%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET678+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 : n014.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 02:47:46 PM UTC 2026
% Result : Theorem 1.04s 1.77s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f197ERROR: Could not build tree for root c_9139ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(domain_of(X1),X0)
=> compose(identity_relation_of(X0),X1) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(range_of(X1),X0)
=> compose(X1,identity_relation_of(X0)) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ilf_type(compose(X0,X1),binary_relation_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),binary_relation_type) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f13,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',p13) ).
fof(f15,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',p15) ).
fof(f19,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',p19) ).
fof(f22,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',p22) ).
fof(f25,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',p25) ).
fof(f26,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',p26) ).
fof(f27,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',p27) ).
fof(f28,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',p28) ).
fof(f32,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/sandbox/benchmark/theBenchmark.p',p32) ).
fof(f33,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(domain(X0,X1,X2),subset_type(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
fof(f34,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/sandbox/benchmark/theBenchmark.p',p34) ).
fof(f35,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/sandbox/benchmark/theBenchmark.p',p35) ).
fof(f38,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p38) ).
fof(f39,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
=> ( compose(identity_relation_of(X0),X1) = X1
& compose(X1,identity_relation_of(X0)) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_45) ).
fof(f40,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
=> ( compose(identity_relation_of(X0),X1) = X1
& compose(X1,identity_relation_of(X0)) = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f41,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ~ subset(domain_of(X1),X0)
| compose(identity_relation_of(X0),X1) = X1 ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f42,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ~ subset(domain_of(X1),X0)
| compose(identity_relation_of(X0),X1) = X1 ) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ~ subset(range_of(X1),X0)
| compose(X1,identity_relation_of(X0)) = X1 ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f44,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ~ subset(range_of(X1),X0)
| compose(X1,identity_relation_of(X0)) = X1 ) ),
inference(flattening,[],[f43]) ).
fof(f46,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ilf_type(compose(X0,X1),binary_relation_type) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f48,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(identity_relation_of(X0),binary_relation_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f49,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f55,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f56,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,[],[f15]) ).
fof(f61,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,[],[f19]) ).
fof(f62,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,[],[f61]) ).
fof(f65,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,[],[f22]) ).
fof(f69,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,[],[f25]) ).
fof(f70,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,[],[f26]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f73,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,[],[f28]) ).
fof(f74,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,[],[f73]) ).
fof(f80,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,[],[f32]) ).
fof(f81,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(domain(X0,X1,X2),subset_type(X0)) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f82,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,[],[f34]) ).
fof(f83,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,[],[f35]) ).
fof(f86,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
& ( compose(identity_relation_of(X0),X1) != X1
| compose(X1,identity_relation_of(X0)) != X1 ) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f92,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ ilf_type(X1,identity_relation_of_type(X0))
| ilf_type(X1,relation_type(X0,X0)) )
& ( ~ ilf_type(X1,relation_type(X0,X0))
| ilf_type(X1,identity_relation_of_type(X0)) ) ) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f98,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,[],[f55]) ).
fof(f99,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,[],[f98]) ).
fof(f102,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,[],[f62]) ).
fof(f103,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,[],[f102]) ).
fof(f104,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(sK6(X0,X1),set_type)
& member(sK6(X0,X1),X0)
& ~ member(sK6(X0,X1),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f103]) ).
fof(f105,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,[],[f65]) ).
fof(f110,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,[],[f71]) ).
fof(f111,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,[],[f110]) ).
fof(f112,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(sK11(X0,X1),set_type)
& member(sK11(X0,X1),X0)
& ~ member(sK11(X0,X1),X1) )
| member(X0,power_set(X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f111]) ).
fof(f113,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,[],[f74]) ).
fof(f118,plain,
( ilf_type(sK14,set_type)
& ilf_type(sK15,identity_relation_of_type(sK14))
& ( sK15 != compose(identity_relation_of(sK14),sK15)
| sK15 != compose(sK15,identity_relation_of(sK14)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f86]) ).
fof(f119,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ subset(domain_of(X1),X0)
| compose(identity_relation_of(X0),X1) = X1 ),
inference(cnf_transformation,[],[f42]) ).
fof(f120,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ subset(range_of(X1),X0)
| compose(X1,identity_relation_of(X0)) = X1 ),
inference(cnf_transformation,[],[f44]) ).
fof(f125,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ilf_type(compose(X0,X1),binary_relation_type) ),
inference(cnf_transformation,[],[f46]) ).
fof(f129,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(identity_relation_of(X0),binary_relation_type) ),
inference(cnf_transformation,[],[f48]) ).
fof(f130,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,identity_relation_of_type(X0))
| ilf_type(X1,relation_type(X0,X0)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f143,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f146,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,[],[f56]) ).
fof(f153,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f154,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f157,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,[],[f105]) ).
fof(f166,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,[],[f69]) ).
fof(f167,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,[],[f112]) ).
fof(f172,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f173,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,[],[f113]) ).
fof(f180,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,[],[f80]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(domain(X0,X1,X2),subset_type(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f182,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,[],[f82]) ).
fof(f183,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,[],[f83]) ).
fof(f186,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f38]) ).
fof(f188,plain,
ilf_type(sK15,identity_relation_of_type(sK14)),
inference(cnf_transformation,[],[f118]) ).
fof(f189,plain,
( sK15 != compose(identity_relation_of(sK14),sK15)
| sK15 != compose(sK15,identity_relation_of(sK14)) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( compose(identity_relation_of(X1),X0) = X0 )
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ subset(domain_of(X0),X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( compose(X0,identity_relation_of(X1)) = X0 )
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ subset(range_of(X0),X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ilf_type(compose(X0,X1),binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_59,plain,
! [X0: $i] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,relation_type(X1,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_72,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_73,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_76,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,[],[f146]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK6(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_86,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,[],[f157]) ).
tcf(c_94,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,[],[f166]) ).
tcf(c_98,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,[],[f167]) ).
tcf(c_99,plain,
! [X0: $i] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_102,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,[],[f173]) ).
tcf(c_108,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,[],[f180]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_110,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,[],[f182]) ).
tcf(c_111,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,[],[f183]) ).
tcf(c_114,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f186]) ).
tcf(c_115,negated_conjecture,
( ( compose(sK15,identity_relation_of(sK14)) != sK15 )
| ( compose(identity_relation_of(sK14),sK15) != sK15 ) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_116,negated_conjecture,
ilf_type(sK15,identity_relation_of_type(sK14)),
inference(cnf_transformation,[],[f188]) ).
tcf(c_178,plain,
! [X0: $i] : ~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_99,c_114,c_99]) ).
tcf(c_181,plain,
! [X0: $i] : ilf_type(identity_relation_of(X0),binary_relation_type),
inference(global_subsumption_just,[status(thm)],[c_59,c_114,c_59]) ).
tcf(c_205,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_114,c_73]) ).
tcf(c_208,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_114,c_72]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK6(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_80,c_114,c_80]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK6(X1,X0),X1)
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_235]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| member(sK6(X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_236,c_114,c_236]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK6(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_237]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ member(sK6(X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_79,c_114,c_79]) ).
tcf(c_251,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_102,c_114,c_102]) ).
tcf(c_258,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_86,c_114,c_86]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,relation_type(X1,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_114,c_61]) ).
tcf(c_282,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_98,c_114,c_98]) ).
tcf(c_283,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_282]) ).
tcf(c_294,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_208]) ).
tcf(c_451,plain,
! [X0: $i,X1: $i] :
( ( compose(identity_relation_of(X1),X0) = X0 )
| ~ relation_like(X0)
| ~ ilf_type(X1,set_type)
| ~ subset(domain_of(X0),X1) ),
inference(bin_hyper_res,[status(thm)],[c_49,c_294]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i] :
( ( compose(X0,identity_relation_of(X1)) = X0 )
| ~ relation_like(X0)
| ~ ilf_type(X1,set_type)
| ~ subset(range_of(X0),X1) ),
inference(bin_hyper_res,[status(thm)],[c_50,c_294]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i] :
( ilf_type(compose(X1,X0),binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X0,binary_relation_type) ),
inference(bin_hyper_res,[status(thm)],[c_55,c_294]) ).
tcf(c_475,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_108,c_114]) ).
tcf(c_478,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_94,c_114]) ).
tcf(c_480,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_109,c_114]) ).
tcf(c_481,plain,
! [X0: $i,X1: $i] :
( ( compose(X0,identity_relation_of(X1)) = X0 )
| ~ relation_like(X0)
| ~ subset(range_of(X0),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_452,c_114]) ).
tcf(c_482,plain,
! [X0: $i,X1: $i] :
( ( compose(identity_relation_of(X1),X0) = X0 )
| ~ relation_like(X0)
| ~ subset(domain_of(X0),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_451,c_114]) ).
tcf(c_483,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_110,c_114]) ).
tcf(c_485,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,relation_type(X1,X1))
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_262,c_114]) ).
tcf(c_486,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_76,c_114]) ).
tcf(c_488,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_111,c_114]) ).
tcf(c_490,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_283,c_114]) ).
tcf(c_492,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_249,c_114]) ).
tcf(c_493,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_251,c_114]) ).
tcf(c_496,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_258,c_114]) ).
tcf(c_612,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_478,c_114]) ).
tcf(c_674,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_486,c_114]) ).
tcf(c_696,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_480,c_114]) ).
tcf(c_707,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_488,c_114]) ).
tcf(c_718,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_475,c_114]) ).
tcf(c_729,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_483,c_114]) ).
tcf(c_755,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_490,c_114]) ).
tcf(c_1818,plain,
! [X0: $i] :
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_205]) ).
tcf(c_1819,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(renaming,[status(thm)],[c_1818]) ).
tcf(c_1820,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_114,c_72]) ).
tcf(c_1824,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,relation_type(X1,X1))
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_485]) ).
tcf(c_1832,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_496]) ).
tcf(c_1844,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_612,c_674]) ).
tcf(c_1845,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(renaming,[status(thm)],[c_1844]) ).
tcf(c_1852,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_718]) ).
tcf(c_1854,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_696]) ).
tcf(c_1856,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_729]) ).
tcf(c_1858,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_707]) ).
tcf(c_1860,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_492]) ).
tcf(c_1864,plain,
! [X0: $i,X1: $i] :
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_238]) ).
tcf(c_1865,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK6(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_1864]) ).
tcf(c_2005,plain,
! [X0: $i,X1: $i] :
( ilf_type(compose(X1,X0),binary_relation_type)
| ~ relation_like(X1)
| ~ relation_like(X0) ),
inference(bin_hyper_res,[status(thm)],[c_453,c_1820]) ).
tcf(c_2659,definition,
iPr_def_10 = identity_relation_of_type(sK14),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2660,definition,
iPr_def_11 = identity_relation_of(sK14),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2661,definition,
iPr_def_12 = compose(iPr_def_11,sK15),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2662,definition,
iPr_def_13 = compose(sK15,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2663,negated_conjecture,
ilf_type(sK15,iPr_def_10),
inference(demodulation,[status(thm)],[c_116,c_2659]) ).
tcf(c_2664,negated_conjecture,
( ( iPr_def_13 != sK15 )
| ( iPr_def_12 != sK15 ) ),
inference(demodulation,[status(thm)],[c_115,c_2662,c_2660,c_2661]) ).
tcf(c_3742,plain,
ilf_type(iPr_def_11,binary_relation_type),
inference(superposition,[status(thm)],[c_2660,c_181]) ).
tcf(c_3758,plain,
relation_like(iPr_def_11),
inference(superposition,[status(thm)],[c_3742,c_1819]) ).
tcf(c_3817,plain,
! [X0: $i,X1: $i] :
( relation_like(X0)
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(superposition,[status(thm)],[c_1824,c_1845]) ).
tcf(c_3833,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2659,c_3817]) ).
tcf(c_3842,plain,
relation_like(sK15),
inference(superposition,[status(thm)],[c_2663,c_3833]) ).
tcf(c_3897,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_1832,c_493]) ).
tcf(c_3898,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3897,c_178]) ).
tcf(c_4169,plain,
! [X0: $i,X1: $i] :
( ( domain(X1,X1,X0) = domain_of(X0) )
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(superposition,[status(thm)],[c_1824,c_1852]) ).
tcf(c_4184,plain,
! [X0: $i,X1: $i] :
( ( range(X1,X1,X0) = range_of(X0) )
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(superposition,[status(thm)],[c_1824,c_1856]) ).
tcf(c_4789,plain,
( ilf_type(iPr_def_13,binary_relation_type)
| ~ relation_like(iPr_def_11)
| ~ relation_like(sK15) ),
inference(superposition,[status(thm)],[c_2662,c_2005]) ).
tcf(c_4791,plain,
ilf_type(iPr_def_13,binary_relation_type),
inference(forward_subsumption_resolution,[status(thm)],[c_4789,c_3758,c_3842]) ).
tcf(c_4813,plain,
relation_like(iPr_def_13),
inference(superposition,[status(thm)],[c_4791,c_1819]) ).
tcf(c_6269,plain,
! [X0: $i] :
( ( domain(sK14,sK14,X0) = domain_of(X0) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2659,c_4169]) ).
tcf(c_6650,plain,
domain(sK14,sK14,sK15) = domain_of(sK15),
inference(superposition,[status(thm)],[c_2663,c_6269]) ).
tcf(c_6673,plain,
( ilf_type(domain_of(sK15),subset_type(sK14))
| ~ ilf_type(sK15,relation_type(sK14,sK14)) ),
inference(superposition,[status(thm)],[c_6650,c_1854]) ).
tcf(c_6694,plain,
( ilf_type(domain_of(sK15),subset_type(sK14))
| ~ ilf_type(sK15,identity_relation_of_type(sK14)) ),
inference(superposition,[status(thm)],[c_1824,c_6673]) ).
tcf(c_6701,plain,
( ilf_type(domain_of(sK15),subset_type(sK14))
| ~ ilf_type(sK15,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_6694,c_2659]) ).
tcf(c_6702,plain,
ilf_type(domain_of(sK15),subset_type(sK14)),
inference(forward_subsumption_resolution,[status(thm)],[c_6701,c_2663]) ).
tcf(c_6703,plain,
member(domain_of(sK15),power_set(sK14)),
inference(superposition,[status(thm)],[c_6702,c_3898]) ).
tcf(c_6708,plain,
! [X0: $i] :
( member(X0,sK14)
| ~ member(X0,domain_of(sK15)) ),
inference(superposition,[status(thm)],[c_6703,c_755]) ).
tcf(c_6734,plain,
! [X0: $i] :
( subset(domain_of(sK15),X0)
| member(sK6(domain_of(sK15),X0),sK14) ),
inference(superposition,[status(thm)],[c_1865,c_6708]) ).
tcf(c_6977,plain,
subset(domain_of(sK15),sK14),
inference(superposition,[status(thm)],[c_6734,c_1860]) ).
tcf(c_7318,plain,
! [X0: $i] :
( ( range(sK14,sK14,X0) = range_of(X0) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2659,c_4184]) ).
tcf(c_7630,plain,
range(sK14,sK14,sK15) = range_of(sK15),
inference(superposition,[status(thm)],[c_2663,c_7318]) ).
tcf(c_7654,plain,
( ilf_type(range_of(sK15),subset_type(sK14))
| ~ ilf_type(sK15,relation_type(sK14,sK14)) ),
inference(superposition,[status(thm)],[c_7630,c_1858]) ).
tcf(c_7668,plain,
( ilf_type(range_of(sK15),subset_type(sK14))
| ~ ilf_type(sK15,identity_relation_of_type(sK14)) ),
inference(superposition,[status(thm)],[c_1824,c_7654]) ).
tcf(c_7675,plain,
( ilf_type(range_of(sK15),subset_type(sK14))
| ~ ilf_type(sK15,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_7668,c_2659]) ).
tcf(c_7676,plain,
ilf_type(range_of(sK15),subset_type(sK14)),
inference(forward_subsumption_resolution,[status(thm)],[c_7675,c_2663]) ).
tcf(c_7677,plain,
member(range_of(sK15),power_set(sK14)),
inference(superposition,[status(thm)],[c_7676,c_3898]) ).
tcf(c_7682,plain,
! [X0: $i] :
( member(X0,sK14)
| ~ member(X0,range_of(sK15)) ),
inference(superposition,[status(thm)],[c_7677,c_755]) ).
tcf(c_7778,plain,
! [X0: $i] :
( subset(range_of(sK15),X0)
| member(sK6(range_of(sK15),X0),sK14) ),
inference(superposition,[status(thm)],[c_1865,c_7682]) ).
tcf(c_7947,plain,
subset(range_of(sK15),sK14),
inference(superposition,[status(thm)],[c_7778,c_1860]) ).
tcf(c_8643,plain,
( ( compose(sK15,identity_relation_of(sK14)) = sK15 )
| ~ relation_like(sK15) ),
inference(superposition,[status(thm)],[c_7947,c_481]) ).
tcf(c_8644,plain,
( ( sK15 = iPr_def_13 )
| ~ relation_like(sK15) ),
inference(light_normalisation,[status(thm)],[c_8643,c_2660,c_2662]) ).
tcf(c_8645,plain,
sK15 = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_8644,c_3842]) ).
tcf(c_8729,plain,
subset(domain_of(iPr_def_13),sK14),
inference(demodulation,[status(thm)],[c_6977,c_8645]) ).
tcf(c_8743,plain,
compose(iPr_def_11,iPr_def_13) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2661,c_8645]) ).
tcf(c_8744,plain,
( ( iPr_def_13 != iPr_def_13 )
| ( iPr_def_12 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_2664,c_8645]) ).
tcf(c_8746,plain,
iPr_def_12 != iPr_def_13,
inference(equality_resolution_simp,[status(thm)],[c_8744]) ).
tcf(c_9137,plain,
( ( compose(identity_relation_of(sK14),iPr_def_13) = iPr_def_13 )
| ~ relation_like(iPr_def_13) ),
inference(superposition,[status(thm)],[c_8729,c_482]) ).
tcf(c_9138,plain,
( ( iPr_def_12 = iPr_def_13 )
| ~ relation_like(iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_9137,c_2660,c_8743]) ).
tcf(c_9139,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9138,c_8746,c_4813]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET678+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:38:48 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 1.04/1.77 % SZS status Started for theBenchmark.p
% 1.04/1.77 % SZS status Theorem for theBenchmark.p
% 1.04/1.77
% 1.04/1.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.04/1.77
% 1.04/1.77 % ------ iProver source info
% 1.04/1.77
% 1.04/1.77 % git: date: 2026-07-19 20:42:38 +0200
% 1.04/1.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.04/1.77 % git: non_committed_changes: false
% 1.04/1.77
% 1.04/1.77 % ------ Parsing...
% 1.04/1.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.04/1.77
% 1.04/1.77 % ------ 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 %
% 1.04/1.77
% 1.04/1.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.04/1.77
% 1.04/1.77 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.04/1.77 % ------ Proving...
% 1.04/1.77 % ------ Problem Properties
% 1.04/1.77
% 1.04/1.77 %
% 1.04/1.77 % clauses 55
% 1.04/1.77 % conjectures 2
% 1.04/1.77 % EPR 10
% 1.04/1.77 % Horn 48
% 1.04/1.77 % unary 13
% 1.04/1.77 % binary 28
% 1.04/1.77 % lits 119
% 1.04/1.77 % lits eq 16
% 1.04/1.77 % fd_pure 0
% 1.04/1.77 % fd_pseudo 0
% 1.04/1.77 % fd_cond 0
% 1.04/1.77 % fd_pseudo_cond 3
% 1.04/1.77 % AC symbols 0
% 1.04/1.77
% 1.04/1.77 % ------ Schedule dynamic 5 is on
% 1.04/1.77
% 1.04/1.77 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.04/1.77
% 1.04/1.77
% 1.04/1.77 % ------
% 1.04/1.77 % Current options:
% 1.04/1.77 % ------
% 1.04/1.77
% 1.04/1.77
% 1.04/1.77 %
% 1.04/1.77
% 1.04/1.77 % ------ Proving...
% 1.04/1.77 %
% 1.04/1.77
% 1.04/1.77 % SZS status Theorem for theBenchmark.p
% 1.04/1.77
% 1.04/1.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.04/1.78
% 1.04/1.78
%------------------------------------------------------------------------------