%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% 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 09:36:16 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 56 ( 22 unt; 0 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 49 ~; 67 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 37 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivityish,axiom,
! [VAR_0] : equalish(VAR_0,VAR_0),
file('theBenchmark.p',reflexivityish) ).
cnf(c_1,plain,
equalish(A,A),
inference(clausify,[status(thm)],[reflexivityish]) ).
fof(symmetryish,axiom,
! [VAR_0,VAR_1] :
( equalish(VAR_1,VAR_0)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetryish) ).
cnf(c_2,plain,
( equalish(B,A)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[symmetryish]) ).
fof(transitivityish,axiom,
! [VAR_0,VAR_1,VAR_2] :
( equalish(VAR_0,VAR_2)
| ~ equalish(VAR_1,VAR_2)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivityish) ).
cnf(c_3,plain,
( equalish(A,C)
| ~ equalish(B,C)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[transitivityish]) ).
fof(element_substitutionish1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( element(VAR_2,VAR_1)
| ~ element(VAR_2,VAR_0)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',element_substitutionish1) ).
cnf(c_4,plain,
( element(C,B)
| ~ element(C,A)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[element_substitutionish1]) ).
fof(c_5,axiom,
! [VAR_0] :
( equalish(VAR_0,m)
| ~ element(VAR_0,m)
| ~ equalish(f(VAR_0),m) ),
file('theBenchmark.p',c_5) ).
cnf(c_8,plain,
( equalish(A,m)
| ~ element(A,m)
| ~ equalish(f(A),m) ),
inference(clausify,[status(thm)],[c_5]) ).
fof(c_6,axiom,
! [VAR_0] :
( equalish(VAR_0,m)
| ~ element(VAR_0,m)
| ~ equalish(f(VAR_0),VAR_0) ),
file('theBenchmark.p',c_6) ).
cnf(c_9,plain,
( equalish(A,m)
| ~ element(A,m)
| ~ equalish(f(A),A) ),
inference(clausify,[status(thm)],[c_6]) ).
fof(c_7,axiom,
! [VAR_0] :
( equalish(VAR_0,m)
| ~ element(VAR_0,m)
| element(VAR_0,f(VAR_0)) ),
file('theBenchmark.p',c_7) ).
cnf(c_10,plain,
( equalish(A,m)
| ~ element(A,m)
| element(A,f(A)) ),
inference(clausify,[status(thm)],[c_7]) ).
fof(c_8_001,axiom,
! [VAR_0] :
( equalish(VAR_0,m)
| ~ element(VAR_0,m)
| element(f(VAR_0),VAR_0) ),
file('theBenchmark.p',c_8) ).
cnf(c_11,plain,
( equalish(A,m)
| ~ element(A,m)
| element(f(A),A) ),
inference(clausify,[status(thm)],[c_8]) ).
fof(c_9_002,axiom,
! [VAR_0,VAR_1] :
( equalish(VAR_1,m)
| element(VAR_1,m)
| equalish(VAR_0,m)
| equalish(VAR_0,VAR_1)
| ~ element(VAR_1,VAR_0)
| ~ element(VAR_0,VAR_1) ),
file('theBenchmark.p',c_9) ).
cnf(c_12,plain,
( equalish(B,m)
| element(B,m)
| equalish(A,m)
| equalish(A,B)
| ~ element(B,A)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[c_9]) ).
fof(c_16,axiom,
! [VAR_0] :
( equalish(VAR_0,k)
| element(VAR_0,k)
| ~ equalish(VAR_0,n) ),
file('theBenchmark.p',c_16) ).
cnf(c_19,plain,
( equalish(A,k)
| element(A,k)
| ~ equalish(A,n) ),
inference(clausify,[status(thm)],[c_16]) ).
fof(c_17,axiom,
! [VAR_0] :
( equalish(VAR_0,k)
| equalish(VAR_0,m)
| equalish(VAR_0,n)
| ~ element(VAR_0,k) ),
file('theBenchmark.p',c_17) ).
cnf(c_20,plain,
( equalish(A,k)
| equalish(A,m)
| equalish(A,n)
| ~ element(A,k) ),
inference(clausify,[status(thm)],[c_17]) ).
fof(c_19_003,axiom,
~ equalish(m,n),
file('theBenchmark.p',c_19) ).
cnf(c_22,plain,
~ equalish(m,n),
inference(clausify,[status(thm)],[c_19]) ).
fof(c_20_004,axiom,
~ equalish(n,k),
file('theBenchmark.p',c_20) ).
cnf(c_23,plain,
~ equalish(n,k),
inference(clausify,[status(thm)],[c_20]) ).
fof(c_23_005,axiom,
equalish(m,k),
file('theBenchmark.p',c_23) ).
cnf(c_26,plain,
equalish(m,k),
inference(clausify,[status(thm)],[c_23]) ).
cnf(c_98,plain,
( equalish(n,k)
| element(n,k) ),
inference(resolve,[status(thm)],[c_19,c_1]) ).
cnf(c_45,plain,
element(n,k),
inference(resolve,[status(thm)],[c_23,c_98]) ).
cnf(c_49,plain,
~ equalish(n,m),
inference(resolve,[status(thm)],[c_2,c_22]) ).
cnf(c_58,plain,
equalish(k,m),
inference(resolve,[status(thm)],[c_26,c_2]) ).
cnf(c_99,plain,
( element(A,m)
| ~ element(A,k) ),
inference(resolve,[status(thm)],[c_4,c_58]) ).
cnf(c_74,plain,
element(n,m),
inference(resolve,[status(thm)],[c_99,c_45]) ).
cnf(c_100,plain,
( equalish(n,m)
| element(f(n),n) ),
inference(resolve,[status(thm)],[c_74,c_11]) ).
cnf(c_76,plain,
element(f(n),n),
inference(resolve,[status(thm)],[c_49,c_100]) ).
cnf(c_101,plain,
( equalish(n,m)
| element(n,f(n)) ),
inference(resolve,[status(thm)],[c_74,c_10]) ).
cnf(c_77,plain,
element(n,f(n)),
inference(resolve,[status(thm)],[c_49,c_101]) ).
cnf(c_102,plain,
( equalish(n,m)
| ~ equalish(f(n),n) ),
inference(resolve,[status(thm)],[c_74,c_9]) ).
cnf(c_78,plain,
~ equalish(f(n),n),
inference(resolve,[status(thm)],[c_49,c_102]) ).
cnf(c_103,plain,
( equalish(n,m)
| ~ equalish(f(n),m) ),
inference(resolve,[status(thm)],[c_74,c_8]) ).
cnf(c_79,plain,
~ equalish(f(n),m),
inference(resolve,[status(thm)],[c_49,c_103]) ).
cnf(c_84,plain,
~ equalish(n,f(n)),
inference(resolve,[status(thm)],[c_2,c_78]) ).
cnf(c_104,plain,
( equalish(A,m)
| ~ equalish(A,k) ),
inference(resolve,[status(thm)],[c_3,c_58]) ).
cnf(c_85,plain,
~ equalish(f(n),k),
inference(resolve,[status(thm)],[c_104,c_79]) ).
cnf(c_105,plain,
( equalish(f(n),k)
| equalish(f(n),m)
| ~ element(f(n),k) ),
inference(resolve,[status(thm)],[c_20,c_78]) ).
cnf(c_106,plain,
( equalish(f(n),k)
| ~ element(f(n),k) ),
inference(resolve,[status(thm)],[c_105,c_79]) ).
cnf(c_87,plain,
~ element(f(n),k),
inference(resolve,[status(thm)],[c_106,c_85]) ).
cnf(c_107,plain,
( element(A,k)
| ~ element(A,m) ),
inference(resolve,[status(thm)],[c_4,c_26]) ).
cnf(c_89,plain,
~ element(f(n),m),
inference(resolve,[status(thm)],[c_107,c_87]) ).
cnf(c_108,plain,
( equalish(f(n),m)
| element(f(n),m)
| equalish(n,m)
| equalish(n,f(n))
| ~ element(n,f(n)) ),
inference(resolve,[status(thm)],[c_76,c_12]) ).
cnf(c_109,plain,
( equalish(f(n),m)
| element(f(n),m)
| equalish(n,m)
| equalish(n,f(n)) ),
inference(resolve,[status(thm)],[c_77,c_108]) ).
cnf(c_110,plain,
( equalish(f(n),m)
| element(f(n),m)
| equalish(n,m) ),
inference(resolve,[status(thm)],[c_84,c_109]) ).
cnf(c_111,plain,
( equalish(f(n),m)
| element(f(n),m) ),
inference(resolve,[status(thm)],[c_49,c_110]) ).
cnf(c_112,plain,
equalish(f(n),m),
inference(resolve,[status(thm)],[c_89,c_111]) ).
cnf(c_97,plain,
$false,
inference(resolve,[status(thm)],[c_79,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n019.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sat Sep 26 17:04:39 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.45 % Process 1795842 was started by sandbox2 on n019,
% 0.16/5.45 % Sat Sep 26 17:04:39 2026
% 0.16/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.45
% 0.16/5.45 % From the command line: assign(max_seconds, 300).
% 0.16/5.48
% 0.16/5.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.48
% 0.16/5.48 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.16/5.48 % Length of proof is 27.
% 0.16/5.48 % Level of proof is 7.
% 0.16/5.48 % Maximum clause weight is 23.000.
% 0.16/5.48 % Given clauses 63.
% 0.16/5.48
% 0.16/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------