%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN352+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 : n011.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 03:34:28 PM UTC 2026
% Result : Theorem 3.36s 6.11s
% Output : Proof 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 88 ( 26 ~; 28 |; 18 &)
% ( 4 <=>; 12 =>; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 2 sgn 10 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,X2)
=> ( ( big_f(Y1,Y2)
=> ( big_f(Y2,Z)
| big_f(X2,Z) ) )
=> ( ( ( big_f(Y1,Y2)
=> ( big_f(X2,Z)
<=> big_f(Y1,Z) ) )
=> big_f(Z,Z) )
=> ( ( big_f(Y1,Z)
<=> big_f(Y2,Z) )
& big_f(Y1,Y2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_4) ).
fof(f0_neg,negated_conjecture,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,X2)
=> ( ( big_f(Y1,Y2)
=> ( big_f(Y2,Z)
| big_f(X2,Z) ) )
=> ( ( ( big_f(Y1,Y2)
=> ( big_f(X2,Z)
<=> big_f(Y1,Z) ) )
=> big_f(Z,Z) )
=> ( ( big_f(Y1,Z)
<=> big_f(Y2,Z) )
& big_f(Y1,Y2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ( big_f(Y2,Z)
& ~ big_f(Y1,Z) )
| ( ~ big_f(Y2,Z)
& big_f(Y1,Z) )
| ~ big_f(Y1,Y2) )
& ( big_f(Z,Z)
| ( ( ( big_f(Y1,Z)
& ~ big_f(X2,Z) )
| ( ~ big_f(Y1,Z)
& big_f(X2,Z) ) )
& big_f(Y1,Y2) ) )
& ( big_f(Y2,Z)
| big_f(X2,Z)
| ~ big_f(Y1,Y2) )
& big_f(X1,X2) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y1,Y2] :
( ( ( big_f(Y2,sk2(Y1,Y2))
& ~ big_f(Y1,sk2(Y1,Y2)) )
| ( ~ big_f(Y2,sk2(Y1,Y2))
& big_f(Y1,sk2(Y1,Y2)) )
| ~ big_f(Y1,Y2) )
& ( big_f(sk2(Y1,Y2),sk2(Y1,Y2))
| ( ( ( big_f(Y1,sk2(Y1,Y2))
& ~ big_f(sk1,sk2(Y1,Y2)) )
| ( ~ big_f(Y1,sk2(Y1,Y2))
& big_f(sk1,sk2(Y1,Y2)) ) )
& big_f(Y1,Y2) ) )
& ( big_f(Y2,sk2(Y1,Y2))
| big_f(sk1,sk2(Y1,Y2))
| ~ big_f(Y1,Y2) )
& big_f(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c9,plain,
( ~ big_f(X2,sk2(X2,X3))
| ~ big_f(X3,sk2(X2,X3))
| ~ big_f(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p26,plain,
( ~ big_f(X0,sk2(X0,X0))
| ~ big_f(X0,X0) ),
inference(factoring,[status(thm)],[c9]) ).
cnf(c2,plain,
( big_f(sk2(X2,X3),sk2(X2,X3))
| big_f(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p32,plain,
( big_f(X0,X1)
| ~ big_f(sk2(X0,X1),sk2(sk2(X0,X1),sk2(X0,X1))) ),
inference(resolution,[status(thm)],[p26,c2]) ).
cnf(c8,plain,
( big_f(X3,sk2(X2,X3))
| big_f(X2,sk2(X2,X3))
| ~ big_f(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p16,plain,
( big_f(X0,sk2(X0,X0))
| ~ big_f(X0,X0) ),
inference(factoring,[status(thm)],[c8]) ).
cnf(p18,plain,
( big_f(X0,X1)
| big_f(sk2(X0,X1),sk2(sk2(X0,X1),sk2(X0,X1))) ),
inference(resolution,[status(thm)],[p16,c2]) ).
cnf(p41,plain,
( big_f(X0,X1)
| big_f(X0,X1) ),
inference(resolution,[status(thm)],[p32,p18]) ).
cnf(p42,plain,
big_f(X0,X1),
inference(factoring,[status(thm)],[p41]) ).
cnf(c0,plain,
big_f(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p27,plain,
( ~ big_f(sk0,sk2(sk0,sk1))
| ~ big_f(sk1,sk2(sk0,sk1)) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(c1,plain,
( big_f(X3,sk2(X2,X3))
| big_f(sk1,sk2(X2,X3))
| ~ big_f(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p11,plain,
( big_f(sk1,sk2(X0,sk1))
| ~ big_f(X0,sk1) ),
inference(factoring,[status(thm)],[c1]) ).
cnf(p14,plain,
big_f(sk1,sk2(sk0,sk1)),
inference(resolution,[status(thm)],[p11,c0]) ).
cnf(p35,plain,
~ big_f(sk0,sk2(sk0,sk1)),
inference(resolution,[status(thm)],[p27,p14]) ).
cnf(p45,plain,
$false,
inference(resolution,[status(thm)],[p42,p35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN352+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.59 % Computer : n011.cluster.edu
% 0.09/5.59 % Model : x86_64 x86_64
% 0.09/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.59 % Memory : 8046.5625MB
% 0.09/5.59 % OS : Linux 6.8.0-71-generic
% 0.09/5.59 % CPULimit : 300
% 0.09/5.59 % WCLimit : 300
% 0.09/5.59 % DateTime : Fri Sep 25 00:57:04 UTC 2026
% 0.14/5.60 % CPUTime :
% 0.14/5.60 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.36/6.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.36/6.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------