%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 02:44:22 PM UTC 2026
% Result : Theorem 4.05s 1.11s
% Output : Proof 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 4 unt; 0 def)
% Number of atoms : 78 ( 6 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 76 ( 24 ~; 28 |; 18 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 63 ( 0 sgn 39 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B,C,D] :
~ ( ! [E,F] :
~ ( D = ordered_pair(E,F)
& in(F,C)
& in(E,B) )
& in(D,A)
& subset(A,cartesian_product2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f8_nnf,plain,
! [A,B,C,D] :
( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,C)
& in(E,B) )
| ~ in(D,A)
| ~ subset(A,cartesian_product2(B,C)) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D] :
( ( D = ordered_pair(sk3(A,B,C,D),sk4(A,B,C,D))
& in(sk4(A,B,C,D),C)
& in(sk3(A,B,C,D),B) )
| ~ in(D,A)
| ~ subset(A,cartesian_product2(B,C)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f8_nnf]) ).
cnf(c12,plain,
( X3 = ordered_pair(sk3(X0,X1,X2,X3),sk4(X0,X1,X2,X3))
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f9,conjecture,
! [A,B,C,D] :
( ( ! [E,F] :
( in(ordered_pair(E,F),A)
=> in(ordered_pair(E,F),D) )
& subset(A,cartesian_product2(B,C)) )
=> subset(A,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).
fof(f9_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( ! [E,F] :
( in(ordered_pair(E,F),A)
=> in(ordered_pair(E,F),D) )
& subset(A,cartesian_product2(B,C)) )
=> subset(A,D) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_nnf,plain,
? [A,B,C,D] :
( ~ subset(A,D)
& ! [E,F] :
( in(ordered_pair(E,F),D)
| ~ in(ordered_pair(E,F),A) )
& subset(A,cartesian_product2(B,C)) ),
inference(nnf_transformation,[status(thm)],[f9_neg]) ).
fof(f9_sk,plain,
! [E,F] :
( ~ subset(sk5,sk8)
& ( in(ordered_pair(E,F),sk8)
| ~ in(ordered_pair(E,F),sk5) )
& subset(sk5,cartesian_product2(sk6,sk7)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6,sk7,sk8])],[f9_nnf]) ).
cnf(c13,plain,
subset(sk5,cartesian_product2(sk6,sk7)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p45,plain,
( X0 = ordered_pair(sk3(sk5,sk6,sk7,X0),sk4(sk5,sk6,sk7,X0))
| ~ in(X0,sk5) ),
inference(resolution,[status(thm)],[c12,c13]) ).
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c3,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p47,plain,
( subset(sk5,X0)
| sk0(sk5,X0) = ordered_pair(sk3(sk5,sk6,sk7,sk0(sk5,X0)),sk4(sk5,sk6,sk7,sk0(sk5,X0))) ),
inference(resolution,[status(thm)],[p45,c3]) ).
cnf(c14,plain,
( in(ordered_pair(X4,X5),sk8)
| ~ in(ordered_pair(X4,X5),sk5) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p48,plain,
( in(ordered_pair(sk3(sk5,sk6,sk7,sk0(sk5,X0)),sk4(sk5,sk6,sk7,sk0(sk5,X0))),sk8)
| ~ in(sk0(sk5,X0),sk5)
| subset(sk5,X0) ),
inference(superposition,[status(thm)],[p47,c14]) ).
cnf(p62,plain,
( subset(sk5,X0)
| in(ordered_pair(sk3(sk5,sk6,sk7,sk0(sk5,X0)),sk4(sk5,sk6,sk7,sk0(sk5,X0))),sk8)
| subset(sk5,X0) ),
inference(resolution,[status(thm)],[p48,c3]) ).
cnf(p63,plain,
( in(ordered_pair(sk3(sk5,sk6,sk7,sk0(sk5,X0)),sk4(sk5,sk6,sk7,sk0(sk5,X0))),sk8)
| subset(sk5,X0) ),
inference(factoring,[status(thm)],[p62]) ).
cnf(p65,plain,
( in(sk0(sk5,X0),sk8)
| subset(sk5,X0)
| subset(sk5,X0) ),
inference(superposition,[status(thm)],[p47,p63]) ).
cnf(p66,plain,
( in(sk0(sk5,X0),sk8)
| subset(sk5,X0) ),
inference(factoring,[status(thm)],[p65]) ).
cnf(c4,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p80,plain,
( subset(sk5,sk8)
| subset(sk5,sk8) ),
inference(resolution,[status(thm)],[p66,c4]) ).
cnf(p81,plain,
subset(sk5,sk8),
inference(factoring,[status(thm)],[p80]) ).
cnf(c15,plain,
~ subset(sk5,sk8),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p82,plain,
$false,
inference(resolution,[status(thm)],[p81,c15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 12:31:57 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.05/1.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.05/1.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------