%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN364+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 : n017.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 09:37:42 AM UTC 2026
% Result : Theorem 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 4 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 77 ( 26 ~; 25 |; 20 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 4 sgn 29 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2115,conjecture,
( ( ! [W] :
( big_q(W)
=> ~ big_m(g(W)) )
& ! [U] :
? [V] :
( ( big_q(f(U,V))
& big_m(U) )
| big_p(U,V) )
& ! [X] :
( ? [Y] : big_p(X,Y)
=> ! [Z] : big_p(Z,Z) ) )
=> ! [U] :
? [V] :
( big_p(U,U)
& big_p(g(U),V) ) ),
file('theBenchmark.p',x2115) ).
fof(x2115_neg,negated_conjecture,
~ ( ( ! [W] :
( big_q(W)
=> ~ big_m(g(W)) )
& ! [U] :
? [V] :
( ( big_q(f(U,V))
& big_m(U) )
| big_p(U,V) )
& ! [X] :
( ? [Y] : big_p(X,Y)
=> ! [Z] : big_p(Z,Z) ) )
=> ! [U] :
? [V] :
( big_p(U,U)
& big_p(g(U),V) ) ),
inference(assume_negation,[status(cth)],[x2115]) ).
fof(nnf_1,plain,
( ? [U] :
! [V] :
( ~ big_p(U,U)
| ~ big_p(g(U),V) )
& ! [W] :
( ~ big_m(g(W))
| ~ big_q(W) )
& ! [X0] :
? [X1] :
( ( big_q(f(X0,X1))
& big_m(X0) )
| big_p(X0,X1) )
& ! [X] :
( ! [Z] : big_p(Z,Z)
| ! [Y] : ~ big_p(X,Y) ) ),
inference(fof_nnf,[status(thm)],[x2115_neg]) ).
fof(sk_x2115_neg_sk,plain,
( ! [V] :
( ~ big_p(sK1,sK1)
| ~ big_p(g(sK1),V) )
& ! [W] :
( ~ big_m(g(W))
| ~ big_q(W) )
& ! [X0] :
( ( big_q(f(X0,sK0(X0)))
& big_m(X0) )
| big_p(X0,sK0(X0)) )
& ! [X] :
( ! [Z] : big_p(Z,Z)
| ! [Y] : ~ big_p(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(U,sK1)],[nnf_1]) ).
fof(sk_x2115_neg,plain,
( ! [VAR_0] :
( ~ big_p(sK1,sK1)
| ~ big_p(g(sK1),VAR_0) )
& ! [VAR_0] :
( ~ big_m(g(VAR_0))
| ~ big_q(VAR_0) )
& ! [VAR_0] :
( big_q(f(VAR_0,sK0(VAR_0)))
| big_p(VAR_0,sK0(VAR_0)) )
& ! [VAR_0] :
( big_m(VAR_0)
| big_p(VAR_0,sK0(VAR_0)) )
& ! [VAR_0,VAR_1,VAR_2] :
( big_p(VAR_2,VAR_2)
| ~ big_p(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_x2115_neg_sk]) ).
cnf(c_2,negated_conjecture,
( ~ big_m(g(A))
| ~ big_q(A) ),
inference(split_conjunct,[status(thm)],[sk_x2115_neg]) ).
cnf(c_3,negated_conjecture,
( big_m(A)
| big_p(A,sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_x2115_neg]) ).
cnf(c_4,negated_conjecture,
( big_q(f(A,sK0(A)))
| big_p(A,sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_x2115_neg]) ).
cnf(c_5,negated_conjecture,
( big_p(g(A),sK0(g(A)))
| ~ big_q(A) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_6,negated_conjecture,
( big_p(g(f(A,sK0(A))),sK0(g(f(A,sK0(A)))))
| big_p(A,sK0(A)) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_7,negated_conjecture,
( big_p(C,C)
| ~ big_p(A,B) ),
inference(split_conjunct,[status(thm)],[sk_x2115_neg]) ).
cnf(c_8,negated_conjecture,
( ~ big_p(sK1,sK1)
| ~ big_p(g(sK1),A) ),
inference(split_conjunct,[status(thm)],[sk_x2115_neg]) ).
cnf(c_9,plain,
( big_p(B,sK0(B))
| big_p(A,A) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_10,plain,
( ~ big_p(sK1,sK1)
| big_p(A,sK0(A)) ),
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_11,plain,
( big_p(B,B)
| big_p(A,A) ),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_12,plain,
big_p(A,A),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_13,plain,
big_p(A,sK0(A)),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_14,negated_conjecture,
~ big_p(g(sK1),A),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_15,plain,
$false,
inference(resolve,[status(thm)],[c_14,c_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN364+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 17:33:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1272707 was started by sandbox on n017,
% 0.09/0.36 % Sat Sep 26 17:33:33 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.37
% 0.09/0.37 % SZS status Theorem for theBenchmark
% 0.09/0.37
% 0.09/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.37 % Length of proof is 15.
% 0.09/0.37 % Level of proof is 8.
% 0.09/0.37 % Maximum clause weight is 16.000.
% 0.09/0.37 % Given clauses 4.
% 0.09/0.37
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------