%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN643-1 : 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 09:39:01 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 19 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 27 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3_is_p15_1,axiom,
p15(f3(c19)),
file('theBenchmark.p',f3_is_p15_1) ).
cnf(c_1,plain,
p15(f3(c19)),
inference(clausify,[status(thm)],[f3_is_p15_1]) ).
fof(f3_is_p15_2,axiom,
p15(f3(c18)),
file('theBenchmark.p',f3_is_p15_2) ).
cnf(c_2,plain,
p15(f3(c18)),
inference(clausify,[status(thm)],[f3_is_p15_2]) ).
fof(p4_5,axiom,
! [VAR_0] : p4(VAR_0,VAR_0),
file('theBenchmark.p',p4_5) ).
cnf(c_5,plain,
p4(A,A),
inference(clausify,[status(thm)],[p4_5]) ).
fof(p4_10,axiom,
p4(f5(f3(c18)),f5(c18)),
file('theBenchmark.p',p4_10) ).
cnf(c_10,plain,
p4(f5(f3(c18)),f5(c18)),
inference(clausify,[status(thm)],[p4_10]) ).
fof(p4_11,axiom,
p4(f5(f3(c19)),f5(c19)),
file('theBenchmark.p',p4_11) ).
cnf(c_11,plain,
p4(f5(f3(c19)),f5(c19)),
inference(clausify,[status(thm)],[p4_11]) ).
fof(p4_24,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_24) ).
cnf(c_24,plain,
( ~ p4(C,B)
| ~ p4(C,A)
| p4(A,B) ),
inference(clausify,[status(thm)],[p4_24]) ).
fof(not_p4_28,axiom,
~ p4(f5(f10(f3(c19),f3(c18))),f9(f5(c19),f5(c18))),
file('theBenchmark.p',not_p4_28) ).
cnf(c_28,plain,
~ p4(f5(f10(f3(c19),f3(c18))),f9(f5(c19),f5(c18))),
inference(clausify,[status(thm)],[not_p4_28]) ).
fof(p4_35,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p4(VAR_0,VAR_2)
| ~ p4(VAR_1,VAR_3)
| p4(f9(VAR_0,VAR_1),f9(VAR_2,VAR_3)) ),
file('theBenchmark.p',p4_35) ).
cnf(c_35,plain,
( ~ p4(A,C)
| ~ p4(B,D)
| p4(f9(A,B),f9(C,D)) ),
inference(clausify,[status(thm)],[p4_35]) ).
fof(p4_37,axiom,
! [VAR_0,VAR_1] :
( ~ p15(VAR_1)
| ~ p15(VAR_0)
| p4(f5(f10(VAR_0,VAR_1)),f9(f5(VAR_0),f5(VAR_1))) ),
file('theBenchmark.p',p4_37) ).
cnf(c_37,plain,
( ~ p15(B)
| ~ p15(A)
| p4(f5(f10(A,B)),f9(f5(A),f5(B))) ),
inference(clausify,[status(thm)],[p4_37]) ).
cnf(c_70,plain,
( ~ p4(B,A)
| p4(A,B) ),
inference(resolve,[status(thm)],[c_24,c_5]) ).
cnf(c_89,plain,
( ~ p4(A,C)
| p4(f9(A,B),f9(C,B)) ),
inference(resolve,[status(thm)],[c_35,c_5]) ).
cnf(c_92,plain,
( ~ p4(B,C)
| p4(f9(A,B),f9(A,C)) ),
inference(resolve,[status(thm)],[c_35,c_5]) ).
cnf(c_141,plain,
p4(f9(f5(f3(c19)),A),f9(f5(c19),A)),
inference(resolve,[status(thm)],[c_89,c_11]) ).
cnf(c_144,plain,
p4(f9(A,f5(f3(c18))),f9(A,f5(c18))),
inference(resolve,[status(thm)],[c_92,c_10]) ).
cnf(c_596,plain,
( ~ p4(A,f9(f5(c19),f5(c18)))
| ~ p4(A,f5(f10(f3(c19),f3(c18)))) ),
inference(resolve,[status(thm)],[c_24,c_28]) ).
cnf(c_442,plain,
~ p4(f9(f5(f3(c19)),f5(c18)),f5(f10(f3(c19),f3(c18)))),
inference(resolve,[status(thm)],[c_596,c_141]) ).
cnf(c_597,plain,
( ~ p4(A,f5(f10(f3(c19),f3(c18))))
| ~ p4(A,f9(f5(f3(c19)),f5(c18))) ),
inference(resolve,[status(thm)],[c_24,c_442]) ).
cnf(c_489,plain,
~ p4(f9(f5(f3(c19)),f5(f3(c18))),f5(f10(f3(c19),f3(c18)))),
inference(resolve,[status(thm)],[c_597,c_144]) ).
cnf(c_594,plain,
~ p4(f5(f10(f3(c19),f3(c18))),f9(f5(f3(c19)),f5(f3(c18)))),
inference(resolve,[status(thm)],[c_70,c_489]) ).
cnf(c_598,plain,
( ~ p15(f3(c18))
| ~ p15(f3(c19)) ),
inference(resolve,[status(thm)],[c_37,c_594]) ).
cnf(c_599,plain,
~ p15(f3(c19)),
inference(resolve,[status(thm)],[c_598,c_2]) ).
cnf(c_595,plain,
$false,
inference(resolve,[status(thm)],[c_1,c_599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN643-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 18:18:04 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 1905035 was started by sandbox2 on n019,
% 0.09/0.37 % Sat Sep 26 18:18:04 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).
% 0.09/0.43
% 0.09/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.43
% 0.09/0.43 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.09/0.43 % Length of proof is 18.
% 0.09/0.43 % Level of proof is 6.
% 0.09/0.43 % Maximum clause weight is 34.000.
% 0.09/0.43 % Given clauses 142.
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------