%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET682+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 02:47:47 PM UTC 2026
% Result : Theorem 3.72s 1.27s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f125ERROR: Could not build tree for root c_4106ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,domain_of(X1))
=> ? [X2] :
( member(X2,range_of(X1))
& ilf_type(X2,set_type) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,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/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f4,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/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f5,axiom,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ? [X1] : ilf_type(X1,member_type(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f12,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/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f14,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/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f18,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/sandbox2/benchmark/theBenchmark.p',p18) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain(X0,X1,X2) = domain_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range(X0,X1,X2) = range_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f23,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(f24,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(f25,conjecture,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,domain(X0,X1,X2))
=> ? [X4] :
( member(X4,range(X0,X1,X2))
& ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_49) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,domain(X0,X1,X2))
=> ? [X4] :
( member(X4,range(X0,X1,X2))
& ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,domain_of(X1))
| ? [X2] :
( member(X2,range_of(X1))
& ilf_type(X2,set_type) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,domain_of(X1))
| ? [X2] :
( member(X2,range_of(X1))
& ilf_type(X2,set_type) ) ) ),
inference(flattening,[],[f27]) ).
fof(f29,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,[],[f2]) ).
fof(f31,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,[],[f4]) ).
fof(f32,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,[],[f31]) ).
fof(f33,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| empty(X0)
| ? [X1] : ilf_type(X1,member_type(X0)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f34,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| empty(X0)
| ? [X1] : ilf_type(X1,member_type(X0)) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f40,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,[],[f12]) ).
fof(f42,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,[],[f14]) ).
fof(f43,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,[],[f42]) ).
fof(f44,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f49,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,[],[f18]) ).
fof(f51,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f53,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f54,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f55,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& ? [X3] :
( ilf_type(X3,member_type(X0))
& member(X3,domain(X0,X1,X2))
& ! [X4] :
( ~ member(X4,range(X0,X1,X2))
| ~ ilf_type(X4,member_type(X1)) ) ) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f56,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ empty(X1)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& ? [X3] :
( ilf_type(X3,member_type(X0))
& member(X3,domain(X0,X1,X2))
& ! [X4] :
( ~ member(X4,range(X0,X1,X2))
| ~ ilf_type(X4,member_type(X1)) ) ) ) ) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,domain_of(X1))
| ( member(sK0(X1),range_of(X1))
& ilf_type(sK0(X1),set_type) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X1))],[f28]) ).
fof(f59,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,[],[f32]) ).
fof(f60,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| empty(X0)
| ilf_type(sK2(X0),member_type(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f34]) ).
fof(f61,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,[],[f35]) ).
fof(f62,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,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ( ilf_type(sK3(X0),set_type)
& member(sK3(X0),X0) )
| empty(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f62]) ).
fof(f67,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,[],[f40]) ).
fof(f69,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,[],[f43]) ).
fof(f70,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,[],[f69]) ).
fof(f71,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(sK6(X0,X1),set_type)
& member(sK6(X0,X1),X0)
& ~ member(sK6(X0,X1),X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f70]) ).
fof(f75,plain,
( ilf_type(sK10,set_type)
& ~ empty(sK10)
& ilf_type(sK11,set_type)
& ~ empty(sK11)
& ilf_type(sK12,relation_type(sK10,sK11))
& ilf_type(sK13,member_type(sK10))
& member(sK13,domain(sK10,sK11,sK12))
& ! [X4] :
( ~ member(X4,range(sK10,sK11,sK12))
| ~ ilf_type(X4,member_type(sK11)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f56]) ).
fof(f76,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,domain_of(X1))
| member(sK0(X1),range_of(X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f78,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,[],[f29]) ).
fof(f81,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,[],[f59]) ).
fof(f82,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,[],[f59]) ).
fof(f83,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| empty(X0)
| ilf_type(sK2(X0),member_type(X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f84,plain,
! [X2,X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f94,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,[],[f67]) ).
fof(f97,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,[],[f71]) ).
fof(f102,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f110,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,[],[f49]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f116,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f24]) ).
fof(f121,plain,
ilf_type(sK12,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f75]) ).
fof(f123,plain,
member(sK13,domain(sK10,sK11,sK12)),
inference(cnf_transformation,[],[f75]) ).
fof(f124,plain,
! [X4] :
( ~ member(X4,range(sK10,sK11,sK12))
| ~ ilf_type(X4,member_type(sK11)) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( member(sK0(X1),range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,domain_of(X1)) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_52,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,[],[f78]) ).
tcf(c_54,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,[],[f82]) ).
tcf(c_55,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,[],[f81]) ).
tcf(c_56,plain,
! [X0: $i] :
( empty(X0)
| ilf_type(sK2(X0),member_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_63,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_67,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,[],[f94]) ).
tcf(c_72,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,[],[f97]) ).
tcf(c_73,plain,
! [X0: $i] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_82,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,[],[f110]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_88,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f116]) ).
tcf(c_89,negated_conjecture,
! [X0: $i] :
( ~ ilf_type(X0,member_type(sK11))
| ~ member(X0,range(sK10,sK11,sK12)) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_90,negated_conjecture,
member(sK13,domain(sK10,sK11,sK12)),
inference(cnf_transformation,[],[f123]) ).
tcf(c_92,negated_conjecture,
ilf_type(sK12,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_139,plain,
! [X0: $i] : ~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_73,c_88,c_73]) ).
tcf(c_157,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_88,c_63]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_88,c_59]) ).
tcf(c_201,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_67,c_88,c_67]) ).
tcf(c_205,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_55,c_88,c_55]) ).
tcf(c_207,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_54,c_88,c_59,c_54]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(renaming,[status(thm)],[c_207]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( member(sK0(X1),range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,domain_of(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_88,c_50]) ).
tcf(c_221,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_72,c_88,c_72]) ).
tcf(c_222,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_221]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_87,c_88]) ).
tcf(c_348,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_201,c_88]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_179,c_88]) ).
tcf(c_350,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_222,c_88]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_208,c_88]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_205,c_88]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_86,c_88]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_84,c_88]) ).
tcf(c_358,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_82,c_88]) ).
tcf(c_359,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_52,c_88]) ).
tcf(c_446,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_358,c_88]) ).
tcf(c_480,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_359,c_88]) ).
tcf(c_502,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_346,c_88]) ).
tcf(c_524,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_355,c_88]) ).
tcf(c_535,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_356,c_88]) ).
tcf(c_547,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_350,c_88]) ).
tcf(c_929,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_157]) ).
tcf(c_937,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_348]) ).
tcf(c_939,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_446,c_480]) ).
tcf(c_941,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_535]) ).
tcf(c_945,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_524]) ).
tcf(c_947,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_502]) ).
tcf(c_951,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_351]) ).
tcf(c_953,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_349]) ).
tcf(c_973,plain,
! [X0: $i] :
( ilf_type(sK2(X0),member_type(X0))
| empty(X0) ),
inference(prop_impl_just,[status(thm)],[c_88,c_56]) ).
tcf(c_974,plain,
! [X0: $i] :
( empty(X0)
| ilf_type(sK2(X0),member_type(X0)) ),
inference(renaming,[status(thm)],[c_973]) ).
tcf(c_1540,definition,
iPr_def_10 = relation_type(sK10,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1542,definition,
iPr_def_12 = domain(sK10,sK11,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1543,definition,
iPr_def_13 = range(sK10,sK11,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1544,definition,
iPr_def_14 = member_type(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1547,negated_conjecture,
ilf_type(sK12,iPr_def_10),
inference(demodulation,[status(thm)],[c_92,c_1540]) ).
tcf(c_1549,negated_conjecture,
member(sK13,iPr_def_12),
inference(demodulation,[status(thm)],[c_90,c_1542]) ).
tcf(c_1550,negated_conjecture,
! [X0: $i] :
( ~ member(X0,iPr_def_13)
| ~ ilf_type(X0,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_89,c_1544,c_1543]) ).
tcf(c_2368,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1540,c_939]) ).
tcf(c_2377,plain,
! [X0: $i] :
( ilf_type(X0,iPr_def_14)
| ~ member(X0,sK11) ),
inference(superposition,[status(thm)],[c_1544,c_951]) ).
tcf(c_2389,plain,
relation_like(sK12),
inference(superposition,[status(thm)],[c_1547,c_2368]) ).
tcf(c_2432,plain,
! [X0: $i] :
( empty(X0)
| member(sK2(X0),X0) ),
inference(superposition,[status(thm)],[c_974,c_352]) ).
tcf(c_2450,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_937,c_352]) ).
tcf(c_2451,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2450,c_139]) ).
tcf(c_2559,plain,
( ilf_type(iPr_def_13,subset_type(sK11))
| ~ ilf_type(sK12,relation_type(sK10,sK11)) ),
inference(superposition,[status(thm)],[c_1543,c_947]) ).
tcf(c_2561,plain,
( ilf_type(iPr_def_13,subset_type(sK11))
| ~ ilf_type(sK12,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_2559,c_1540]) ).
tcf(c_2562,plain,
ilf_type(iPr_def_13,subset_type(sK11)),
inference(forward_subsumption_resolution,[status(thm)],[c_2561,c_1547]) ).
tcf(c_2571,plain,
! [X0: $i] :
( ( domain(sK10,sK11,X0) = domain_of(X0) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1540,c_941]) ).
tcf(c_2581,plain,
! [X0: $i] :
( ( range(sK10,sK11,X0) = range_of(X0) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1540,c_945]) ).
tcf(c_2621,plain,
member(iPr_def_13,power_set(sK11)),
inference(superposition,[status(thm)],[c_2562,c_2451]) ).
tcf(c_2879,plain,
! [X0: $i] :
( member(X0,sK11)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2621,c_547]) ).
tcf(c_2972,plain,
! [X0: $i] : ~ member(X0,iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_2879,c_1550,c_2377,c_2879]) ).
tcf(c_2978,plain,
empty(iPr_def_13),
inference(superposition,[status(thm)],[c_2432,c_2972]) ).
tcf(c_3428,plain,
domain(sK10,sK11,sK12) = domain_of(sK12),
inference(superposition,[status(thm)],[c_1547,c_2571]) ).
tcf(c_3433,plain,
domain_of(sK12) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3428,c_1542]) ).
tcf(c_3446,plain,
! [X0: $i] :
( member(sK0(sK12),range_of(sK12))
| ~ ilf_type(sK12,binary_relation_type)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3433,c_210]) ).
tcf(c_3973,plain,
( member(sK0(sK12),range_of(sK12))
| ~ ilf_type(sK12,binary_relation_type) ),
inference(superposition,[status(thm)],[c_1549,c_3446]) ).
tcf(c_3988,plain,
( ~ empty(range_of(sK12))
| ~ ilf_type(sK12,binary_relation_type) ),
inference(superposition,[status(thm)],[c_3973,c_953]) ).
tcf(c_3998,plain,
( ~ relation_like(sK12)
| ~ empty(range_of(sK12)) ),
inference(superposition,[status(thm)],[c_929,c_3988]) ).
tcf(c_3999,plain,
~ empty(range_of(sK12)),
inference(forward_subsumption_resolution,[status(thm)],[c_3998,c_2389]) ).
tcf(c_4094,plain,
range(sK10,sK11,sK12) = range_of(sK12),
inference(superposition,[status(thm)],[c_1547,c_2581]) ).
tcf(c_4101,plain,
range_of(sK12) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_4094,c_1543]) ).
tcf(c_4103,plain,
~ empty(iPr_def_13),
inference(demodulation,[status(thm)],[c_3999,c_4101]) ).
tcf(c_4106,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4103,c_2978]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET682+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 11:37:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 3.72/1.27 % SZS status Started for theBenchmark.p
% 3.72/1.27 % SZS status Theorem for theBenchmark.p
% 3.72/1.27
% 3.72/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.72/1.27
% 3.72/1.27 % ------ iProver source info
% 3.72/1.27
% 3.72/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.72/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.72/1.27 % git: non_committed_changes: false
% 3.72/1.27
% 3.72/1.27 % ------ Parsing...
% 3.72/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.72/1.27
% 3.72/1.27 % ------ 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 %
% 3.72/1.27
% 3.72/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.72/1.27
% 3.72/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.72/1.27 % ------ Proving...
% 3.72/1.27 % ------ Problem Properties
% 3.72/1.27
% 3.72/1.27 %
% 3.72/1.27 % clauses 40
% 3.72/1.27 % conjectures 6
% 3.72/1.27 % EPR 12
% 3.72/1.27 % Horn 35
% 3.72/1.27 % unary 15
% 3.72/1.27 % binary 21
% 3.72/1.27 % lits 69
% 3.72/1.27 % lits eq 9
% 3.72/1.27 % fd_pure 0
% 3.72/1.27 % fd_pseudo 0
% 3.72/1.27 % fd_cond 0
% 3.72/1.27 % fd_pseudo_cond 0
% 3.72/1.27 % AC symbols 0
% 3.72/1.27
% 3.72/1.27 % ------ Schedule dynamic 5 is on
% 3.72/1.27
% 3.72/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.72/1.27
% 3.72/1.27
% 3.72/1.27 % ------
% 3.72/1.27 % Current options:
% 3.72/1.27 % ------
% 3.72/1.27
% 3.72/1.27
% 3.72/1.27 %
% 3.72/1.27
% 3.72/1.27 % ------ Proving...
% 3.72/1.27 %
% 3.72/1.27
% 3.72/1.27 % SZS status Theorem for theBenchmark.p
% 3.72/1.27
% 3.72/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.72/1.28
% 3.72/1.28
%------------------------------------------------------------------------------