%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN350+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 : 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 : Fri Sep 25 03:34:27 PM UTC 2026
% Result : Theorem 4.31s 6.28s
% Output : Proof 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 57 ( 20 ~; 15 |; 14 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 24 ( 3 sgn 8 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
! [X] :
? [Y1,Y2] :
! [Z] :
( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( big_f(X,Z)
<=> ( ( big_f(Y1,Z)
=> big_f(Y1,Y2) )
& big_f(Y2,Z) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_2) ).
fof(f0_neg,negated_conjecture,
~ ! [X] :
? [Y1,Y2] :
! [Z] :
( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( big_f(X,Z)
<=> ( ( big_f(Y1,Z)
=> big_f(Y1,Y2) )
& big_f(Y2,Z) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [X] :
! [Y1,Y2] :
? [Z] :
( ( ( ( big_f(Y1,Y2)
| ~ big_f(Y1,Z) )
& big_f(Y2,Z)
& ~ big_f(X,Z) )
| ( ( ( ~ big_f(Y1,Y2)
& big_f(Y1,Z) )
| ~ big_f(Y2,Z) )
& big_f(X,Z) ) )
& ( ~ big_f(Z,X)
| big_f(X,Z) )
& ( big_f(Z,X)
| ~ big_f(X,Z) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y1,Y2] :
( ( ( ( big_f(Y1,Y2)
| ~ big_f(Y1,sk1(Y1,Y2)) )
& big_f(Y2,sk1(Y1,Y2))
& ~ big_f(sk0,sk1(Y1,Y2)) )
| ( ( ( ~ big_f(Y1,Y2)
& big_f(Y1,sk1(Y1,Y2)) )
| ~ big_f(Y2,sk1(Y1,Y2)) )
& big_f(sk0,sk1(Y1,Y2)) ) )
& ( ~ big_f(sk1(Y1,Y2),sk0)
| big_f(sk0,sk1(Y1,Y2)) )
& ( big_f(sk1(Y1,Y2),sk0)
| ~ big_f(sk0,sk1(Y1,Y2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c8,plain,
( ~ big_f(sk0,sk1(X1,X2))
| ~ big_f(X1,X2)
| ~ big_f(X2,sk1(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p15,plain,
( ~ big_f(X0,sk0)
| ~ big_f(sk0,sk1(X0,sk0)) ),
inference(factoring,[status(thm)],[c8]) ).
cnf(c3,plain,
( big_f(X2,sk1(X1,X2))
| big_f(sk0,sk1(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p11,plain,
big_f(sk0,sk1(X0,sk0)),
inference(factoring,[status(thm)],[c3]) ).
cnf(p20,plain,
~ big_f(X0,sk0),
inference(resolution,[status(thm)],[p15,p11]) ).
cnf(c0,plain,
( big_f(sk1(X1,X2),sk0)
| ~ big_f(sk0,sk1(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p16,plain,
big_f(sk1(X0,sk0),sk0),
inference(resolution,[status(thm)],[p11,c0]) ).
cnf(p23,plain,
$false,
inference(resolution,[status(thm)],[p20,p16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN350+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.57 % Computer : n008.cluster.edu
% 0.10/5.57 % Model : x86_64 x86_64
% 0.10/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.57 % Memory : 8046.5625MB
% 0.10/5.57 % OS : Linux 6.8.0-71-generic
% 0.10/5.57 % CPULimit : 300
% 0.10/5.57 % WCLimit : 300
% 0.10/5.57 % DateTime : Fri Sep 25 00:57:16 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.31/6.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.31/6.28 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------