%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN918+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 : Fri Sep 25 03:36:19 PM UTC 2026
% Result : Theorem 2.13s 6.11s
% Output : Proof 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 121 ( 36 ~; 47 |; 24 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 49 ( 9 sgn 18 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ! [X] :
( ( ( g(X)
& f(X) )
=> h(X) )
=> ? [Y] :
( ~ g(Y)
& f(Y) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f0_neg,negated_conjecture,
~ ( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ! [X] :
( ( ( g(X)
& f(X) )
=> h(X) )
=> ? [Y] :
( ~ g(Y)
& f(Y) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,W,Z,R,V] :
( ( h(V)
| ~ g(V)
| ~ f(V) )
& ( g(R)
| ~ h(R)
| ~ f(R) )
& ( h(Z)
| ~ f(Z)
| g(W)
| ~ f(W) )
& ( ( ~ g(sk0(X))
& f(sk0(X)) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c6,plain,
( h(X3)
| ~ f(X3)
| g(X2)
| ~ f(X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p11,plain,
( h(X0)
| g(X0)
| ~ f(X0) ),
inference(factoring,[status(thm)],[c6]) ).
cnf(c0,plain,
( f(sk0(X0))
| f(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p14,plain,
( f(X0)
| h(sk0(X0))
| g(sk0(X0)) ),
inference(resolution,[status(thm)],[p11,c0]) ).
cnf(c7,plain,
( g(X4)
| ~ h(X4)
| ~ f(X4) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p9,plain,
( f(X0)
| g(sk0(X0))
| ~ h(sk0(X0)) ),
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(p16,plain,
( f(X0)
| g(sk0(X0))
| f(X0)
| g(sk0(X0)) ),
inference(resolution,[status(thm)],[p14,p9]) ).
cnf(p23,plain,
( f(X0)
| f(X0)
| g(sk0(X0)) ),
inference(factoring,[status(thm)],[p16]) ).
cnf(p25,plain,
( f(X0)
| g(sk0(X0)) ),
inference(factoring,[status(thm)],[p23]) ).
cnf(c1,plain,
( ~ g(sk0(X0))
| f(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p26,plain,
( f(X0)
| f(X0) ),
inference(resolution,[status(thm)],[p25,c1]) ).
cnf(p30,plain,
f(X0),
inference(factoring,[status(thm)],[p26]) ).
cnf(p33,plain,
( h(X1)
| ~ f(X1)
| g(X0) ),
inference(resolution,[status(thm)],[p30,c6]) ).
cnf(p39,plain,
( h(X1)
| g(X0) ),
inference(resolution,[status(thm)],[p33,p30]) ).
cnf(p31,plain,
( g(X0)
| ~ h(X0) ),
inference(resolution,[status(thm)],[p30,c7]) ).
cnf(p41,plain,
( g(X1)
| g(X0) ),
inference(resolution,[status(thm)],[p39,p31]) ).
cnf(p43,plain,
g(X0),
inference(factoring,[status(thm)],[p41]) ).
cnf(c8,plain,
( h(X5)
| ~ g(X5)
| ~ f(X5) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p32,plain,
( h(X0)
| ~ g(X0) ),
inference(resolution,[status(thm)],[p30,c8]) ).
cnf(p44,plain,
h(X0),
inference(resolution,[status(thm)],[p43,p32]) ).
cnf(c5,plain,
( ~ g(sk0(X0))
| ~ h(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p45,plain,
~ g(sk0(X0)),
inference(resolution,[status(thm)],[p44,c5]) ).
cnf(p46,plain,
$false,
inference(resolution,[status(thm)],[p45,p43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN918+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/5.37 % Computer : n004.cluster.edu
% 0.07/5.37 % Model : x86_64 x86_64
% 0.07/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.37 % Memory : 8046.5625MB
% 0.07/5.37 % OS : Linux 6.8.0-71-generic
% 0.07/5.37 % CPULimit : 300
% 0.07/5.37 % WCLimit : 300
% 0.07/5.37 % DateTime : Fri Sep 25 02:34:27 UTC 2026
% 0.07/5.37 % CPUTime :
% 0.07/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.13/6.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.13/6.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------