%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN056+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 : n004.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 03:33:37 PM UTC 2026
% Result : Theorem 0.14s 5.78s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 48 ( 10 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 130 ( 49 ~; 59 |; 13 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 37 ( 2 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ( big_q(Y)
& big_p(X) )
=> ( big_r(X)
<=> big_s(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26_2) ).
fof(f1_nnf,plain,
! [X,Y] :
( ( ( ~ big_s(Y)
| big_r(X) )
& ( big_s(Y)
| ~ big_r(X) ) )
| ~ big_q(Y)
| ~ big_p(X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( ( ( ~ big_s(Y)
| big_r(X) )
& ( big_s(Y)
| ~ big_r(X) ) )
| ~ big_q(Y)
| ~ big_p(X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( big_s(X1)
| ~ big_r(X0)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f0,axiom,
( ? [X] : big_p(X)
<=> ? [Y] : big_q(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26_1) ).
fof(f0_nnf,plain,
( ( ! [Y] : ~ big_q(Y)
| ? [X] : big_p(X) )
& ( ? [Y] : big_q(Y)
| ! [X] : ~ big_p(X) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ~ big_q(Y)
| big_p(sk1) )
& ( big_q(sk0)
| ~ big_p(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c1,plain,
( ~ big_q(X1)
| big_p(sk1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f2,conjecture,
( ! [X] :
( big_p(X)
=> big_r(X) )
<=> ! [Y] :
( big_q(Y)
=> big_s(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26) ).
fof(f2_neg,negated_conjecture,
~ ( ! [X] :
( big_p(X)
=> big_r(X) )
<=> ! [Y] :
( big_q(Y)
=> big_s(Y) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
( ( ! [Y] :
( big_s(Y)
| ~ big_q(Y) )
& ? [X] :
( ~ big_r(X)
& big_p(X) ) )
| ( ? [Y] :
( ~ big_s(Y)
& big_q(Y) )
& ! [X] :
( big_r(X)
| ~ big_p(X) ) ) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
! [X,Y] :
( ( ( big_s(Y)
| ~ big_q(Y) )
& ~ big_r(sk3)
& big_p(sk3) )
| ( ~ big_s(sk2)
& big_q(sk2)
& ( big_r(X)
| ~ big_p(X) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f2_nnf]) ).
cnf(c7,plain,
( big_p(sk3)
| big_q(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p13,plain,
( big_p(sk3)
| big_p(sk1) ),
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(c0,plain,
( big_q(sk0)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p14,plain,
( big_q(sk0)
| big_p(sk1) ),
inference(resolution,[status(thm)],[p13,c0]) ).
cnf(p16,plain,
( big_p(sk1)
| big_p(sk1) ),
inference(resolution,[status(thm)],[p14,c1]) ).
cnf(p17,plain,
big_p(sk1),
inference(factoring,[status(thm)],[p16]) ).
cnf(p21,plain,
( big_s(X0)
| ~ big_r(sk1)
| ~ big_q(X0) ),
inference(resolution,[status(thm)],[c2,p17]) ).
cnf(p24,plain,
( big_p(sk3)
| big_s(sk2)
| ~ big_r(sk1) ),
inference(resolution,[status(thm)],[p21,c7]) ).
cnf(c4,plain,
( big_p(sk3)
| big_r(X0)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p19,plain,
( big_p(sk3)
| big_r(sk1) ),
inference(resolution,[status(thm)],[p17,c4]) ).
cnf(p30,plain,
( big_p(sk3)
| big_p(sk3)
| big_s(sk2) ),
inference(resolution,[status(thm)],[p24,p19]) ).
cnf(p32,plain,
( big_p(sk3)
| big_s(sk2) ),
inference(factoring,[status(thm)],[p30]) ).
cnf(c10,plain,
( big_p(sk3)
| ~ big_s(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p34,plain,
( big_p(sk3)
| big_p(sk3) ),
inference(resolution,[status(thm)],[p32,c10]) ).
cnf(p39,plain,
big_p(sk3),
inference(factoring,[status(thm)],[p34]) ).
cnf(c3,plain,
( ~ big_s(X1)
| big_r(X0)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p41,plain,
( ~ big_s(X0)
| big_r(sk3)
| ~ big_q(X0) ),
inference(resolution,[status(thm)],[p39,c3]) ).
cnf(p18,plain,
big_q(sk0),
inference(resolution,[status(thm)],[p17,c0]) ).
cnf(p43,plain,
( ~ big_s(sk0)
| big_r(sk3) ),
inference(resolution,[status(thm)],[p41,p18]) ).
cnf(c6,plain,
( big_s(X1)
| ~ big_q(X1)
| big_r(X0)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p28,plain,
( big_s(X0)
| ~ big_q(X0)
| big_r(sk1) ),
inference(resolution,[status(thm)],[c6,p17]) ).
cnf(p31,plain,
( big_s(sk0)
| big_r(sk1) ),
inference(resolution,[status(thm)],[p28,p18]) ).
cnf(p23,plain,
( ~ big_s(X0)
| big_r(sk1)
| ~ big_q(X0) ),
inference(resolution,[status(thm)],[c3,p17]) ).
cnf(p27,plain,
( ~ big_s(sk0)
| big_r(sk1) ),
inference(resolution,[status(thm)],[p23,p18]) ).
cnf(p33,plain,
( big_r(sk1)
| big_r(sk1) ),
inference(resolution,[status(thm)],[p31,p27]) ).
cnf(p37,plain,
big_r(sk1),
inference(factoring,[status(thm)],[p33]) ).
cnf(p25,plain,
( big_s(sk0)
| ~ big_r(sk1) ),
inference(resolution,[status(thm)],[p21,p18]) ).
cnf(p38,plain,
big_s(sk0),
inference(resolution,[status(thm)],[p37,p25]) ).
cnf(p44,plain,
big_r(sk3),
inference(resolution,[status(thm)],[p43,p38]) ).
cnf(c8,plain,
( ~ big_r(sk3)
| big_q(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p45,plain,
big_q(sk2),
inference(resolution,[status(thm)],[p44,c8]) ).
cnf(p46,plain,
( big_s(sk2)
| ~ big_r(sk1) ),
inference(resolution,[status(thm)],[p45,p21]) ).
cnf(p48,plain,
big_s(sk2),
inference(resolution,[status(thm)],[p46,p37]) ).
cnf(c11,plain,
( ~ big_r(sk3)
| ~ big_s(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p49,plain,
~ big_r(sk3),
inference(resolution,[status(thm)],[p48,c11]) ).
cnf(p51,plain,
$false,
inference(resolution,[status(thm)],[p49,p44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN056+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n004.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 23:58:13 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/5.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.78 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------