%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN312-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 09:37:31 AM UTC 2026
% Result : Unsatisfiable 0.03s 0.31s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 20 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 25 ~; 13 |; 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 : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 33 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p(VAR_3,VAR_1,VAR_2)
| ~ p(VAR_0,VAR_3,VAR_2)
| p(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause1) ).
cnf(c_1,plain,
( ~ p(D,B,C)
| ~ p(A,D,C)
| p(A,B,C) ),
inference(clausify,[status(thm)],[clause1]) ).
fof(clause2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p(VAR_2,VAR_1,VAR_0)
| p(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause2) ).
cnf(c_2,plain,
( ~ p(C,B,A)
| p(A,B,C) ),
inference(clausify,[status(thm)],[clause2]) ).
fof(clause3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p(VAR_1,VAR_0,VAR_2)
| p(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',clause3) ).
cnf(c_3,plain,
( ~ p(B,A,C)
| p(A,B,C) ),
inference(clausify,[status(thm)],[clause3]) ).
fof(clause4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p(VAR_0,VAR_1,VAR_2)
| p(VAR_0,VAR_1,f(VAR_2)) ),
file('theBenchmark.p',clause4) ).
cnf(c_4,plain,
( ~ p(A,B,C)
| p(A,B,f(C)) ),
inference(clausify,[status(thm)],[clause4]) ).
fof(clause5,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p(VAR_0,VAR_1,VAR_2)
| p(g(VAR_0),VAR_1,VAR_2) ),
file('theBenchmark.p',clause5) ).
cnf(c_5,plain,
( ~ p(A,B,C)
| p(g(A),B,C) ),
inference(clausify,[status(thm)],[clause5]) ).
fof(clause6,axiom,
p(a,f(b),c),
file('theBenchmark.p',clause6) ).
cnf(c_6,plain,
p(a,f(b),c),
inference(clausify,[status(thm)],[clause6]) ).
fof(clause7,axiom,
p(f(b),d,c),
file('theBenchmark.p',clause7) ).
cnf(c_7,plain,
p(f(b),d,c),
inference(clausify,[status(thm)],[clause7]) ).
fof(clause8,axiom,
~ p(f(g(a)),f(g(d)),f(g(c))),
file('theBenchmark.p',clause8) ).
cnf(c_8,plain,
~ p(f(g(a)),f(g(d)),f(g(c))),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_121,plain,
( ~ p(f(b),A,c)
| p(a,A,c) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_17,plain,
p(a,d,c),
inference(resolve,[status(thm)],[c_121,c_7]) ).
cnf(c_18,plain,
~ p(f(g(a)),f(g(d)),g(c)),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_28,plain,
~ p(g(c),f(g(d)),f(g(a))),
inference(resolve,[status(thm)],[c_18,c_2]) ).
cnf(c_32,plain,
~ p(c,f(g(d)),f(g(a))),
inference(resolve,[status(thm)],[c_28,c_5]) ).
cnf(c_36,plain,
~ p(c,f(g(d)),g(a)),
inference(resolve,[status(thm)],[c_32,c_4]) ).
cnf(c_41,plain,
p(d,a,c),
inference(resolve,[status(thm)],[c_3,c_17]) ).
cnf(c_43,plain,
p(g(d),a,c),
inference(resolve,[status(thm)],[c_5,c_41]) ).
cnf(c_58,plain,
~ p(g(a),f(g(d)),c),
inference(resolve,[status(thm)],[c_36,c_2]) ).
cnf(c_62,plain,
~ p(a,f(g(d)),c),
inference(resolve,[status(thm)],[c_58,c_5]) ).
cnf(c_66,plain,
~ p(f(g(d)),a,c),
inference(resolve,[status(thm)],[c_62,c_3]) ).
cnf(c_87,plain,
~ p(c,a,f(g(d))),
inference(resolve,[status(thm)],[c_66,c_2]) ).
cnf(c_96,plain,
~ p(c,a,g(d)),
inference(resolve,[status(thm)],[c_87,c_4]) ).
cnf(c_119,plain,
~ p(g(d),a,c),
inference(resolve,[status(thm)],[c_96,c_2]) ).
cnf(c_120,plain,
$false,
inference(resolve,[status(thm)],[c_119,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN312-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 26 17:32:04 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 1140249 was started by sandbox2 on n012,
% 0.03/0.30 % Sat Sep 26 17:32:04 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 0.03/0.31
% 0.03/0.31 % SZS status Unsatisfiable for theBenchmark
% 0.03/0.31
% 0.03/0.31 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.31 % Length of proof is 22.
% 0.03/0.31 % Level of proof is 11.
% 0.03/0.31 % Maximum clause weight is 12.000.
% 0.03/0.31 % Given clauses 37.
% 0.03/0.31
% 0.03/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------