%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET645+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 02:47:40 PM UTC 2026
% Result : Theorem 4.26s 1.28s
% Output : CNFRefutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 86 ( 11 unt; 0 def)
% Number of atoms : 351 ( 1 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 452 ( 187 ~; 184 |; 42 &)
% ( 10 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 214 ( 0 sgn 202 !; 12 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f21,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f22,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_7) ).
fof(f23,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ) ) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f27,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f33,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f36,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( member(X0,power_set(X1))
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f37,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( member(X0,power_set(X1))
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f39,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f40,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(flattening,[],[f39]) ).
fof(f49,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,relation_type(X0,X1))
& member(ordered_pair(X2,X3),X4)
& ( ~ member(X3,X1)
| ~ member(X2,X0) ) ) ) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f50,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,relation_type(X0,X1))
& member(ordered_pair(X2,X3),X4)
& ( ~ member(X3,X1)
| ~ member(X2,X0) ) ) ) ) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ( member(X1,X3)
& member(X0,X2) ) )
& ( ~ member(X1,X3)
| ~ member(X0,X2)
| member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ) ) ) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f52,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ( member(X1,X3)
& member(X0,X2) ) )
& ( ~ member(X1,X3)
| ~ member(X0,X2)
| member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ) ) ) ) ),
inference(flattening,[],[f51]) ).
fof(f55,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) )
& ( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ) ) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f61,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X0,power_set(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f62,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X0,power_set(X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X0,power_set(X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( ilf_type(sK3(X0,X1),set_type)
& member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f62]) ).
fof(f64,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ( ~ ilf_type(X0,member_type(X1))
| member(X0,X1) )
& ( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ) ) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f72,plain,
( ilf_type(sK9,set_type)
& ilf_type(sK10,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK12,set_type)
& ilf_type(sK13,relation_type(sK9,sK10))
& member(ordered_pair(sK11,sK12),sK13)
& ( ~ member(sK12,sK10)
| ~ member(sK11,sK9) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12),skolemize(X4,sK13)],[f50]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
inference(cnf_transformation,[],[f52]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f79,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(X3,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[],[f27]) ).
fof(f86,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[],[f55]) ).
fof(f94,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f99,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f100,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,member_type(X1))
| member(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f114,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f21]) ).
fof(f119,plain,
ilf_type(sK13,relation_type(sK9,sK10)),
inference(cnf_transformation,[],[f72]) ).
fof(f120,plain,
member(ordered_pair(sK11,sK12),sK13),
inference(cnf_transformation,[],[f72]) ).
fof(f121,plain,
( ~ member(sK12,sK10)
| ~ member(sK11,sK9) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1)) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_74,plain,
! [X0: $i] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,member_type(X1)) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_90,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f114]) ).
tcf(c_91,negated_conjecture,
( ~ member(sK12,sK10)
| ~ member(sK11,sK9) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_92,negated_conjecture,
member(ordered_pair(sK11,sK12),sK13),
inference(cnf_transformation,[],[f120]) ).
tcf(c_93,negated_conjecture,
ilf_type(sK13,relation_type(sK9,sK10)),
inference(cnf_transformation,[],[f119]) ).
tcf(c_139,plain,
! [X0: $i] : ~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_74,c_90,c_74]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_77,c_90,c_77]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_90,c_63]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,power_set(X1))
| ~ member(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_90,c_73]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_232]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_90,c_51]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_90,c_50]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_233,c_90]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_208,c_90]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_215,c_90]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_90]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_238,c_90]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_236,c_90]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_265,c_90]) ).
tcf(c_410,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_258,c_90]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_268,c_90,c_90]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_269,c_90,c_90]) ).
tcf(c_548,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,member_type(X1))
| ( power_set(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_260]) ).
tcf(c_549,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(unflattening,[status(thm)],[c_548]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_392]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_262]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(prop_impl_just,[status(thm)],[c_424]) ).
tcf(c_627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(prop_impl_just,[status(thm)],[c_436]) ).
tcf(c_2147,plain,
! [X0: $i,X1: $i] :
( empty(power_set(X1))
| member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(superposition,[status(thm)],[c_623,c_260]) ).
tcf(c_2150,plain,
! [X0: $i,X1: $i] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_2147,c_262,c_549]) ).
tcf(c_2151,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_2150]) ).
tcf(c_3042,plain,
! [X0: $i,X1: $i] :
( empty(power_set(X1))
| member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(superposition,[status(thm)],[c_623,c_260]) ).
tcf(c_3044,plain,
! [X0: $i,X1: $i] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_3042,c_2151]) ).
tcf(c_3045,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_3044]) ).
tcf(c_3047,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,power_set(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(superposition,[status(thm)],[c_619,c_3045]) ).
tcf(c_3110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,cross_product(X1,X2))
| ~ member(X3,X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(superposition,[status(thm)],[c_3047,c_410]) ).
tcf(c_3118,plain,
! [X0: $i] :
( member(X0,cross_product(sK9,sK10))
| ~ member(X0,sK13) ),
inference(superposition,[status(thm)],[c_93,c_3110]) ).
tcf(c_3138,plain,
! [X0: $i,X1: $i] :
( member(X1,sK10)
| ~ member(ordered_pair(X0,X1),sK13) ),
inference(superposition,[status(thm)],[c_3118,c_627]) ).
tcf(c_3139,plain,
! [X0: $i,X1: $i] :
( member(X0,sK9)
| ~ member(ordered_pair(X0,X1),sK13) ),
inference(superposition,[status(thm)],[c_3118,c_625]) ).
tcf(c_3152,plain,
member(sK12,sK10),
inference(superposition,[status(thm)],[c_92,c_3138]) ).
tcf(c_3156,plain,
member(sK11,sK9),
inference(superposition,[status(thm)],[c_92,c_3139]) ).
tcf(c_3158,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3156,c_3152,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET645+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n002.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 11:35:34 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.39 Running first-order theorem proving
% 0.03/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.41
% 0.03/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.41
% 0.03/0.41 % Detected problem language: tptp
% 0.03/0.42 % Proving...
% 4.26/1.28 % SZS status Started for theBenchmark.p
% 4.26/1.28 % SZS status Theorem for theBenchmark.p
% 4.26/1.28
% 4.26/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.26/1.28
% 4.26/1.28 % ------ iProver source info
% 4.26/1.28
% 4.26/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.26/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.26/1.28 % git: non_committed_changes: false
% 4.26/1.28
% 4.26/1.28 % ------ Parsing...
% 4.26/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.26/1.28
% 4.26/1.28 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.26/1.28
% 4.26/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.26/1.28
% 4.26/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.26/1.28 % ------ Proving...
% 4.26/1.28 % ------ Problem Properties
% 4.26/1.28
% 4.26/1.28 %
% 4.26/1.28 % clauses 31
% 4.26/1.28 % conjectures 3
% 4.26/1.28 % EPR 4
% 4.26/1.28 % Horn 25
% 4.26/1.28 % unary 8
% 4.26/1.28 % binary 17
% 4.26/1.28 % lits 60
% 4.26/1.28 % lits eq 6
% 4.26/1.28 % fd_pure 0
% 4.26/1.28 % fd_pseudo 0
% 4.26/1.28 % fd_cond 0
% 4.26/1.28 % fd_pseudo_cond 2
% 4.26/1.28 % AC symbols 0
% 4.26/1.28
% 4.26/1.28 % ------ Input Options Time Limit: Unbounded
% 4.26/1.28
% 4.26/1.28
% 4.26/1.28 % ------
% 4.26/1.28 % Current options:
% 4.26/1.28 % ------
% 4.26/1.28
% 4.26/1.28
% 4.26/1.28 %
% 4.26/1.28
% 4.26/1.28 % ------ Proving...
% 4.26/1.28 %
% 4.26/1.28
% 4.26/1.28 % SZS status Theorem for theBenchmark.p
% 4.26/1.28
% 4.26/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.26/1.29
% 4.26/1.29
%------------------------------------------------------------------------------