%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN077-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 09:36:59 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 6 unt; 0 def)
% Number of atoms : 100 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 99 ( 40 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_1,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ big_f(VAR_0,f(VAR_1)) ),
file('theBenchmark.p',clause_1) ).
cnf(c_1,plain,
( A = B
| ~ big_f(A,f(B)) ),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_2,axiom,
! [VAR_0,VAR_1] :
( big_f(VAR_0,f(VAR_1))
| VAR_0 != VAR_1 ),
file('theBenchmark.p',clause_2) ).
cnf(c_2,plain,
( big_f(A,f(B))
| A != B ),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_3,axiom,
! [VAR_0,VAR_1] :
( big_f(g(VAR_0,VAR_1),VAR_1)
| ~ big_f(VAR_0,VAR_1)
| ~ big_f(VAR_0,a) ),
file('theBenchmark.p',clause_3) ).
cnf(c_3,plain,
( big_f(g(A,B),B)
| ~ big_f(A,B)
| ~ big_f(A,a) ),
inference(clausify,[status(thm)],[clause_3]) ).
fof(clause_4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ big_f(VAR_2,VAR_1)
| ~ big_f(VAR_2,g(VAR_0,VAR_1))
| ~ big_f(VAR_0,VAR_1)
| ~ big_f(VAR_0,a) ),
file('theBenchmark.p',clause_4) ).
cnf(c_4,plain,
( ~ big_f(C,B)
| ~ big_f(C,g(A,B))
| ~ big_f(A,B)
| ~ big_f(A,a) ),
inference(clausify,[status(thm)],[clause_4]) ).
fof(clause_5,axiom,
! [VAR_0] :
( big_f(VAR_0,a)
| big_f(VAR_0,h(VAR_0)) ),
file('theBenchmark.p',clause_5) ).
cnf(c_5,plain,
( big_f(A,a)
| big_f(A,h(A)) ),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_6,axiom,
! [VAR_0,VAR_1] :
( big_f(VAR_1,a)
| big_f(i(VAR_1,VAR_0),VAR_0)
| ~ big_f(VAR_0,h(VAR_1)) ),
file('theBenchmark.p',clause_6) ).
cnf(c_6,plain,
( big_f(B,a)
| big_f(i(B,A),A)
| ~ big_f(A,h(B)) ),
inference(clausify,[status(thm)],[clause_6]) ).
fof(clause_7,axiom,
! [VAR_0,VAR_1] :
( ~ big_f(VAR_1,h(VAR_0))
| big_f(i(VAR_0,VAR_1),h(VAR_0))
| big_f(VAR_0,a) ),
file('theBenchmark.p',clause_7) ).
cnf(c_7,plain,
( ~ big_f(B,h(A))
| big_f(i(A,B),h(A))
| big_f(A,a) ),
inference(clausify,[status(thm)],[clause_7]) ).
cnf(c_11,plain,
( ~ big_f(A,g(A,B))
| ~ big_f(A,B)
| ~ big_f(A,a) ),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_12,plain,
big_f(A,f(A)),
inference(xxres,[status(thm)],[c_2]) ).
cnf(c_162,plain,
( big_f(A,a)
| big_f(A,a)
| big_f(i(A,A),A) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_13,plain,
( big_f(A,a)
| big_f(i(A,A),A) ),
inference(copy,[status(thm)],[c_162]) ).
cnf(c_163,plain,
( big_f(A,a)
| big_f(i(A,A),h(A))
| big_f(A,a) ),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_14,plain,
( big_f(i(A,A),h(A))
| big_f(A,a) ),
inference(copy,[status(thm)],[c_163]) ).
cnf(c_16,plain,
( big_f(g(A,f(A)),f(A))
| ~ big_f(A,a) ),
inference(resolve,[status(thm)],[c_12,c_3]) ).
cnf(c_23,plain,
( ~ big_f(B,A)
| ~ big_f(B,g(i(a,a),A))
| ~ big_f(i(a,a),A)
| big_f(a,a) ),
inference(resolve,[status(thm)],[c_13,c_4]) ).
cnf(c_25,plain,
( big_f(g(i(a,a),A),A)
| ~ big_f(i(a,a),A)
| big_f(a,a) ),
inference(resolve,[status(thm)],[c_13,c_3]) ).
cnf(c_164,plain,
( big_f(a,a)
| big_f(g(i(a,a),h(a)),h(a))
| big_f(a,a) ),
inference(resolve,[status(thm)],[c_25,c_14]) ).
cnf(c_68,plain,
( big_f(g(i(a,a),h(a)),h(a))
| big_f(a,a) ),
inference(copy,[status(thm)],[c_164]) ).
cnf(c_165,plain,
( big_f(i(a,g(i(a,a),h(a))),h(a))
| big_f(a,a)
| big_f(a,a) ),
inference(resolve,[status(thm)],[c_68,c_7]) ).
cnf(c_69,plain,
( big_f(i(a,g(i(a,a),h(a))),h(a))
| big_f(a,a) ),
inference(copy,[status(thm)],[c_165]) ).
cnf(c_166,plain,
( big_f(a,a)
| big_f(i(a,g(i(a,a),h(a))),g(i(a,a),h(a)))
| big_f(a,a) ),
inference(resolve,[status(thm)],[c_68,c_6]) ).
cnf(c_70,plain,
( big_f(i(a,g(i(a,a),h(a))),g(i(a,a),h(a)))
| big_f(a,a) ),
inference(copy,[status(thm)],[c_166]) ).
cnf(c_167,plain,
( big_f(a,a)
| ~ big_f(A,h(a))
| ~ big_f(A,g(i(a,a),h(a)))
| big_f(a,a) ),
inference(resolve,[status(thm)],[c_23,c_14]) ).
cnf(c_74,plain,
( ~ big_f(A,h(a))
| ~ big_f(A,g(i(a,a),h(a)))
| big_f(a,a) ),
inference(copy,[status(thm)],[c_167]) ).
cnf(c_168,plain,
( ~ big_f(i(a,g(i(a,a),h(a))),h(a))
| big_f(a,a)
| big_f(a,a) ),
inference(resolve,[status(thm)],[c_70,c_74]) ).
cnf(c_124,plain,
( ~ big_f(i(a,g(i(a,a),h(a))),h(a))
| big_f(a,a) ),
inference(copy,[status(thm)],[c_168]) ).
cnf(c_169,plain,
( big_f(a,a)
| big_f(a,a) ),
inference(resolve,[status(thm)],[c_124,c_69]) ).
cnf(c_127,plain,
big_f(a,a),
inference(copy,[status(thm)],[c_169]) ).
cnf(c_128,plain,
big_f(g(a,f(a)),f(a)),
inference(resolve,[status(thm)],[c_127,c_16]) ).
cnf(c_157,plain,
g(a,f(a)) = a,
inference(resolve,[status(thm)],[c_128,c_1]) ).
cnf(c_170,plain,
( ~ big_f(a,a)
| ~ big_f(a,f(a))
| ~ big_f(a,a) ),
inference(paramod,[status(thm)],[c_157,c_11]) ).
cnf(c_171,plain,
( ~ big_f(a,f(a))
| ~ big_f(a,a) ),
inference(copy,[status(thm)],[c_170]) ).
cnf(c_172,plain,
~ big_f(a,f(a)),
inference(resolve,[status(thm)],[c_127,c_171]) ).
cnf(c_161,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN077-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.34 % Computer : n003.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8046.5625MB
% 0.11/0.34 % OS : Linux 6.8.0-71-generic
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Sat Sep 26 17:11:09 UTC 2026
% 0.11/0.34 % CPUTime :
% 0.11/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.34 % Process 3379917 was started by sandbox on n003,
% 0.11/0.34 % Sat Sep 26 17:11:09 2026
% 0.11/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.35
% 0.11/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.12/0.37 % Length of proof is 23.
% 0.12/0.37 % Level of proof is 9.
% 0.12/0.37 % Maximum clause weight is 38.000.
% 0.12/0.37 % Given clauses 67.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------