%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN353-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 09:37:40 AM UTC 2026
% Result : Unsatisfiable 2.61s 0.75s
% Output : CNFRefutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 11
% Syntax : Number of formulae : 90 ( 10 unt; 0 def)
% Number of atoms : 236 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 213 ( 67 ~; 146 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 171 ( 7 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( f(VAR_2,VAR_0,VAR_1)
| f(VAR_1,VAR_2,VAR_0)
| ~ f(a,a,z(VAR_0,VAR_1,VAR_2))
| ~ f(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause1) ).
cnf(c_1,plain,
( f(C,A,B)
| f(B,C,A)
| ~ f(a,a,z(A,B,C))
| ~ f(A,B,C) ),
inference(clausify,[status(thm)],[clause1]) ).
fof(clause2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ f(VAR_2,VAR_1,z(VAR_1,VAR_2,VAR_0))
| f(VAR_1,VAR_2,VAR_0)
| ~ f(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause2) ).
cnf(c_2,plain,
( ~ f(C,B,z(B,C,A))
| f(B,C,A)
| ~ f(A,B,C) ),
inference(clausify,[status(thm)],[clause2]) ).
fof(clause3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ f(VAR_2,VAR_1,z(VAR_1,VAR_2,VAR_0))
| f(VAR_2,VAR_0,VAR_1)
| ~ f(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause3) ).
cnf(c_3,plain,
( ~ f(C,B,z(B,C,A))
| f(C,A,B)
| ~ f(A,B,C) ),
inference(clausify,[status(thm)],[clause3]) ).
fof(clause4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( f(VAR_2,VAR_1,z(VAR_1,VAR_2,VAR_0))
| f(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause4) ).
cnf(c_4,plain,
( f(C,B,z(B,C,A))
| f(A,B,C) ),
inference(clausify,[status(thm)],[clause4]) ).
fof(clause6,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ f(VAR_2,z(VAR_2,VAR_0,VAR_1),VAR_0)
| f(VAR_2,VAR_0,VAR_1)
| ~ f(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause6) ).
cnf(c_6,plain,
( ~ f(C,z(C,A,B),A)
| f(C,A,B)
| ~ f(A,B,C) ),
inference(clausify,[status(thm)],[clause6]) ).
fof(clause7,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ f(VAR_2,z(VAR_2,VAR_0,VAR_1),VAR_0)
| f(VAR_1,VAR_2,VAR_0)
| ~ f(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause7) ).
cnf(c_7,plain,
( ~ f(C,z(C,A,B),A)
| f(B,C,A)
| ~ f(A,B,C) ),
inference(clausify,[status(thm)],[clause7]) ).
fof(clause8,axiom,
! [VAR_0,VAR_1,VAR_2] :
( f(VAR_2,z(VAR_2,VAR_0,VAR_1),VAR_0)
| f(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause8) ).
cnf(c_8,plain,
( f(C,z(C,A,B),A)
| f(A,B,C) ),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause10,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ f(z(VAR_1,VAR_2,VAR_0),VAR_2,VAR_1)
| f(VAR_1,VAR_2,VAR_0)
| f(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause10) ).
cnf(c_10,plain,
( ~ f(z(B,C,A),C,B)
| f(B,C,A)
| f(A,B,C) ),
inference(clausify,[status(thm)],[clause10]) ).
fof(clause11,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ f(z(VAR_2,VAR_0,VAR_1),VAR_0,VAR_2)
| f(VAR_2,VAR_0,VAR_1)
| f(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause11) ).
cnf(c_11,plain,
( ~ f(z(C,A,B),A,C)
| f(C,A,B)
| f(A,B,C) ),
inference(clausify,[status(thm)],[clause11]) ).
fof(clause12,axiom,
! [VAR_0,VAR_1,VAR_2] :
( f(z(VAR_1,VAR_2,VAR_0),VAR_2,VAR_1)
| ~ f(VAR_2,VAR_0,VAR_1)
| ~ f(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause12) ).
cnf(c_12,plain,
( f(z(B,C,A),C,B)
| ~ f(C,A,B)
| ~ f(A,B,C) ),
inference(clausify,[status(thm)],[clause12]) ).
fof(clause17,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ f(z(VAR_0,VAR_1,VAR_2),z(VAR_0,VAR_1,VAR_2),z(VAR_0,VAR_1,VAR_2))
| ~ f(VAR_2,VAR_0,VAR_1)
| ~ f(VAR_1,VAR_2,VAR_0)
| ~ f(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause17) ).
cnf(c_17,plain,
( ~ f(z(A,B,C),z(A,B,C),z(A,B,C))
| ~ f(C,A,B)
| ~ f(B,C,A)
| ~ f(A,B,C) ),
inference(clausify,[status(thm)],[clause17]) ).
cnf(c_20,plain,
( ~ f(z(A,A,A),A,A)
| f(A,A,A) ),
inference(factor,[status(thm)],[c_10]) ).
cnf(c_678,plain,
( f(A,a,a)
| f(a,A,a)
| ~ f(a,a,A)
| f(A,a,a) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_27,plain,
( f(a,A,a)
| ~ f(a,a,A)
| f(A,a,a) ),
inference(copy,[status(thm)],[c_678]) ).
cnf(c_45,plain,
( f(A,B,C)
| f(C,A,B)
| ~ f(a,a,z(B,C,A))
| f(A,z(A,B,C),B) ),
inference(resolve,[status(thm)],[c_8,c_1]) ).
cnf(c_66,plain,
( f(A,C,z(C,A,B))
| f(z(C,A,B),A,C)
| ~ f(A,B,C) ),
inference(resolve,[status(thm)],[c_12,c_4]) ).
cnf(c_68,plain,
( f(B,z(B,C,A),C)
| f(z(B,C,A),C,B)
| ~ f(A,B,C) ),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_115,plain,
( f(A,a,a)
| f(a,z(a,a,A),a)
| f(z(a,a,A),a,a) ),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_679,plain,
( f(a,a,A)
| f(A,a,a)
| f(A,a,a)
| f(a,z(a,a,A),a) ),
inference(resolve,[status(thm)],[c_115,c_10]) ).
cnf(c_215,plain,
( f(a,a,A)
| f(A,a,a)
| f(a,z(a,a,A),a) ),
inference(copy,[status(thm)],[c_679]) ).
cnf(c_680,plain,
( f(a,z(a,a,A),a)
| f(z(a,a,A),a,a)
| f(a,z(a,a,A),a)
| f(z(a,a,A),a,a) ),
inference(resolve,[status(thm)],[c_115,c_68]) ).
cnf(c_681,plain,
( f(a,z(a,a,A),a)
| f(a,z(a,a,A),a)
| f(z(a,a,A),a,a) ),
inference(copy,[status(thm)],[c_680]) ).
cnf(c_224,plain,
( f(a,z(a,a,A),a)
| f(z(a,a,A),a,a) ),
inference(copy,[status(thm)],[c_681]) ).
cnf(c_682,plain,
( ~ f(a,a,z(a,a,z(a,a,A)))
| f(a,z(a,a,A),a)
| f(a,z(a,a,A),a) ),
inference(resolve,[status(thm)],[c_224,c_3]) ).
cnf(c_227,plain,
( ~ f(a,a,z(a,a,z(a,a,A)))
| f(a,z(a,a,A),a) ),
inference(copy,[status(thm)],[c_682]) ).
cnf(c_683,plain,
( ~ f(a,z(a,a,z(a,a,A)),a)
| f(z(a,a,A),a,a)
| f(z(a,a,A),a,a) ),
inference(resolve,[status(thm)],[c_224,c_7]) ).
cnf(c_231,plain,
( ~ f(a,z(a,a,z(a,a,A)),a)
| f(z(a,a,A),a,a) ),
inference(copy,[status(thm)],[c_683]) ).
cnf(c_684,plain,
( f(A,a,a)
| ~ f(a,A,a)
| f(a,a,A)
| f(A,a,a) ),
inference(resolve,[status(thm)],[c_215,c_7]) ).
cnf(c_237,plain,
( ~ f(a,A,a)
| f(a,a,A)
| f(A,a,a) ),
inference(copy,[status(thm)],[c_684]) ).
cnf(c_685,plain,
( f(z(a,a,A),a,a)
| f(a,a,z(a,a,A))
| f(z(a,a,A),a,a) ),
inference(resolve,[status(thm)],[c_237,c_224]) ).
cnf(c_248,plain,
( f(a,a,z(a,a,A))
| f(z(a,a,A),a,a) ),
inference(copy,[status(thm)],[c_685]) ).
cnf(c_260,plain,
( f(a,a,A)
| f(a,A,a)
| f(a,a,z(a,a,A)) ),
inference(resolve,[status(thm)],[c_248,c_11]) ).
cnf(c_686,plain,
( f(a,A,a)
| ~ f(A,a,a)
| f(a,a,A)
| f(a,A,a) ),
inference(resolve,[status(thm)],[c_260,c_3]) ).
cnf(c_287,plain,
( ~ f(A,a,a)
| f(a,a,A)
| f(a,A,a) ),
inference(copy,[status(thm)],[c_686]) ).
cnf(c_687,plain,
( f(a,a,z(a,a,A))
| f(a,a,z(a,a,A))
| f(a,z(a,a,A),a) ),
inference(resolve,[status(thm)],[c_287,c_248]) ).
cnf(c_309,plain,
( f(a,a,z(a,a,A))
| f(a,z(a,a,A),a) ),
inference(copy,[status(thm)],[c_687]) ).
cnf(c_314,plain,
( f(a,a,A)
| ~ f(a,A,a)
| f(a,a,z(a,a,A)) ),
inference(resolve,[status(thm)],[c_309,c_6]) ).
cnf(c_688,plain,
( f(a,a,A)
| f(a,a,z(a,a,A))
| f(a,a,A)
| f(a,a,z(a,a,A)) ),
inference(resolve,[status(thm)],[c_314,c_260]) ).
cnf(c_689,plain,
( f(a,a,A)
| f(a,a,A)
| f(a,a,z(a,a,A)) ),
inference(copy,[status(thm)],[c_688]) ).
cnf(c_338,plain,
( f(a,a,A)
| f(a,a,z(a,a,A)) ),
inference(copy,[status(thm)],[c_689]) ).
cnf(c_690,plain,
( f(a,a,A)
| ~ f(A,a,a)
| f(a,a,A) ),
inference(resolve,[status(thm)],[c_338,c_2]) ).
cnf(c_347,plain,
( ~ f(A,a,a)
| f(a,a,A) ),
inference(copy,[status(thm)],[c_690]) ).
cnf(c_691,plain,
( f(a,a,z(a,a,A))
| f(a,a,z(a,a,A)) ),
inference(resolve,[status(thm)],[c_347,c_248]) ).
cnf(c_356,plain,
f(a,a,z(a,a,A)),
inference(copy,[status(thm)],[c_691]) ).
cnf(c_359,plain,
f(a,z(a,a,A),a),
inference(resolve,[status(thm)],[c_356,c_227]) ).
cnf(c_364,plain,
f(z(a,a,A),a,a),
inference(resolve,[status(thm)],[c_359,c_231]) ).
cnf(c_377,plain,
( f(a,A,a)
| ~ f(A,a,a) ),
inference(resolve,[status(thm)],[c_356,c_3]) ).
cnf(c_381,plain,
( f(A,a,a)
| ~ f(a,A,a) ),
inference(resolve,[status(thm)],[c_359,c_7]) ).
cnf(c_382,plain,
( f(a,a,A)
| ~ f(a,A,a) ),
inference(resolve,[status(thm)],[c_359,c_6]) ).
cnf(c_387,plain,
( f(a,a,A)
| f(a,A,a) ),
inference(resolve,[status(thm)],[c_364,c_11]) ).
cnf(c_692,plain,
( f(a,a,A)
| f(a,a,A) ),
inference(resolve,[status(thm)],[c_387,c_382]) ).
cnf(c_393,plain,
f(a,a,A),
inference(copy,[status(thm)],[c_692]) ).
cnf(c_693,plain,
( f(a,A,a)
| f(A,a,a)
| f(a,A,a) ),
inference(resolve,[status(thm)],[c_387,c_27]) ).
cnf(c_399,plain,
( f(A,a,a)
| f(a,A,a) ),
inference(copy,[status(thm)],[c_693]) ).
cnf(c_405,plain,
( f(A,B,C)
| f(C,A,B)
| f(A,z(A,B,C),B) ),
inference(resolve,[status(thm)],[c_393,c_45]) ).
cnf(c_407,plain,
( f(C,A,B)
| f(B,C,A)
| ~ f(A,B,C) ),
inference(resolve,[status(thm)],[c_393,c_1]) ).
cnf(c_415,plain,
( ~ f(z(a,A,a),z(a,A,a),z(a,A,a))
| ~ f(A,a,a)
| ~ f(a,A,a) ),
inference(resolve,[status(thm)],[c_393,c_17]) ).
cnf(c_694,plain,
( f(A,a,a)
| f(A,a,a) ),
inference(resolve,[status(thm)],[c_399,c_381]) ).
cnf(c_424,plain,
f(A,a,a),
inference(copy,[status(thm)],[c_694]) ).
cnf(c_695,plain,
( f(a,A,a)
| f(a,A,a) ),
inference(resolve,[status(thm)],[c_399,c_377]) ).
cnf(c_425,plain,
f(a,A,a),
inference(copy,[status(thm)],[c_695]) ).
cnf(c_696,plain,
( ~ f(z(a,A,a),z(a,A,a),z(a,A,a))
| ~ f(A,a,a) ),
inference(resolve,[status(thm)],[c_425,c_415]) ).
cnf(c_430,plain,
~ f(z(a,A,a),z(a,A,a),z(a,A,a)),
inference(resolve,[status(thm)],[c_424,c_696]) ).
cnf(c_439,plain,
~ f(z(z(a,A,a),z(a,A,a),z(a,A,a)),z(a,A,a),z(a,A,a)),
inference(resolve,[status(thm)],[c_20,c_430]) ).
cnf(c_480,plain,
( f(B,C,A)
| f(B,A,z(A,B,C))
| f(z(A,B,C),B,A) ),
inference(resolve,[status(thm)],[c_407,c_8]) ).
cnf(c_697,plain,
( f(B,A,z(A,B,C))
| f(z(A,B,C),B,A)
| f(B,A,z(A,B,C))
| f(z(A,B,C),B,A) ),
inference(resolve,[status(thm)],[c_480,c_66]) ).
cnf(c_698,plain,
( f(B,A,z(A,B,C))
| f(B,A,z(A,B,C))
| f(z(A,B,C),B,A) ),
inference(copy,[status(thm)],[c_697]) ).
cnf(c_607,plain,
( f(B,A,z(A,B,C))
| f(z(A,B,C),B,A) ),
inference(copy,[status(thm)],[c_698]) ).
cnf(c_699,plain,
( f(B,z(B,A,C),A)
| f(A,B,z(B,A,C))
| f(A,B,z(B,A,C)) ),
inference(resolve,[status(thm)],[c_607,c_407]) ).
cnf(c_608,plain,
( f(B,z(B,A,C),A)
| f(A,B,z(B,A,C)) ),
inference(copy,[status(thm)],[c_699]) ).
cnf(c_625,plain,
( f(A,B,C)
| ~ f(C,A,B)
| f(A,z(A,B,C),B) ),
inference(resolve,[status(thm)],[c_608,c_2]) ).
cnf(c_700,plain,
( f(A,B,C)
| f(A,z(A,B,C),B)
| f(A,B,C)
| f(A,z(A,B,C),B) ),
inference(resolve,[status(thm)],[c_625,c_405]) ).
cnf(c_701,plain,
( f(A,B,C)
| f(A,B,C)
| f(A,z(A,B,C),B) ),
inference(copy,[status(thm)],[c_700]) ).
cnf(c_655,plain,
( f(A,B,C)
| f(A,z(A,B,C),B) ),
inference(copy,[status(thm)],[c_701]) ).
cnf(c_702,plain,
( f(A,B,C)
| ~ f(B,C,A)
| f(A,B,C) ),
inference(resolve,[status(thm)],[c_655,c_6]) ).
cnf(c_663,plain,
( ~ f(B,C,A)
| f(A,B,C) ),
inference(copy,[status(thm)],[c_702]) ).
cnf(c_703,plain,
( f(z(A,B,C),B,A)
| f(z(A,B,C),B,A) ),
inference(resolve,[status(thm)],[c_663,c_607]) ).
cnf(c_676,plain,
f(z(A,B,C),B,A),
inference(copy,[status(thm)],[c_703]) ).
cnf(c_677,plain,
$false,
inference(resolve,[status(thm)],[c_676,c_439]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN353-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 17:37:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2667661 was started by sandbox2 on n005,
% 0.09/0.37 % Sat Sep 26 17:37:01 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 2.61/0.75
% 2.61/0.75 % SZS status Unsatisfiable for theBenchmark
% 2.61/0.75
% 2.61/0.75 % Proof 1 at 0.30 (+ 0.07) seconds.
% 2.61/0.75 % Length of proof is 53.
% 2.61/0.75 % Level of proof is 25.
% 2.61/0.75 % Maximum clause weight is 29.000.
% 2.61/0.75 % Given clauses 175.
% 2.61/0.75
% 2.61/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------