%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN687-1 : 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 : n019.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 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 31 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p4_4,axiom,
! [VAR_0] : p4(VAR_0,VAR_0),
file('theBenchmark.p',p4_4) ).
cnf(c_4,plain,
p4(A,A),
inference(clausify,[status(thm)],[p4_4]) ).
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(p4_23,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p4(VAR_2,VAR_1)
| ~ p4(VAR_2,VAR_0)
| p4(VAR_0,VAR_1) ),
file('theBenchmark.p',p4_23) ).
cnf(c_23,plain,
( ~ p4(C,B)
| ~ p4(C,A)
| p4(A,B) ),
inference(clausify,[status(thm)],[p4_23]) ).
fof(not_p4_40,axiom,
! [VAR_0] : ~ p4(f5(VAR_0,f7(c38,VAR_0)),f5(f9(c39,VAR_0),f7(c38,VAR_0))),
file('theBenchmark.p',not_p4_40) ).
cnf(c_40,plain,
~ p4(f5(A,f7(c38,A)),f5(f9(c39,A),f7(c38,A))),
inference(clausify,[status(thm)],[not_p4_40]) ).
fof(p4_55,axiom,
! [VAR_0,VAR_1,VAR_2] :
( p35(f12(c37,f14(f16(f18(c40,VAR_0),VAR_2),VAR_1)),VAR_1)
| p4(f5(f9(c39,VAR_0),VAR_1),f5(f9(c39,VAR_2),VAR_1)) ),
file('theBenchmark.p',p4_55) ).
cnf(c_55,plain,
( p35(f12(c37,f14(f16(f18(c40,A),C),B)),B)
| p4(f5(f9(c39,A),B),f5(f9(c39,C),B)) ),
inference(clausify,[status(thm)],[p4_55]) ).
fof(p4_56,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p4(f5(VAR_0,f14(f16(f18(c40,VAR_0),VAR_2),VAR_1)),f5(VAR_2,f14(f16(f18(c40,VAR_0),VAR_2),VAR_1)))
| p4(f5(f9(c39,VAR_0),VAR_1),f5(f9(c39,VAR_2),VAR_1)) ),
file('theBenchmark.p',p4_56) ).
cnf(c_56,plain,
( ~ p4(f5(A,f14(f16(f18(c40,A),C),B)),f5(C,f14(f16(f18(c40,A),C),B)))
| p4(f5(f9(c39,A),B),f5(f9(c39,C),B)) ),
inference(clausify,[status(thm)],[p4_56]) ).
fof(p4_57,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p35(f12(VAR_0,VAR_2),f30(f32(c45,VAR_0),VAR_1))
| ~ p34(c36,VAR_0)
| p4(f5(f26(f28(c46,VAR_0),VAR_1),VAR_3),f5(f9(VAR_1,f26(f28(c46,VAR_0),VAR_1)),VAR_3))
| p4(f5(f26(f28(c46,VAR_0),VAR_1),VAR_2),f5(f26(f28(c47,VAR_0),VAR_1),VAR_2)) ),
file('theBenchmark.p',p4_57) ).
cnf(c_57,plain,
( ~ p35(f12(A,C),f30(f32(c45,A),B))
| ~ p34(c36,A)
| p4(f5(f26(f28(c46,A),B),D),f5(f9(B,f26(f28(c46,A),B)),D))
| p4(f5(f26(f28(c46,A),B),C),f5(f26(f28(c47,A),B),C)) ),
inference(clausify,[status(thm)],[p4_57]) ).
fof(p4_58,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p4(f5(f9(VAR_1,f26(f28(c46,VAR_0),VAR_1)),f30(f32(c45,VAR_0),VAR_1)),f5(f9(VAR_1,f26(f28(c47,VAR_0),VAR_1)),f30(f32(c45,VAR_0),VAR_1)))
| ~ p34(c36,VAR_0)
| p4(f5(f26(f28(c46,VAR_0),VAR_1),VAR_2),f5(f9(VAR_1,f26(f28(c46,VAR_0),VAR_1)),VAR_2)) ),
file('theBenchmark.p',p4_58) ).
cnf(c_58,plain,
( ~ p4(f5(f9(B,f26(f28(c46,A),B)),f30(f32(c45,A),B)),f5(f9(B,f26(f28(c47,A),B)),f30(f32(c45,A),B)))
| ~ p34(c36,A)
| p4(f5(f26(f28(c46,A),B),C),f5(f9(B,f26(f28(c46,A),B)),C)) ),
inference(clausify,[status(thm)],[p4_58]) ).
cnf(c_64,plain,
( ~ p4(B,A)
| p4(A,B) ),
inference(resolve,[status(thm)],[c_23,c_4]) ).
cnf(c_142,plain,
( ~ p4(A,f5(f9(c39,B),f7(c38,B)))
| ~ p4(A,f5(B,f7(c38,B))) ),
inference(resolve,[status(thm)],[c_23,c_40]) ).
cnf(c_84,plain,
~ p4(f5(f9(c39,A),f7(c38,A)),f5(A,f7(c38,A))),
inference(resolve,[status(thm)],[c_142,c_4]) ).
cnf(c_143,plain,
( ~ p4(f5(f9(c39,f26(f28(c46,A),c39)),f30(f32(c45,A),c39)),f5(f9(c39,f26(f28(c47,A),c39)),f30(f32(c45,A),c39)))
| ~ p34(c36,A) ),
inference(resolve,[status(thm)],[c_58,c_40]) ).
cnf(c_119,plain,
~ p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),
inference(resolve,[status(thm)],[c_143,c_19]) ).
cnf(c_121,plain,
~ p4(f5(f9(c39,A),f14(f16(f18(c40,f9(c39,A)),A),f7(c38,f9(c39,A)))),f5(A,f14(f16(f18(c40,f9(c39,A)),A),f7(c38,f9(c39,A))))),
inference(resolve,[status(thm)],[c_56,c_84]) ).
cnf(c_122,plain,
~ p4(f5(f26(f28(c46,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f5(f26(f28(c47,c37),c39),f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39)))),
inference(resolve,[status(thm)],[c_56,c_119]) ).
cnf(c_137,plain,
~ p4(f5(A,f14(f16(f18(c40,f9(c39,A)),A),f7(c38,f9(c39,A)))),f5(f9(c39,A),f14(f16(f18(c40,f9(c39,A)),A),f7(c38,f9(c39,A))))),
inference(resolve,[status(thm)],[c_64,c_121]) ).
cnf(c_144,plain,
( ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39))
| ~ p34(c36,c37)
| p4(f5(f26(f28(c46,c37),c39),A),f5(f9(c39,f26(f28(c46,c37),c39)),A)) ),
inference(resolve,[status(thm)],[c_57,c_122]) ).
cnf(c_145,plain,
( ~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39))
| ~ p34(c36,c37) ),
inference(resolve,[status(thm)],[c_144,c_137]) ).
cnf(c_140,plain,
~ p35(f12(c37,f14(f16(f18(c40,f26(f28(c46,c37),c39)),f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),f30(f32(c45,c37),c39)),
inference(resolve,[status(thm)],[c_145,c_19]) ).
cnf(c_146,plain,
p4(f5(f9(c39,f26(f28(c46,c37),c39)),f30(f32(c45,c37),c39)),f5(f9(c39,f26(f28(c47,c37),c39)),f30(f32(c45,c37),c39))),
inference(resolve,[status(thm)],[c_140,c_55]) ).
cnf(c_141,plain,
$false,
inference(resolve,[status(thm)],[c_119,c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN687-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n019.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 18:20:33 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 1910447 was started by sandbox2 on n019,
% 0.19/0.44 % Sat Sep 26 18:20:33 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.19/0.48 % Length of proof is 16.
% 0.19/0.48 % Level of proof is 5.
% 0.19/0.48 % Maximum clause weight is 86.000.
% 0.19/0.48 % Given clauses 107.
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------