%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN690-1 : TPTP v9.3.1. Released v2.5.0.
% 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 09:39:07 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.68s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 16 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 52 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 10 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p2_14,axiom,
! [VAR_0] : p2(VAR_0,VAR_0),
file('theBenchmark.p',p2_14) ).
cnf(c_14,plain,
p2(A,A),
inference(clausify,[status(thm)],[p2_14]) ).
fof(p34_19,axiom,
p34(c36,c37),
file('theBenchmark.p',p34_19) ).
cnf(c_19,plain,
p34(c36,c37),
inference(clausify,[status(thm)],[p34_19]) ).
fof(not_p2_20,axiom,
~ p2(c38,c40),
file('theBenchmark.p',not_p2_20) ).
cnf(c_20,plain,
~ p2(c38,c40),
inference(clausify,[status(thm)],[not_p2_20]) ).
fof(p4_21,axiom,
! [VAR_0] : p4(f5(c40,VAR_0),f5(f7(c39,c40),VAR_0)),
file('theBenchmark.p',p4_21) ).
cnf(c_21,plain,
p4(f5(c40,A),f5(f7(c39,c40),A)),
inference(clausify,[status(thm)],[p4_21]) ).
fof(p4_22,axiom,
! [VAR_0] : p4(f5(c38,VAR_0),f5(f7(c39,c38),VAR_0)),
file('theBenchmark.p',p4_22) ).
cnf(c_22,plain,
p4(f5(c38,A),f5(f7(c39,c38),A)),
inference(clausify,[status(thm)],[p4_22]) ).
fof(p2_36,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p2(VAR_2,VAR_1)
| ~ p2(VAR_2,VAR_0)
| p2(VAR_0,VAR_1) ),
file('theBenchmark.p',p2_36) ).
cnf(c_36,plain,
( ~ p2(C,B)
| ~ p2(C,A)
| p2(A,B) ),
inference(clausify,[status(thm)],[p2_36]) ).
fof(p4_57,axiom,
! [VAR_0,VAR_1,VAR_2] :
( p35(f10(c37,f12(f14(f16(c41,VAR_0),VAR_2),VAR_1)),VAR_1)
| p4(f5(f7(c39,VAR_0),VAR_1),f5(f7(c39,VAR_2),VAR_1)) ),
file('theBenchmark.p',p4_57) ).
cnf(c_57,plain,
( p35(f10(c37,f12(f14(f16(c41,A),C),B)),B)
| p4(f5(f7(c39,A),B),f5(f7(c39,C),B)) ),
inference(clausify,[status(thm)],[p4_57]) ).
fof(p4_58,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p4(f5(VAR_0,f12(f14(f16(c41,VAR_0),VAR_2),VAR_1)),f5(VAR_2,f12(f14(f16(c41,VAR_0),VAR_2),VAR_1)))
| p4(f5(f7(c39,VAR_0),VAR_1),f5(f7(c39,VAR_2),VAR_1)) ),
file('theBenchmark.p',p4_58) ).
cnf(c_58,plain,
( ~ p4(f5(A,f12(f14(f16(c41,A),C),B)),f5(C,f12(f14(f16(c41,A),C),B)))
| p4(f5(f7(c39,A),B),f5(f7(c39,C),B)) ),
inference(clausify,[status(thm)],[p4_58]) ).
fof(p2_61,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ p4(f5(VAR_1,f18(f20(f22(f24(c45,VAR_2),VAR_3),VAR_0),VAR_1)),f5(f7(VAR_3,VAR_1),f18(f20(f22(f24(c45,VAR_2),VAR_3),VAR_0),VAR_1)))
| ~ p4(f5(VAR_0,f18(f20(f22(f24(c45,VAR_2),VAR_3),VAR_0),VAR_1)),f5(f7(VAR_3,VAR_0),f18(f20(f22(f24(c45,VAR_2),VAR_3),VAR_0),VAR_1)))
| ~ p35(f10(VAR_2,VAR_4),f30(f32(c42,VAR_2),VAR_3))
| ~ p34(c36,VAR_2)
| p4(f5(f26(f28(c43,VAR_2),VAR_3),VAR_4),f5(f26(f28(c44,VAR_2),VAR_3),VAR_4))
| p2(VAR_0,VAR_1) ),
file('theBenchmark.p',p2_61) ).
cnf(c_61,plain,
( ~ p4(f5(B,f18(f20(f22(f24(c45,C),D),A),B)),f5(f7(D,B),f18(f20(f22(f24(c45,C),D),A),B)))
| ~ p4(f5(A,f18(f20(f22(f24(c45,C),D),A),B)),f5(f7(D,A),f18(f20(f22(f24(c45,C),D),A),B)))
| ~ p35(f10(C,E),f30(f32(c42,C),D))
| ~ p34(c36,C)
| p4(f5(f26(f28(c43,C),D),E),f5(f26(f28(c44,C),D),E))
| p2(A,B) ),
inference(clausify,[status(thm)],[p2_61]) ).
fof(p2_62,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p4(f5(f7(VAR_3,f26(f28(c43,VAR_2),VAR_3)),f30(f32(c42,VAR_2),VAR_3)),f5(f7(VAR_3,f26(f28(c44,VAR_2),VAR_3)),f30(f32(c42,VAR_2),VAR_3)))
| ~ p4(f5(VAR_1,f18(f20(f22(f24(c45,VAR_2),VAR_3),VAR_0),VAR_1)),f5(f7(VAR_3,VAR_1),f18(f20(f22(f24(c45,VAR_2),VAR_3),VAR_0),VAR_1)))
| ~ p4(f5(VAR_0,f18(f20(f22(f24(c45,VAR_2),VAR_3),VAR_0),VAR_1)),f5(f7(VAR_3,VAR_0),f18(f20(f22(f24(c45,VAR_2),VAR_3),VAR_0),VAR_1)))
| ~ p34(c36,VAR_2)
| p2(VAR_0,VAR_1) ),
file('theBenchmark.p',p2_62) ).
cnf(c_62,plain,
( ~ p4(f5(f7(D,f26(f28(c43,C),D)),f30(f32(c42,C),D)),f5(f7(D,f26(f28(c44,C),D)),f30(f32(c42,C),D)))
| ~ p4(f5(B,f18(f20(f22(f24(c45,C),D),A),B)),f5(f7(D,B),f18(f20(f22(f24(c45,C),D),A),B)))
| ~ p4(f5(A,f18(f20(f22(f24(c45,C),D),A),B)),f5(f7(D,A),f18(f20(f22(f24(c45,C),D),A),B)))
| ~ p34(c36,C)
| p2(A,B) ),
inference(clausify,[status(thm)],[p2_62]) ).
cnf(c_128,plain,
( ~ p2(A,c40)
| ~ p2(A,c38) ),
inference(resolve,[status(thm)],[c_36,c_20]) ).
cnf(c_81,plain,
~ p2(c40,c38),
inference(resolve,[status(thm)],[c_128,c_14]) ).
cnf(c_129,plain,
( ~ p4(f5(f7(B,f26(f28(c43,A),B)),f30(f32(c42,A),B)),f5(f7(B,f26(f28(c44,A),B)),f30(f32(c42,A),B)))
| ~ p4(f5(c40,f18(f20(f22(f24(c45,A),B),c38),c40)),f5(f7(B,c40),f18(f20(f22(f24(c45,A),B),c38),c40)))
| ~ p4(f5(c38,f18(f20(f22(f24(c45,A),B),c38),c40)),f5(f7(B,c38),f18(f20(f22(f24(c45,A),B),c38),c40)))
| ~ p34(c36,A) ),
inference(resolve,[status(thm)],[c_62,c_20]) ).
cnf(c_130,plain,
( ~ p4(f5(f7(A,f26(f28(c43,c37),A)),f30(f32(c42,c37),A)),f5(f7(A,f26(f28(c44,c37),A)),f30(f32(c42,c37),A)))
| ~ p4(f5(c40,f18(f20(f22(f24(c45,c37),A),c38),c40)),f5(f7(A,c40),f18(f20(f22(f24(c45,c37),A),c38),c40)))
| ~ p4(f5(c38,f18(f20(f22(f24(c45,c37),A),c38),c40)),f5(f7(A,c38),f18(f20(f22(f24(c45,c37),A),c38),c40))) ),
inference(resolve,[status(thm)],[c_129,c_19]) ).
cnf(c_131,plain,
( ~ p4(f5(f7(c39,f26(f28(c43,c37),c39)),f30(f32(c42,c37),c39)),f5(f7(c39,f26(f28(c44,c37),c39)),f30(f32(c42,c37),c39)))
| ~ p4(f5(c40,f18(f20(f22(f24(c45,c37),c39),c38),c40)),f5(f7(c39,c40),f18(f20(f22(f24(c45,c37),c39),c38),c40))) ),
inference(resolve,[status(thm)],[c_130,c_22]) ).
cnf(c_109,plain,
~ p4(f5(f7(c39,f26(f28(c43,c37),c39)),f30(f32(c42,c37),c39)),f5(f7(c39,f26(f28(c44,c37),c39)),f30(f32(c42,c37),c39))),
inference(resolve,[status(thm)],[c_131,c_21]) ).
cnf(c_110,plain,
p35(f10(c37,f12(f14(f16(c41,f26(f28(c43,c37),c39)),f26(f28(c44,c37),c39)),f30(f32(c42,c37),c39))),f30(f32(c42,c37),c39)),
inference(resolve,[status(thm)],[c_109,c_57]) ).
cnf(c_111,plain,
~ p4(f5(f26(f28(c43,c37),c39),f12(f14(f16(c41,f26(f28(c43,c37),c39)),f26(f28(c44,c37),c39)),f30(f32(c42,c37),c39))),f5(f26(f28(c44,c37),c39),f12(f14(f16(c41,f26(f28(c43,c37),c39)),f26(f28(c44,c37),c39)),f30(f32(c42,c37),c39)))),
inference(resolve,[status(thm)],[c_58,c_109]) ).
cnf(c_132,plain,
( ~ p4(f5(c38,f18(f20(f22(f24(c45,A),B),c40),c38)),f5(f7(B,c38),f18(f20(f22(f24(c45,A),B),c40),c38)))
| ~ p4(f5(c40,f18(f20(f22(f24(c45,A),B),c40),c38)),f5(f7(B,c40),f18(f20(f22(f24(c45,A),B),c40),c38)))
| ~ p35(f10(A,C),f30(f32(c42,A),B))
| ~ p34(c36,A)
| p4(f5(f26(f28(c43,A),B),C),f5(f26(f28(c44,A),B),C)) ),
inference(resolve,[status(thm)],[c_61,c_81]) ).
cnf(c_133,plain,
( ~ p4(f5(c38,f18(f20(f22(f24(c45,c37),c39),c40),c38)),f5(f7(c39,c38),f18(f20(f22(f24(c45,c37),c39),c40),c38)))
| ~ p4(f5(c40,f18(f20(f22(f24(c45,c37),c39),c40),c38)),f5(f7(c39,c40),f18(f20(f22(f24(c45,c37),c39),c40),c38)))
| ~ p35(f10(c37,f12(f14(f16(c41,f26(f28(c43,c37),c39)),f26(f28(c44,c37),c39)),f30(f32(c42,c37),c39))),f30(f32(c42,c37),c39))
| ~ p34(c36,c37) ),
inference(resolve,[status(thm)],[c_132,c_111]) ).
cnf(c_134,plain,
( ~ p4(f5(c38,f18(f20(f22(f24(c45,c37),c39),c40),c38)),f5(f7(c39,c38),f18(f20(f22(f24(c45,c37),c39),c40),c38)))
| ~ p4(f5(c40,f18(f20(f22(f24(c45,c37),c39),c40),c38)),f5(f7(c39,c40),f18(f20(f22(f24(c45,c37),c39),c40),c38)))
| ~ p35(f10(c37,f12(f14(f16(c41,f26(f28(c43,c37),c39)),f26(f28(c44,c37),c39)),f30(f32(c42,c37),c39))),f30(f32(c42,c37),c39)) ),
inference(resolve,[status(thm)],[c_133,c_19]) ).
cnf(c_135,plain,
( ~ p4(f5(c38,f18(f20(f22(f24(c45,c37),c39),c40),c38)),f5(f7(c39,c38),f18(f20(f22(f24(c45,c37),c39),c40),c38)))
| ~ p35(f10(c37,f12(f14(f16(c41,f26(f28(c43,c37),c39)),f26(f28(c44,c37),c39)),f30(f32(c42,c37),c39))),f30(f32(c42,c37),c39)) ),
inference(resolve,[status(thm)],[c_134,c_21]) ).
cnf(c_136,plain,
~ p35(f10(c37,f12(f14(f16(c41,f26(f28(c43,c37),c39)),f26(f28(c44,c37),c39)),f30(f32(c42,c37),c39))),f30(f32(c42,c37),c39)),
inference(resolve,[status(thm)],[c_135,c_22]) ).
cnf(c_127,plain,
$false,
inference(resolve,[status(thm)],[c_110,c_136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN690-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.63 % Computer : n008.cluster.edu
% 0.16/0.63 % Model : x86_64 x86_64
% 0.16/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.63 % Memory : 8046.5625MB
% 0.16/0.63 % OS : Linux 6.8.0-71-generic
% 0.16/0.63 % CPULimit : 300
% 0.16/0.63 % WCLimit : 300
% 0.16/0.63 % DateTime : Sat Sep 26 18:20:55 UTC 2026
% 0.16/0.64 % CPUTime :
% 0.16/0.64 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.64 % Process 75199 was started by sandbox2 on n008,
% 0.16/0.64 % Sat Sep 26 18:20:55 2026
% 0.16/0.64 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/0.65
% 0.21/0.65 % From the command line: assign(max_seconds, 300).
% 0.21/0.68
% 0.21/0.68 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.68
% 0.21/0.68 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.21/0.68 % Length of proof is 15.
% 0.21/0.68 % Level of proof is 3.
% 0.21/0.68 % Maximum clause weight is 113.000.
% 0.21/0.68 % Given clauses 95.
% 0.21/0.68
% 0.21/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------