%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN065+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 09:36:56 AM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 11 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 5 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 23 ( 3 sgn 10 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel36_2,axiom,
! [X] :
? [Y] : big_g(X,Y),
file('theBenchmark.p',pel36_2) ).
fof(pel36_3,axiom,
! [X,Y] :
( ( big_g(X,Y)
| big_f(X,Y) )
=> ! [Z] :
( ( big_g(Y,Z)
| big_f(Y,Z) )
=> big_h(X,Z) ) ),
file('theBenchmark.p',pel36_3) ).
fof(pel36,conjecture,
! [X] :
? [Y] : big_h(X,Y),
file('theBenchmark.p',pel36) ).
fof(pel36_neg,negated_conjecture,
~ ! [X] :
? [Y] : big_h(X,Y),
inference(assume_negation,[status(cth)],[pel36]) ).
fof(nnf_4,plain,
? [X] :
! [Y] : ~ big_h(X,Y),
inference(fof_nnf,[status(thm)],[pel36_neg]) ).
fof(sk_pel36_neg,plain,
! [Y] : ~ big_h(sK0,Y),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_4]) ).
cnf(c_5,negated_conjecture,
~ big_h(sK0,A),
inference(split_conjunct,[status(thm)],[sk_pel36_neg]) ).
cnf(c_6,plain,
( big_h(A,C)
| ~ big_g(B,C)
| ~ big_g(A,B) ),
inference(clausify,[status(thm)],[pel36_3]) ).
cnf(c_13,negated_conjecture,
( ~ big_g(A,B)
| ~ big_g(sK0,A) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
fof(nnf_2,plain,
! [X] :
? [Y] : big_g(X,Y),
inference(fof_nnf,[status(thm)],[pel36_2]) ).
fof(sk_pel36_2,plain,
! [X] : big_g(X,sK1(X)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Y,sK1(X))],[nnf_2]) ).
cnf(c_14,plain,
big_g(A,sK1(A)),
inference(split_conjunct,[status(thm)],[sk_pel36_2]) ).
cnf(c_16,plain,
~ big_g(sK0,A),
inference(resolve,[status(thm)],[c_14,c_13]) ).
cnf(c_17,plain,
$false,
inference(resolve,[status(thm)],[c_16,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN065+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n011.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sat Sep 26 17:08:45 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 1117063 was started by sandbox on n011,
% 0.17/0.45 % Sat Sep 26 17:08:45 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.47
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47
% 0.17/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.47 % Length of proof is 9.
% 0.17/0.47 % Level of proof is 4.
% 0.17/0.47 % Maximum clause weight is 6.000.
% 0.17/0.47 % Given clauses 5.
% 0.17/0.47
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------