%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN012-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 09:36:15 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 5 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 68 ( 27 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 67 ( 5 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_1,axiom,
! [VAR_0,VAR_1] :
( big_g(VAR_1,g(VAR_0,VAR_1))
| ~ big_f(VAR_0,g(VAR_0,VAR_1))
| ~ big_f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_1) ).
cnf(c_1,plain,
( big_g(B,g(A,B))
| ~ big_f(A,g(A,B))
| ~ big_f(A,B) ),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_2,axiom,
! [VAR_0,VAR_1] :
( ~ big_g(VAR_1,g(VAR_0,VAR_1))
| big_f(VAR_0,g(VAR_0,VAR_1))
| ~ big_f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_2) ).
cnf(c_2,plain,
( ~ big_g(B,g(A,B))
| big_f(A,g(A,B))
| ~ big_f(A,B) ),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_3,axiom,
! [VAR_0,VAR_1] :
( big_g(g(VAR_0,VAR_1),g(VAR_0,VAR_1))
| ~ big_f(g(VAR_0,VAR_1),g(VAR_0,VAR_1))
| ~ big_f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_3) ).
cnf(c_3,plain,
( big_g(g(A,B),g(A,B))
| ~ big_f(g(A,B),g(A,B))
| ~ big_f(A,B) ),
inference(clausify,[status(thm)],[clause_3]) ).
fof(clause_4,axiom,
! [VAR_0,VAR_1] :
( big_f(g(VAR_0,VAR_1),g(VAR_0,VAR_1))
| big_f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_4) ).
cnf(c_4,plain,
( big_f(g(A,B),g(A,B))
| big_f(A,B) ),
inference(clausify,[status(thm)],[clause_4]) ).
fof(clause_5,axiom,
! [VAR_0,VAR_1] :
( ~ big_g(g(VAR_0,VAR_1),g(VAR_0,VAR_1))
| big_f(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_5) ).
cnf(c_5,plain,
( ~ big_g(g(A,B),g(A,B))
| big_f(A,B) ),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_6,axiom,
! [VAR_0,VAR_1] :
( big_g(g(VAR_0,VAR_1),g(VAR_0,VAR_1))
| big_g(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_6) ).
cnf(c_6,plain,
( big_g(g(A,B),g(A,B))
| big_g(A,B) ),
inference(clausify,[status(thm)],[clause_6]) ).
fof(clause_7,axiom,
! [VAR_0,VAR_1] :
( ~ big_g(g(VAR_0,VAR_1),g(VAR_0,VAR_1))
| ~ big_g(VAR_0,VAR_1) ),
file('theBenchmark.p',clause_7) ).
cnf(c_7,plain,
( ~ big_g(g(A,B),g(A,B))
| ~ big_g(A,B) ),
inference(clausify,[status(thm)],[clause_7]) ).
cnf(c_8,plain,
( big_f(A,B)
| big_g(A,B) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_9,plain,
( ~ big_g(A,B)
| big_f(g(A,B),g(A,B)) ),
inference(resolve,[status(thm)],[c_8,c_7]) ).
cnf(c_10,plain,
( big_f(B,g(B,A))
| ~ big_f(B,A)
| big_f(A,g(B,A)) ),
inference(resolve,[status(thm)],[c_8,c_2]) ).
cnf(c_11,plain,
( ~ big_f(A,A)
| big_f(A,g(A,A)) ),
inference(factor,[status(thm)],[c_10]) ).
cnf(c_12,plain,
( big_f(A,B)
| big_f(g(A,B),g(g(A,B),g(A,B))) ),
inference(resolve,[status(thm)],[c_11,c_4]) ).
cnf(c_15,plain,
( big_g(g(A,B),g(g(A,B),g(A,B)))
| ~ big_f(g(A,B),g(A,B))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_12,c_1]) ).
cnf(c_38,plain,
( big_f(A,B)
| big_g(g(A,B),g(g(A,B),g(A,B)))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_15,c_4]) ).
cnf(c_19,plain,
( big_g(g(A,B),g(g(A,B),g(A,B)))
| big_f(A,B) ),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_20,plain,
( big_f(g(g(A,B),g(g(A,B),g(A,B))),g(g(A,B),g(g(A,B),g(A,B))))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_19,c_9]) ).
cnf(c_22,plain,
( big_g(g(g(A,B),g(g(A,B),g(A,B))),g(g(A,B),g(g(A,B),g(A,B))))
| ~ big_f(g(A,B),g(g(A,B),g(A,B)))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_20,c_3]) ).
cnf(c_39,plain,
( big_f(A,B)
| big_g(g(g(A,B),g(g(A,B),g(A,B))),g(g(A,B),g(g(A,B),g(A,B))))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_22,c_12]) ).
cnf(c_29,plain,
( big_g(g(g(A,B),g(g(A,B),g(A,B))),g(g(A,B),g(g(A,B),g(A,B))))
| big_f(A,B) ),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_31,plain,
( ~ big_g(g(A,B),g(g(A,B),g(A,B)))
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_29,c_7]) ).
cnf(c_40,plain,
( big_f(A,B)
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_31,c_19]) ).
cnf(c_33,plain,
big_f(A,B),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_41,plain,
( big_g(g(A,B),g(A,B))
| ~ big_f(g(A,B),g(A,B)) ),
inference(resolve,[status(thm)],[c_33,c_3]) ).
cnf(c_34,plain,
big_g(g(A,B),g(A,B)),
inference(resolve,[status(thm)],[c_33,c_41]) ).
cnf(c_42,plain,
( big_g(B,g(A,B))
| ~ big_f(A,g(A,B)) ),
inference(resolve,[status(thm)],[c_33,c_1]) ).
cnf(c_35,plain,
big_g(A,g(B,A)),
inference(resolve,[status(thm)],[c_33,c_42]) ).
cnf(c_36,plain,
~ big_g(A,B),
inference(resolve,[status(thm)],[c_34,c_7]) ).
cnf(c_37,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN012-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 17:09:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2275727 was started by sandbox2 on n001,
% 0.11/0.37 % Sat Sep 26 17:09:45 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.39 % Length of proof is 23.
% 0.11/0.39 % Level of proof is 14.
% 0.11/0.39 % Maximum clause weight is 37.000.
% 0.11/0.39 % Given clauses 24.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------