%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN354+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 2.52s 0.77s
% Output : Proof 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 97 ( 32 ~; 31 |; 18 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 1 sgn 10 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,X2)
=> ( big_g(X1,X2)
=> ( ( ( big_g(X2,Z)
<=> big_g(Y2,Z) )
=> ( big_f(Y1,Y2)
=> big_f(X2,Y2) ) )
=> ( ( big_g(X2,Z)
<=> big_g(Y1,Z) )
=> ( big_f(Y1,Y2)
& big_f(X2,Y1)
& big_f(X1,Y1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_20_1) ).
fof(f0_neg,negated_conjecture,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,X2)
=> ( big_g(X1,X2)
=> ( ( ( big_g(X2,Z)
<=> big_g(Y2,Z) )
=> ( big_f(Y1,Y2)
=> big_f(X2,Y2) ) )
=> ( ( big_g(X2,Z)
<=> big_g(Y1,Z) )
=> ( big_f(Y1,Y2)
& big_f(X2,Y1)
& big_f(X1,Y1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ~ big_f(Y1,Y2)
| ~ big_f(X2,Y1)
| ~ big_f(X1,Y1) )
& ( ~ big_g(Y1,Z)
| big_g(X2,Z) )
& ( big_g(Y1,Z)
| ~ big_g(X2,Z) )
& ( big_f(X2,Y2)
| ~ big_f(Y1,Y2)
| ( big_g(Y2,Z)
& ~ big_g(X2,Z) )
| ( ~ big_g(Y2,Z)
& big_g(X2,Z) ) )
& big_g(X1,X2)
& big_f(X1,X2) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y1,Y2] :
( ( ~ big_f(Y1,Y2)
| ~ big_f(sk1,Y1)
| ~ big_f(sk0,Y1) )
& ( ~ big_g(Y1,sk2(Y1,Y2))
| big_g(sk1,sk2(Y1,Y2)) )
& ( big_g(Y1,sk2(Y1,Y2))
| ~ big_g(sk1,sk2(Y1,Y2)) )
& ( big_f(sk1,Y2)
| ~ big_f(Y1,Y2)
| ( big_g(Y2,sk2(Y1,Y2))
& ~ big_g(sk1,sk2(Y1,Y2)) )
| ( ~ big_g(Y2,sk2(Y1,Y2))
& big_g(sk1,sk2(Y1,Y2)) ) )
& big_g(sk0,sk1)
& big_f(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c4,plain,
( big_f(sk1,X3)
| ~ big_f(X2,X3)
| ~ big_g(sk1,sk2(X2,X3))
| ~ big_g(X3,sk2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p17,plain,
( big_f(sk1,sk1)
| ~ big_f(X0,sk1)
| ~ big_g(sk1,sk2(X0,sk1)) ),
inference(factoring,[status(thm)],[c4]) ).
cnf(c3,plain,
( big_f(sk1,X3)
| ~ big_f(X2,X3)
| big_g(X3,sk2(X2,X3))
| big_g(sk1,sk2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p13,plain,
( big_f(sk1,sk1)
| ~ big_f(X0,sk1)
| big_g(sk1,sk2(X0,sk1)) ),
inference(factoring,[status(thm)],[c3]) ).
cnf(c0,plain,
big_f(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p15,plain,
( big_f(sk1,sk1)
| big_g(sk1,sk2(sk0,sk1)) ),
inference(resolution,[status(thm)],[p13,c0]) ).
cnf(p18,plain,
( big_f(sk1,sk1)
| big_f(sk1,sk1)
| ~ big_f(sk0,sk1) ),
inference(resolution,[status(thm)],[p17,p15]) ).
cnf(p19,plain,
( big_f(sk1,sk1)
| ~ big_f(sk0,sk1) ),
inference(factoring,[status(thm)],[p18]) ).
cnf(p20,plain,
big_f(sk1,sk1),
inference(resolution,[status(thm)],[p19,c0]) ).
cnf(c8,plain,
( ~ big_f(X2,X3)
| ~ big_f(sk1,X2)
| ~ big_f(sk0,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p10,plain,
( ~ big_f(sk1,sk1)
| ~ big_f(sk0,sk1) ),
inference(factoring,[status(thm)],[c8]) ).
cnf(p12,plain,
~ big_f(sk1,sk1),
inference(resolution,[status(thm)],[p10,c0]) ).
cnf(p21,plain,
$false,
inference(resolution,[status(thm)],[p20,p12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN354+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.33 % Computer : n001.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Fri Sep 25 01:03:38 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.52/0.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.52/0.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------