%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN729+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 09:39:13 AM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 74 ( 26 ~; 17 |; 23 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn 17 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm72,conjecture,
( ( ! [W] :
( p(W)
=> ( p(h(W))
& p(g(W)) ) )
& ! [X] :
? [Y] :
( p(X)
=> ( p(Y)
& l(X,g(h(Y))) ) ) )
=> ! [X] :
( p(X)
=> ? [Y] :
( p(Y)
& l(X,Y) ) ) ),
file('theBenchmark.p',thm72) ).
fof(thm72_neg,negated_conjecture,
~ ( ( ! [W] :
( p(W)
=> ( p(h(W))
& p(g(W)) ) )
& ! [X] :
? [Y] :
( p(X)
=> ( p(Y)
& l(X,g(h(Y))) ) ) )
=> ! [X] :
( p(X)
=> ? [Y] :
( p(Y)
& l(X,Y) ) ) ),
inference(assume_negation,[status(cth)],[thm72]) ).
fof(nnf_1,plain,
( ? [X] :
( ! [Y] :
( ~ p(Y)
| ~ l(X,Y) )
& p(X) )
& ! [W] :
( ( p(h(W))
& p(g(W)) )
| ~ p(W) )
& ! [X0] :
? [X1] :
( ( p(X1)
& l(X0,g(h(X1))) )
| ~ p(X0) ) ),
inference(fof_nnf,[status(thm)],[thm72_neg]) ).
fof(sk_thm72_neg_sk,plain,
( ! [Y] :
( ~ p(Y)
| ~ l(sK0,Y) )
& p(sK0)
& ! [W] :
( ( p(h(W))
& p(g(W)) )
| ~ p(W) )
& ! [X0] :
( ( p(sK1(X0))
& l(X0,g(h(sK1(X0)))) )
| ~ p(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X1,sK1(X0)),skolemize(X,sK0)],[nnf_1]) ).
fof(sk_thm72_neg,plain,
( ! [VAR_0] :
( ~ p(VAR_0)
| ~ l(sK0,VAR_0) )
& p(sK0)
& ! [VAR_0] :
( p(h(VAR_0))
| ~ p(VAR_0) )
& ! [VAR_0] :
( p(g(VAR_0))
| ~ p(VAR_0) )
& ! [VAR_0] :
( p(sK1(VAR_0))
| ~ p(VAR_0) )
& ! [VAR_0] :
( l(VAR_0,g(h(sK1(VAR_0))))
| ~ p(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_thm72_neg_sk]) ).
cnf(c_2,negated_conjecture,
( ~ p(A)
| ~ l(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_thm72_neg]) ).
cnf(c_3,negated_conjecture,
( l(A,g(h(sK1(A))))
| ~ p(A) ),
inference(split_conjunct,[status(thm)],[sk_thm72_neg]) ).
cnf(c_4,negated_conjecture,
( ~ p(sK0)
| ~ p(g(h(sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_5,negated_conjecture,
p(sK0),
inference(split_conjunct,[status(thm)],[sk_thm72_neg]) ).
cnf(c_6,negated_conjecture,
( p(h(A))
| ~ p(A) ),
inference(split_conjunct,[status(thm)],[sk_thm72_neg]) ).
cnf(c_7,negated_conjecture,
( p(g(A))
| ~ p(A) ),
inference(split_conjunct,[status(thm)],[sk_thm72_neg]) ).
cnf(c_8,negated_conjecture,
( p(sK1(A))
| ~ p(A) ),
inference(split_conjunct,[status(thm)],[sk_thm72_neg]) ).
cnf(c_9,negated_conjecture,
~ p(g(h(sK1(sK0)))),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_12,negated_conjecture,
p(sK1(sK0)),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_13,plain,
~ p(h(sK1(sK0))),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_18,negated_conjecture,
~ p(sK1(sK0)),
inference(resolve,[status(thm)],[c_13,c_6]) ).
cnf(c_17,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_12,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN729+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.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 18:23:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 81199 was started by sandbox2 on n008,
% 0.11/0.38 % Sat Sep 26 18:23:24 2026
% 0.11/0.38 % 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 Theorem 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 12.
% 0.11/0.39 % Level of proof is 5.
% 0.11/0.39 % Maximum clause weight is 7.000.
% 0.11/0.39 % Given clauses 7.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------