%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET958+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 : n011.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 5.47s 1.22s
% Output : Proof 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 3 unt; 0 def)
% Number of atoms : 63 ( 6 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 64 ( 22 ~; 24 |; 12 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 28 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(c4,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(c3,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f8,conjecture,
! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> subset(A,B) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B] :
( ~ subset(A,B)
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
& ! [C] :
( ? [D,E] : C = ordered_pair(D,E)
| ~ in(C,A) ) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
! [C,D] :
( ~ subset(sk3,sk4)
& ( in(ordered_pair(C,D),sk4)
| ~ in(ordered_pair(C,D),sk3) )
& ( C = ordered_pair(sk5(C),sk6(C))
| ~ in(C,sk3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5,sk6])],[f8_nnf]) ).
cnf(c10,plain,
( X2 = ordered_pair(sk5(X2),sk6(X2))
| ~ in(X2,sk3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p14,plain,
( sk0(sk3,X0) = ordered_pair(sk5(sk0(sk3,X0)),sk6(sk0(sk3,X0)))
| subset(sk3,X0) ),
inference(resolution,[status(thm)],[c3,c10]) ).
cnf(c11,plain,
( in(ordered_pair(X2,X3),sk4)
| ~ in(ordered_pair(X2,X3),sk3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p16,plain,
( in(ordered_pair(sk5(sk0(sk3,X0)),sk6(sk0(sk3,X0))),sk4)
| ~ in(sk0(sk3,X0),sk3)
| subset(sk3,X0) ),
inference(superposition,[status(thm)],[p14,c11]) ).
cnf(p18,plain,
( subset(sk3,X0)
| in(ordered_pair(sk5(sk0(sk3,X0)),sk6(sk0(sk3,X0))),sk4)
| subset(sk3,X0) ),
inference(resolution,[status(thm)],[p16,c3]) ).
cnf(p19,plain,
( in(ordered_pair(sk5(sk0(sk3,X0)),sk6(sk0(sk3,X0))),sk4)
| subset(sk3,X0) ),
inference(factoring,[status(thm)],[p18]) ).
cnf(p21,plain,
( in(sk0(sk3,X0),sk4)
| subset(sk3,X0)
| subset(sk3,X0) ),
inference(superposition,[status(thm)],[p14,p19]) ).
cnf(p22,plain,
( in(sk0(sk3,X0),sk4)
| subset(sk3,X0) ),
inference(factoring,[status(thm)],[p21]) ).
cnf(p24,plain,
( subset(sk3,sk4)
| subset(sk3,sk4) ),
inference(resolution,[status(thm)],[c4,p22]) ).
cnf(p25,plain,
subset(sk3,sk4),
inference(factoring,[status(thm)],[p24]) ).
cnf(c12,plain,
~ subset(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p26,plain,
$false,
inference(resolution,[status(thm)],[p25,c12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET958+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:26:57 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.47/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.47/1.22 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------