%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN014-2 : 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 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 11 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(c_19,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,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_001,axiom,
equalish(m,k),
file('theBenchmark.p',c_23) ).
cnf(c_26,plain,
equalish(m,k),
inference(clausify,[status(thm)],[c_23]) ).
cnf(c_50,plain,
equalish(k,n),
inference(resolve,[status(thm)],[c_23,c_2]) ).
cnf(c_58,plain,
( equalish(m,A)
| ~ equalish(k,A) ),
inference(resolve,[status(thm)],[c_3,c_26]) ).
cnf(c_59,plain,
~ equalish(k,n),
inference(resolve,[status(thm)],[c_58,c_22]) ).
cnf(c_57,plain,
$false,
inference(resolve,[status(thm)],[c_50,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN014-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n019.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 17:04:18 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 1795429 was started by sandbox2 on n019,
% 0.15/0.42 % Sat Sep 26 17:04:18 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.44
% 0.15/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.44
% 0.15/0.44 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.44 % Length of proof is 7.
% 0.15/0.44 % Level of proof is 2.
% 0.15/0.44 % Maximum clause weight is 9.000.
% 0.15/0.44 % Given clauses 26.
% 0.15/0.44
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------