%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN351+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 03:34:27 PM UTC 2026
% Result : Theorem 2.36s 0.78s
% Output : Proof 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 4 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 60 ( 17 ~; 11 |; 18 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 4 sgn 10 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,Y2,X1,Z)
=> ( ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
=> ( big_f(X1,Y1,X1,Y2)
=> ( ( big_f(X1,Z,Y1,Z)
=> ( big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) )
& ( big_f(X1,Y2,Y1,Y2)
=> big_f(X1,Z,Y1,Z) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_3) ).
fof(f0_neg,negated_conjecture,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,Y2,X1,Z)
=> ( ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
=> ( big_f(X1,Y1,X1,Y2)
=> ( ( big_f(X1,Z,Y1,Z)
=> ( big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) )
& ( big_f(X1,Y2,Y1,Y2)
=> big_f(X1,Z,Y1,Z) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ( ( ( big_f(X1,Y2,Y1,Y2)
& ~ big_f(X1,Y1,X1,Y2) )
| ( ~ big_f(X1,Y2,Y1,Y2)
& big_f(X1,Y1,X1,Y2) ) )
& big_f(X1,Z,Y1,Z) )
| ( ~ big_f(X1,Z,Y1,Z)
& big_f(X1,Y2,Y1,Y2) ) )
& big_f(X1,Y1,X1,Y2)
& ( ~ big_f(Y1,X2,Y1,Y2)
| big_f(X1,Y1,X1,Y2) )
& ( big_f(Y1,X2,Y1,Y2)
| ~ big_f(X1,Y1,X1,Y2) )
& big_f(X1,Y2,X1,Z) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y2,Y1] :
( ( ( ( ( big_f(sk0,Y2,Y1,Y2)
& ~ big_f(sk0,Y1,sk0,Y2) )
| ( ~ big_f(sk0,Y2,Y1,Y2)
& big_f(sk0,Y1,sk0,Y2) ) )
& big_f(sk0,sk2(Y1,Y2),Y1,sk2(Y1,Y2)) )
| ( ~ big_f(sk0,sk2(Y1,Y2),Y1,sk2(Y1,Y2))
& big_f(sk0,Y2,Y1,Y2) ) )
& big_f(sk0,Y1,sk0,Y2)
& ( ~ big_f(Y1,sk1,Y1,Y2)
| big_f(sk0,Y1,sk0,Y2) )
& ( big_f(Y1,sk1,Y1,Y2)
| ~ big_f(sk0,Y1,sk0,Y2) )
& big_f(sk0,Y2,sk0,sk2(Y1,Y2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c12,plain,
( ~ big_f(sk0,X2,sk0,X3)
| ~ big_f(sk0,X3,X2,X3)
| ~ big_f(sk0,sk2(X2,X3),X2,sk2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c3,plain,
big_f(sk0,X2,sk0,X3),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p17,plain,
( ~ big_f(sk0,sk0,sk0,X0)
| ~ big_f(sk0,X0,sk0,X0) ),
inference(resolution,[status(thm)],[c12,c3]) ).
cnf(p19,plain,
~ big_f(sk0,sk0,sk0,X0),
inference(resolution,[status(thm)],[p17,c3]) ).
cnf(c0,plain,
big_f(sk0,X3,sk0,sk2(X2,X3)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p20,plain,
$false,
inference(resolution,[status(thm)],[p19,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN351+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Sep 25 00:58:51 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.36/0.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.36/0.78 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------