%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN334+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 : n026.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 4.62s 1.10s
% Output : Proof 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 32 ( 5 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 108 ( 34 ~; 46 |; 14 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 65 ( 5 sgn 6 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
? [X,Y] :
! [Z] :
( ( big_f(X,Y)
=> ( big_f(X,Z)
<=> big_g(Y,Z) ) )
=> ( ( big_f(X,Y)
<=> ( big_f(Z,Z)
=> big_g(Z,Z) ) )
=> ( big_g(X,Y)
<=> big_g(Z,Z) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_6) ).
fof(f0_neg,negated_conjecture,
~ ? [X,Y] :
! [Z] :
( ( big_f(X,Y)
=> ( big_f(X,Z)
<=> big_g(Y,Z) ) )
=> ( ( big_f(X,Y)
<=> ( big_f(Z,Z)
=> big_g(Z,Z) ) )
=> ( big_g(X,Y)
<=> big_g(Z,Z) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
! [X,Y] :
? [Z] :
( ( ( big_g(Z,Z)
& ~ big_g(X,Y) )
| ( ~ big_g(Z,Z)
& big_g(X,Y) ) )
& ( ( ~ big_g(Z,Z)
& big_f(Z,Z) )
| big_f(X,Y) )
& ( big_g(Z,Z)
| ~ big_f(Z,Z)
| ~ big_f(X,Y) )
& ( ( ( ~ big_g(Y,Z)
| big_f(X,Z) )
& ( big_g(Y,Z)
| ~ big_f(X,Z) ) )
| ~ big_f(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ( big_g(sk0(X,Y),sk0(X,Y))
& ~ big_g(X,Y) )
| ( ~ big_g(sk0(X,Y),sk0(X,Y))
& big_g(X,Y) ) )
& ( ( ~ big_g(sk0(X,Y),sk0(X,Y))
& big_f(sk0(X,Y),sk0(X,Y)) )
| big_f(X,Y) )
& ( big_g(sk0(X,Y),sk0(X,Y))
| ~ big_f(sk0(X,Y),sk0(X,Y))
| ~ big_f(X,Y) )
& ( ( ( ~ big_g(Y,sk0(X,Y))
| big_f(X,sk0(X,Y)) )
& ( big_g(Y,sk0(X,Y))
| ~ big_f(X,sk0(X,Y)) ) )
| ~ big_f(X,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( ~ big_g(X1,sk0(X0,X1))
| big_f(X0,sk0(X0,X1))
| ~ big_f(X0,X1) ),
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(p13,plain,
( big_f(X0,X1)
| ~ big_g(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1)))
| big_f(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))) ),
inference(resolution,[status(thm)],[c1,c3]) ).
cnf(c6,plain,
( big_g(sk0(X0,X1),sk0(X0,X1))
| big_g(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c4,plain,
( ~ big_g(sk0(X0,X1),sk0(X0,X1))
| big_f(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p9,plain,
( big_f(X0,X1)
| big_g(X0,X1) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(p18,plain,
( big_f(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1)))
| big_f(X0,X1)
| big_f(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))) ),
inference(resolution,[status(thm)],[p13,p9]) ).
cnf(p19,plain,
( big_f(X0,X1)
| big_f(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))) ),
inference(factoring,[status(thm)],[p18]) ).
cnf(c2,plain,
( big_g(sk0(X0,X1),sk0(X0,X1))
| ~ big_f(sk0(X0,X1),sk0(X0,X1))
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p22,plain,
( big_g(sk0(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))),sk0(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))))
| ~ big_f(sk0(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))),sk0(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))))
| big_f(X0,X1) ),
inference(resolution,[status(thm)],[p19,c2]) ).
cnf(c0,plain,
( big_g(X1,sk0(X0,X1))
| ~ big_f(X0,sk0(X0,X1))
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p10,plain,
( big_f(X0,X1)
| big_g(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1)))
| ~ big_f(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))) ),
inference(resolution,[status(thm)],[c0,c3]) ).
cnf(p23,plain,
( big_f(X0,X1)
| big_g(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1)))
| big_f(X0,X1) ),
inference(resolution,[status(thm)],[p19,p10]) ).
cnf(p24,plain,
( big_g(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1)))
| big_f(X0,X1) ),
inference(factoring,[status(thm)],[p23]) ).
cnf(c7,plain,
( ~ big_g(X0,X1)
| ~ big_g(sk0(X0,X1),sk0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p11,plain,
( big_f(sk0(X0,X1),sk0(X0,X1))
| ~ big_g(X0,X1) ),
inference(resolution,[status(thm)],[c7,p9]) ).
cnf(p25,plain,
( big_f(sk0(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))),sk0(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))))
| big_f(X0,X1) ),
inference(resolution,[status(thm)],[p24,p11]) ).
cnf(p34,plain,
( big_f(X0,X1)
| big_g(sk0(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))),sk0(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))))
| big_f(X0,X1) ),
inference(resolution,[status(thm)],[p22,p25]) ).
cnf(p35,plain,
( big_g(sk0(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))),sk0(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1))))
| big_f(X0,X1) ),
inference(factoring,[status(thm)],[p34]) ).
cnf(p36,plain,
( ~ big_g(sk0(X0,X1),sk0(sk0(X0,X1),sk0(X0,X1)))
| big_f(X0,X1) ),
inference(resolution,[status(thm)],[p35,c7]) ).
cnf(p38,plain,
( big_f(X0,X1)
| big_f(X0,X1) ),
inference(resolution,[status(thm)],[p36,p24]) ).
cnf(p39,plain,
big_f(X0,X1),
inference(factoring,[status(thm)],[p38]) ).
cnf(p41,plain,
( big_g(sk0(X0,X1),sk0(X0,X1))
| ~ big_f(sk0(X0,X1),sk0(X0,X1)) ),
inference(resolution,[status(thm)],[p39,c2]) ).
cnf(p43,plain,
big_g(sk0(X0,X1),sk0(X0,X1)),
inference(resolution,[status(thm)],[p41,p39]) ).
cnf(p44,plain,
~ big_g(X0,X1),
inference(resolution,[status(thm)],[p43,c7]) ).
cnf(p40,plain,
( big_g(X1,sk0(X0,X1))
| ~ big_f(X0,sk0(X0,X1)) ),
inference(resolution,[status(thm)],[p39,c0]) ).
cnf(p42,plain,
big_g(X0,sk0(X1,X0)),
inference(resolution,[status(thm)],[p40,p39]) ).
cnf(p45,plain,
$false,
inference(resolution,[status(thm)],[p44,p42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN334+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 00:55:10 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.62/1.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.62/1.10 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------