%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 02:43:29 PM UTC 2026
% Result : Theorem 9.31s 6.73s
% Output : Proof 9.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 5 unt; 0 def)
% Number of atoms : 123 ( 13 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 128 ( 45 ~; 53 |; 22 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 2 sgn 34 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f2_nnf,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D] :
( ( ( ~ member(sk0(B,C),C)
& member(sk0(B,C),B) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ subset(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c7,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f0_nnf,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [D,B,C] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p17,plain,
( member(sk0(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c7,c0]) ).
fof(f4,conjecture,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( ~ member(E,D)
& member(E,C) ) )
=> B = difference(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th20) ).
fof(f4_neg,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( ~ member(E,D)
& member(E,C) ) )
=> B = difference(C,D) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [B,C,D] :
( B != difference(C,D)
& ! [E] :
( ( member(E,D)
| ~ member(E,C)
| member(E,B) )
& ( ( ~ member(E,D)
& member(E,C) )
| ~ member(E,B) ) ) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
! [E] :
( sk1 != difference(sk2,sk3)
& ( member(E,sk3)
| ~ member(E,sk2)
| member(E,sk1) )
& ( ( ~ member(E,sk3)
& member(E,sk2) )
| ~ member(E,sk1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f4_nnf]) ).
cnf(c12,plain,
( member(X3,sk3)
| ~ member(X3,sk2)
| member(X3,sk1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p49,plain,
( member(sk0(difference(sk2,X0),X1),sk3)
| member(sk0(difference(sk2,X0),X1),sk1)
| subset(difference(sk2,X0),X1) ),
inference(resolution,[status(thm)],[p17,c12]) ).
cnf(c1,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p18,plain,
( ~ member(sk0(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(p173,plain,
( subset(difference(sk2,sk3),X0)
| member(sk0(difference(sk2,sk3),X0),sk1)
| subset(difference(sk2,sk3),X0) ),
inference(resolution,[status(thm)],[p49,p18]) ).
cnf(p467,plain,
( member(sk0(difference(sk2,sk3),X0),sk1)
| subset(difference(sk2,sk3),X0) ),
inference(factoring,[status(thm)],[p173]) ).
cnf(c8,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p469,plain,
( subset(difference(sk2,sk3),sk1)
| subset(difference(sk2,sk3),sk1) ),
inference(resolution,[status(thm)],[p467,c8]) ).
cnf(p480,plain,
subset(difference(sk2,sk3),sk1),
inference(factoring,[status(thm)],[p469]) ).
cnf(c10,plain,
( member(X3,sk2)
| ~ member(X3,sk1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p14,plain,
( member(sk0(sk1,X0),sk2)
| subset(sk1,X0) ),
inference(resolution,[status(thm)],[c7,c10]) ).
cnf(c2,plain,
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p20,plain,
( member(sk0(sk1,X0),X1)
| member(sk0(sk1,X0),difference(sk2,X1))
| subset(sk1,X0) ),
inference(resolution,[status(thm)],[p14,c2]) ).
cnf(p36,plain,
( member(sk0(sk1,difference(sk2,X0)),X0)
| subset(sk1,difference(sk2,X0))
| subset(sk1,difference(sk2,X0)) ),
inference(resolution,[status(thm)],[c8,p20]) ).
cnf(p118,plain,
( member(sk0(sk1,difference(sk2,X0)),X0)
| subset(sk1,difference(sk2,X0)) ),
inference(factoring,[status(thm)],[p36]) ).
cnf(c11,plain,
( ~ member(X3,sk3)
| ~ member(X3,sk1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p15,plain,
( ~ member(sk0(sk1,X0),sk3)
| subset(sk1,X0) ),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(p123,plain,
( subset(sk1,difference(sk2,sk3))
| subset(sk1,difference(sk2,sk3)) ),
inference(resolution,[status(thm)],[p118,p15]) ).
cnf(p127,plain,
subset(sk1,difference(sk2,sk3)),
inference(factoring,[status(thm)],[p123]) ).
fof(f1,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f1_nnf,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p128,plain,
( ~ subset(difference(sk2,sk3),sk1)
| sk1 = difference(sk2,sk3) ),
inference(resolution,[status(thm)],[p127,c5]) ).
cnf(p483,plain,
sk1 = difference(sk2,sk3),
inference(resolution,[status(thm)],[p480,p128]) ).
cnf(c13,plain,
sk1 != difference(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p484,plain,
$false,
inference(resolution,[status(thm)],[p483,c13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n020.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Thu Sep 24 11:20:54 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.31/6.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.31/6.73 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------