%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET616+3 : TPTP v9.3.1. Released v2.2.0.
% 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 02:43:36 PM UTC 2026
% Result : Theorem 30.04s 4.25s
% Output : Proof 30.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 16 unt; 0 def)
% Number of atoms : 121 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 108 ( 40 ~; 46 |; 16 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 9 sgn 28 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,conjecture,
! [B,C] :
( difference(B,C) = difference(C,B)
=> B = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th90) ).
fof(f6_neg,negated_conjecture,
~ ! [B,C] :
( difference(B,C) = difference(C,B)
=> B = C ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [B,C] :
( B != C
& difference(B,C) = difference(C,B) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( sk3 != sk4
& difference(sk3,sk4) = difference(sk4,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f6_nnf]) ).
cnf(c20,plain,
difference(sk3,sk4) = difference(sk4,sk3),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f1,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f1_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)],[f1]) ).
fof(f1_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)],[f1_nnf]) ).
cnf(c4,plain,
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p24,plain,
( member(X0,sk4)
| ~ member(X0,difference(sk3,sk4)) ),
inference(superposition,[status(thm)],[c20,c4]) ).
fof(f4,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f4_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)],[f4]) ).
fof(f4_sk,plain,
! [B,C,D] :
( ( ( ~ member(sk2(B,C),C)
& member(sk2(B,C),B) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ subset(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f4_nnf]) ).
cnf(c17,plain,
( member(sk2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p34,plain,
( subset(difference(sk3,sk4),X0)
| member(sk2(difference(sk3,sk4),X0),sk4) ),
inference(resolution,[status(thm)],[p24,c17]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p31,plain,
( ~ member(sk2(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c17,c5]) ).
cnf(p118,plain,
( subset(difference(sk3,sk4),X0)
| subset(difference(sk3,sk4),X0) ),
inference(resolution,[status(thm)],[p34,p31]) ).
cnf(p119,plain,
subset(difference(sk3,sk4),X0),
inference(factoring,[status(thm)],[p118]) ).
cnf(p30,plain,
( member(sk2(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c17,c4]) ).
cnf(p79,plain,
( subset(difference(X0,X0),X1)
| subset(difference(X0,X0),X1) ),
inference(resolution,[status(thm)],[p31,p30]) ).
cnf(p80,plain,
subset(difference(X0,X0),X1),
inference(factoring,[status(thm)],[p79]) ).
fof(f2,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f2_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)],[f2]) ).
fof(f2_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c9,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p81,plain,
( ~ subset(X1,difference(X0,X0))
| difference(X0,X0) = X1 ),
inference(resolution,[status(thm)],[p80,c9]) ).
cnf(p95,plain,
difference(X0,X0) = difference(X1,X1),
inference(resolution,[status(thm)],[p81,p80]) ).
cnf(p97,plain,
( ~ subset(X1,difference(X2,X2))
| difference(X0,X0) = X1 ),
inference(superposition,[status(thm)],[p95,p81]) ).
cnf(p123,plain,
difference(X0,X0) = difference(sk3,sk4),
inference(resolution,[status(thm)],[p119,p97]) ).
cnf(p138,plain,
difference(X0,X0) = difference(sk4,sk3),
inference(superposition,[status(thm)],[p123,c20]) ).
cnf(p178,plain,
difference(sk4,sk3) = difference(sk3,sk4),
inference(superposition,[status(thm)],[p138,p123]) ).
cnf(c6,plain,
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p49,plain,
( subset(X0,X1)
| member(sk2(X0,X1),X2)
| member(sk2(X0,X1),difference(X0,X2)) ),
inference(resolution,[status(thm)],[c6,c17]) ).
cnf(p237,plain,
( subset(sk4,X0)
| member(sk2(sk4,X0),sk3)
| member(sk2(sk4,X0),difference(sk3,sk4)) ),
inference(superposition,[status(thm)],[p178,p49]) ).
cnf(c18,plain,
( ~ member(sk2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p53,plain,
( subset(difference(X0,X1),X0)
| subset(difference(X0,X1),X0) ),
inference(resolution,[status(thm)],[p30,c18]) ).
cnf(p59,plain,
subset(difference(X0,X1),X0),
inference(factoring,[status(thm)],[p53]) ).
cnf(p61,plain,
( ~ subset(X0,difference(X0,X1))
| difference(X0,X1) = X0 ),
inference(resolution,[status(thm)],[p59,c9]) ).
cnf(p83,plain,
difference(difference(X0,X0),X1) = difference(X0,X0),
inference(resolution,[status(thm)],[p80,p61]) ).
cnf(p89,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X1)) ),
inference(superposition,[status(thm)],[p83,c5]) ).
cnf(p90,plain,
~ member(X0,difference(X1,X1)),
inference(factoring,[status(thm)],[p89]) ).
cnf(p146,plain,
~ member(X0,difference(sk3,sk4)),
inference(superposition,[status(thm)],[p123,p90]) ).
cnf(p5345,plain,
( subset(sk4,X0)
| member(sk2(sk4,X0),sk3) ),
inference(resolution,[status(thm)],[p237,p146]) ).
cnf(p5346,plain,
( subset(sk4,sk3)
| subset(sk4,sk3) ),
inference(resolution,[status(thm)],[p5345,c18]) ).
cnf(p5364,plain,
subset(sk4,sk3),
inference(factoring,[status(thm)],[p5346]) ).
cnf(p236,plain,
( subset(sk3,X0)
| member(sk2(sk3,X0),sk4) ),
inference(resolution,[status(thm)],[p49,p146]) ).
cnf(p238,plain,
( subset(sk3,sk4)
| subset(sk3,sk4) ),
inference(resolution,[status(thm)],[p236,c18]) ).
cnf(p240,plain,
subset(sk3,sk4),
inference(factoring,[status(thm)],[p238]) ).
cnf(p241,plain,
( ~ subset(sk4,sk3)
| sk3 = sk4 ),
inference(resolution,[status(thm)],[p240,c9]) ).
cnf(p5367,plain,
sk3 = sk4,
inference(resolution,[status(thm)],[p5364,p241]) ).
cnf(c21,plain,
sk3 != sk4,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p5368,plain,
$false,
inference(resolution,[status(thm)],[p5367,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET616+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 11:28:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 30.04/4.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.04/4.25 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------