%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN331+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 : n010.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 03:34:23 PM UTC 2026
% Result : Theorem 3.59s 1.08s
% Output : Proof 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 4 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 46 ( 11 ~; 13 |; 12 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 22 ( 3 sgn 6 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
? [X,Y] :
! [Z] :
( big_f(X,Z)
=> ( big_f(Y,Z)
=> ( ( big_f(X,Y)
<=> big_f(Z,Z) )
=> ( ( big_f(Z,Z)
| big_f(Y,X) )
=> ( big_f(Z,Y)
| big_f(Z,X) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_3) ).
fof(f0_neg,negated_conjecture,
~ ? [X,Y] :
! [Z] :
( big_f(X,Z)
=> ( big_f(Y,Z)
=> ( ( big_f(X,Y)
<=> big_f(Z,Z) )
=> ( ( big_f(Z,Z)
| big_f(Y,X) )
=> ( big_f(Z,Y)
| big_f(Z,X) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
! [X,Y] :
? [Z] :
( ~ big_f(Z,Y)
& ~ big_f(Z,X)
& ( big_f(Z,Z)
| big_f(Y,X) )
& ( ~ big_f(Z,Z)
| big_f(X,Y) )
& ( big_f(Z,Z)
| ~ big_f(X,Y) )
& big_f(Y,Z)
& big_f(X,Z) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y] :
( ~ big_f(sk0(X,Y),Y)
& ~ big_f(sk0(X,Y),X)
& ( big_f(sk0(X,Y),sk0(X,Y))
| big_f(Y,X) )
& ( ~ big_f(sk0(X,Y),sk0(X,Y))
| big_f(X,Y) )
& ( big_f(sk0(X,Y),sk0(X,Y))
| ~ big_f(X,Y) )
& big_f(Y,sk0(X,Y))
& big_f(X,sk0(X,Y)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c4,plain,
( big_f(sk0(X0,X1),sk0(X0,X1))
| big_f(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c3,plain,
( ~ big_f(sk0(X0,X1),sk0(X0,X1))
| big_f(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p10,plain,
( big_f(X1,X0)
| big_f(X0,X1) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(p14,plain,
big_f(X0,X0),
inference(factoring,[status(thm)],[p10]) ).
cnf(p15,plain,
big_f(X0,X1),
inference(resolution,[status(thm)],[p14,c3]) ).
cnf(c5,plain,
~ big_f(sk0(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p16,plain,
$false,
inference(resolution,[status(thm)],[p15,c5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN331+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.36 % Computer : n010.cluster.edu
% 0.03/0.36 % Model : x86_64 x86_64
% 0.03/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.36 % Memory : 8046.5625MB
% 0.03/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Fri Sep 25 00:52:15 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.59/1.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.59/1.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------