TSTP Solution File: SET678+3 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET678+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 03:01:13 EDT 2024
% Result : Theorem 7.39s 1.63s
% Output : CNFRefutation 7.39s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% 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,[],[f39]) ).
fof(f41,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f15]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( compose(identity_relation_of(X0),X1) = X1
| ~ subset(domain_of(X1),X0)
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( compose(identity_relation_of(X0),X1) = X1
| ~ subset(domain_of(X1),X0)
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( compose(X1,identity_relation_of(X0)) = X1
| ~ subset(range_of(X1),X0)
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( compose(X1,identity_relation_of(X0)) = X1
| ~ subset(range_of(X1),X0)
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f44]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ilf_type(compose(X0,X1),binary_relation_type)
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f49,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f56,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f41]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f19]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f62]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f25]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f26]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f74]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f32]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f33]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f34]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f35]) ).
fof(f87,plain,
? [X0] :
( ? [X1] :
( ( compose(identity_relation_of(X0),X1) != X1
| compose(X1,identity_relation_of(X0)) != X1 )
& ilf_type(X1,identity_relation_of_type(X0)) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f40]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ( ( 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)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f50]) ).
fof(f103,plain,
! [X0] :
( ( ( 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) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f56]) ).
fof(f104,plain,
! [X0] :
( ( ( 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) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f103]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f63]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0)
& ilf_type(sK6(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0)
& ilf_type(sK6(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f110,f111]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ( ( 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)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f66]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f72]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f122]) ).
fof(f124,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK11(X0,X1),X1)
& member(sK11(X0,X1),X0)
& ilf_type(sK11(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK11(X0,X1),X1)
& member(sK11(X0,X1),X0)
& ilf_type(sK11(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f123,f124]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f75]) ).
fof(f133,plain,
( ? [X0] :
( ? [X1] :
( ( compose(identity_relation_of(X0),X1) != X1
| compose(X1,identity_relation_of(X0)) != X1 )
& ilf_type(X1,identity_relation_of_type(X0)) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ( compose(identity_relation_of(sK14),X1) != X1
| compose(X1,identity_relation_of(sK14)) != X1 )
& ilf_type(X1,identity_relation_of_type(sK14)) )
& ilf_type(sK14,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f134,plain,
( ? [X1] :
( ( compose(identity_relation_of(sK14),X1) != X1
| compose(X1,identity_relation_of(sK14)) != X1 )
& ilf_type(X1,identity_relation_of_type(sK14)) )
=> ( ( sK15 != compose(identity_relation_of(sK14),sK15)
| sK15 != compose(sK15,identity_relation_of(sK14)) )
& ilf_type(sK15,identity_relation_of_type(sK14)) ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
( ( sK15 != compose(identity_relation_of(sK14),sK15)
| sK15 != compose(sK15,identity_relation_of(sK14)) )
& ilf_type(sK15,identity_relation_of_type(sK14))
& ilf_type(sK14,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f87,f134,f133]) ).
fof(f136,plain,
! [X0,X1] :
( compose(identity_relation_of(X0),X1) = X1
| ~ subset(domain_of(X1),X0)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f43]) ).
fof(f137,plain,
! [X0,X1] :
( compose(X1,identity_relation_of(X0)) = X1
| ~ subset(range_of(X1),X0)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f45]) ).
fof(f142,plain,
! [X0,X1] :
( ilf_type(compose(X0,X1),binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f47]) ).
fof(f146,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f49]) ).
fof(f147,plain,
! [X0,X1] :
( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f159,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f104]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f57]) ).
fof(f170,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK6(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f112]) ).
fof(f171,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f112]) ).
fof(f174,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f113]) ).
fof(f183,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f184,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f125]) ).
fof(f188,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f73]) ).
fof(f190,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f126]) ).
fof(f197,plain,
! [X2,X0,X1] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f81]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f82]) ).
fof(f199,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f203,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f38]) ).
fof(f205,plain,
ilf_type(sK15,identity_relation_of_type(sK14)),
inference(cnf_transformation,[],[f135]) ).
fof(f206,plain,
( sK15 != compose(identity_relation_of(sK14),sK15)
| sK15 != compose(sK15,identity_relation_of(sK14)) ),
inference(cnf_transformation,[],[f135]) ).
cnf(c_49,plain,
( ~ subset(domain_of(X0),X1)
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| compose(identity_relation_of(X1),X0) = X0 ),
inference(cnf_transformation,[],[f136]) ).
cnf(c_50,plain,
( ~ subset(range_of(X0),X1)
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| compose(X0,identity_relation_of(X1)) = X0 ),
inference(cnf_transformation,[],[f137]) ).
cnf(c_55,plain,
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ilf_type(compose(X0,X1),binary_relation_type) ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_59,plain,
( ~ ilf_type(X0,set_type)
| ilf_type(identity_relation_of(X0),binary_relation_type) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_61,plain,
( ~ ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,relation_type(X1,X1)) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_72,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f214]) ).
cnf(c_73,plain,
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| relation_like(X0) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_75,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_79,plain,
( ~ member(sK6(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_80,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_86,plain,
( ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(power_set(X1))) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_94,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| relation_like(X0) ),
inference(cnf_transformation,[],[f183]) ).
cnf(c_98,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_100,plain,
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f188]) ).
cnf(c_102,plain,
( ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f190]) ).
cnf(c_108,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| domain(X1,X2,X0) = domain_of(X0) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_109,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_110,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| range(X1,X2,X0) = range_of(X0) ),
inference(cnf_transformation,[],[f199]) ).
cnf(c_111,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(cnf_transformation,[],[f200]) ).
cnf(c_114,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f203]) ).
cnf(c_115,negated_conjecture,
( compose(identity_relation_of(sK14),sK15) != sK15
| compose(sK15,identity_relation_of(sK14)) != sK15 ),
inference(cnf_transformation,[],[f206]) ).
cnf(c_116,negated_conjecture,
ilf_type(sK15,identity_relation_of_type(sK14)),
inference(cnf_transformation,[],[f205]) ).
cnf(c_175,plain,
~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_100,c_114,c_100]) ).
cnf(c_181,plain,
ilf_type(identity_relation_of(X0),binary_relation_type),
inference(global_subsumption_just,[status(thm)],[c_59,c_114,c_59]) ).
cnf(c_205,plain,
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_114,c_73]) ).
cnf(c_208,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_114,c_72]) ).
cnf(c_235,plain,
( ~ ilf_type(X1,set_type)
| member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_80,c_114,c_80]) ).
cnf(c_236,plain,
( ~ ilf_type(X0,set_type)
| member(sK6(X1,X0),X1)
| subset(X1,X0) ),
inference(renaming,[status(thm)],[c_235]) ).
cnf(c_237,plain,
( member(sK6(X1,X0),X1)
| subset(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_236,c_114,c_236]) ).
cnf(c_238,plain,
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_237]) ).
cnf(c_249,plain,
( ~ member(sK6(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| subset(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_79,c_114,c_79]) ).
cnf(c_251,plain,
( ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| empty(X1) ),
inference(global_subsumption_just,[status(thm)],[c_102,c_114,c_102]) ).
cnf(c_258,plain,
( ~ 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_86,c_114,c_86]) ).
cnf(c_262,plain,
( ~ ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X1,set_type)
| ilf_type(X0,relation_type(X1,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_114,c_61]) ).
cnf(c_282,plain,
( ~ member(X2,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_98,c_114,c_98]) ).
cnf(c_283,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(renaming,[status(thm)],[c_282]) ).
cnf(c_294,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_208]) ).
cnf(c_451,plain,
( ~ subset(domain_of(X0),X1)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X0)
| compose(identity_relation_of(X1),X0) = X0 ),
inference(bin_hyper_res,[status(thm)],[c_49,c_294]) ).
cnf(c_452,plain,
( ~ subset(range_of(X0),X1)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X0)
| compose(X0,identity_relation_of(X1)) = X0 ),
inference(bin_hyper_res,[status(thm)],[c_50,c_294]) ).
cnf(c_453,plain,
( ~ ilf_type(X0,binary_relation_type)
| ~ relation_like(X1)
| ilf_type(compose(X1,X0),binary_relation_type) ),
inference(bin_hyper_res,[status(thm)],[c_55,c_294]) ).
cnf(c_475,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| domain(X1,X2,X0) = domain_of(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_108,c_114]) ).
cnf(c_478,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| relation_like(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_94,c_114]) ).
cnf(c_480,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_109,c_114]) ).
cnf(c_481,plain,
( ~ subset(range_of(X0),X1)
| ~ relation_like(X0)
| compose(X0,identity_relation_of(X1)) = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[c_452,c_114]) ).
cnf(c_482,plain,
( ~ subset(domain_of(X0),X1)
| ~ relation_like(X0)
| compose(identity_relation_of(X1),X0) = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[c_451,c_114]) ).
cnf(c_483,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| range(X1,X2,X0) = range_of(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_110,c_114]) ).
cnf(c_485,plain,
( ~ ilf_type(X0,identity_relation_of_type(X1))
| ilf_type(X0,relation_type(X1,X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_262,c_114]) ).
cnf(c_487,plain,
( ~ 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_75,c_114]) ).
cnf(c_488,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_111,c_114]) ).
cnf(c_490,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_283,c_114]) ).
cnf(c_492,plain,
( ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_249,c_114]) ).
cnf(c_493,plain,
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_251,c_114]) ).
cnf(c_496,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_258,c_114]) ).
cnf(c_612,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_478,c_114]) ).
cnf(c_685,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_487,c_114]) ).
cnf(c_696,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_480,c_114]) ).
cnf(c_707,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_488,c_114]) ).
cnf(c_718,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| domain(X1,X2,X0) = domain_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_475,c_114]) ).
cnf(c_729,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| range(X1,X2,X0) = range_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_483,c_114]) ).
cnf(c_755,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_490,c_114]) ).
cnf(c_1818,plain,
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_205]) ).
cnf(c_1819,plain,
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(renaming,[status(thm)],[c_1818]) ).
cnf(c_1820,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_114,c_72]) ).
cnf(c_1824,plain,
( ~ ilf_type(X0,identity_relation_of_type(X1))
| ilf_type(X0,relation_type(X1,X1)) ),
inference(prop_impl_just,[status(thm)],[c_485]) ).
cnf(c_1832,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_496]) ).
cnf(c_1844,plain,
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_612,c_685]) ).
cnf(c_1845,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(renaming,[status(thm)],[c_1844]) ).
cnf(c_1852,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| domain(X1,X2,X0) = domain_of(X0) ),
inference(prop_impl_just,[status(thm)],[c_718]) ).
cnf(c_1854,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_696]) ).
cnf(c_1856,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| range(X1,X2,X0) = range_of(X0) ),
inference(prop_impl_just,[status(thm)],[c_729]) ).
cnf(c_1858,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(prop_impl_just,[status(thm)],[c_707]) ).
cnf(c_1860,plain,
( ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_492]) ).
cnf(c_1864,plain,
( subset(X0,X1)
| member(sK6(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_238]) ).
cnf(c_1865,plain,
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_1864]) ).
cnf(c_2005,plain,
( ~ relation_like(X0)
| ~ relation_like(X1)
| ilf_type(compose(X1,X0),binary_relation_type) ),
inference(bin_hyper_res,[status(thm)],[c_453,c_1820]) ).
cnf(c_2659,plain,
identity_relation_of_type(sK14) = sP0_iProver_def,
definition ).
cnf(c_2660,plain,
identity_relation_of(sK14) = sP1_iProver_def,
definition ).
cnf(c_2661,plain,
compose(sP1_iProver_def,sK15) = sP2_iProver_def,
definition ).
cnf(c_2662,plain,
compose(sK15,sP1_iProver_def) = sP3_iProver_def,
definition ).
cnf(c_2663,negated_conjecture,
ilf_type(sK15,sP0_iProver_def),
inference(demodulation,[status(thm)],[c_116,c_2659]) ).
cnf(c_2664,negated_conjecture,
( sP2_iProver_def != sK15
| sP3_iProver_def != sK15 ),
inference(demodulation,[status(thm)],[c_115,c_2662,c_2660,c_2661]) ).
cnf(c_3742,plain,
ilf_type(sP1_iProver_def,binary_relation_type),
inference(superposition,[status(thm)],[c_2660,c_181]) ).
cnf(c_3758,plain,
relation_like(sP1_iProver_def),
inference(superposition,[status(thm)],[c_3742,c_1819]) ).
cnf(c_3817,plain,
( ~ ilf_type(X0,identity_relation_of_type(X1))
| relation_like(X0) ),
inference(superposition,[status(thm)],[c_1824,c_1845]) ).
cnf(c_3833,plain,
( ~ ilf_type(X0,sP0_iProver_def)
| relation_like(X0) ),
inference(superposition,[status(thm)],[c_2659,c_3817]) ).
cnf(c_3842,plain,
relation_like(sK15),
inference(superposition,[status(thm)],[c_2663,c_3833]) ).
cnf(c_3897,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1))
| empty(power_set(X1)) ),
inference(superposition,[status(thm)],[c_1832,c_493]) ).
cnf(c_3898,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3897,c_175]) ).
cnf(c_4169,plain,
( ~ ilf_type(X0,identity_relation_of_type(X1))
| domain(X1,X1,X0) = domain_of(X0) ),
inference(superposition,[status(thm)],[c_1824,c_1852]) ).
cnf(c_4184,plain,
( ~ ilf_type(X0,identity_relation_of_type(X1))
| range(X1,X1,X0) = range_of(X0) ),
inference(superposition,[status(thm)],[c_1824,c_1856]) ).
cnf(c_4817,plain,
( ~ relation_like(sK15)
| ~ relation_like(sP1_iProver_def)
| ilf_type(sP3_iProver_def,binary_relation_type) ),
inference(superposition,[status(thm)],[c_2662,c_2005]) ).
cnf(c_4819,plain,
ilf_type(sP3_iProver_def,binary_relation_type),
inference(forward_subsumption_resolution,[status(thm)],[c_4817,c_3758,c_3842]) ).
cnf(c_4833,plain,
relation_like(sP3_iProver_def),
inference(superposition,[status(thm)],[c_4819,c_1819]) ).
cnf(c_6289,plain,
( ~ ilf_type(X0,sP0_iProver_def)
| domain(sK14,sK14,X0) = domain_of(X0) ),
inference(superposition,[status(thm)],[c_2659,c_4169]) ).
cnf(c_6698,plain,
domain(sK14,sK14,sK15) = domain_of(sK15),
inference(superposition,[status(thm)],[c_2663,c_6289]) ).
cnf(c_6754,plain,
( ~ ilf_type(sK15,relation_type(sK14,sK14))
| ilf_type(domain_of(sK15),subset_type(sK14)) ),
inference(superposition,[status(thm)],[c_6698,c_1854]) ).
cnf(c_6763,plain,
( ~ ilf_type(sK15,identity_relation_of_type(sK14))
| ilf_type(domain_of(sK15),subset_type(sK14)) ),
inference(superposition,[status(thm)],[c_1824,c_6754]) ).
cnf(c_6770,plain,
( ~ ilf_type(sK15,sP0_iProver_def)
| ilf_type(domain_of(sK15),subset_type(sK14)) ),
inference(light_normalisation,[status(thm)],[c_6763,c_2659]) ).
cnf(c_6771,plain,
ilf_type(domain_of(sK15),subset_type(sK14)),
inference(forward_subsumption_resolution,[status(thm)],[c_6770,c_2663]) ).
cnf(c_6772,plain,
member(domain_of(sK15),power_set(sK14)),
inference(superposition,[status(thm)],[c_6771,c_3898]) ).
cnf(c_6802,plain,
( ~ member(X0,domain_of(sK15))
| member(X0,sK14) ),
inference(superposition,[status(thm)],[c_6772,c_755]) ).
cnf(c_6818,plain,
( member(sK6(domain_of(sK15),X0),sK14)
| subset(domain_of(sK15),X0) ),
inference(superposition,[status(thm)],[c_1865,c_6802]) ).
cnf(c_7069,plain,
subset(domain_of(sK15),sK14),
inference(superposition,[status(thm)],[c_6818,c_1860]) ).
cnf(c_7450,plain,
( ~ ilf_type(X0,sP0_iProver_def)
| range(sK14,sK14,X0) = range_of(X0) ),
inference(superposition,[status(thm)],[c_2659,c_4184]) ).
cnf(c_7767,plain,
range(sK14,sK14,sK15) = range_of(sK15),
inference(superposition,[status(thm)],[c_2663,c_7450]) ).
cnf(c_7792,plain,
( ~ ilf_type(sK15,relation_type(sK14,sK14))
| ilf_type(range_of(sK15),subset_type(sK14)) ),
inference(superposition,[status(thm)],[c_7767,c_1858]) ).
cnf(c_7825,plain,
( ~ ilf_type(sK15,identity_relation_of_type(sK14))
| ilf_type(range_of(sK15),subset_type(sK14)) ),
inference(superposition,[status(thm)],[c_1824,c_7792]) ).
cnf(c_7832,plain,
( ~ ilf_type(sK15,sP0_iProver_def)
| ilf_type(range_of(sK15),subset_type(sK14)) ),
inference(light_normalisation,[status(thm)],[c_7825,c_2659]) ).
cnf(c_7833,plain,
ilf_type(range_of(sK15),subset_type(sK14)),
inference(forward_subsumption_resolution,[status(thm)],[c_7832,c_2663]) ).
cnf(c_7834,plain,
member(range_of(sK15),power_set(sK14)),
inference(superposition,[status(thm)],[c_7833,c_3898]) ).
cnf(c_7839,plain,
( ~ member(X0,range_of(sK15))
| member(X0,sK14) ),
inference(superposition,[status(thm)],[c_7834,c_755]) ).
cnf(c_7906,plain,
( member(sK6(range_of(sK15),X0),sK14)
| subset(range_of(sK15),X0) ),
inference(superposition,[status(thm)],[c_1865,c_7839]) ).
cnf(c_8103,plain,
subset(range_of(sK15),sK14),
inference(superposition,[status(thm)],[c_7906,c_1860]) ).
cnf(c_8839,plain,
( ~ relation_like(sK15)
| compose(sK15,identity_relation_of(sK14)) = sK15 ),
inference(superposition,[status(thm)],[c_8103,c_481]) ).
cnf(c_8840,plain,
( ~ relation_like(sK15)
| sK15 = sP3_iProver_def ),
inference(light_normalisation,[status(thm)],[c_8839,c_2660,c_2662]) ).
cnf(c_8841,plain,
sK15 = sP3_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_8840,c_3842]) ).
cnf(c_8925,plain,
subset(domain_of(sP3_iProver_def),sK14),
inference(demodulation,[status(thm)],[c_7069,c_8841]) ).
cnf(c_8939,plain,
compose(sP1_iProver_def,sP3_iProver_def) = sP2_iProver_def,
inference(demodulation,[status(thm)],[c_2661,c_8841]) ).
cnf(c_8940,plain,
( sP2_iProver_def != sP3_iProver_def
| sP3_iProver_def != sP3_iProver_def ),
inference(demodulation,[status(thm)],[c_2664,c_8841]) ).
cnf(c_8942,plain,
sP2_iProver_def != sP3_iProver_def,
inference(equality_resolution_simp,[status(thm)],[c_8940]) ).
cnf(c_9341,plain,
( ~ relation_like(sP3_iProver_def)
| compose(identity_relation_of(sK14),sP3_iProver_def) = sP3_iProver_def ),
inference(superposition,[status(thm)],[c_8925,c_482]) ).
cnf(c_9342,plain,
( ~ relation_like(sP3_iProver_def)
| sP2_iProver_def = sP3_iProver_def ),
inference(light_normalisation,[status(thm)],[c_9341,c_2660,c_8939]) ).
cnf(c_9343,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9342,c_8942,c_4833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SET678+3 : TPTP v8.1.2. Released v2.2.0.
% 0.05/0.11 % Command : run_iprover %s %d THM
% 0.10/0.32 % Computer : n008.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu May 2 20:39:57 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.17/0.43 Running first-order theorem proving
% 0.17/0.43 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.39/1.63 % SZS status Started for theBenchmark.p
% 7.39/1.63 % SZS status Theorem for theBenchmark.p
% 7.39/1.63
% 7.39/1.63 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.39/1.63
% 7.39/1.63 ------ iProver source info
% 7.39/1.63
% 7.39/1.63 git: date: 2024-05-02 19:28:25 +0000
% 7.39/1.63 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.39/1.63 git: non_committed_changes: false
% 7.39/1.63
% 7.39/1.63 ------ Parsing...
% 7.39/1.63 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.39/1.63
% 7.39/1.63 ------ 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
% 7.39/1.63
% 7.39/1.63 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.39/1.63
% 7.39/1.63 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.39/1.63 ------ Proving...
% 7.39/1.63 ------ Problem Properties
% 7.39/1.63
% 7.39/1.63
% 7.39/1.63 clauses 55
% 7.39/1.63 conjectures 2
% 7.39/1.63 EPR 10
% 7.39/1.63 Horn 48
% 7.39/1.63 unary 13
% 7.39/1.63 binary 28
% 7.39/1.63 lits 119
% 7.39/1.63 lits eq 16
% 7.39/1.63 fd_pure 0
% 7.39/1.63 fd_pseudo 0
% 7.39/1.63 fd_cond 0
% 7.39/1.63 fd_pseudo_cond 3
% 7.39/1.63 AC symbols 0
% 7.39/1.63
% 7.39/1.63 ------ Schedule dynamic 5 is on
% 7.39/1.63
% 7.39/1.63 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.39/1.63
% 7.39/1.63
% 7.39/1.63 ------
% 7.39/1.63 Current options:
% 7.39/1.63 ------
% 7.39/1.63
% 7.39/1.63
% 7.39/1.63
% 7.39/1.63
% 7.39/1.63 ------ Proving...
% 7.39/1.63
% 7.39/1.63
% 7.39/1.63 % SZS status Theorem for theBenchmark.p
% 7.39/1.63
% 7.39/1.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.39/1.63
% 7.39/1.64
%------------------------------------------------------------------------------