%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET201+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 : n001.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 02:42:52 PM UTC 2026
% Result : Theorem 21.04s 3.14s
% Output : Proof 21.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 6
% Syntax : Number of formulae : 89 ( 73 unt; 0 def)
% Number of atoms : 129 ( 69 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 67 ( 27 ~; 20 |; 15 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 108 ( 8 sgn 32 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f2_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c6,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t9,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t60,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(orient,[status(thm)],[t9]) ).
fof(f5,conjecture,
! [B,C,D,E] :
( ( subset(D,E)
& subset(B,C) )
=> subset(intersection(B,D),intersection(C,E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th41) ).
fof(f5_neg,negated_conjecture,
~ ! [B,C,D,E] :
( ( subset(D,E)
& subset(B,C) )
=> subset(intersection(B,D),intersection(C,E)) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [B,C,D,E] :
( ~ subset(intersection(B,D),intersection(C,E))
& subset(D,E)
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( ~ subset(intersection(sk2,sk4),intersection(sk3,sk5))
& subset(sk4,sk5)
& subset(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f5_nnf]) ).
cnf(c16,plain,
~ subset(intersection(sk2,sk4),intersection(sk3,sk5)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t11,plain,
subset(intersection(sk2,sk4),intersection(sk3,sk5)) = false,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t56,plain,
subset(intersection(sk2,sk4),intersection(sk3,sk5)) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t62,plain,
subset(intersection(sk2,sk4),intersection(sk3,sk5)) = false,
inference(rw,[status(thm)],[t56]) ).
cnf(t2125,plain,
subset(intersection(sk4,sk2),intersection(sk3,sk5)) = false,
inference(step,[status(thm)],[t62,t60]) ).
cnf(t2126,plain,
subset(intersection(sk4,sk2),intersection(sk5,sk3)) = false,
inference(step,[status(thm)],[t2125,t60]) ).
cnf(t69,plain,
subset(intersection(sk4,sk2),intersection(sk5,sk3)) = false,
inference(orient,[status(thm)],[t2126]) ).
fof(f1,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f1_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)],[f1]) ).
fof(f1_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])],[f1_nnf]) ).
cnf(c5,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t15,plain,
ifeq(member(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t38,plain,
ifeq(member(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(orient,[status(thm)],[t15]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f0_nnf,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [D,B,C] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c2,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t20,plain,
ifeq(member(X1,X2),true,ifeq(member(X1,X3),true,member(X1,intersection(X2,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t31,plain,
ifeq(member(X1,X2),true,ifeq(member(X1,X3),true,member(X1,intersection(X2,X3)),true),true) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t18,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t39,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(c15,plain,
subset(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t7,plain,
subset(sk4,sk5) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t52,plain,
subset(sk4,sk5) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t53,plain,
true = ifeq(true,true,ifeq(member(X1,sk4),true,member(X1,sk5),true),true),
inference(cp,[status(thm)],[t39,t52]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t2128,plain,
true = ifeq(member(X1,sk4),true,member(X1,sk5),true),
inference(step,[status(thm)],[t53,t22]) ).
cnf(t84,plain,
ifeq(member(X1,sk4),true,member(X1,sk5),true) = true,
inference(orient,[status(thm)],[t2128]) ).
cnf(c0,plain,
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t13,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t35,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X2),true) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(c4,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t12,plain,
or(subset(X1,X2),member(sk0(X1,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t44,plain,
or(subset(X1,X2),member(sk0(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t70,plain,
true = or(false,member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),intersection(sk4,sk2))),
inference(cp,[status(thm)],[t44,t69]) ).
cnf(t3,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t26,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t2129,plain,
true = member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),intersection(sk4,sk2)),
inference(step,[status(thm)],[t70,t26]) ).
cnf(t90,plain,
member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),intersection(sk4,sk2)) = true,
inference(orient,[status(thm)],[t2129]) ).
cnf(t95,plain,
true = ifeq(true,true,member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk4),true),
inference(cp,[status(thm)],[t35,t90]) ).
cnf(t2130,plain,
true = member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk4),
inference(step,[status(thm)],[t95,t22]) ).
cnf(t104,plain,
member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk4) = true,
inference(orient,[status(thm)],[t2130]) ).
cnf(t105,plain,
true = ifeq(true,true,member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk5),true),
inference(cp,[status(thm)],[t84,t104]) ).
cnf(t2132,plain,
true = member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk5),
inference(step,[status(thm)],[t105,t22]) ).
cnf(t128,plain,
member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk5) = true,
inference(orient,[status(thm)],[t2132]) ).
cnf(t137,plain,
true = ifeq(true,true,ifeq(member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),X1),true,member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),intersection(sk5,X1)),true),true),
inference(cp,[status(thm)],[t31,t128]) ).
cnf(t2210,plain,
true = ifeq(member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),X1),true,member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),intersection(sk5,X1)),true),
inference(step,[status(thm)],[t137,t22]) ).
cnf(t2039,plain,
ifeq(member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),X1),true,member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),intersection(sk5,X1)),true) = true,
inference(orient,[status(thm)],[t2210]) ).
cnf(c14,plain,
subset(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t6,plain,
subset(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t49,plain,
subset(sk2,sk3) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t50,plain,
true = ifeq(true,true,ifeq(member(X1,sk2),true,member(X1,sk3),true),true),
inference(cp,[status(thm)],[t39,t49]) ).
cnf(t2127,plain,
true = ifeq(member(X1,sk2),true,member(X1,sk3),true),
inference(step,[status(thm)],[t50,t22]) ).
cnf(t78,plain,
ifeq(member(X1,sk2),true,member(X1,sk3),true) = true,
inference(orient,[status(thm)],[t2127]) ).
cnf(c1,plain,
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t14,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t32,plain,
ifeq(member(X1,intersection(X2,X3)),true,member(X1,X3),true) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t97,plain,
true = ifeq(true,true,member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk2),true),
inference(cp,[status(thm)],[t32,t90]) ).
cnf(t2131,plain,
true = member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk2),
inference(step,[status(thm)],[t97,t22]) ).
cnf(t116,plain,
member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk2) = true,
inference(orient,[status(thm)],[t2131]) ).
cnf(t117,plain,
true = ifeq(true,true,member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk3),true),
inference(cp,[status(thm)],[t78,t116]) ).
cnf(t2133,plain,
true = member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk3),
inference(step,[status(thm)],[t117,t22]) ).
cnf(t139,plain,
member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),sk3) = true,
inference(orient,[status(thm)],[t2133]) ).
cnf(t2068,plain,
true = ifeq(true,true,member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),intersection(sk5,sk3)),true),
inference(cp,[status(thm)],[t2039,t139]) ).
cnf(t2211,plain,
true = member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),intersection(sk5,sk3)),
inference(step,[status(thm)],[t2068,t22]) ).
cnf(t2079,plain,
member(sk0(intersection(sk4,sk2),intersection(sk5,sk3)),intersection(sk5,sk3)) = true,
inference(orient,[status(thm)],[t2211]) ).
cnf(t2084,plain,
true = ifeq(true,true,subset(intersection(sk4,sk2),intersection(sk5,sk3)),true),
inference(cp,[status(thm)],[t38,t2079]) ).
cnf(t2215,plain,
true = subset(intersection(sk4,sk2),intersection(sk5,sk3)),
inference(step,[status(thm)],[t2084,t22]) ).
cnf(t2216,plain,
true = false,
inference(step,[status(thm)],[t2215,t69]) ).
cnf(t2119,plain,
false = true,
inference(orient,[status(thm)],[t2216]) ).
cnf(t2217,plain,
subset(intersection(sk4,sk2),intersection(sk5,sk3)) = true,
inference(step,[status(thm)],[t69,t2119]) ).
cnf(t2120,plain,
subset(intersection(sk4,sk2),intersection(sk5,sk3)) = true,
inference(orient,[status(thm)],[t2217]) ).
cnf(goal_0,negated_conjecture,
subset(intersection(sk2,sk4),intersection(sk3,sk5)) != true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(g0_0,plain,
subset(intersection(sk4,sk2),intersection(sk3,sk5)) != true,
inference(rw,[status(thm)],[goal_0,t60]) ).
cnf(g0_1,plain,
subset(intersection(sk4,sk2),intersection(sk5,sk3)) != true,
inference(rw,[status(thm)],[g0_0,t60]) ).
cnf(g0_2,plain,
true != true,
inference(rw,[status(thm)],[g0_1,t2120]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET201+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n001.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 10:20:22 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 21.04/3.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.04/3.14 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------