%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN094-1.005 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:37:02 AM UTC 2026
% Result : Unsatisfiable 0.03s 0.41s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 40
% Syntax : Number of formulae : 153 ( 24 unt; 0 def)
% Number of atoms : 364 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 339 ( 128 ~; 211 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 40 ( 39 usr; 40 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(u_s3_goal_1,axiom,
( ~ q_0
| ~ p_0
| u_1 ),
file('theBenchmark.p',u_s3_goal_1) ).
cnf(c_1,plain,
( ~ q_0
| ~ p_0
| u_1 ),
inference(clausify,[status(thm)],[u_s3_goal_1]) ).
fof(u_1_s3_goal_1,axiom,
~ u_1,
file('theBenchmark.p',u_1_s3_goal_1) ).
cnf(c_2,plain,
~ u_1,
inference(clausify,[status(thm)],[u_1_s3_goal_1]) ).
fof(u_s3_type11_2,axiom,
( ~ q_2
| ~ q_1
| p_0
| u_3 ),
file('theBenchmark.p',u_s3_type11_2) ).
cnf(c_5,plain,
( ~ q_2
| ~ q_1
| p_0
| u_3 ),
inference(clausify,[status(thm)],[u_s3_type11_2]) ).
fof(u_3_s3_type11_2,axiom,
( ~ u_3
| p_0 ),
file('theBenchmark.p',u_3_s3_type11_2) ).
cnf(c_6,plain,
( ~ u_3
| p_0 ),
inference(clausify,[status(thm)],[u_3_s3_type11_2]) ).
fof(u_s3_type11_3,axiom,
( ~ p_3
| ~ p_2
| p_1
| u_4 ),
file('theBenchmark.p',u_s3_type11_3) ).
cnf(c_7,plain,
( ~ p_3
| ~ p_2
| p_1
| u_4 ),
inference(clausify,[status(thm)],[u_s3_type11_3]) ).
fof(u_4_s3_type11_3,axiom,
( ~ u_4
| p_1 ),
file('theBenchmark.p',u_4_s3_type11_3) ).
cnf(c_8,plain,
( ~ u_4
| p_1 ),
inference(clausify,[status(thm)],[u_4_s3_type11_3]) ).
fof(u_s3_type11_6,axiom,
( ~ q_4
| ~ q_3
| p_2
| u_7 ),
file('theBenchmark.p',u_s3_type11_6) ).
cnf(c_13,plain,
( ~ q_4
| ~ q_3
| p_2
| u_7 ),
inference(clausify,[status(thm)],[u_s3_type11_6]) ).
fof(u_7_s3_type11_6,axiom,
( ~ u_7
| p_2 ),
file('theBenchmark.p',u_7_s3_type11_6) ).
cnf(c_14,plain,
( ~ u_7
| p_2 ),
inference(clausify,[status(thm)],[u_7_s3_type11_6]) ).
fof(u_s3_type11_7,axiom,
( ~ p_5
| ~ p_4
| p_3
| u_8 ),
file('theBenchmark.p',u_s3_type11_7) ).
cnf(c_15,plain,
( ~ p_5
| ~ p_4
| p_3
| u_8 ),
inference(clausify,[status(thm)],[u_s3_type11_7]) ).
fof(u_8_s3_type11_7,axiom,
( ~ u_8
| p_3 ),
file('theBenchmark.p',u_8_s3_type11_7) ).
cnf(c_16,plain,
( ~ u_8
| p_3 ),
inference(clausify,[status(thm)],[u_8_s3_type11_7]) ).
fof(u_s3_type11_9,axiom,
( ~ p_6
| ~ p_5
| p_4
| u_10 ),
file('theBenchmark.p',u_s3_type11_9) ).
cnf(c_19,plain,
( ~ p_6
| ~ p_5
| p_4
| u_10 ),
inference(clausify,[status(thm)],[u_s3_type11_9]) ).
fof(u_10_s3_type11_9,axiom,
( ~ u_10
| p_4 ),
file('theBenchmark.p',u_10_s3_type11_9) ).
cnf(c_20,plain,
( ~ u_10
| p_4 ),
inference(clausify,[status(thm)],[u_10_s3_type11_9]) ).
fof(u_s3_type11_12,axiom,
( ~ q_7
| ~ q_6
| p_5
| u_13 ),
file('theBenchmark.p',u_s3_type11_12) ).
cnf(c_25,plain,
( ~ q_7
| ~ q_6
| p_5
| u_13 ),
inference(clausify,[status(thm)],[u_s3_type11_12]) ).
fof(u_13_s3_type11_12,axiom,
( ~ u_13
| p_5 ),
file('theBenchmark.p',u_13_s3_type11_12) ).
cnf(c_26,plain,
( ~ u_13
| p_5 ),
inference(clausify,[status(thm)],[u_13_s3_type11_12]) ).
fof(u_s3_type11_13,axiom,
( ~ p_8
| ~ p_7
| p_6
| u_14 ),
file('theBenchmark.p',u_s3_type11_13) ).
cnf(c_27,plain,
( ~ p_8
| ~ p_7
| p_6
| u_14 ),
inference(clausify,[status(thm)],[u_s3_type11_13]) ).
fof(u_14_s3_type11_13,axiom,
( ~ u_14
| p_6 ),
file('theBenchmark.p',u_14_s3_type11_13) ).
cnf(c_28,plain,
( ~ u_14
| p_6 ),
inference(clausify,[status(thm)],[u_14_s3_type11_13]) ).
fof(u_s3_type11_15,axiom,
( ~ p_9
| ~ p_8
| p_7
| u_16 ),
file('theBenchmark.p',u_s3_type11_15) ).
cnf(c_31,plain,
( ~ p_9
| ~ p_8
| p_7
| u_16 ),
inference(clausify,[status(thm)],[u_s3_type11_15]) ).
fof(u_16_s3_type11_15,axiom,
( ~ u_16
| p_7 ),
file('theBenchmark.p',u_16_s3_type11_15) ).
cnf(c_32,plain,
( ~ u_16
| p_7 ),
inference(clausify,[status(thm)],[u_16_s3_type11_15]) ).
fof(u_s3_type12_1,axiom,
( ~ q_2
| ~ p_1
| q_0
| u_18 ),
file('theBenchmark.p',u_s3_type12_1) ).
cnf(c_35,plain,
( ~ q_2
| ~ p_1
| q_0
| u_18 ),
inference(clausify,[status(thm)],[u_s3_type12_1]) ).
fof(u_18_s3_type12_1,axiom,
( ~ u_18
| q_0 ),
file('theBenchmark.p',u_18_s3_type12_1) ).
cnf(c_36,plain,
( ~ u_18
| q_0 ),
inference(clausify,[status(thm)],[u_18_s3_type12_1]) ).
fof(u_s3_type12_3,axiom,
( ~ q_3
| ~ p_2
| q_1
| u_20 ),
file('theBenchmark.p',u_s3_type12_3) ).
cnf(c_39,plain,
( ~ q_3
| ~ p_2
| q_1
| u_20 ),
inference(clausify,[status(thm)],[u_s3_type12_3]) ).
fof(u_20_s3_type12_3,axiom,
( ~ u_20
| q_1 ),
file('theBenchmark.p',u_20_s3_type12_3) ).
cnf(c_40,plain,
( ~ u_20
| q_1 ),
inference(clausify,[status(thm)],[u_20_s3_type12_3]) ).
fof(u_s3_type12_6,axiom,
( ~ p_4
| ~ q_3
| q_2
| u_23 ),
file('theBenchmark.p',u_s3_type12_6) ).
cnf(c_45,plain,
( ~ p_4
| ~ q_3
| q_2
| u_23 ),
inference(clausify,[status(thm)],[u_s3_type12_6]) ).
fof(u_23_s3_type12_6,axiom,
( ~ u_23
| q_2 ),
file('theBenchmark.p',u_23_s3_type12_6) ).
cnf(c_46,plain,
( ~ u_23
| q_2 ),
inference(clausify,[status(thm)],[u_23_s3_type12_6]) ).
fof(u_s3_type12_7,axiom,
( ~ q_5
| ~ p_4
| q_3
| u_24 ),
file('theBenchmark.p',u_s3_type12_7) ).
cnf(c_47,plain,
( ~ q_5
| ~ p_4
| q_3
| u_24 ),
inference(clausify,[status(thm)],[u_s3_type12_7]) ).
fof(u_24_s3_type12_7,axiom,
( ~ u_24
| q_3 ),
file('theBenchmark.p',u_24_s3_type12_7) ).
cnf(c_48,plain,
( ~ u_24
| q_3 ),
inference(clausify,[status(thm)],[u_24_s3_type12_7]) ).
fof(u_s3_type12_9,axiom,
( ~ q_6
| ~ p_5
| q_4
| u_26 ),
file('theBenchmark.p',u_s3_type12_9) ).
cnf(c_51,plain,
( ~ q_6
| ~ p_5
| q_4
| u_26 ),
inference(clausify,[status(thm)],[u_s3_type12_9]) ).
fof(u_26_s3_type12_9,axiom,
( ~ u_26
| q_4 ),
file('theBenchmark.p',u_26_s3_type12_9) ).
cnf(c_52,plain,
( ~ u_26
| q_4 ),
inference(clausify,[status(thm)],[u_26_s3_type12_9]) ).
fof(u_s3_type12_12,axiom,
( ~ p_7
| ~ q_6
| q_5
| u_29 ),
file('theBenchmark.p',u_s3_type12_12) ).
cnf(c_57,plain,
( ~ p_7
| ~ q_6
| q_5
| u_29 ),
inference(clausify,[status(thm)],[u_s3_type12_12]) ).
fof(u_29_s3_type12_12,axiom,
( ~ u_29
| q_5 ),
file('theBenchmark.p',u_29_s3_type12_12) ).
cnf(c_58,plain,
( ~ u_29
| q_5 ),
inference(clausify,[status(thm)],[u_29_s3_type12_12]) ).
fof(u_s3_type12_13,axiom,
( ~ q_8
| ~ p_7
| q_6
| u_30 ),
file('theBenchmark.p',u_s3_type12_13) ).
cnf(c_59,plain,
( ~ q_8
| ~ p_7
| q_6
| u_30 ),
inference(clausify,[status(thm)],[u_s3_type12_13]) ).
fof(u_30_s3_type12_13,axiom,
( ~ u_30
| q_6 ),
file('theBenchmark.p',u_30_s3_type12_13) ).
cnf(c_60,plain,
( ~ u_30
| q_6 ),
inference(clausify,[status(thm)],[u_30_s3_type12_13]) ).
fof(u_s3_type12_16,axiom,
( ~ p_9
| ~ q_8
| q_7
| u_33 ),
file('theBenchmark.p',u_s3_type12_16) ).
cnf(c_65,plain,
( ~ p_9
| ~ q_8
| q_7
| u_33 ),
inference(clausify,[status(thm)],[u_s3_type12_16]) ).
fof(u_33_s3_type12_16,axiom,
( ~ u_33
| q_7 ),
file('theBenchmark.p',u_33_s3_type12_16) ).
cnf(c_66,plain,
( ~ u_33
| q_7 ),
inference(clausify,[status(thm)],[u_33_s3_type12_16]) ).
fof(u_t3_1,axiom,
( p_8
| u_38 ),
file('theBenchmark.p',u_t3_1) ).
cnf(c_75,plain,
( p_8
| u_38 ),
inference(clausify,[status(thm)],[u_t3_1]) ).
fof(u_38_t3_1,axiom,
( ~ u_38
| p_8 ),
file('theBenchmark.p',u_38_t3_1) ).
cnf(c_76,plain,
( ~ u_38
| p_8 ),
inference(clausify,[status(thm)],[u_38_t3_1]) ).
fof(u_t3_2,axiom,
( p_9
| u_39 ),
file('theBenchmark.p',u_t3_2) ).
cnf(c_77,plain,
( p_9
| u_39 ),
inference(clausify,[status(thm)],[u_t3_2]) ).
fof(u_39_t3_2,axiom,
( ~ u_39
| p_9 ),
file('theBenchmark.p',u_39_t3_2) ).
cnf(c_78,plain,
( ~ u_39
| p_9 ),
inference(clausify,[status(thm)],[u_39_t3_2]) ).
fof(u_t3_3,axiom,
( q_8
| u_40 ),
file('theBenchmark.p',u_t3_3) ).
cnf(c_79,plain,
( q_8
| u_40 ),
inference(clausify,[status(thm)],[u_t3_3]) ).
fof(u_40_t3_3,axiom,
( ~ u_40
| q_8 ),
file('theBenchmark.p',u_40_t3_3) ).
cnf(c_80,plain,
( ~ u_40
| q_8 ),
inference(clausify,[status(thm)],[u_40_t3_3]) ).
cnf(c_83,plain,
( ~ q_0
| ~ p_0 ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_211,plain,
( p_8
| p_8 ),
inference(resolve,[status(thm)],[c_76,c_75]) ).
cnf(c_88,plain,
p_8,
inference(copy,[status(thm)],[c_211]) ).
cnf(c_91,plain,
( ~ p_9
| p_7
| u_16 ),
inference(resolve,[status(thm)],[c_88,c_31]) ).
cnf(c_92,plain,
( ~ p_7
| p_6
| u_14 ),
inference(resolve,[status(thm)],[c_88,c_27]) ).
cnf(c_212,plain,
( p_9
| p_9 ),
inference(resolve,[status(thm)],[c_78,c_77]) ).
cnf(c_94,plain,
p_9,
inference(copy,[status(thm)],[c_212]) ).
cnf(c_95,plain,
( p_7
| u_16 ),
inference(resolve,[status(thm)],[c_94,c_91]) ).
cnf(c_96,plain,
( ~ q_8
| q_7
| u_33 ),
inference(resolve,[status(thm)],[c_94,c_65]) ).
cnf(c_213,plain,
( q_8
| q_8 ),
inference(resolve,[status(thm)],[c_80,c_79]) ).
cnf(c_100,plain,
q_8,
inference(copy,[status(thm)],[c_213]) ).
cnf(c_101,plain,
( q_7
| u_33 ),
inference(resolve,[status(thm)],[c_100,c_96]) ).
cnf(c_102,plain,
( ~ p_7
| q_6
| u_30 ),
inference(resolve,[status(thm)],[c_100,c_59]) ).
cnf(c_214,plain,
( p_7
| p_7 ),
inference(resolve,[status(thm)],[c_95,c_32]) ).
cnf(c_108,plain,
p_7,
inference(copy,[status(thm)],[c_214]) ).
cnf(c_111,plain,
( q_6
| u_30 ),
inference(resolve,[status(thm)],[c_108,c_102]) ).
cnf(c_112,plain,
( p_6
| u_14 ),
inference(resolve,[status(thm)],[c_108,c_92]) ).
cnf(c_113,plain,
( ~ q_6
| q_5
| u_29 ),
inference(resolve,[status(thm)],[c_108,c_57]) ).
cnf(c_215,plain,
( q_7
| q_7 ),
inference(resolve,[status(thm)],[c_101,c_66]) ).
cnf(c_115,plain,
q_7,
inference(copy,[status(thm)],[c_215]) ).
cnf(c_122,plain,
( ~ q_6
| p_5
| u_13 ),
inference(resolve,[status(thm)],[c_115,c_25]) ).
cnf(c_216,plain,
( q_6
| q_6 ),
inference(resolve,[status(thm)],[c_111,c_60]) ).
cnf(c_123,plain,
q_6,
inference(copy,[status(thm)],[c_216]) ).
cnf(c_126,plain,
( p_5
| u_13 ),
inference(resolve,[status(thm)],[c_123,c_122]) ).
cnf(c_127,plain,
( q_5
| u_29 ),
inference(resolve,[status(thm)],[c_123,c_113]) ).
cnf(c_128,plain,
( ~ p_5
| q_4
| u_26 ),
inference(resolve,[status(thm)],[c_123,c_51]) ).
cnf(c_217,plain,
( p_6
| p_6 ),
inference(resolve,[status(thm)],[c_112,c_28]) ).
cnf(c_130,plain,
p_6,
inference(copy,[status(thm)],[c_217]) ).
cnf(c_136,plain,
( ~ p_5
| p_4
| u_10 ),
inference(resolve,[status(thm)],[c_130,c_19]) ).
cnf(c_218,plain,
( p_5
| p_5 ),
inference(resolve,[status(thm)],[c_126,c_26]) ).
cnf(c_137,plain,
p_5,
inference(copy,[status(thm)],[c_218]) ).
cnf(c_141,plain,
( p_4
| u_10 ),
inference(resolve,[status(thm)],[c_137,c_136]) ).
cnf(c_142,plain,
( q_4
| u_26 ),
inference(resolve,[status(thm)],[c_137,c_128]) ).
cnf(c_145,plain,
( ~ p_4
| p_3
| u_8 ),
inference(resolve,[status(thm)],[c_137,c_15]) ).
cnf(c_219,plain,
( q_5
| q_5 ),
inference(resolve,[status(thm)],[c_127,c_58]) ).
cnf(c_146,plain,
q_5,
inference(copy,[status(thm)],[c_219]) ).
cnf(c_153,plain,
( ~ p_4
| q_3
| u_24 ),
inference(resolve,[status(thm)],[c_146,c_47]) ).
cnf(c_220,plain,
( p_4
| p_4 ),
inference(resolve,[status(thm)],[c_141,c_20]) ).
cnf(c_155,plain,
p_4,
inference(copy,[status(thm)],[c_220]) ).
cnf(c_158,plain,
( q_3
| u_24 ),
inference(resolve,[status(thm)],[c_155,c_153]) ).
cnf(c_159,plain,
( p_3
| u_8 ),
inference(resolve,[status(thm)],[c_155,c_145]) ).
cnf(c_160,plain,
( ~ q_3
| q_2
| u_23 ),
inference(resolve,[status(thm)],[c_155,c_45]) ).
cnf(c_221,plain,
( q_4
| q_4 ),
inference(resolve,[status(thm)],[c_142,c_52]) ).
cnf(c_162,plain,
q_4,
inference(copy,[status(thm)],[c_221]) ).
cnf(c_168,plain,
( ~ q_3
| p_2
| u_7 ),
inference(resolve,[status(thm)],[c_162,c_13]) ).
cnf(c_222,plain,
( q_3
| q_3 ),
inference(resolve,[status(thm)],[c_158,c_48]) ).
cnf(c_171,plain,
q_3,
inference(copy,[status(thm)],[c_222]) ).
cnf(c_174,plain,
( p_2
| u_7 ),
inference(resolve,[status(thm)],[c_171,c_168]) ).
cnf(c_175,plain,
( q_2
| u_23 ),
inference(resolve,[status(thm)],[c_171,c_160]) ).
cnf(c_176,plain,
( ~ p_2
| q_1
| u_20 ),
inference(resolve,[status(thm)],[c_171,c_39]) ).
cnf(c_223,plain,
( p_3
| p_3 ),
inference(resolve,[status(thm)],[c_159,c_16]) ).
cnf(c_178,plain,
p_3,
inference(copy,[status(thm)],[c_223]) ).
cnf(c_184,plain,
( ~ p_2
| p_1
| u_4 ),
inference(resolve,[status(thm)],[c_178,c_7]) ).
cnf(c_224,plain,
( p_2
| p_2 ),
inference(resolve,[status(thm)],[c_174,c_14]) ).
cnf(c_185,plain,
p_2,
inference(copy,[status(thm)],[c_224]) ).
cnf(c_188,plain,
( p_1
| u_4 ),
inference(resolve,[status(thm)],[c_185,c_184]) ).
cnf(c_189,plain,
( q_1
| u_20 ),
inference(resolve,[status(thm)],[c_185,c_176]) ).
cnf(c_225,plain,
( q_2
| q_2 ),
inference(resolve,[status(thm)],[c_175,c_46]) ).
cnf(c_192,plain,
q_2,
inference(copy,[status(thm)],[c_225]) ).
cnf(c_197,plain,
( ~ p_1
| q_0
| u_18 ),
inference(resolve,[status(thm)],[c_192,c_35]) ).
cnf(c_198,plain,
( ~ q_1
| p_0
| u_3 ),
inference(resolve,[status(thm)],[c_192,c_5]) ).
cnf(c_226,plain,
( p_1
| p_1 ),
inference(resolve,[status(thm)],[c_188,c_8]) ).
cnf(c_199,plain,
p_1,
inference(copy,[status(thm)],[c_226]) ).
cnf(c_200,plain,
( q_0
| u_18 ),
inference(resolve,[status(thm)],[c_199,c_197]) ).
cnf(c_227,plain,
( q_1
| q_1 ),
inference(resolve,[status(thm)],[c_189,c_40]) ).
cnf(c_202,plain,
q_1,
inference(copy,[status(thm)],[c_227]) ).
cnf(c_203,plain,
( p_0
| u_3 ),
inference(resolve,[status(thm)],[c_202,c_198]) ).
cnf(c_228,plain,
( q_0
| q_0 ),
inference(resolve,[status(thm)],[c_200,c_36]) ).
cnf(c_205,plain,
q_0,
inference(copy,[status(thm)],[c_228]) ).
cnf(c_207,plain,
~ p_0,
inference(resolve,[status(thm)],[c_205,c_83]) ).
cnf(c_208,plain,
u_3,
inference(resolve,[status(thm)],[c_207,c_203]) ).
cnf(c_229,plain,
~ u_3,
inference(resolve,[status(thm)],[c_207,c_6]) ).
cnf(c_210,plain,
$false,
inference(resolve,[status(thm)],[c_208,c_229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN094-1.005 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.03/0.37 % CPULimit : 300
% 0.03/0.37 % WCLimit : 300
% 0.03/0.37 % DateTime : Sat Sep 26 17:11:55 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.37 % Process 4126742 was started by sandbox2 on n008,
% 0.03/0.37 % Sat Sep 26 17:11:55 2026
% 0.03/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.38
% 0.03/0.38 % From the command line: assign(max_seconds, 300).
% 0.03/0.41
% 0.03/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.03/0.41
% 0.03/0.41 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.03/0.41 % Length of proof is 94.
% 0.03/0.41 % Level of proof is 21.
% 0.03/0.41 % Maximum clause weight is 4.000.
% 0.03/0.41 % Given clauses 119.
% 0.03/0.41
% 0.03/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------