%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET648+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 02:47:41 PM UTC 2026
% Result : Theorem 7.72s 12.03s
% Output : CNFRefutation 8.67s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f144ERROR: Could not build tree for root c_5425ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X0,X1)
=> ( subset(cross_product(X2,X0),cross_product(X2,X1))
& subset(cross_product(X0,X2),cross_product(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
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)
=> ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
fof(f15,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',p15) ).
fof(f20,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',p20) ).
fof(f22,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',p22) ).
fof(f24,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(f27,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(range_of(X1),X0)
=> ilf_type(X1,relation_type(domain_of(X1),X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_10) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(range_of(X1),X0)
=> ilf_type(X1,relation_type(domain_of(X1),X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f30,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ) ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ subset(X0,X1)
| ( subset(cross_product(X2,X0),cross_product(X2,X1))
& subset(cross_product(X0,X2),cross_product(X1,X2)) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ subset(X0,X1)
| ( subset(cross_product(X2,X0),cross_product(X2,X1))
& subset(cross_product(X0,X2),cross_product(X1,X2)) ) ) ) ),
inference(flattening,[],[f32]) ).
fof(f34,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(f40,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f41,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( subset(X0,X1)
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f42,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( subset(X0,X1)
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(flattening,[],[f41]) ).
fof(f45,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,[],[f15]) ).
fof(f51,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,[],[f20]) ).
fof(f52,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,[],[f51]) ).
fof(f54,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,[],[f22]) ).
fof(f55,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,[],[f54]) ).
fof(f58,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f61,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,binary_relation_type)
& subset(range_of(X1),X0)
& ~ ilf_type(X1,relation_type(domain_of(X1),X0)) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f62,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,binary_relation_type)
& subset(range_of(X1),X0)
& ~ ilf_type(X1,relation_type(domain_of(X1),X0)) ) ),
inference(flattening,[],[f61]) ).
fof(f70,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ ilf_type(X0,binary_relation_type)
| ( ilf_type(X0,set_type)
& relation_like(X0) ) )
& ( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f71,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ ilf_type(X0,binary_relation_type)
| ( ilf_type(X0,set_type)
& relation_like(X0) ) )
& ( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ) ) ),
inference(flattening,[],[f70]) ).
fof(f73,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,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) )
| subset(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f74,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,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) )
| subset(X0,X1) ) ) ) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ subset(X0,X1)
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( ilf_type(sK4(X0,X1),set_type)
& member(sK4(X0,X1),X0)
& ~ member(sK4(X0,X1),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f74]) ).
fof(f76,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,[],[f45]) ).
fof(f81,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,[],[f52]) ).
fof(f82,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,[],[f81]) ).
fof(f83,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(sK9(X0,X1),set_type)
& member(sK9(X0,X1),X0)
& ~ member(sK9(X0,X1),X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f82]) ).
fof(f84,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,[],[f55]) ).
fof(f86,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0) )
| empty(X0) ) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f87,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0) )
| empty(X0) ) ) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ( ilf_type(sK11(X0),set_type)
& member(sK11(X0),X0) )
| empty(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X1,sK11(X0))],[f87]) ).
fof(f89,plain,
( ilf_type(sK12,set_type)
& ilf_type(sK13,binary_relation_type)
& subset(range_of(sK13),sK12)
& ~ ilf_type(sK13,relation_type(domain_of(sK13),sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f62]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f91,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(cnf_transformation,[],[f31]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1)
| subset(cross_product(X2,X0),cross_product(X2,X1)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f106,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f109,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f116,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f128,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK9(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f129,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK9(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f133,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f135,plain,
! [X2,X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f139,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f141,plain,
ilf_type(sK13,binary_relation_type),
inference(cnf_transformation,[],[f89]) ).
fof(f142,plain,
subset(range_of(sK13),sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f143,plain,
~ ilf_type(sK13,relation_type(domain_of(sK13),sK12)),
inference(cnf_transformation,[],[f89]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_50,plain,
! [X0: $i] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cross_product(X2,X0),cross_product(X2,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_64,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_65,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_70,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)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK9(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_97,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f139]) ).
tcf(c_98,negated_conjecture,
~ ilf_type(sK13,relation_type(domain_of(sK13),sK12)),
inference(cnf_transformation,[],[f143]) ).
tcf(c_99,negated_conjecture,
subset(range_of(sK13),sK12),
inference(cnf_transformation,[],[f142]) ).
tcf(c_100,negated_conjecture,
ilf_type(sK13,binary_relation_type),
inference(cnf_transformation,[],[f141]) ).
tcf(c_170,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_65,c_97,c_65]) ).
tcf(c_173,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_97,c_64]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK9(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_97,c_85]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( member(X1,power_set(X0))
| member(sK9(X1,X0),X1)
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_209]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] :
( member(X1,power_set(X0))
| member(sK9(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_210,c_97,c_210]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK9(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_211]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_90,c_97,c_95,c_90]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_218]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ member(sK9(X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_84,c_97,c_84]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_97,c_73]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ member(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_70,c_97,c_70]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(renaming,[status(thm)],[c_251]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cross_product(X2,X0),cross_product(X2,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_97,c_52]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_97,c_49]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(renaming,[status(thm)],[c_257]) ).
tcf(c_269,plain,
! [X0: $i] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_50,c_173]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cross_product(X2,X0),cross_product(X2,X1))
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_253,c_97]) ).
tcf(c_404,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_252,c_97]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_258,c_97]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_53,c_97]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_225,c_97]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_219,c_97]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ member(sK9(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_221,c_97]) ).
tcf(c_558,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cross_product(X2,X0),cross_product(X2,X1))
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_403,c_97]) ).
tcf(c_597,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_411,c_97]) ).
tcf(c_609,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_404,c_97]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_406,c_97]) ).
tcf(c_921,plain,
! [X0: $i] :
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_170]) ).
tcf(c_922,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(renaming,[status(thm)],[c_921]) ).
tcf(c_925,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_597]) ).
tcf(c_926,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(renaming,[status(thm)],[c_925]) ).
tcf(c_929,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_414]) ).
tcf(c_930,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(renaming,[status(thm)],[c_929]) ).
tcf(c_935,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cross_product(X2,X0),cross_product(X2,X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_558]) ).
tcf(c_943,plain,
! [X0: $i] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_269]) ).
tcf(c_955,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_418]) ).
tcf(c_959,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ member(sK9(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_419]) ).
tcf(c_963,plain,
! [X0: $i,X1: $i] :
( member(sK9(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(prop_impl_just,[status(thm)],[c_212]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| member(sK9(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_963]) ).
tcf(c_2297,plain,
( ilf_type(sK13,relation_type(domain_of(sK13),sK12))
| ~ ilf_type(sK13,subset_type(cross_product(domain_of(sK13),sK12))) ),
inference(instantiation,[status(thm)],[c_926]) ).
tcf(c_2301,plain,
( ilf_type(sK13,subset_type(cross_product(domain_of(sK13),sK12)))
| ~ ilf_type(sK13,member_type(power_set(cross_product(domain_of(sK13),sK12)))) ),
inference(instantiation,[status(thm)],[c_930]) ).
tcf(c_2308,plain,
( ilf_type(sK13,member_type(power_set(cross_product(domain_of(sK13),sK12))))
| ~ member(sK13,power_set(cross_product(domain_of(sK13),sK12))) ),
inference(instantiation,[status(thm)],[c_955]) ).
tcf(c_2329,plain,
( member(sK13,power_set(cross_product(domain_of(sK13),sK12)))
| ~ member(sK9(sK13,cross_product(domain_of(sK13),sK12)),cross_product(domain_of(sK13),sK12)) ),
inference(instantiation,[status(thm)],[c_959]) ).
tcf(c_2330,plain,
( member(sK13,power_set(cross_product(domain_of(sK13),sK12)))
| member(sK9(sK13,cross_product(domain_of(sK13),sK12)),sK13) ),
inference(instantiation,[status(thm)],[c_964]) ).
tcf(c_2491,plain,
! [X0: $i,X1: $i] :
( subset(X1,cross_product(domain_of(sK13),sK12))
| ~ subset(X1,X0)
| ~ subset(X0,cross_product(domain_of(sK13),sK12)) ),
inference(instantiation,[status(thm)],[c_623]) ).
tcf(c_2678,plain,
relation_like(sK13),
inference(superposition,[status(thm)],[c_100,c_922]) ).
tcf(c_2815,plain,
! [X0: $i] :
( subset(cross_product(domain_of(sK13),X0),cross_product(domain_of(sK13),sK12))
| ~ subset(X0,sK12) ),
inference(instantiation,[status(thm)],[c_935]) ).
tcf(c_2964,plain,
! [X0: $i,X1: $i] :
( subset(X1,cross_product(domain_of(sK13),sK12))
| ~ subset(X1,cross_product(domain_of(sK13),X0))
| ~ subset(cross_product(domain_of(sK13),X0),cross_product(domain_of(sK13),sK12)) ),
inference(instantiation,[status(thm)],[c_2491]) ).
tcf(c_3217,plain,
! [X0: $i,X1: $i] :
( member(sK9(sK13,X0),X0)
| ~ subset(X1,X0)
| ~ member(sK9(sK13,X0),X1) ),
inference(instantiation,[status(thm)],[c_609]) ).
tcf(c_3781,plain,
( subset(sK13,cross_product(domain_of(sK13),range_of(sK13)))
| ~ relation_like(sK13) ),
inference(instantiation,[status(thm)],[c_943]) ).
tcf(c_3913,plain,
( subset(cross_product(domain_of(sK13),range_of(sK13)),cross_product(domain_of(sK13),sK12))
| ~ subset(range_of(sK13),sK12) ),
inference(instantiation,[status(thm)],[c_2815]) ).
tcf(c_4286,plain,
( subset(sK13,cross_product(domain_of(sK13),sK12))
| ~ subset(sK13,cross_product(domain_of(sK13),range_of(sK13)))
| ~ subset(cross_product(domain_of(sK13),range_of(sK13)),cross_product(domain_of(sK13),sK12)) ),
inference(instantiation,[status(thm)],[c_2964]) ).
tcf(c_5424,plain,
( member(sK9(sK13,cross_product(domain_of(sK13),sK12)),cross_product(domain_of(sK13),sK12))
| ~ subset(sK13,cross_product(domain_of(sK13),sK12))
| ~ member(sK9(sK13,cross_product(domain_of(sK13),sK12)),sK13) ),
inference(instantiation,[status(thm)],[c_3217]) ).
tcf(c_5425,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5424,c_4286,c_3913,c_3781,c_2678,c_2329,c_2330,c_2308,c_2301,c_2297,c_98,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET648+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/10.61 % Computer : n002.cluster.edu
% 0.13/10.61 % Model : x86_64 x86_64
% 0.13/10.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.61 % Memory : 8046.5625MB
% 0.13/10.61 % OS : Linux 6.8.0-71-generic
% 0.13/10.61 % CPULimit : 300
% 0.13/10.61 % WCLimit : 300
% 0.13/10.61 % DateTime : Thu Sep 24 11:36:17 UTC 2026
% 0.13/10.62 % CPUTime :
% 0.13/10.62 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/10.66 Running first-order theorem proving
% 0.13/10.66 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
% 0.13/10.67
% 0.13/10.67 % ======== iProver multi-core TPTP/SMT =========
% 0.13/10.67
% 0.13/10.67 % Detected problem language: tptp
% 0.13/10.69 % Proving...
% 7.72/12.03 % SZS status Started for theBenchmark.p
% 7.72/12.03 % SZS status Theorem for theBenchmark.p
% 7.72/12.03
% 7.72/12.03 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.72/12.03
% 7.72/12.03 % ------ iProver source info
% 7.72/12.03
% 7.72/12.03 % git: date: 2026-07-19 20:42:38 +0200
% 7.72/12.03 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.72/12.03 % git: non_committed_changes: false
% 7.72/12.03
% 7.72/12.03 % ------ Parsing...
% 7.72/12.03 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.72/12.03
% 7.72/12.03 % ------ Preprocessing... sup_sim: 0 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 %
% 7.72/12.03
% 7.72/12.03 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.72/12.03
% 7.72/12.03 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.72/12.03 % ------ Proving...
% 7.72/12.03 % ------ Problem Properties
% 7.72/12.03
% 7.72/12.03 %
% 7.72/12.03 % clauses 39
% 7.72/12.03 % conjectures 3
% 7.72/12.03 % EPR 10
% 7.72/12.03 % Horn 33
% 7.72/12.03 % unary 9
% 7.72/12.03 % binary 21
% 7.72/12.03 % lits 78
% 8.67/12.03 % lits eq 2
% 8.67/12.03 % fd_pure 0
% 8.67/12.03 % fd_pseudo 0
% 8.67/12.03 % fd_cond 0
% 8.67/12.03 % fd_pseudo_cond 0
% 8.67/12.03 % AC symbols 0
% 8.67/12.03
% 8.67/12.03 % ------ Input Options Time Limit: Unbounded
% 8.67/12.03
% 8.67/12.03
% 8.67/12.03 % ------
% 8.67/12.03 % Current options:
% 8.67/12.03 % ------
% 8.67/12.03
% 8.67/12.03
% 8.67/12.03 %
% 8.67/12.03
% 8.67/12.03 % ------ Proving...
% 8.67/12.03 %
% 8.67/12.03
% 8.67/12.03 % SZS status Theorem for theBenchmark.p
% 8.67/12.03
% 8.67/12.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.67/12.04
% 8.67/12.04
%------------------------------------------------------------------------------