%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET640+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 : n012.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 02:43:41 PM UTC 2026
% Result : Theorem 8.27s 1.51s
% Output : Proof 8.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 13
% Syntax : Number of formulae : 132 ( 98 unt; 0 def)
% Number of atoms : 293 ( 88 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 260 ( 99 ~; 90 |; 37 &)
% ( 5 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-4 aty)
% Number of variables : 198 ( 15 sgn 62 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f5_nnf,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk3(B,C),C)
& member(sk3(B,C),B)
& ilf_type(sk3(B,C),set_type) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type)
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f5_nnf]) ).
cnf(c14,plain,
( ~ member(sk3(X0,X1),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t60,plain,
ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,set_type),true,ifeq(member(sk3(X1,X2),X2),true,subset(X1,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
fof(f18,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f18_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c40,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t3,plain,
ilf_type(X1,set_type) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t85,plain,
ilf_type(X1,set_type) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t1037,plain,
ifeq(true,true,ifeq(ilf_type(X2,set_type),true,ifeq(member(sk3(X1,X2),X2),true,subset(X1,X2),true),true),true) = true,
inference(step,[status(thm)],[t60,t85]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t82,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t1038,plain,
ifeq(ilf_type(X2,set_type),true,ifeq(member(sk3(X1,X2),X2),true,subset(X1,X2),true),true) = true,
inference(step,[status(thm)],[t1037,t82]) ).
cnf(t1039,plain,
ifeq(true,true,ifeq(member(sk3(X1,X2),X2),true,subset(X1,X2),true),true) = true,
inference(step,[status(thm)],[t1038,t85]) ).
cnf(t1040,plain,
ifeq(member(sk3(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(step,[status(thm)],[t1039,t82]) ).
cnf(t120,plain,
ifeq(member(sk3(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(orient,[status(thm)],[t1040]) ).
fof(f10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
fof(f10_nnf,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk5(B,C),C)
& member(sk5(B,C),B)
& ilf_type(sk5(B,C),set_type) )
| member(B,power_set(C)) )
& ( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f10_nnf]) ).
cnf(c20,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t78,plain,
ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,set_type),true,ifeq(member(X1,power_set(X2)),true,ifeq(ilf_type(X3,set_type),true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t1027,plain,
ifeq(true,true,ifeq(ilf_type(X2,set_type),true,ifeq(member(X1,power_set(X2)),true,ifeq(ilf_type(X3,set_type),true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true),true),true) = true,
inference(step,[status(thm)],[t78,t85]) ).
cnf(t1028,plain,
ifeq(ilf_type(X2,set_type),true,ifeq(member(X1,power_set(X2)),true,ifeq(ilf_type(X3,set_type),true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true),true) = true,
inference(step,[status(thm)],[t1027,t82]) ).
cnf(t1029,plain,
ifeq(true,true,ifeq(member(X1,power_set(X2)),true,ifeq(ilf_type(X3,set_type),true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true),true) = true,
inference(step,[status(thm)],[t1028,t85]) ).
cnf(t1030,plain,
ifeq(member(X1,power_set(X2)),true,ifeq(ilf_type(X3,set_type),true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true) = true,
inference(step,[status(thm)],[t1029,t82]) ).
cnf(t1031,plain,
ifeq(member(X1,power_set(X2)),true,ifeq(true,true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true) = true,
inference(step,[status(thm)],[t1030,t85]) ).
cnf(t1032,plain,
ifeq(member(X1,power_set(X2)),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(step,[status(thm)],[t1031,t82]) ).
cnf(t118,plain,
ifeq(member(X1,power_set(X2)),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t1032]) ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f3_nnf,plain,
! [B] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C,D,E] :
( ( ( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c9,plain,
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi9,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,relation_type(X0,X1)),true,ilf_type(X2,subset_type(cross_product(X0,X1))),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f19,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(C,D))
=> ( subset(B,E)
=> subset(B,cross_product(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_2) ).
fof(f19_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(C,D))
=> ( subset(B,E)
=> subset(B,cross_product(C,D)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f19_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ subset(B,cross_product(C,D))
& subset(B,E)
& ilf_type(E,relation_type(C,D)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f19_neg]) ).
fof(f19_sk,plain,
( ~ subset(sk11,cross_product(sk12,sk13))
& subset(sk11,sk14)
& ilf_type(sk14,relation_type(sk12,sk13))
& ilf_type(sk13,set_type)
& ilf_type(sk12,set_type)
& ilf_type(sk11,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12,sk13,sk14])],[f19_nnf]) ).
cnf(c42,plain,
ilf_type(sk12,set_type),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi40,negated_conjecture,
ilf_type(sk12,set_type) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(c43,plain,
ilf_type(sk13,set_type),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi41,negated_conjecture,
ilf_type(sk13,set_type) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(c44,plain,
ilf_type(sk14,relation_type(sk12,sk13)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi42,negated_conjecture,
ilf_type(sk14,relation_type(sk12,sk13)) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(h12,plain,
ilf_type(sk14,subset_type(cross_product(sk12,sk13))) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi40,hi41,hi42]) ).
fof(f7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
fof(f7_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [B,C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c16,plain,
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi16,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X1,subset_type(X0)),true,ilf_type(X1,member_type(power_set(X0))),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(hi38,axiom,
ilf_type(X0,set_type) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(h50,plain,
ilf_type(sk14,member_type(power_set(cross_product(sk12,sk13)))) = true,
inference(hyper_resolution,[status(thm)],[hi16,hi38,hi38,h12]) ).
fof(f12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
fof(f12_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [B,C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c26,plain,
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi25,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X0,member_type(X1)),true,or(empty(X1),member(X0,X1)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t42,plain,
or(empty(power_set(cross_product(sk12,sk13))),member(sk14,power_set(cross_product(sk12,sk13)))) = true,
inference(hyper_resolution,[status(thm)],[hi25,hi38,hi38,h50]) ).
cnf(t151,plain,
or(empty(power_set(cross_product(sk12,sk13))),member(sk14,power_set(cross_product(sk12,sk13)))) = true,
inference(orient,[status(thm)],[t42]) ).
cnf(t19,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t181,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t19]) ).
fof(f11,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
fof(f11_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c24,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t35,plain,
or(not(ilf_type(X1,set_type)),not(empty(power_set(X1)))) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t1094,plain,
or(not(true),not(empty(power_set(X1)))) = true,
inference(step,[status(thm)],[t35,t85]) ).
cnf(t153,plain,
or(not(true),not(empty(power_set(X1)))) = true,
inference(orient,[status(thm)],[t1094]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t190,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t1106,plain,
or(false,not(empty(power_set(X1)))) = true,
inference(step,[status(thm)],[t153,t190]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t84,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t1107,plain,
not(empty(power_set(X1))) = true,
inference(step,[status(thm)],[t1106,t84]) ).
cnf(t192,plain,
not(empty(power_set(X1))) = true,
inference(rw,[status(thm)],[t1107]) ).
cnf(t194,plain,
not(empty(power_set(X1))) = true,
inference(orient,[status(thm)],[t192]) ).
cnf(t195,plain,
false = ifeq(true,true,empty(power_set(X1)),false),
inference(cp,[status(thm)],[t181,t194]) ).
cnf(t1112,plain,
false = empty(power_set(X1)),
inference(step,[status(thm)],[t195,t82]) ).
cnf(t196,plain,
empty(power_set(X1)) = false,
inference(orient,[status(thm)],[t1112]) ).
cnf(t1116,plain,
or(false,member(sk14,power_set(cross_product(sk12,sk13)))) = true,
inference(step,[status(thm)],[t151,t196]) ).
cnf(t1117,plain,
member(sk14,power_set(cross_product(sk12,sk13))) = true,
inference(step,[status(thm)],[t1116,t84]) ).
cnf(t205,plain,
member(sk14,power_set(cross_product(sk12,sk13))) = true,
inference(rw,[status(thm)],[t1117]) ).
cnf(t234,plain,
member(sk14,power_set(cross_product(sk12,sk13))) = true,
inference(orient,[status(thm)],[t205]) ).
cnf(t238,plain,
true = ifeq(true,true,ifeq(member(X1,sk14),true,member(X1,cross_product(sk12,sk13)),true),true),
inference(cp,[status(thm)],[t118,t234]) ).
cnf(t1209,plain,
true = ifeq(member(X1,sk14),true,member(X1,cross_product(sk12,sk13)),true),
inference(step,[status(thm)],[t238,t82]) ).
cnf(t598,plain,
ifeq(member(X1,sk14),true,member(X1,cross_product(sk12,sk13)),true) = true,
inference(orient,[status(thm)],[t1209]) ).
cnf(c11,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t77,plain,
ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,set_type),true,ifeq(subset(X1,X2),true,ifeq(ilf_type(X3,set_type),true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t1041,plain,
ifeq(true,true,ifeq(ilf_type(X2,set_type),true,ifeq(subset(X1,X2),true,ifeq(ilf_type(X3,set_type),true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true),true),true) = true,
inference(step,[status(thm)],[t77,t85]) ).
cnf(t1042,plain,
ifeq(ilf_type(X2,set_type),true,ifeq(subset(X1,X2),true,ifeq(ilf_type(X3,set_type),true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true),true) = true,
inference(step,[status(thm)],[t1041,t82]) ).
cnf(t1043,plain,
ifeq(true,true,ifeq(subset(X1,X2),true,ifeq(ilf_type(X3,set_type),true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true),true) = true,
inference(step,[status(thm)],[t1042,t85]) ).
cnf(t1044,plain,
ifeq(subset(X1,X2),true,ifeq(ilf_type(X3,set_type),true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true) = true,
inference(step,[status(thm)],[t1043,t82]) ).
cnf(t1045,plain,
ifeq(subset(X1,X2),true,ifeq(true,true,ifeq(member(X3,X1),true,member(X3,X2),true),true),true) = true,
inference(step,[status(thm)],[t1044,t85]) ).
cnf(t1046,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(step,[status(thm)],[t1045,t82]) ).
cnf(t121,plain,
ifeq(subset(X1,X2),true,ifeq(member(X3,X1),true,member(X3,X2),true),true) = true,
inference(orient,[status(thm)],[t1046]) ).
cnf(c45,plain,
subset(sk11,sk14),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t12,plain,
subset(sk11,sk14) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t154,plain,
subset(sk11,sk14) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t155,plain,
true = ifeq(true,true,ifeq(member(X1,sk11),true,member(X1,sk14),true),true),
inference(cp,[status(thm)],[t121,t154]) ).
cnf(t1150,plain,
true = ifeq(member(X1,sk11),true,member(X1,sk14),true),
inference(step,[status(thm)],[t155,t82]) ).
cnf(t371,plain,
ifeq(member(X1,sk11),true,member(X1,sk14),true) = true,
inference(orient,[status(thm)],[t1150]) ).
cnf(c13,plain,
( member(sk3(X0,X1),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t56,plain,
ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,set_type),true,or(subset(X1,X2),member(sk3(X1,X2),X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t1061,plain,
ifeq(true,true,ifeq(ilf_type(X2,set_type),true,or(subset(X1,X2),member(sk3(X1,X2),X1)),true),true) = true,
inference(step,[status(thm)],[t56,t85]) ).
cnf(t1062,plain,
ifeq(ilf_type(X2,set_type),true,or(subset(X1,X2),member(sk3(X1,X2),X1)),true) = true,
inference(step,[status(thm)],[t1061,t82]) ).
cnf(t1063,plain,
ifeq(true,true,or(subset(X1,X2),member(sk3(X1,X2),X1)),true) = true,
inference(step,[status(thm)],[t1062,t85]) ).
cnf(t1064,plain,
or(subset(X1,X2),member(sk3(X1,X2),X1)) = true,
inference(step,[status(thm)],[t1063,t82]) ).
cnf(t125,plain,
or(subset(X1,X2),member(sk3(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t1064]) ).
cnf(c46,plain,
~ subset(sk11,cross_product(sk12,sk13)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t18,plain,
subset(sk11,cross_product(sk12,sk13)) = false,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t182,plain,
subset(sk11,cross_product(sk12,sk13)) = false,
inference(orient,[status(thm)],[t18]) ).
cnf(t183,plain,
true = or(false,member(sk3(sk11,cross_product(sk12,sk13)),sk11)),
inference(cp,[status(thm)],[t125,t182]) ).
cnf(t1122,plain,
true = member(sk3(sk11,cross_product(sk12,sk13)),sk11),
inference(step,[status(thm)],[t183,t84]) ).
cnf(t245,plain,
member(sk3(sk11,cross_product(sk12,sk13)),sk11) = true,
inference(orient,[status(thm)],[t1122]) ).
cnf(t373,plain,
true = ifeq(true,true,member(sk3(sk11,cross_product(sk12,sk13)),sk14),true),
inference(cp,[status(thm)],[t371,t245]) ).
cnf(t1169,plain,
true = member(sk3(sk11,cross_product(sk12,sk13)),sk14),
inference(step,[status(thm)],[t373,t82]) ).
cnf(t440,plain,
member(sk3(sk11,cross_product(sk12,sk13)),sk14) = true,
inference(orient,[status(thm)],[t1169]) ).
cnf(t602,plain,
true = ifeq(true,true,member(sk3(sk11,cross_product(sk12,sk13)),cross_product(sk12,sk13)),true),
inference(cp,[status(thm)],[t598,t440]) ).
cnf(t1275,plain,
true = member(sk3(sk11,cross_product(sk12,sk13)),cross_product(sk12,sk13)),
inference(step,[status(thm)],[t602,t82]) ).
cnf(t913,plain,
member(sk3(sk11,cross_product(sk12,sk13)),cross_product(sk12,sk13)) = true,
inference(orient,[status(thm)],[t1275]) ).
cnf(t917,plain,
true = ifeq(true,true,subset(sk11,cross_product(sk12,sk13)),true),
inference(cp,[status(thm)],[t120,t913]) ).
cnf(t1276,plain,
true = subset(sk11,cross_product(sk12,sk13)),
inference(step,[status(thm)],[t917,t82]) ).
cnf(t1277,plain,
true = false,
inference(step,[status(thm)],[t1276,t182]) ).
cnf(t931,plain,
false = true,
inference(orient,[status(thm)],[t1277]) ).
fof(f14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f14_nnf,plain,
! [B] :
( ( ( ? [C] :
( member(C,B)
& ilf_type(C,set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [B,C] :
( ( ( ( member(sk7(B),B)
& ilf_type(sk7(B),set_type) )
| empty(B) )
& ( ~ member(C,B)
| ~ ilf_type(C,set_type)
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f14_nnf]) ).
cnf(c29,plain,
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c24,c29,c46]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t931]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET640+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Thu Sep 24 11:32:35 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.27/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.27/1.51 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------