(e22,e22) = e23,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_236,plain,
op1(j(e22),j(e22)) = j(op2(e22,e22)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_343,plain,
op1(j(e22),j(e22)) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_166,c_236]) ).
tff(c_2247,plain,
op1(e10,e10) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_2240,c_2240,c_343]) ).
tff(c_2250,plain,
j(e23) = e13,
inference(demodulation,[status(thm),theory(equality)],[c_140,c_2247]) ).
tff(c_204,plain,
h(j(e23)) = e23,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_2260,plain,
h(e13) = e23,
inference(demodulation,[status(thm),theory(equality)],[c_2250,c_204]) ).
tff(c_2249,plain,
h(e10) = e22,
inference(demodulation,[status(thm),theory(equality)],[c_2240,c_206]) ).
tff(c_2270,plain,
op2(e22,h(e13)) = h(e11),
inference(demodulation,[status(thm),theory(equality)],[c_2249,c_359]) ).
tff(c_2302,plain,
h(e11) = e20,
inference(demodulation,[status(thm),theory(equality)],[c_164,c_2260,c_2270]) ).
tff(c_2303,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_848,c_2302]) ).
tff(c_2304,plain,
( ( j(e22) = e11 )
| ( j(e22) = e12 )
| ( j(e22) = e13 )
| ( j(e22) = e14 ) ),
inference(splitRight,[status(thm)],[c_316]) ).
tff(c_2430,plain,
j(e22) = e14,
inference(splitLeft,[status(thm)],[c_2304]) ).
tff(c_2442,plain,
op1(e14,e14) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_2430,c_2430,c_343]) ).
tff(c_2445,plain,
j(e23) = e11,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_2442]) ).
tff(c_156,plain,
op2(e23,e22) = e24,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_226,plain,
op1(j(e23),j(e22)) = j(op2(e23,e22)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_348,plain,
op1(j(e23),j(e22)) = j(e24),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_226]) ).
tff(c_2441,plain,
op1(j(e23),e14) = j(e24),
inference(demodulation,[status(thm),theory(equality)],[c_2430,c_348]) ).
tff(c_2545,plain,
j(e24) = e13,
inference(demodulation,[status(thm),theory(equality)],[c_122,c_2445,c_2441]) ).
tff(c_162,plain,
op2(e22,e24) = e22,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_232,plain,
op1(j(e22),j(e24)) = j(op2(e22,e24)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_345,plain,
op1(j(e22),j(e24)) = j(e22),
inference(demodulation,[status(thm),theory(equality)],[c_162,c_232]) ).
tff(c_2432,plain,
op1(e14,j(e24)) = e14,
inference(demodulation,[status(thm),theory(equality)],[c_2430,c_2430,c_345]) ).
tff(c_2546,plain,
op1(e14,e13) = e14,
inference(demodulation,[status(thm),theory(equality)],[c_2545,c_2432]) ).
tff(c_2552,plain,
e14 = e13,
inference(demodulation,[status(thm),theory(equality)],[c_94,c_2546]) ).
tff(c_2554,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2,c_2552]) ).
tff(c_2555,plain,
( ( j(e22) = e13 )
| ( j(e22) = e12 )
| ( j(e22) = e11 ) ),
inference(splitRight,[status(thm)],[c_2304]) ).
tff(c_2577,plain,
j(e22) = e11,
inference(splitLeft,[status(thm)],[c_2555]) ).
tff(c_2590,plain,
op1(e11,e11) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_2577,c_2577,c_343]) ).
tff(c_2593,plain,
j(e23) = e14,
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2590]) ).
tff(c_2607,plain,
h(e14) = e23,
inference(demodulation,[status(thm),theory(equality)],[c_2593,c_204]) ).
tff(c_2592,plain,
h(e11) = e22,
inference(demodulation,[status(thm),theory(equality)],[c_2577,c_206]) ).
tff(c_292,plain,
op2(h(e11),h(e14)) = h(op1(e11,e14)),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_365,plain,
op2(h(e11),h(e14)) = h(e13),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_292]) ).
tff(c_2615,plain,
op2(e22,h(e14)) = h(e13),
inference(demodulation,[status(thm),theory(equality)],[c_2592,c_365]) ).
tff(c_2763,plain,
h(e13) = e20,
inference(demodulation,[status(thm),theory(equality)],[c_164,c_2607,c_2615]) ).
tff(c_2764,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2326,c_2763]) ).
tff(c_2765,plain,
( ( j(e22) = e12 )
| ( j(e22) = e13 ) ),
inference(splitRight,[status(thm)],[c_2555]) ).
tff(c_2767,plain,
j(e22) = e13,
inference(splitLeft,[status(thm)],[c_2765]) ).
tff(c_2782,plain,
op1(e13,e13) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_2767,c_2767,c_343]) ).
tff(c_2785,plain,
j(e23) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_104,c_2782]) ).
tff(c_2787,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2104,c_2785]) ).
tff(c_2788,plain,
j(e22) = e12,
inference(splitRight,[status(thm)],[c_2765]) ).
tff(c_2805,plain,
h(e12) = e22,
inference(demodulation,[status(thm),theory(equality)],[c_2788,c_206]) ).
tff(c_116,plain,
op1(e12,e12) = e12,
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_2803,plain,
op1(e12,e12) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_2788,c_2788,c_343]) ).
tff(c_2806,plain,
j(e23) = e12,
inference(demodulation,[status(thm),theory(equality)],[c_116,c_2803]) ).
tff(c_2821,plain,
h(e12) = e23,
inference(demodulation,[status(thm),theory(equality)],[c_2806,c_204]) ).
tff(c_2846,plain,
e23 = e22,
inference(demodulation,[status(thm),theory(equality)],[c_2805,c_2821]) ).
tff(c_2847,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26,c_2846]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : ALG180+1 : TPTP v9.0.0. Released v2.7.0.
% 0.06/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Apr 6 07:07:49 EDT 2025
% 0.14/0.35 % CPUTime :
% 9.64/3.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.68/3.32
% 9.68/3.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------