%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN321+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 : n014.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 03:34:20 PM UTC 2026
% Result : Theorem 4.25s 1.08s
% Output : Proof 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 4 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 43 ( 14 ~; 11 |; 8 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 40 ( 11 sgn 15 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
? [X,Y] :
( ( ? [Z] : big_f(X,Z)
=> ! [Z] : big_g(X,Z) )
=> ( ! [Z] :
( big_g(Z,Z)
=> big_f(Z,Y) )
=> ( big_f(X,Y)
<=> ! [Z] : big_g(X,Z) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_3_2) ).
fof(f0_neg,negated_conjecture,
~ ? [X,Y] :
( ( ? [Z] : big_f(X,Z)
=> ! [Z] : big_g(X,Z) )
=> ( ! [Z] :
( big_g(Z,Z)
=> big_f(Z,Y) )
=> ( big_f(X,Y)
<=> ! [Z] : big_g(X,Z) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
! [X,Y] :
( ( ( ! [Z] : big_g(X,Z)
& ~ big_f(X,Y) )
| ( ? [Z] : ~ big_g(X,Z)
& big_f(X,Y) ) )
& ! [Z] :
( big_f(Z,Y)
| ~ big_g(Z,Z) )
& ( ! [Z] : big_g(X,Z)
| ! [Z] : ~ big_f(X,Z) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Z,Y] :
( ( ( big_g(X,Z)
& ~ big_f(X,Y) )
| ( ~ big_g(X,sk0(X,Y))
& big_f(X,Y) ) )
& ( big_f(Z,Y)
| ~ big_g(Z,Z) )
& ( big_g(X,Z)
| ~ big_f(X,Z) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c4,plain,
( ~ big_f(X0,X1)
| ~ big_g(X0,sk0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c3,plain,
( big_g(X0,X2)
| big_f(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c0,plain,
( big_g(X0,X2)
| ~ big_f(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p6,plain,
( big_g(X0,X2)
| big_g(X0,X1) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(p8,plain,
big_g(X0,X1),
inference(factoring,[status(thm)],[p6]) ).
cnf(p10,plain,
~ big_f(X0,X1),
inference(resolution,[status(thm)],[c4,p8]) ).
cnf(c1,plain,
( big_f(X2,X1)
| ~ big_g(X2,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p9,plain,
big_f(X0,X1),
inference(resolution,[status(thm)],[p8,c1]) ).
cnf(p11,plain,
$false,
inference(resolution,[status(thm)],[p10,p9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN321+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 00:49:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.25/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.25/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------