%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET598+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 : n018.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 02:43:33 PM UTC 2026
% Result : Theorem 24.44s 3.94s
% Output : Proof 24.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 75 ( 21 unt; 0 def)
% Number of atoms : 207 ( 48 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 212 ( 80 ~; 102 |; 24 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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; 4 con; 0-2 aty)
% Number of variables : 65 ( 2 sgn 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( ( subset(B,D)
& subset(B,C) )
=> subset(B,intersection(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subsets) ).
fof(f1_nnf,plain,
! [B,C,D] :
( subset(B,intersection(C,D))
| ~ subset(B,D)
| ~ subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( subset(B,intersection(C,D))
| ~ subset(B,D)
| ~ subset(B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( subset(X0,intersection(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f8,conjecture,
! [B,C,D] :
( B = intersection(C,D)
<=> ( ! [E] :
( ( subset(E,D)
& subset(E,C) )
=> subset(E,B) )
& subset(B,D)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th57) ).
fof(f8_neg,negated_conjecture,
~ ! [B,C,D] :
( B = intersection(C,D)
<=> ( ! [E] :
( ( subset(E,D)
& subset(E,C) )
=> subset(E,B) )
& subset(B,D)
& subset(B,C) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [B,C,D] :
( ( ! [E] :
( subset(E,B)
| ~ subset(E,D)
| ~ subset(E,C) )
& subset(B,D)
& subset(B,C)
& B != intersection(C,D) )
| ( ( ? [E] :
( ~ subset(E,B)
& subset(E,D)
& subset(E,C) )
| ~ subset(B,D)
| ~ subset(B,C) )
& B = intersection(C,D) ) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
! [E] :
( ( ( subset(E,sk2)
| ~ subset(E,sk4)
| ~ subset(E,sk3) )
& subset(sk2,sk4)
& subset(sk2,sk3)
& sk2 != intersection(sk3,sk4) )
| ( ( ( ~ subset(sk5,sk2)
& subset(sk5,sk4)
& subset(sk5,sk3) )
| ~ subset(sk2,sk4)
| ~ subset(sk2,sk3) )
& sk2 = intersection(sk3,sk4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f8_nnf]) ).
cnf(c20,plain,
( subset(sk2,sk3)
| sk2 = intersection(sk3,sk4) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f0,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(f0_nnf,plain,
! [B,C] : subset(intersection(B,C),B),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] : subset(intersection(B,C),B),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
subset(intersection(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p39,plain,
( subset(sk2,sk3)
| subset(sk2,sk3) ),
inference(superposition,[status(thm)],[c20,c0]) ).
cnf(p41,plain,
subset(sk2,sk3),
inference(factoring,[status(thm)],[p39]) ).
cnf(p102,plain,
( subset(sk2,intersection(sk3,X0))
| ~ subset(sk2,X0) ),
inference(resolution,[status(thm)],[c1,p41]) ).
cnf(c21,plain,
( subset(sk2,sk4)
| sk2 = intersection(sk3,sk4) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f5,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f5_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c11,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p49,plain,
subset(intersection(X0,X1),X1),
inference(superposition,[status(thm)],[c11,c0]) ).
cnf(p55,plain,
( subset(sk2,sk4)
| subset(sk2,sk4) ),
inference(superposition,[status(thm)],[c21,p49]) ).
cnf(p56,plain,
subset(sk2,sk4),
inference(factoring,[status(thm)],[p55]) ).
cnf(p111,plain,
subset(sk2,intersection(sk3,sk4)),
inference(resolution,[status(thm)],[p102,p56]) ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f4_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)],[f4]) ).
fof(f4_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c10,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(c22,plain,
( subset(X3,sk2)
| ~ subset(X3,sk4)
| ~ subset(X3,sk3)
| sk2 = intersection(sk3,sk4) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p36,plain,
( subset(intersection(sk3,X0),sk2)
| ~ subset(intersection(sk3,X0),sk4)
| sk2 = intersection(sk3,sk4) ),
inference(resolution,[status(thm)],[c0,c22]) ).
cnf(p51,plain,
( subset(intersection(sk3,X0),sk2)
| ~ subset(intersection(X0,sk3),sk4)
| sk2 = intersection(sk3,sk4) ),
inference(superposition,[status(thm)],[c11,p36]) ).
cnf(p53,plain,
( subset(intersection(sk3,sk4),sk2)
| sk2 = intersection(sk3,sk4) ),
inference(resolution,[status(thm)],[p51,c0]) ).
cnf(p91,plain,
( sk2 = intersection(sk3,sk4)
| ~ subset(sk2,intersection(sk3,sk4))
| intersection(sk3,sk4) = sk2 ),
inference(resolution,[status(thm)],[c10,p53]) ).
cnf(p123,plain,
( sk2 = intersection(sk3,sk4)
| intersection(sk3,sk4) = sk2 ),
inference(resolution,[status(thm)],[p111,p91]) ).
cnf(c26,plain,
( subset(X3,sk2)
| ~ subset(X3,sk4)
| ~ subset(X3,sk3)
| subset(sk5,sk3)
| ~ subset(sk2,sk4)
| ~ subset(sk2,sk3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p45,plain,
( subset(X0,sk2)
| ~ subset(X0,sk4)
| ~ subset(X0,sk3)
| subset(sk5,sk3)
| ~ subset(sk2,sk4) ),
inference(resolution,[status(thm)],[p41,c26]) ).
cnf(p60,plain,
( subset(X0,sk2)
| ~ subset(X0,sk4)
| ~ subset(X0,sk3)
| subset(sk5,sk3) ),
inference(resolution,[status(thm)],[p56,p45]) ).
cnf(p64,plain,
( subset(intersection(sk3,X0),sk2)
| ~ subset(intersection(sk3,X0),sk4)
| subset(sk5,sk3) ),
inference(resolution,[status(thm)],[p60,c0]) ).
cnf(p70,plain,
( subset(intersection(sk3,sk4),sk2)
| subset(sk5,sk3) ),
inference(resolution,[status(thm)],[p64,p49]) ).
cnf(p94,plain,
( subset(sk5,sk3)
| ~ subset(sk2,intersection(sk3,sk4))
| intersection(sk3,sk4) = sk2 ),
inference(resolution,[status(thm)],[c10,p70]) ).
cnf(p121,plain,
( subset(sk5,sk3)
| intersection(sk3,sk4) = sk2 ),
inference(resolution,[status(thm)],[p111,p94]) ).
cnf(p174,plain,
( sk2 = intersection(sk3,sk4)
| subset(sk5,sk3) ),
inference(superposition,[status(thm)],[p121,c11]) ).
cnf(c23,plain,
( sk2 != intersection(sk3,sk4)
| subset(sk5,sk3)
| ~ subset(sk2,sk4)
| ~ subset(sk2,sk3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p42,plain,
( sk2 != intersection(sk3,sk4)
| subset(sk5,sk3)
| ~ subset(sk2,sk4) ),
inference(resolution,[status(thm)],[p41,c23]) ).
cnf(p57,plain,
( sk2 != intersection(sk3,sk4)
| subset(sk5,sk3) ),
inference(resolution,[status(thm)],[p56,p42]) ).
cnf(p251,plain,
( subset(sk5,sk3)
| subset(sk5,sk3) ),
inference(resolution,[status(thm)],[p174,p57]) ).
cnf(p253,plain,
subset(sk5,sk3),
inference(factoring,[status(thm)],[p251]) ).
cnf(p257,plain,
( subset(sk5,intersection(sk3,X0))
| ~ subset(sk5,X0) ),
inference(resolution,[status(thm)],[p253,c1]) ).
cnf(c30,plain,
( subset(X3,sk2)
| ~ subset(X3,sk4)
| ~ subset(X3,sk3)
| subset(sk5,sk4)
| ~ subset(sk2,sk4)
| ~ subset(sk2,sk3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p46,plain,
( subset(X0,sk2)
| ~ subset(X0,sk4)
| ~ subset(X0,sk3)
| subset(sk5,sk4)
| ~ subset(sk2,sk4) ),
inference(resolution,[status(thm)],[p41,c30]) ).
cnf(p61,plain,
( subset(X0,sk2)
| ~ subset(X0,sk4)
| ~ subset(X0,sk3)
| subset(sk5,sk4) ),
inference(resolution,[status(thm)],[p56,p46]) ).
cnf(p67,plain,
( subset(intersection(sk3,X0),sk2)
| ~ subset(intersection(sk3,X0),sk4)
| subset(sk5,sk4) ),
inference(resolution,[status(thm)],[p61,c0]) ).
cnf(p73,plain,
( subset(intersection(sk3,sk4),sk2)
| subset(sk5,sk4) ),
inference(resolution,[status(thm)],[p67,p49]) ).
cnf(p95,plain,
( subset(sk5,sk4)
| ~ subset(sk2,intersection(sk3,sk4))
| intersection(sk3,sk4) = sk2 ),
inference(resolution,[status(thm)],[c10,p73]) ).
cnf(p122,plain,
( subset(sk5,sk4)
| intersection(sk3,sk4) = sk2 ),
inference(resolution,[status(thm)],[p111,p95]) ).
cnf(p182,plain,
( sk2 = intersection(sk3,sk4)
| subset(sk5,sk4) ),
inference(superposition,[status(thm)],[p122,c11]) ).
cnf(c27,plain,
( sk2 != intersection(sk3,sk4)
| subset(sk5,sk4)
| ~ subset(sk2,sk4)
| ~ subset(sk2,sk3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p43,plain,
( sk2 != intersection(sk3,sk4)
| subset(sk5,sk4)
| ~ subset(sk2,sk4) ),
inference(resolution,[status(thm)],[p41,c27]) ).
cnf(p58,plain,
( sk2 != intersection(sk3,sk4)
| subset(sk5,sk4) ),
inference(resolution,[status(thm)],[p56,p43]) ).
cnf(p259,plain,
( subset(sk5,sk4)
| subset(sk5,sk4) ),
inference(resolution,[status(thm)],[p182,p58]) ).
cnf(p260,plain,
subset(sk5,sk4),
inference(factoring,[status(thm)],[p259]) ).
cnf(p267,plain,
subset(sk5,intersection(sk3,sk4)),
inference(resolution,[status(thm)],[p257,p260]) ).
cnf(p430,plain,
( subset(sk5,sk2)
| sk2 = intersection(sk3,sk4) ),
inference(superposition,[status(thm)],[p123,p267]) ).
cnf(p436,plain,
( subset(sk5,sk2)
| subset(sk5,sk2) ),
inference(superposition,[status(thm)],[p430,p267]) ).
cnf(p437,plain,
subset(sk5,sk2),
inference(factoring,[status(thm)],[p436]) ).
cnf(c31,plain,
( sk2 != intersection(sk3,sk4)
| ~ subset(sk5,sk2)
| ~ subset(sk2,sk4)
| ~ subset(sk2,sk3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p44,plain,
( sk2 != intersection(sk3,sk4)
| ~ subset(sk5,sk2)
| ~ subset(sk2,sk4) ),
inference(resolution,[status(thm)],[p41,c31]) ).
cnf(p59,plain,
( sk2 != intersection(sk3,sk4)
| ~ subset(sk5,sk2) ),
inference(resolution,[status(thm)],[p56,p44]) ).
cnf(p438,plain,
sk2 != intersection(sk3,sk4),
inference(resolution,[status(thm)],[p437,p59]) ).
cnf(p443,plain,
( sk2 != sk2
| sk2 = intersection(sk3,sk4) ),
inference(superposition,[status(thm)],[p123,p438]) ).
cnf(p506,plain,
sk2 = intersection(sk3,sk4),
inference(equality_resolution,[status(thm)],[p443]) ).
cnf(p508,plain,
intersection(sk3,sk4) = sk2,
inference(superposition,[status(thm)],[p506,c11]) ).
cnf(p586,plain,
sk2 != sk2,
inference(demodulation,[status(thm)],[p508,p438]) ).
cnf(p593,plain,
$false,
inference(equality_resolution,[status(thm)],[p586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET598+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 : n018.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 11:26:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.44/3.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.44/3.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------