%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN059+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 : n008.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 03:33:38 PM UTC 2026
% Result : Theorem 4.35s 1.03s
% Output : Proof 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 3
% Syntax : Number of formulae : 87 ( 18 unt; 0 def)
% Number of atoms : 255 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 249 ( 81 ~; 138 |; 22 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 51 ( 15 sgn 16 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,conjecture,
( ( ! [U] :
( big_g(U)
=> big_j(U) )
& ! [X] :
( big_f(X)
=> big_h(X) ) )
<=> ! [W,Y] :
( ( big_g(Y)
& big_f(W) )
=> ( big_j(Y)
& big_h(W) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel29) ).
fof(f2_neg,negated_conjecture,
~ ( ( ! [U] :
( big_g(U)
=> big_j(U) )
& ! [X] :
( big_f(X)
=> big_h(X) ) )
<=> ! [W,Y] :
( ( big_g(Y)
& big_f(W) )
=> ( big_j(Y)
& big_h(W) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
( ( ! [W,Y] :
( ( big_j(Y)
& big_h(W) )
| ~ big_g(Y)
| ~ big_f(W) )
& ( ? [U] :
( ~ big_j(U)
& big_g(U) )
| ? [X] :
( ~ big_h(X)
& big_f(X) ) ) )
| ( ? [W,Y] :
( ( ~ big_j(Y)
| ~ big_h(W) )
& big_g(Y)
& big_f(W) )
& ! [U] :
( big_j(U)
| ~ big_g(U) )
& ! [X] :
( big_h(X)
| ~ big_f(X) ) ) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
! [X,U,W,Y] :
( ( ( ( big_j(Y)
& big_h(W) )
| ~ big_g(Y)
| ~ big_f(W) )
& ( ( ~ big_j(sk5)
& big_g(sk5) )
| ( ~ big_h(sk4)
& big_f(sk4) ) ) )
| ( ( ~ big_j(sk3)
| ~ big_h(sk2) )
& big_g(sk3)
& big_f(sk2)
& ( big_j(U)
| ~ big_g(U) )
& ( big_h(X)
| ~ big_f(X) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f2_nnf]) ).
cnf(c19,plain,
( big_j(X3)
| ~ big_g(X3)
| ~ big_f(X2)
| big_f(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f0,axiom,
? [X] : big_f(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel29_1) ).
fof(f0_nnf,plain,
? [X] : big_f(X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
big_f(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
big_f(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p48,plain,
( big_j(X0)
| ~ big_g(X0)
| big_f(sk2) ),
inference(resolution,[status(thm)],[c19,c0]) ).
cnf(c14,plain,
( big_g(sk5)
| big_f(sk4)
| big_f(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p55,plain,
( big_f(sk4)
| big_f(sk2)
| big_j(sk5)
| big_f(sk2) ),
inference(resolution,[status(thm)],[p48,c14]) ).
cnf(p64,plain,
( big_f(sk4)
| big_j(sk5)
| big_f(sk2) ),
inference(factoring,[status(thm)],[p55]) ).
cnf(c15,plain,
( ~ big_j(sk5)
| big_f(sk4)
| big_f(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p68,plain,
( big_f(sk4)
| big_f(sk2)
| big_f(sk4)
| big_f(sk2) ),
inference(resolution,[status(thm)],[p64,c15]) ).
cnf(p71,plain,
( big_f(sk4)
| big_f(sk4)
| big_f(sk2) ),
inference(factoring,[status(thm)],[p68]) ).
cnf(p75,plain,
( big_f(sk4)
| big_f(sk2) ),
inference(factoring,[status(thm)],[p71]) ).
cnf(c6,plain,
( big_h(X2)
| ~ big_g(X3)
| ~ big_f(X2)
| big_h(X0)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p36,plain,
( big_h(X0)
| ~ big_g(X1)
| big_h(X0)
| ~ big_f(X0) ),
inference(factoring,[status(thm)],[c6]) ).
cnf(p51,plain,
( ~ big_g(X1)
| big_h(X0)
| ~ big_f(X0) ),
inference(factoring,[status(thm)],[p36]) ).
cnf(p77,plain,
( ~ big_g(X0)
| big_h(sk4)
| big_f(sk2) ),
inference(resolution,[status(thm)],[p75,p51]) ).
fof(f1,axiom,
? [Y] : big_g(Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel29_2) ).
fof(f1_nnf,plain,
? [Y] : big_g(Y),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
big_g(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c1,plain,
big_g(sk1),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p83,plain,
( big_h(sk4)
| big_f(sk2) ),
inference(resolution,[status(thm)],[p77,c1]) ).
cnf(c16,plain,
( big_g(sk5)
| ~ big_h(sk4)
| big_f(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p87,plain,
( big_g(sk5)
| big_f(sk2)
| big_f(sk2) ),
inference(resolution,[status(thm)],[p83,c16]) ).
cnf(p91,plain,
( big_g(sk5)
| big_f(sk2) ),
inference(factoring,[status(thm)],[p87]) ).
cnf(p93,plain,
( big_j(sk5)
| big_f(sk2)
| big_f(sk2) ),
inference(resolution,[status(thm)],[p91,p48]) ).
cnf(p96,plain,
( big_j(sk5)
| big_f(sk2) ),
inference(factoring,[status(thm)],[p93]) ).
cnf(c17,plain,
( ~ big_j(sk5)
| ~ big_h(sk4)
| big_f(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p88,plain,
( ~ big_j(sk5)
| big_f(sk2)
| big_f(sk2) ),
inference(resolution,[status(thm)],[p83,c17]) ).
cnf(p92,plain,
( ~ big_j(sk5)
| big_f(sk2) ),
inference(factoring,[status(thm)],[p88]) ).
cnf(p97,plain,
( big_f(sk2)
| big_f(sk2) ),
inference(resolution,[status(thm)],[p96,p92]) ).
cnf(p98,plain,
big_f(sk2),
inference(factoring,[status(thm)],[p97]) ).
cnf(p103,plain,
( ~ big_g(X0)
| big_h(sk2) ),
inference(resolution,[status(thm)],[p98,p51]) ).
cnf(p108,plain,
big_h(sk2),
inference(resolution,[status(thm)],[p103,c1]) ).
cnf(c26,plain,
( big_g(sk5)
| big_f(sk4)
| ~ big_j(sk3)
| ~ big_h(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p112,plain,
( big_g(sk5)
| big_f(sk4)
| ~ big_j(sk3) ),
inference(resolution,[status(thm)],[p108,c26]) ).
cnf(c25,plain,
( big_j(X3)
| ~ big_g(X3)
| ~ big_f(X2)
| big_g(sk3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p50,plain,
( big_j(X0)
| ~ big_g(X0)
| big_g(sk3) ),
inference(resolution,[status(thm)],[c25,c0]) ).
cnf(c20,plain,
( big_g(sk5)
| big_f(sk4)
| big_g(sk3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p59,plain,
( big_f(sk4)
| big_g(sk3)
| big_j(sk5)
| big_g(sk3) ),
inference(resolution,[status(thm)],[p50,c20]) ).
cnf(p65,plain,
( big_f(sk4)
| big_j(sk5)
| big_g(sk3) ),
inference(factoring,[status(thm)],[p59]) ).
cnf(c21,plain,
( ~ big_j(sk5)
| big_f(sk4)
| big_g(sk3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p70,plain,
( big_f(sk4)
| big_g(sk3)
| big_f(sk4)
| big_g(sk3) ),
inference(resolution,[status(thm)],[p65,c21]) ).
cnf(p73,plain,
( big_f(sk4)
| big_f(sk4)
| big_g(sk3) ),
inference(factoring,[status(thm)],[p70]) ).
cnf(p76,plain,
( big_f(sk4)
| big_g(sk3) ),
inference(factoring,[status(thm)],[p73]) ).
cnf(c13,plain,
( big_j(X3)
| ~ big_g(X3)
| ~ big_f(X2)
| big_j(X1)
| ~ big_g(X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p44,plain,
( big_j(X0)
| ~ big_f(X1)
| big_j(X0)
| ~ big_g(X0) ),
inference(factoring,[status(thm)],[c13]) ).
cnf(p52,plain,
( ~ big_f(X1)
| big_j(X0)
| ~ big_g(X0) ),
inference(factoring,[status(thm)],[p44]) ).
cnf(p82,plain,
( ~ big_f(X0)
| big_j(sk3)
| big_f(sk4) ),
inference(resolution,[status(thm)],[p76,p52]) ).
cnf(p86,plain,
( big_j(sk3)
| big_f(sk4) ),
inference(resolution,[status(thm)],[p82,c0]) ).
cnf(p117,plain,
( big_f(sk4)
| big_g(sk5)
| big_f(sk4) ),
inference(resolution,[status(thm)],[p112,p86]) ).
cnf(p121,plain,
( big_g(sk5)
| big_f(sk4) ),
inference(factoring,[status(thm)],[p117]) ).
cnf(p123,plain,
( ~ big_f(X0)
| big_j(sk5)
| big_f(sk4) ),
inference(resolution,[status(thm)],[p121,p52]) ).
cnf(p124,plain,
( big_j(sk5)
| big_f(sk4) ),
inference(resolution,[status(thm)],[p123,c0]) ).
cnf(c27,plain,
( ~ big_j(sk5)
| big_f(sk4)
| ~ big_j(sk3)
| ~ big_h(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p113,plain,
( ~ big_j(sk5)
| big_f(sk4)
| ~ big_j(sk3) ),
inference(resolution,[status(thm)],[p108,c27]) ).
cnf(p118,plain,
( big_f(sk4)
| ~ big_j(sk5)
| big_f(sk4) ),
inference(resolution,[status(thm)],[p113,p86]) ).
cnf(p122,plain,
( ~ big_j(sk5)
| big_f(sk4) ),
inference(factoring,[status(thm)],[p118]) ).
cnf(p125,plain,
( big_f(sk4)
| big_f(sk4) ),
inference(resolution,[status(thm)],[p124,p122]) ).
cnf(p126,plain,
big_f(sk4),
inference(factoring,[status(thm)],[p125]) ).
cnf(p127,plain,
( ~ big_g(X0)
| big_h(sk4) ),
inference(resolution,[status(thm)],[p126,p51]) ).
cnf(p128,plain,
big_h(sk4),
inference(resolution,[status(thm)],[p127,c1]) ).
cnf(c22,plain,
( big_g(sk5)
| ~ big_h(sk4)
| big_g(sk3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p129,plain,
( big_g(sk5)
| big_g(sk3) ),
inference(resolution,[status(thm)],[p128,c22]) ).
cnf(p131,plain,
( big_j(sk5)
| big_g(sk3)
| big_g(sk3) ),
inference(resolution,[status(thm)],[p129,p50]) ).
cnf(p133,plain,
( big_j(sk5)
| big_g(sk3) ),
inference(factoring,[status(thm)],[p131]) ).
cnf(c23,plain,
( ~ big_j(sk5)
| ~ big_h(sk4)
| big_g(sk3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p130,plain,
( ~ big_j(sk5)
| big_g(sk3) ),
inference(resolution,[status(thm)],[p128,c23]) ).
cnf(p134,plain,
( big_g(sk3)
| big_g(sk3) ),
inference(resolution,[status(thm)],[p133,p130]) ).
cnf(p135,plain,
big_g(sk3),
inference(factoring,[status(thm)],[p134]) ).
cnf(p138,plain,
( ~ big_f(X0)
| big_j(sk3) ),
inference(resolution,[status(thm)],[p135,p52]) ).
cnf(p141,plain,
big_j(sk3),
inference(resolution,[status(thm)],[p138,c0]) ).
cnf(c28,plain,
( big_g(sk5)
| ~ big_h(sk4)
| ~ big_j(sk3)
| ~ big_h(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p114,plain,
( big_g(sk5)
| ~ big_h(sk4)
| ~ big_j(sk3) ),
inference(resolution,[status(thm)],[p108,c28]) ).
cnf(p142,plain,
( big_g(sk5)
| ~ big_h(sk4) ),
inference(resolution,[status(thm)],[p141,p114]) ).
cnf(p144,plain,
big_g(sk5),
inference(resolution,[status(thm)],[p142,p128]) ).
cnf(p146,plain,
( ~ big_f(X0)
| big_j(sk5) ),
inference(resolution,[status(thm)],[p144,p52]) ).
cnf(p147,plain,
big_j(sk5),
inference(resolution,[status(thm)],[p146,c0]) ).
cnf(c29,plain,
( ~ big_j(sk5)
| ~ big_h(sk4)
| ~ big_j(sk3)
| ~ big_h(sk2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p115,plain,
( ~ big_j(sk5)
| ~ big_h(sk4)
| ~ big_j(sk3) ),
inference(resolution,[status(thm)],[p108,c29]) ).
cnf(p143,plain,
( ~ big_j(sk5)
| ~ big_h(sk4) ),
inference(resolution,[status(thm)],[p141,p115]) ).
cnf(p145,plain,
~ big_j(sk5),
inference(resolution,[status(thm)],[p143,p128]) ).
cnf(p148,plain,
$false,
inference(resolution,[status(thm)],[p147,p145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN059+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 00:00:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.35/1.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.35/1.03 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------