%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN349+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 : n019.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 0.15s 5.81s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 5 unt; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 138 ( 47 ~; 55 |; 26 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 40 ( 0 sgn 8 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
? [X1] :
! [X2] :
? [X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X2,X4) )
=> ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<=> big_f(X4,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_17_5) ).
fof(f0_neg,negated_conjecture,
~ ? [X1] :
! [X2] :
? [X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X2,X4) )
=> ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<=> big_f(X4,X2) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
! [X1] :
? [X2] :
! [X3] :
? [X4] :
( ( ( big_f(X4,X2)
& ( ( big_f(X3,X4)
& ( ( big_f(X4,X3)
& ~ big_f(X1,X4) )
| ( ~ big_f(X4,X3)
& big_f(X1,X4) ) ) )
| ( ~ big_f(X3,X4)
& ( ~ big_f(X4,X3)
| big_f(X1,X4) )
& ( big_f(X4,X3)
| ~ big_f(X1,X4) ) ) ) )
| ( ~ big_f(X4,X2)
& ( ~ big_f(X3,X4)
| ( ( ~ big_f(X4,X3)
| big_f(X1,X4) )
& ( big_f(X4,X3)
| ~ big_f(X1,X4) ) ) )
& ( big_f(X3,X4)
| ( big_f(X4,X3)
& ~ big_f(X1,X4) )
| ( ~ big_f(X4,X3)
& big_f(X1,X4) ) ) ) )
& ( ~ big_f(X2,X4)
| big_f(X1,X4) )
& ( big_f(X2,X4)
| ~ big_f(X1,X4) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X1,X3] :
( ( ( big_f(sk1(X1,X3),sk0(X1))
& ( ( big_f(X3,sk1(X1,X3))
& ( ( big_f(sk1(X1,X3),X3)
& ~ big_f(X1,sk1(X1,X3)) )
| ( ~ big_f(sk1(X1,X3),X3)
& big_f(X1,sk1(X1,X3)) ) ) )
| ( ~ big_f(X3,sk1(X1,X3))
& ( ~ big_f(sk1(X1,X3),X3)
| big_f(X1,sk1(X1,X3)) )
& ( big_f(sk1(X1,X3),X3)
| ~ big_f(X1,sk1(X1,X3)) ) ) ) )
| ( ~ big_f(sk1(X1,X3),sk0(X1))
& ( ~ big_f(X3,sk1(X1,X3))
| ( ( ~ big_f(sk1(X1,X3),X3)
| big_f(X1,sk1(X1,X3)) )
& ( big_f(sk1(X1,X3),X3)
| ~ big_f(X1,sk1(X1,X3)) ) ) )
& ( big_f(X3,sk1(X1,X3))
| ( big_f(sk1(X1,X3),X3)
& ~ big_f(X1,sk1(X1,X3)) )
| ( ~ big_f(sk1(X1,X3),X3)
& big_f(X1,sk1(X1,X3)) ) ) ) )
& ( ~ big_f(sk0(X1),sk1(X1,X3))
| big_f(X1,sk1(X1,X3)) )
& ( big_f(sk0(X1),sk1(X1,X3))
| ~ big_f(X1,sk1(X1,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c107,plain,
( big_f(X2,sk1(X0,X2))
| ~ big_f(sk1(X0,X2),X2)
| big_f(X0,sk1(X0,X2))
| ~ big_f(sk1(X0,X2),sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p118,plain,
( big_f(sk0(X0),sk1(X0,sk0(X0)))
| big_f(X0,sk1(X0,sk0(X0)))
| ~ big_f(sk1(X0,sk0(X0)),sk0(X0)) ),
inference(factoring,[status(thm)],[c107]) ).
cnf(c33,plain,
( big_f(sk1(X0,X2),sk0(X0))
| big_f(X2,sk1(X0,X2))
| big_f(sk1(X0,X2),X2)
| big_f(X0,sk1(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p115,plain,
( big_f(sk0(X0),sk1(X0,sk0(X0)))
| big_f(sk1(X0,sk0(X0)),sk0(X0))
| big_f(X0,sk1(X0,sk0(X0))) ),
inference(factoring,[status(thm)],[c33]) ).
cnf(p122,plain,
( big_f(sk0(X0),sk1(X0,sk0(X0)))
| big_f(X0,sk1(X0,sk0(X0)))
| big_f(sk0(X0),sk1(X0,sk0(X0)))
| big_f(X0,sk1(X0,sk0(X0))) ),
inference(resolution,[status(thm)],[p118,p115]) ).
cnf(p123,plain,
( big_f(sk0(X0),sk1(X0,sk0(X0)))
| big_f(sk0(X0),sk1(X0,sk0(X0)))
| big_f(X0,sk1(X0,sk0(X0))) ),
inference(factoring,[status(thm)],[p122]) ).
cnf(p125,plain,
( big_f(sk0(X0),sk1(X0,sk0(X0)))
| big_f(X0,sk1(X0,sk0(X0))) ),
inference(factoring,[status(thm)],[p123]) ).
cnf(c1,plain,
( ~ big_f(sk0(X0),sk1(X0,X2))
| big_f(X0,sk1(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p126,plain,
( big_f(X0,sk1(X0,sk0(X0)))
| big_f(X0,sk1(X0,sk0(X0))) ),
inference(resolution,[status(thm)],[p125,c1]) ).
cnf(p127,plain,
big_f(X0,sk1(X0,sk0(X0))),
inference(factoring,[status(thm)],[p126]) ).
cnf(c81,plain,
( big_f(sk1(X0,X2),sk0(X0))
| ~ big_f(X2,sk1(X0,X2))
| big_f(sk1(X0,X2),X2)
| ~ big_f(X0,sk1(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p117,plain,
( ~ big_f(sk0(X0),sk1(X0,sk0(X0)))
| big_f(sk1(X0,sk0(X0)),sk0(X0))
| ~ big_f(X0,sk1(X0,sk0(X0))) ),
inference(factoring,[status(thm)],[c81]) ).
cnf(p130,plain,
( ~ big_f(sk0(X0),sk1(X0,sk0(X0)))
| big_f(sk1(X0,sk0(X0)),sk0(X0)) ),
inference(resolution,[status(thm)],[p127,p117]) ).
cnf(c0,plain,
( big_f(sk0(X0),sk1(X0,X2))
| ~ big_f(X0,sk1(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p128,plain,
big_f(sk0(X0),sk1(X0,sk0(X0))),
inference(resolution,[status(thm)],[p127,c0]) ).
cnf(p131,plain,
big_f(sk1(X0,sk0(X0)),sk0(X0)),
inference(resolution,[status(thm)],[p130,p128]) ).
cnf(c110,plain,
( ~ big_f(X0,sk1(X0,X2))
| ~ big_f(sk1(X0,X2),X2)
| ~ big_f(X2,sk1(X0,X2))
| ~ big_f(sk1(X0,X2),sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p120,plain,
( ~ big_f(X0,sk1(X0,sk0(X0)))
| ~ big_f(sk0(X0),sk1(X0,sk0(X0)))
| ~ big_f(sk1(X0,sk0(X0)),sk0(X0)) ),
inference(factoring,[status(thm)],[c110]) ).
cnf(p132,plain,
( ~ big_f(X0,sk1(X0,sk0(X0)))
| ~ big_f(sk0(X0),sk1(X0,sk0(X0))) ),
inference(resolution,[status(thm)],[p131,p120]) ).
cnf(p133,plain,
~ big_f(X0,sk1(X0,sk0(X0))),
inference(resolution,[status(thm)],[p132,p128]) ).
cnf(p134,plain,
$false,
inference(resolution,[status(thm)],[p133,p127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN349+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n019.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 00:56:26 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/5.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.81 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------