%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 09:36:49 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 4 unt; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 138 ( 44 ~; 94 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 222 ( 117 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c_5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( q(f1(VAR_0,VAR_1),VAR_3)
| s(f1(VAR_0,VAR_1),VAR_2)
| p(f1(VAR_0,VAR_1),f1(VAR_0,VAR_1)) ),
file('theBenchmark.p',c_5) ).
cnf(c_6,plain,
( q(f1(A,B),D)
| s(f1(A,B),C)
| p(f1(A,B),f1(A,B)) ),
inference(clausify,[status(thm)],[c_5]) ).
fof(c_3,axiom,
! [VAR_0,VAR_1] :
( ~ s(VAR_1,VAR_1)
| ~ s(VAR_0,f1(VAR_0,VAR_1))
| p(f1(VAR_0,VAR_1),f1(VAR_0,VAR_1)) ),
file('theBenchmark.p',c_3) ).
cnf(c_8,plain,
( ~ s(B,B)
| ~ s(A,f1(A,B))
| p(f1(A,B),f1(A,B)) ),
inference(clausify,[status(thm)],[c_3]) ).
fof(c_12,axiom,
! [VAR_0,VAR_1] :
( ~ s(VAR_1,VAR_1)
| ~ s(VAR_0,f1(VAR_0,VAR_1))
| ~ p(VAR_0,VAR_0) ),
file('theBenchmark.p',c_12) ).
cnf(c_12_001,plain,
( ~ s(B,B)
| ~ s(A,f1(A,B))
| ~ p(A,A) ),
inference(clausify,[status(thm)],[c_12]) ).
fof(c_14,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( q(f1(VAR_0,VAR_1),VAR_3)
| s(f1(VAR_0,VAR_1),VAR_2)
| ~ p(VAR_0,VAR_0) ),
file('theBenchmark.p',c_14) ).
cnf(c_14_002,plain,
( q(f1(A,B),D)
| s(f1(A,B),C)
| ~ p(A,A) ),
inference(clausify,[status(thm)],[c_14]) ).
fof(c_16,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ q(VAR_2,f1(VAR_0,VAR_2))
| ~ q(VAR_1,VAR_1)
| ~ p(VAR_0,VAR_0) ),
file('theBenchmark.p',c_16) ).
cnf(c_16_003,plain,
( ~ q(C,f1(A,C))
| ~ q(B,B)
| ~ p(A,A) ),
inference(clausify,[status(thm)],[c_16]) ).
cnf(c_26,plain,
( q(f1(C,D),F)
| s(f1(C,D),E)
| ~ q(B,f1(f1(C,D),B))
| ~ q(A,A) ),
inference(resolve,[status(thm)],[c_16,c_6]) ).
cnf(c_40,plain,
( q(f1(A,B),V6)
| s(f1(A,B),F)
| q(f1(f1(A,B),C),E)
| s(f1(f1(A,B),C),D) ),
inference(resolve,[status(thm)],[c_14,c_6]) ).
cnf(c_54,plain,
( ~ s(B,B)
| ~ s(A,f1(A,B))
| ~ s(C,C)
| ~ s(f1(A,B),f1(f1(A,B),C)) ),
inference(resolve,[status(thm)],[c_12,c_8]) ).
fof(c_25,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ q(VAR_3,f1(VAR_1,VAR_3))
| ~ q(VAR_2,VAR_2)
| s(VAR_0,VAR_1) ),
file('theBenchmark.p',c_25) ).
cnf(c_79,plain,
( ~ q(D,f1(B,D))
| ~ q(C,C)
| s(A,B) ),
inference(clausify,[status(thm)],[c_25]) ).
fof(c_21,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ s(VAR_2,VAR_2)
| ~ s(VAR_1,f1(VAR_1,VAR_2))
| s(VAR_0,VAR_1) ),
file('theBenchmark.p',c_21) ).
cnf(c_83,plain,
( ~ s(C,C)
| ~ s(B,f1(B,C))
| s(A,B) ),
inference(clausify,[status(thm)],[c_21]) ).
cnf(c_95,plain,
( ~ s(A,f1(A,B))
| ~ s(B,B)
| ~ s(f1(A,B),f1(f1(A,B),B)) ),
inference(factor,[status(thm)],[c_54]) ).
cnf(c_456,plain,
( q(f1(F,V6),V10)
| s(f1(F,V6),V9)
| s(f1(f1(F,V6),V7),V8)
| q(f1(B,C),E)
| s(f1(B,C),D)
| ~ q(A,f1(f1(B,C),A)) ),
inference(resolve,[status(thm)],[c_26,c_40]) ).
cnf(c_121,plain,
( q(f1(V10,V11),V15)
| s(f1(V10,V11),V14)
| s(f1(f1(V10,V11),V12),V13)
| q(f1(E,F),V9)
| s(f1(E,F),V8)
| s(f1(f1(E,F),V6),V7)
| q(f1(A,B),D)
| s(f1(A,B),C) ),
inference(resolve,[status(thm)],[c_456,c_40]) ).
cnf(c_149,plain,
( q(f1(V7,V8),V12)
| s(f1(V7,V8),V11)
| s(f1(f1(V7,V8),V9),V10)
| q(f1(A,B),V6)
| s(f1(f1(A,B),E),F)
| q(f1(A,B),D)
| s(f1(A,B),C) ),
inference(factor,[status(thm)],[c_121]) ).
cnf(c_170,plain,
( q(f1(A,B),V9)
| s(f1(f1(A,B),V7),V8)
| q(f1(A,B),V6)
| s(f1(f1(A,B),E),F)
| q(f1(A,B),D)
| s(f1(A,B),C) ),
inference(factor,[status(thm)],[c_149]) ).
cnf(c_185,plain,
( q(f1(A,B),V8)
| s(f1(f1(A,B),V6),V7)
| s(f1(f1(A,B),E),F)
| q(f1(A,B),D)
| s(f1(A,B),C) ),
inference(factor,[status(thm)],[c_170]) ).
cnf(c_195,plain,
( s(f1(f1(A,B),V6),V7)
| s(f1(f1(A,B),E),F)
| q(f1(A,B),D)
| s(f1(A,B),C) ),
inference(factor,[status(thm)],[c_185]) ).
cnf(c_200,plain,
( s(f1(f1(A,B),E),F)
| q(f1(A,B),D)
| s(f1(A,B),C) ),
inference(factor,[status(thm)],[c_195]) ).
cnf(c_457,plain,
( s(f1(f1(D,E),V6),V7)
| s(f1(D,E),F)
| ~ q(C,f1(B,C))
| s(A,B) ),
inference(resolve,[status(thm)],[c_79,c_200]) ).
cnf(c_306,plain,
( s(f1(f1(V7,V8),V10),V11)
| s(f1(V7,V8),V9)
| s(f1(f1(C,D),F),V6)
| s(f1(C,D),E)
| s(A,B) ),
inference(resolve,[status(thm)],[c_457,c_200]) ).
cnf(c_323,plain,
( s(f1(f1(F,V6),V8),V9)
| s(f1(F,V6),V7)
| s(f1(f1(A,B),D),E)
| s(f1(A,B),C) ),
inference(factor,[status(thm)],[c_306]) ).
cnf(c_328,plain,
( s(f1(f1(A,B),F),V6)
| s(f1(f1(A,B),D),E)
| s(f1(A,B),C) ),
inference(factor,[status(thm)],[c_323]) ).
cnf(c_331,plain,
( s(f1(f1(A,B),D),E)
| s(f1(A,B),C) ),
inference(factor,[status(thm)],[c_328]) ).
cnf(c_368,plain,
( ~ s(f1(A,B),f1(f1(A,B),D))
| ~ s(D,D)
| s(f1(A,B),C) ),
inference(resolve,[status(thm)],[c_331,c_95]) ).
cnf(c_458,plain,
( s(f1(B,C),F)
| ~ s(E,E)
| s(A,f1(f1(B,C),D)) ),
inference(resolve,[status(thm)],[c_83,c_331]) ).
cnf(c_398,plain,
( s(f1(F,V6),V7)
| s(f1(B,C),E)
| s(A,f1(f1(B,C),D)) ),
inference(resolve,[status(thm)],[c_458,c_331]) ).
cnf(c_424,plain,
( s(f1(D,E),F)
| s(f1(A,B),f1(f1(A,B),C)) ),
inference(factor,[status(thm)],[c_398]) ).
cnf(c_429,plain,
s(f1(A,B),f1(f1(A,B),C)),
inference(factor,[status(thm)],[c_424]) ).
cnf(c_438,plain,
( ~ s(D,D)
| s(f1(A,B),C) ),
inference(resolve,[status(thm)],[c_429,c_368]) ).
cnf(c_439,plain,
( ~ s(B,f1(B,A))
| ~ s(A,A) ),
inference(resolve,[status(thm)],[c_429,c_95]) ).
cnf(c_450,plain,
( s(f1(D,E),F)
| s(f1(A,B),C) ),
inference(resolve,[status(thm)],[c_438,c_331]) ).
cnf(c_451,plain,
s(f1(A,B),C),
inference(factor,[status(thm)],[c_450]) ).
cnf(c_454,plain,
~ s(A,f1(A,f1(B,C))),
inference(resolve,[status(thm)],[c_439,c_451]) ).
cnf(c_455,plain,
$false,
inference(resolve,[status(thm)],[c_454,c_451]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 17:08:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2268902 was started by sandbox on n002,
% 0.09/0.36 % Sat Sep 26 17:08:20 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.46
% 0.13/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.46
% 0.13/0.46 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.13/0.46 % Length of proof is 31.
% 0.13/0.46 % Level of proof is 19.
% 0.13/0.46 % Maximum clause weight is 69.000.
% 0.13/0.46 % Given clauses 66.
% 0.13/0.46
% 0.13/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------