%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET644+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 : 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 02:47:40 PM UTC 2026
% Result : Theorem 10.29s 2.26s
% Output : CNFRefutation 10.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 111 ( 18 unt; 1 def)
% Number of atoms : 484 ( 26 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 633 ( 265 ~; 256 |; 66 &)
% ( 13 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 278 ( 0 sgn 252 !; 26 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,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',p2) ).
fof(f5,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',p5) ).
fof(f14,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',p14) ).
fof(f19,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',p19) ).
fof(f20,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',p20) ).
fof(f21,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',p21) ).
fof(f23,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( relation_like(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
=> ? [X2] :
( ? [X3] :
( X1 = ordered_pair(X2,X3)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
fof(f24,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(f28,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ( member(X2,X3)
=> ? [X4] :
( ? [X5] :
( member(X5,X1)
& member(X4,X0)
& X2 = ordered_pair(X4,X5)
& ilf_type(X5,set_type) )
& ilf_type(X4,set_type) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_6) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ( member(X2,X3)
=> ? [X4] :
( ? [X5] :
( member(X5,X1)
& member(X4,X0)
& X2 = ordered_pair(X4,X5)
& ilf_type(X5,set_type) )
& ilf_type(X4,set_type) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f32,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,[],[f2]) ).
fof(f35,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,[],[f5]) ).
fof(f43,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,[],[f14]) ).
fof(f49,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,[],[f19]) ).
fof(f50,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,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f52,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,[],[f21]) ).
fof(f53,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,[],[f52]) ).
fof(f56,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( relation_like(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0)
| ? [X2] :
( ? [X3] :
( X1 = ordered_pair(X2,X3)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f57,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( relation_like(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0)
| ? [X2] :
( ? [X3] :
( X1 = ordered_pair(X2,X3)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f62,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X0,X1))
& member(X2,X3)
& ! [X4] :
( ! [X5] :
( ~ member(X5,X1)
| ~ member(X4,X0)
| ordered_pair(X4,X5) != X2
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) ) ) ) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X0,X1))
& member(X2,X3)
& ! [X4] :
( ! [X5] :
( ~ member(X5,X1)
| ~ member(X4,X0)
| ordered_pair(X4,X5) != X2
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) ) ) ) ) ),
inference(flattening,[],[f62]) ).
fof(f65,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,[],[f32]) ).
fof(f66,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,[],[f65]) ).
fof(f74,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,[],[f43]) ).
fof(f83,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,[],[f50]) ).
fof(f84,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,[],[f83]) ).
fof(f85,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(sK7(X0,X1),set_type)
& member(sK7(X0,X1),X0)
& ~ member(sK7(X0,X1),X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f84]) ).
fof(f86,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,[],[f53]) ).
fof(f88,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ relation_like(X0)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0)
| ? [X2] :
( ? [X3] :
( X1 = ordered_pair(X2,X3)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0)
& ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| relation_like(X0) ) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f89,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ relation_like(X0)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X0)
| ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) ) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0)
& ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| relation_like(X0) ) ) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ relation_like(X0)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X0)
| ( ordered_pair(sK10(X4),sK11(X4)) = X4
& ilf_type(sK11(X4),set_type)
& ilf_type(sK10(X4),set_type) ) ) )
& ( ( ilf_type(sK9(X0),set_type)
& member(sK9(X0),X0)
& ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK9(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| relation_like(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X1,sK9(X0)),skolemize(X5,sK10(X4)),skolemize(X6,sK11(X4))],[f89]) ).
fof(f94,plain,
( ilf_type(sK13,set_type)
& ilf_type(sK14,set_type)
& ilf_type(sK15,set_type)
& ilf_type(sK16,relation_type(sK13,sK14))
& member(sK15,sK16)
& ! [X4] :
( ! [X5] :
( ~ member(X5,sK14)
| ~ member(X4,sK13)
| ordered_pair(X4,X5) != sK15
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16)],[f63]) ).
fof(f98,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,[],[f66]) ).
fof(f99,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,[],[f66]) ).
fof(f104,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,[],[f35]) ).
fof(f118,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,[],[f74]) ).
fof(f131,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,[],[f85]) ).
fof(f136,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f137,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,[],[f86]) ).
fof(f140,plain,
! [X0,X4] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ~ ilf_type(X4,set_type)
| ~ member(X4,X0)
| ordered_pair(sK10(X4),sK11(X4)) = X4 ),
inference(cnf_transformation,[],[f90]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f151,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f155,plain,
ilf_type(sK16,relation_type(sK13,sK14)),
inference(cnf_transformation,[],[f94]) ).
fof(f156,plain,
member(sK15,sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f157,plain,
! [X4,X5] :
( ~ member(X5,sK14)
| ~ member(X4,sK13)
| ordered_pair(X4,X5) != sK15
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_53,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,[],[f99]) ).
tcf(c_54,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,[],[f98]) ).
tcf(c_59,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,[],[f104]) ).
tcf(c_72,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,[],[f118]) ).
tcf(c_87,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,[],[f131]) ).
tcf(c_88,plain,
! [X0: $i] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_91,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,[],[f137]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ( ordered_pair(sK10(X0),sK11(X0)) = X0 )
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_104,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f151]) ).
tcf(c_105,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ member(X1,sK14)
| ~ member(X0,sK13)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ( ordered_pair(X0,X1) != sK15 ) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_106,negated_conjecture,
member(sK15,sK16),
inference(cnf_transformation,[],[f156]) ).
tcf(c_107,negated_conjecture,
ilf_type(sK16,relation_type(sK13,sK14)),
inference(cnf_transformation,[],[f155]) ).
tcf(c_167,plain,
! [X0: $i] : ~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_88,c_104,c_88]) ).
tcf(c_258,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_91,c_104,c_91]) ).
tcf(c_265,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_72,c_104,c_72]) ).
tcf(c_285,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ member(X1,sK14)
| ~ member(X0,sK13)
| ~ ilf_type(X1,set_type)
| ( ordered_pair(X0,X1) != sK15 ) ),
inference(global_subsumption_just,[status(thm)],[c_105,c_104,c_105]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i] :
( ( ordered_pair(sK10(X0),sK11(X0)) = X0 )
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_98,c_104,c_98]) ).
tcf(c_291,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_87,c_104,c_87]) ).
tcf(c_292,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_291]) ).
tcf(c_295,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_54,c_104,c_54]) ).
tcf(c_297,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_53,c_104,c_53]) ).
tcf(c_452,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_59,c_104]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_99,c_104]) ).
tcf(c_455,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_297,c_104]) ).
tcf(c_456,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_295,c_104]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_258,c_104]) ).
tcf(c_463,plain,
! [X0: $i,X1: $i] :
( ~ member(X1,sK14)
| ~ member(X0,sK13)
| ( ordered_pair(X0,X1) != sK15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_285,c_104]) ).
tcf(c_464,plain,
! [X0: $i,X1: $i] :
( ( ordered_pair(sK10(X0),sK11(X0)) = X0 )
| ~ relation_like(X1)
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_287,c_104]) ).
tcf(c_468,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_292,c_104]) ).
tcf(c_470,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_265,c_104]) ).
tcf(c_568,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_454,c_104]) ).
tcf(c_614,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_452,c_104]) ).
tcf(c_657,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_468,c_104]) ).
tcf(c_671,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_455,c_104,c_104]) ).
tcf(c_683,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_456,c_104,c_104]) ).
tcf(c_1065,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_614]) ).
tcf(c_1073,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_470]) ).
tcf(c_1079,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_671]) ).
tcf(c_1081,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_683]) ).
tcf(c_1087,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_568,c_614]) ).
tcf(c_1703,definition,
iPr_def_10 = relation_type(sK13,sK14),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1704,plain,
! [X0: $i,X1: $i] :
( ~ member(X1,sK14)
| ~ member(X0,sK13)
| ( ordered_pair(X0,X1) != sK15 ) ),
inference(demodulation,[status(thm)],[c_463]) ).
tcf(c_1705,negated_conjecture,
ilf_type(sK16,iPr_def_10),
inference(demodulation,[status(thm)],[c_107,c_1703]) ).
tcf(c_1706,negated_conjecture,
member(sK15,sK16),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_19764,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1703,c_1087]) ).
tcf(c_19785,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_1073,c_458]) ).
tcf(c_19786,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19785,c_167]) ).
tcf(c_19828,plain,
relation_like(sK16),
inference(superposition,[status(thm)],[c_1705,c_19764]) ).
tcf(c_19889,plain,
( ( ordered_pair(sK10(sK15),sK11(sK15)) = sK15 )
| ~ relation_like(sK16) ),
inference(superposition,[status(thm)],[c_1706,c_464]) ).
tcf(c_19892,plain,
ordered_pair(sK10(sK15),sK11(sK15)) = sK15,
inference(forward_subsumption_resolution,[status(thm)],[c_19889,c_19828]) ).
tcf(c_19965,plain,
! [X0: $i,X1: $i] :
( member(sK11(sK15),X1)
| ~ member(sK15,cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_19892,c_1081]) ).
tcf(c_19966,plain,
! [X0: $i,X1: $i] :
( member(sK10(sK15),X0)
| ~ member(sK15,cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_19892,c_1079]) ).
tcf(c_19968,plain,
( ~ member(sK11(sK15),sK14)
| ~ member(sK10(sK15),sK13) ),
inference(superposition,[status(thm)],[c_19892,c_1704]) ).
tcf(c_20022,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_1065,c_19786]) ).
tcf(c_20904,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_20022,c_657]) ).
tcf(c_21728,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(sK13,sK14))
| ~ ilf_type(X1,iPr_def_10)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_1703,c_20904]) ).
tcf(c_21770,plain,
( member(sK15,cross_product(sK13,sK14))
| ~ ilf_type(sK16,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1706,c_21728]) ).
tcf(c_21802,plain,
member(sK15,cross_product(sK13,sK14)),
inference(forward_subsumption_resolution,[status(thm)],[c_21770,c_1705]) ).
tcf(c_21938,plain,
member(sK10(sK15),sK13),
inference(superposition,[status(thm)],[c_21802,c_19966]) ).
tcf(c_21939,plain,
member(sK11(sK15),sK14),
inference(superposition,[status(thm)],[c_21802,c_19965]) ).
tcf(c_21944,plain,
~ member(sK11(sK15),sK14),
inference(backward_subsumption_resolution,[status(thm)],[c_19968,c_21938]) ).
tcf(c_21945,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_21944,c_21939]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET644+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 : 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 11:35:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 10.29/2.26 % SZS status Started for theBenchmark.p
% 10.29/2.26 % SZS status Theorem for theBenchmark.p
% 10.29/2.26
% 10.29/2.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.29/2.26
% 10.29/2.26 % ------ iProver source info
% 10.29/2.26
% 10.29/2.26 % git: date: 2026-07-19 20:42:38 +0200
% 10.29/2.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.29/2.26 % git: non_committed_changes: false
% 10.29/2.26
% 10.29/2.26 % ------ Parsing...
% 10.29/2.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.29/2.26
% 10.29/2.26 % ------ 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 %
% 10.29/2.26
% 10.29/2.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.29/2.26
% 10.29/2.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.29/2.26 % ------ Proving...
% 10.29/2.26 % ------ Problem Properties
% 10.29/2.26
% 10.29/2.26 %
% 10.29/2.26 % clauses 41
% 10.29/2.26 % conjectures 2
% 10.29/2.26 % EPR 11
% 10.29/2.26 % Horn 34
% 10.29/2.26 % unary 11
% 10.29/2.26 % binary 20
% 10.29/2.26 % lits 81
% 10.29/2.26 % lits eq 10
% 10.29/2.26 % fd_pure 0
% 10.29/2.26 % fd_pseudo 0
% 10.29/2.26 % fd_cond 0
% 10.29/2.26 % fd_pseudo_cond 3
% 10.29/2.26 % AC symbols 0
% 10.29/2.26
% 10.29/2.26 % ------ Schedule dynamic 5 is on
% 10.29/2.26
% 10.29/2.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.29/2.26
% 10.29/2.26
% 10.29/2.26 % ------
% 10.29/2.26 % Current options:
% 10.29/2.26 % ------
% 10.29/2.26
% 10.29/2.26
% 10.29/2.26 %
% 10.29/2.26
% 10.29/2.26 % ------ Proving...
% 10.29/2.26 %
% 10.29/2.26
% 10.29/2.26 % SZS status Theorem for theBenchmark.p
% 10.29/2.26
% 10.29/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.29/2.26
% 10.29/2.26
%------------------------------------------------------------------------------