%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN347+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 : n007.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 03:34:26 PM UTC 2026
% Result : Theorem 3.16s 0.83s
% Output : Proof 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 4 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 82 ( 28 ~; 32 |; 16 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 10 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
! [Z1,Z2] :
? [X1,X2] :
! [Y] :
( ( big_f(Z1,Y)
<=> big_f(Z2,Y) )
| ( ( big_f(X1,Y)
<=> big_f(X2,Y) )
<=> big_f(Z1,Z2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_17_3) ).
fof(f0_neg,negated_conjecture,
~ ! [Z1,Z2] :
? [X1,X2] :
! [Y] :
( ( big_f(Z1,Y)
<=> big_f(Z2,Y) )
| ( ( big_f(X1,Y)
<=> big_f(X2,Y) )
<=> big_f(Z1,Z2) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [Z1,Z2] :
! [X1,X2] :
? [Y] :
( ( ( big_f(Z2,Y)
& ~ big_f(Z1,Y) )
| ( ~ big_f(Z2,Y)
& big_f(Z1,Y) ) )
& ( ( big_f(Z1,Z2)
& ( ( big_f(X2,Y)
& ~ big_f(X1,Y) )
| ( ~ big_f(X2,Y)
& big_f(X1,Y) ) ) )
| ( ~ big_f(Z1,Z2)
& ( ~ big_f(X2,Y)
| big_f(X1,Y) )
& ( big_f(X2,Y)
| ~ big_f(X1,Y) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X1,X2] :
( ( ( big_f(sk1,sk2(X1,X2))
& ~ big_f(sk0,sk2(X1,X2)) )
| ( ~ big_f(sk1,sk2(X1,X2))
& big_f(sk0,sk2(X1,X2)) ) )
& ( ( big_f(sk0,sk1)
& ( ( big_f(X2,sk2(X1,X2))
& ~ big_f(X1,sk2(X1,X2)) )
| ( ~ big_f(X2,sk2(X1,X2))
& big_f(X1,sk2(X1,X2)) ) ) )
| ( ~ big_f(sk0,sk1)
& ( ~ big_f(X2,sk2(X1,X2))
| big_f(X1,sk2(X1,X2)) )
& ( big_f(X2,sk2(X1,X2))
| ~ big_f(X1,sk2(X1,X2)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c4,plain,
( big_f(sk0,sk1)
| big_f(X3,sk2(X2,X3))
| ~ big_f(X2,sk2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c16,plain,
( big_f(sk1,sk2(X2,X3))
| big_f(sk0,sk2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p19,plain,
( big_f(sk0,sk2(sk1,X0))
| big_f(sk0,sk1)
| big_f(X0,sk2(sk1,X0)) ),
inference(resolution,[status(thm)],[c4,c16]) ).
cnf(p23,plain,
( big_f(sk0,sk1)
| big_f(sk0,sk2(sk1,sk0)) ),
inference(factoring,[status(thm)],[p19]) ).
cnf(c9,plain,
( big_f(sk0,sk1)
| ~ big_f(X3,sk2(X2,X3))
| big_f(X2,sk2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p24,plain,
( big_f(sk0,sk1)
| big_f(sk1,sk2(sk1,sk0))
| big_f(sk0,sk1) ),
inference(resolution,[status(thm)],[p23,c9]) ).
cnf(p25,plain,
( big_f(sk1,sk2(sk1,sk0))
| big_f(sk0,sk1) ),
inference(factoring,[status(thm)],[p24]) ).
cnf(c17,plain,
( ~ big_f(sk0,sk2(X2,X3))
| ~ big_f(sk1,sk2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p26,plain,
( ~ big_f(sk0,sk2(sk1,sk0))
| big_f(sk0,sk1) ),
inference(resolution,[status(thm)],[p25,c17]) ).
cnf(p27,plain,
( big_f(sk0,sk1)
| big_f(sk0,sk1) ),
inference(resolution,[status(thm)],[p26,p23]) ).
cnf(p28,plain,
big_f(sk0,sk1),
inference(factoring,[status(thm)],[p27]) ).
cnf(c12,plain,
( ~ big_f(X2,sk2(X2,X3))
| ~ big_f(X3,sk2(X2,X3))
| ~ big_f(sk0,sk1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p22,plain,
( ~ big_f(X0,sk2(X0,X0))
| ~ big_f(sk0,sk1) ),
inference(factoring,[status(thm)],[c12]) ).
cnf(p32,plain,
~ big_f(X0,sk2(X0,X0)),
inference(resolution,[status(thm)],[p28,p22]) ).
cnf(c11,plain,
( big_f(X3,sk2(X2,X3))
| big_f(X2,sk2(X2,X3))
| ~ big_f(sk0,sk1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p21,plain,
( big_f(X0,sk2(X0,X0))
| ~ big_f(sk0,sk1) ),
inference(factoring,[status(thm)],[c11]) ).
cnf(p30,plain,
big_f(X0,sk2(X0,X0)),
inference(resolution,[status(thm)],[p28,p21]) ).
cnf(p37,plain,
$false,
inference(resolution,[status(thm)],[p32,p30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN347+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 00:53:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.16/0.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.16/0.83 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------