%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN077+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 : n012.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 03:33:44 PM UTC 2026
% Result : Theorem 8.98s 1.54s
% Output : Proof 8.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 36 ( 4 unt; 0 def)
% Number of atoms : 112 ( 6 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 120 ( 44 ~; 57 |; 14 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 18 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [W] :
! [X] :
( big_f(X,W)
<=> ! [U] :
( big_f(X,U)
=> ? [Y] :
( ~ ? [Z] :
( big_f(Z,Y)
& big_f(Z,U) )
& big_f(Y,U) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel54) ).
fof(f1_neg,negated_conjecture,
~ ~ ? [W] :
! [X] :
( big_f(X,W)
<=> ! [U] :
( big_f(X,U)
=> ? [Y] :
( ~ ? [Z] :
( big_f(Z,Y)
& big_f(Z,U) )
& big_f(Y,U) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f1_nnf,plain,
? [W] :
! [X] :
( ( ? [U] :
( ! [Y] :
( ? [Z] :
( big_f(Z,Y)
& big_f(Z,U) )
| ~ big_f(Y,U) )
& big_f(X,U) )
| big_f(X,W) )
& ( ! [U] :
( ? [Y] :
( ! [Z] :
( ~ big_f(Z,Y)
| ~ big_f(Z,U) )
& big_f(Y,U) )
| ~ big_f(X,U) )
| ~ big_f(X,W) ) ),
inference(nnf_transformation,[status(thm)],[f1_neg]) ).
fof(f1_sk,plain,
! [X,U,Z,Y] :
( ( ( ( ( big_f(sk4(X,Y),Y)
& big_f(sk4(X,Y),sk3(X)) )
| ~ big_f(Y,sk3(X)) )
& big_f(X,sk3(X)) )
| big_f(X,sk1) )
& ( ( ( ~ big_f(Z,sk2(X,U))
| ~ big_f(Z,U) )
& big_f(sk2(X,U),U) )
| ~ big_f(X,U)
| ~ big_f(X,sk1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3,sk4])],[f1_nnf]) ).
cnf(c3,plain,
( ~ big_f(X4,sk2(X1,X2))
| ~ big_f(X4,X2)
| ~ big_f(X1,X2)
| ~ big_f(X1,sk1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c6,plain,
( big_f(sk4(X1,X3),X3)
| ~ big_f(X3,sk3(X1))
| big_f(X1,sk1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c4,plain,
( big_f(X1,sk3(X1))
| big_f(X1,sk1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p8,plain,
( big_f(X0,sk1)
| big_f(sk4(X0,X0),X0)
| big_f(X0,sk1) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(p9,plain,
( big_f(sk4(X0,X0),X0)
| big_f(X0,sk1) ),
inference(factoring,[status(thm)],[p8]) ).
cnf(p28,plain,
( big_f(sk1,sk1)
| ~ big_f(X1,sk2(sk4(sk1,sk1),X0))
| ~ big_f(X1,X0)
| ~ big_f(sk4(sk1,sk1),X0) ),
inference(resolution,[status(thm)],[c3,p9]) ).
cnf(c5,plain,
( big_f(sk4(X1,X3),sk3(X1))
| ~ big_f(X3,sk3(X1))
| big_f(X1,sk1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p20,plain,
( big_f(X0,sk1)
| big_f(sk4(X0,X0),sk3(X0))
| big_f(X0,sk1) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(p22,plain,
( big_f(sk4(X0,X0),sk3(X0))
| big_f(X0,sk1) ),
inference(factoring,[status(thm)],[p20]) ).
cnf(p128,plain,
( big_f(sk1,sk1)
| big_f(sk1,sk1)
| ~ big_f(X0,sk2(sk4(sk1,sk1),sk3(sk1)))
| ~ big_f(X0,sk3(sk1)) ),
inference(resolution,[status(thm)],[p28,p22]) ).
cnf(p374,plain,
( big_f(sk1,sk1)
| ~ big_f(X0,sk2(sk4(sk1,sk1),sk3(sk1)))
| ~ big_f(X0,sk3(sk1)) ),
inference(factoring,[status(thm)],[p128]) ).
cnf(c2,plain,
( big_f(sk2(X1,X2),X2)
| ~ big_f(X1,X2)
| ~ big_f(X1,sk1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p10,plain,
( big_f(sk2(sk4(sk1,sk1),X0),X0)
| ~ big_f(sk4(sk1,sk1),X0)
| big_f(sk1,sk1) ),
inference(resolution,[status(thm)],[p9,c2]) ).
cnf(p41,plain,
( big_f(sk1,sk1)
| big_f(sk2(sk4(sk1,sk1),sk3(sk1)),sk3(sk1))
| big_f(sk1,sk1) ),
inference(resolution,[status(thm)],[p10,p22]) ).
cnf(p97,plain,
( big_f(sk2(sk4(sk1,sk1),sk3(sk1)),sk3(sk1))
| big_f(sk1,sk1) ),
inference(factoring,[status(thm)],[p41]) ).
cnf(p99,plain,
( big_f(sk4(sk1,sk2(sk4(sk1,sk1),sk3(sk1))),sk3(sk1))
| big_f(sk1,sk1)
| big_f(sk1,sk1) ),
inference(resolution,[status(thm)],[p97,c5]) ).
cnf(p178,plain,
( big_f(sk4(sk1,sk2(sk4(sk1,sk1),sk3(sk1))),sk3(sk1))
| big_f(sk1,sk1) ),
inference(factoring,[status(thm)],[p99]) ).
cnf(p382,plain,
( big_f(sk1,sk1)
| big_f(sk1,sk1)
| ~ big_f(sk4(sk1,sk2(sk4(sk1,sk1),sk3(sk1))),sk2(sk4(sk1,sk1),sk3(sk1))) ),
inference(resolution,[status(thm)],[p374,p178]) ).
cnf(p825,plain,
( big_f(sk1,sk1)
| ~ big_f(sk4(sk1,sk2(sk4(sk1,sk1),sk3(sk1))),sk2(sk4(sk1,sk1),sk3(sk1))) ),
inference(factoring,[status(thm)],[p382]) ).
cnf(p98,plain,
( big_f(sk4(sk1,sk2(sk4(sk1,sk1),sk3(sk1))),sk2(sk4(sk1,sk1),sk3(sk1)))
| big_f(sk1,sk1)
| big_f(sk1,sk1) ),
inference(resolution,[status(thm)],[p97,c6]) ).
cnf(p693,plain,
( big_f(sk4(sk1,sk2(sk4(sk1,sk1),sk3(sk1))),sk2(sk4(sk1,sk1),sk3(sk1)))
| big_f(sk1,sk1) ),
inference(factoring,[status(thm)],[p98]) ).
cnf(p826,plain,
( big_f(sk1,sk1)
| big_f(sk1,sk1) ),
inference(resolution,[status(thm)],[p825,p693]) ).
cnf(p827,plain,
big_f(sk1,sk1),
inference(factoring,[status(thm)],[p826]) ).
cnf(p27,plain,
( ~ big_f(X0,sk2(X0,X1))
| ~ big_f(X0,X1)
| ~ big_f(X0,sk1) ),
inference(factoring,[status(thm)],[c3]) ).
cnf(p834,plain,
( ~ big_f(sk1,sk2(sk1,X0))
| ~ big_f(sk1,X0) ),
inference(resolution,[status(thm)],[p827,p27]) ).
fof(f0,axiom,
! [Y] :
? [Z] :
! [X] :
( big_f(X,Z)
<=> X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel54_1) ).
fof(f0_nnf,plain,
! [Y] :
? [Z] :
! [X] :
( ( X != Y
| big_f(X,Z) )
& ( X = Y
| ~ big_f(X,Z) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( X != Y
| big_f(X,sk0(Y)) )
& ( X = Y
| ~ big_f(X,sk0(Y)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( X2 != X0
| big_f(X2,sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p17,plain,
big_f(X0,sk0(X0)),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(p907,plain,
~ big_f(sk1,sk1),
inference(resolution,[status(thm)],[p834,p17]) ).
cnf(p911,plain,
$false,
inference(resolution,[status(thm)],[p907,p827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN077+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 00:06:36 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.98/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.98/1.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------