%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN075+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 : n009.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 03:33:43 PM UTC 2026
% Result : Theorem 4.79s 1.07s
% Output : Proof 4.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 74 ( 46 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 80 ( 30 ~; 30 |; 15 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn 16 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [W] :
! [Y] :
( ? [Z] :
! [X] :
( big_f(X,Y)
<=> X = Z )
<=> Y = W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel52) ).
fof(f1_neg,negated_conjecture,
~ ? [W] :
! [Y] :
( ? [Z] :
! [X] :
( big_f(X,Y)
<=> X = Z )
<=> Y = W ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f1_nnf,plain,
! [W] :
? [Y] :
( ( Y = W
& ! [Z] :
? [X] :
( ( X = Z
& ~ big_f(X,Y) )
| ( X != Z
& big_f(X,Y) ) ) )
| ( Y != W
& ? [Z] :
! [X] :
( ( X != Z
| big_f(X,Y) )
& ( X = Z
| ~ big_f(X,Y) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1_neg]) ).
fof(f1_sk,plain,
! [X,W,Z] :
( ( sk2(W) = W
& ( ( sk4(W,Z) = Z
& ~ big_f(sk4(W,Z),sk2(W)) )
| ( sk4(W,Z) != Z
& big_f(sk4(W,Z),sk2(W)) ) ) )
| ( sk2(W) != W
& ( X != sk3(W)
| big_f(X,sk2(W)) )
& ( X = sk3(W)
| ~ big_f(X,sk2(W)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f1_nnf]) ).
cnf(c15,plain,
( ~ big_f(sk4(X0,X2),sk2(X0))
| sk4(X0,X2) != X2
| sk2(X0) != X0 ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c12,plain,
( sk2(X0) = X0
| X3 != sk3(X0)
| big_f(X3,sk2(X0)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p23,plain,
( sk2(X0) = X0
| big_f(sk3(X0),sk2(X0)) ),
inference(equality_resolution,[status(thm)],[c12]) ).
fof(f0,axiom,
? [Z,W] :
! [X,Y] :
( big_f(X,Y)
<=> ( Y = W
& X = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel52_1) ).
fof(f0_nnf,plain,
? [Z,W] :
! [X,Y] :
( ( Y != W
| X != Z
| big_f(X,Y) )
& ( ( Y = W
& X = Z )
| ~ big_f(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( Y != sk1
| X != sk0
| big_f(X,Y) )
& ( ( Y = sk1
& X = sk0 )
| ~ big_f(X,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c1,plain,
( X3 = sk1
| ~ big_f(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p25,plain,
( sk2(X0) = sk1
| sk2(X0) = X0 ),
inference(resolution,[status(thm)],[p23,c1]) ).
cnf(p35,plain,
sk2(sk1) = sk1,
inference(factoring,[status(thm)],[p25]) ).
cnf(p170,plain,
( ~ big_f(sk4(sk1,X0),sk1)
| sk4(sk1,X0) != X0 ),
inference(resolution,[status(thm)],[c15,p35]) ).
cnf(c14,plain,
( sk4(X0,X2) = X2
| big_f(sk4(X0,X2),sk2(X0))
| sk2(X0) != X0 ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p129,plain,
( sk4(sk1,X0) = X0
| big_f(sk4(sk1,X0),sk1) ),
inference(resolution,[status(thm)],[c14,p35]) ).
cnf(c0,plain,
( X2 = sk0
| ~ big_f(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p154,plain,
( sk4(sk1,X0) = sk0
| sk4(sk1,X0) = X0 ),
inference(resolution,[status(thm)],[p129,c0]) ).
cnf(p179,plain,
sk4(sk1,sk0) = sk0,
inference(factoring,[status(thm)],[p154]) ).
cnf(p206,plain,
~ big_f(sk0,sk1),
inference(resolution,[status(thm)],[p170,p179]) ).
cnf(c2,plain,
( X3 != sk1
| X2 != sk0
| big_f(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p18,plain,
( X0 != sk1
| big_f(sk0,X0) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p20,plain,
big_f(sk0,sk1),
inference(equality_resolution,[status(thm)],[p18]) ).
cnf(p207,plain,
$false,
inference(resolution,[status(thm)],[p206,p20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN075+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 00:05:44 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.79/1.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.79/1.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------