%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN328+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 03:34:22 PM UTC 2026
% Result : Theorem 0.15s 10.79s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 38 ( 5 unt; 0 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 158 ( 43 ~; 71 |; 24 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 43 ( 4 sgn 6 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
? [X] :
! [Y,Z] :
( ( ( big_f(Y)
=> big_g(Y) )
<=> big_f(X) )
=> ( ( ( big_f(Y)
=> big_h(Y) )
<=> big_g(X) )
=> ( ( ( ( big_f(Y)
=> big_g(Y) )
=> big_h(Y) )
<=> big_h(X) )
=> ( big_h(Z)
& big_g(Z)
& big_f(Z) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_12_3) ).
fof(f0_neg,negated_conjecture,
~ ? [X] :
! [Y,Z] :
( ( ( big_f(Y)
=> big_g(Y) )
<=> big_f(X) )
=> ( ( ( big_f(Y)
=> big_h(Y) )
<=> big_g(X) )
=> ( ( ( ( big_f(Y)
=> big_g(Y) )
=> big_h(Y) )
<=> big_h(X) )
=> ( big_h(Z)
& big_g(Z)
& big_f(Z) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
! [X] :
? [Y,Z] :
( ( ~ big_h(Z)
| ~ big_g(Z)
| ~ big_f(Z) )
& ( ~ big_h(X)
| big_h(Y)
| ( ~ big_g(Y)
& big_f(Y) ) )
& ( big_h(X)
| ( ~ big_h(Y)
& ( big_g(Y)
| ~ big_f(Y) ) ) )
& ( ~ big_g(X)
| big_h(Y)
| ~ big_f(Y) )
& ( big_g(X)
| ( ~ big_h(Y)
& big_f(Y) ) )
& ( ~ big_f(X)
| big_g(Y)
| ~ big_f(Y) )
& ( big_f(X)
| ( ~ big_g(Y)
& big_f(Y) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X] :
( ( ~ big_h(sk1(X))
| ~ big_g(sk1(X))
| ~ big_f(sk1(X)) )
& ( ~ big_h(X)
| big_h(sk0(X))
| ( ~ big_g(sk0(X))
& big_f(sk0(X)) ) )
& ( big_h(X)
| ( ~ big_h(sk0(X))
& ( big_g(sk0(X))
| ~ big_f(sk0(X)) ) ) )
& ( ~ big_g(X)
| big_h(sk0(X))
| ~ big_f(sk0(X)) )
& ( big_g(X)
| ( ~ big_h(sk0(X))
& big_f(sk0(X)) ) )
& ( ~ big_f(X)
| big_g(sk0(X))
| ~ big_f(sk0(X)) )
& ( big_f(X)
| ( ~ big_g(sk0(X))
& big_f(sk0(X)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c6,plain,
( big_h(X0)
| big_g(sk0(X0))
| ~ big_f(sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c0,plain,
( big_f(X0)
| big_f(sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p13,plain,
( big_f(X0)
| big_h(X0)
| big_g(sk0(X0)) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(c1,plain,
( big_f(X0)
| ~ big_g(sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p17,plain,
( big_f(X0)
| big_f(X0)
| big_h(X0) ),
inference(resolution,[status(thm)],[p13,c1]) ).
cnf(p20,plain,
( big_f(X0)
| big_h(X0) ),
inference(factoring,[status(thm)],[p17]) ).
cnf(c7,plain,
( big_h(X0)
| ~ big_h(sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p21,plain,
( big_h(X0)
| big_f(sk0(X0)) ),
inference(resolution,[status(thm)],[p20,c7]) ).
cnf(c5,plain,
( ~ big_g(X0)
| big_h(sk0(X0))
| ~ big_f(sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p23,plain,
( ~ big_g(X0)
| big_h(sk0(X0))
| big_h(X0) ),
inference(resolution,[status(thm)],[p21,c5]) ).
cnf(c3,plain,
( big_g(X0)
| big_f(sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c2,plain,
( ~ big_f(X0)
| big_g(sk0(X0))
| ~ big_f(sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p11,plain,
( ~ big_f(X0)
| big_g(sk0(X0))
| big_g(X0) ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(p15,plain,
( big_f(X0)
| big_g(sk0(sk0(X0)))
| big_g(sk0(X0)) ),
inference(resolution,[status(thm)],[p11,c0]) ).
cnf(p30,plain,
( big_f(X0)
| big_g(sk0(X0))
| big_h(sk0(sk0(sk0(X0))))
| big_h(sk0(sk0(X0))) ),
inference(resolution,[status(thm)],[p23,p15]) ).
cnf(p34,plain,
( big_h(sk0(sk0(X0)))
| big_f(X0)
| big_g(sk0(X0))
| big_h(sk0(sk0(X0))) ),
inference(resolution,[status(thm)],[p30,c7]) ).
cnf(p38,plain,
( big_f(X0)
| big_g(sk0(X0))
| big_h(sk0(sk0(X0))) ),
inference(factoring,[status(thm)],[p34]) ).
cnf(c4,plain,
( big_g(X0)
| ~ big_h(sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p43,plain,
( big_g(sk0(X0))
| big_f(X0)
| big_g(sk0(X0)) ),
inference(resolution,[status(thm)],[p38,c4]) ).
cnf(p49,plain,
( big_f(X0)
| big_g(sk0(X0)) ),
inference(factoring,[status(thm)],[p43]) ).
cnf(p52,plain,
( big_f(X0)
| big_f(X0) ),
inference(resolution,[status(thm)],[p49,c1]) ).
cnf(p57,plain,
big_f(X0),
inference(factoring,[status(thm)],[p52]) ).
cnf(c10,plain,
( ~ big_h(sk1(X0))
| ~ big_g(sk1(X0))
| ~ big_f(sk1(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p59,plain,
( ~ big_h(sk1(X0))
| ~ big_g(sk1(X0)) ),
inference(resolution,[status(thm)],[p57,c10]) ).
cnf(p24,plain,
( big_h(X0)
| big_g(sk0(X0))
| big_h(X0) ),
inference(resolution,[status(thm)],[p21,c6]) ).
cnf(p32,plain,
( big_g(sk0(X0))
| big_h(X0) ),
inference(factoring,[status(thm)],[p24]) ).
cnf(p36,plain,
( big_h(sk0(sk0(X0)))
| big_h(sk0(X0))
| big_h(X0) ),
inference(resolution,[status(thm)],[p32,p23]) ).
cnf(p40,plain,
( big_h(sk0(X0))
| big_h(sk0(X0))
| big_h(X0) ),
inference(resolution,[status(thm)],[p36,c7]) ).
cnf(p47,plain,
( big_h(sk0(X0))
| big_h(X0) ),
inference(factoring,[status(thm)],[p40]) ).
cnf(p51,plain,
( big_h(X0)
| big_h(X0) ),
inference(resolution,[status(thm)],[p47,c7]) ).
cnf(p56,plain,
big_h(X0),
inference(factoring,[status(thm)],[p51]) ).
cnf(p58,plain,
big_g(X0),
inference(resolution,[status(thm)],[p56,c4]) ).
cnf(p60,plain,
~ big_h(sk1(X0)),
inference(resolution,[status(thm)],[p59,p58]) ).
cnf(p61,plain,
$false,
inference(resolution,[status(thm)],[p60,p56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN328+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/10.38 % Computer : n002.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Fri Sep 25 00:53:30 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/10.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/10.79 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------