TSTP Solution File: SET681+3 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET681+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 : Mon Jun 24 14:35:24 EDT 2024
% Result : Theorem 7.94s 1.69s
% Output : CNFRefutation 7.94s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f187)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,range_of(X1))
<=> ? [X2] :
( member(ordered_pair(X2,X0),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)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(ordered_pair(X0,X1),X2)
=> ( member(X1,range_of(X2))
& member(X0,domain_of(X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f6,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',p6) ).
fof(f8,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',p8) ).
fof(f10,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',p10) ).
fof(f19,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',p19) ).
fof(f22,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',p22) ).
fof(f23,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',p23) ).
fof(f26,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',p26) ).
fof(f27,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain_of(X2) = domain(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f28,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/sandbox2/benchmark/theBenchmark.p',p28) ).
fof(f29,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range_of(X2) = range(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
fof(f31,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(f32,conjecture,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,range(X1,X0,X2))
<=> ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_48) ).
fof(f33,negated_conjecture,
~ ! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,range(X1,X0,X2))
<=> ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,member_type(X1)) ) ) ) ) ) ),
inference(negated_conjecture,[],[f32]) ).
fof(f34,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,[],[f6]) ).
fof(f35,plain,
! [X0] :
( ! [X1] :
( ( member(X0,range_of(X1))
<=> ? [X2] :
( member(ordered_pair(X2,X0),X1)
& ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,range_of(X2))
& member(X0,domain_of(X2)) )
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,range_of(X2))
& member(X0,domain_of(X2)) )
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f36]) ).
fof(f42,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,[],[f34]) ).
fof(f44,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,[],[f8]) ).
fof(f45,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,[],[f44]) ).
fof(f48,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f10]) ).
fof(f56,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,[],[f19]) ).
fof(f59,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,[],[f22]) ).
fof(f60,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,[],[f59]) ).
fof(f61,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
fof(f66,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,[],[f26]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f68,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,[],[f28]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f71,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( member(X3,range(X1,X0,X2))
<~> ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,member_type(X1)) ) )
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f72,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( member(X3,range(X1,X0,X2))
<~> ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,member_type(X1)) ) )
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X2] :
( member(ordered_pair(X2,X0),X1)
& ilf_type(X2,set_type) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f35]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X3] :
( member(ordered_pair(X3,X0),X1)
& ilf_type(X3,set_type) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X3] :
( member(ordered_pair(X3,X0),X1)
& ilf_type(X3,set_type) )
=> ( member(ordered_pair(sK0(X0,X1),X0),X1)
& ilf_type(sK0(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ( member(ordered_pair(sK0(X0,X1),X0),X1)
& ilf_type(sK0(X0,X1),set_type) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f74,f75]) ).
fof(f80,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,[],[f45]) ).
fof(f83,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f48]) ).
fof(f84,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK3(X0),X0)
& ilf_type(sK3(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK3(X0),X0)
& ilf_type(sK3(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f84,f85]) ).
fof(f91,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,[],[f56]) ).
fof(f99,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,[],[f60]) ).
fof(f100,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,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0)
& ilf_type(sK7(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0)
& ilf_type(sK7(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,[sK7])],[f100,f101]) ).
fof(f109,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,member_type(X1)) )
| ~ member(X3,range(X1,X0,X2)) )
& ( ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,member_type(X1)) )
| member(X3,range(X1,X0,X2)) )
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(nnf_transformation,[],[f72]) ).
fof(f110,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,member_type(X1)) )
| ~ member(X3,range(X1,X0,X2)) )
& ( ? [X4] :
( member(ordered_pair(X4,X3),X2)
& ilf_type(X4,member_type(X1)) )
| member(X3,range(X1,X0,X2)) )
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,member_type(X1)) )
| ~ member(X3,range(X1,X0,X2)) )
& ( ? [X5] :
( member(ordered_pair(X5,X3),X2)
& ilf_type(X5,member_type(X1)) )
| member(X3,range(X1,X0,X2)) )
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,member_type(X1)) )
| ~ member(X3,range(X1,X0,X2)) )
& ( ? [X5] :
( member(ordered_pair(X5,X3),X2)
& ilf_type(X5,member_type(X1)) )
| member(X3,range(X1,X0,X2)) )
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,member_type(X1)) )
| ~ member(X3,range(X1,sK11,X2)) )
& ( ? [X5] :
( member(ordered_pair(X5,X3),X2)
& ilf_type(X5,member_type(X1)) )
| member(X3,range(X1,sK11,X2)) )
& ilf_type(X3,member_type(sK11)) )
& ilf_type(X2,relation_type(X1,sK11)) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(sK11,set_type)
& ~ empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f113,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,member_type(X1)) )
| ~ member(X3,range(X1,sK11,X2)) )
& ( ? [X5] :
( member(ordered_pair(X5,X3),X2)
& ilf_type(X5,member_type(X1)) )
| member(X3,range(X1,sK11,X2)) )
& ilf_type(X3,member_type(sK11)) )
& ilf_type(X2,relation_type(X1,sK11)) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,member_type(sK12)) )
| ~ member(X3,range(sK12,sK11,X2)) )
& ( ? [X5] :
( member(ordered_pair(X5,X3),X2)
& ilf_type(X5,member_type(sK12)) )
| member(X3,range(sK12,sK11,X2)) )
& ilf_type(X3,member_type(sK11)) )
& ilf_type(X2,relation_type(sK12,sK11)) )
& ilf_type(sK12,set_type)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
( ? [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ member(ordered_pair(X4,X3),X2)
| ~ ilf_type(X4,member_type(sK12)) )
| ~ member(X3,range(sK12,sK11,X2)) )
& ( ? [X5] :
( member(ordered_pair(X5,X3),X2)
& ilf_type(X5,member_type(sK12)) )
| member(X3,range(sK12,sK11,X2)) )
& ilf_type(X3,member_type(sK11)) )
& ilf_type(X2,relation_type(sK12,sK11)) )
=> ( ? [X3] :
( ( ! [X4] :
( ~ member(ordered_pair(X4,X3),sK13)
| ~ ilf_type(X4,member_type(sK12)) )
| ~ member(X3,range(sK12,sK11,sK13)) )
& ( ? [X5] :
( member(ordered_pair(X5,X3),sK13)
& ilf_type(X5,member_type(sK12)) )
| member(X3,range(sK12,sK11,sK13)) )
& ilf_type(X3,member_type(sK11)) )
& ilf_type(sK13,relation_type(sK12,sK11)) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
( ? [X3] :
( ( ! [X4] :
( ~ member(ordered_pair(X4,X3),sK13)
| ~ ilf_type(X4,member_type(sK12)) )
| ~ member(X3,range(sK12,sK11,sK13)) )
& ( ? [X5] :
( member(ordered_pair(X5,X3),sK13)
& ilf_type(X5,member_type(sK12)) )
| member(X3,range(sK12,sK11,sK13)) )
& ilf_type(X3,member_type(sK11)) )
=> ( ( ! [X4] :
( ~ member(ordered_pair(X4,sK14),sK13)
| ~ ilf_type(X4,member_type(sK12)) )
| ~ member(sK14,range(sK12,sK11,sK13)) )
& ( ? [X5] :
( member(ordered_pair(X5,sK14),sK13)
& ilf_type(X5,member_type(sK12)) )
| member(sK14,range(sK12,sK11,sK13)) )
& ilf_type(sK14,member_type(sK11)) ) ),
introduced(choice_axiom,[]) ).
fof(f116,plain,
( ? [X5] :
( member(ordered_pair(X5,sK14),sK13)
& ilf_type(X5,member_type(sK12)) )
=> ( member(ordered_pair(sK15,sK14),sK13)
& ilf_type(sK15,member_type(sK12)) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
( ( ! [X4] :
( ~ member(ordered_pair(X4,sK14),sK13)
| ~ ilf_type(X4,member_type(sK12)) )
| ~ member(sK14,range(sK12,sK11,sK13)) )
& ( ( member(ordered_pair(sK15,sK14),sK13)
& ilf_type(sK15,member_type(sK12)) )
| member(sK14,range(sK12,sK11,sK13)) )
& ilf_type(sK14,member_type(sK11))
& ilf_type(sK13,relation_type(sK12,sK11))
& ilf_type(sK12,set_type)
& ~ empty(sK12)
& ilf_type(sK11,set_type)
& ~ empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15])],[f111,f116,f115,f114,f113,f112]) ).
fof(f119,plain,
! [X0,X1] :
( member(ordered_pair(sK0(X0,X1),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f76]) ).
fof(f120,plain,
! [X2,X0,X1] :
( member(X0,range_of(X1))
| ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f76]) ).
fof(f121,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f37]) ).
fof(f122,plain,
! [X2,X0,X1] :
( member(X1,range_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f37]) ).
fof(f129,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,[],[f42]) ).
fof(f131,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,[],[f80]) ).
fof(f132,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(cnf_transformation,[],[f80]) ).
fof(f134,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f86]) ).
fof(f147,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,[],[f91]) ).
fof(f155,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,[],[f102]) ).
fof(f159,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f61]) ).
fof(f168,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,[],[f66]) ).
fof(f169,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f170,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,[],[f68]) ).
fof(f171,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f69]) ).
fof(f173,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f31]) ).
fof(f178,plain,
ilf_type(sK13,relation_type(sK12,sK11)),
inference(cnf_transformation,[],[f117]) ).
fof(f181,plain,
( member(ordered_pair(sK15,sK14),sK13)
| member(sK14,range(sK12,sK11,sK13)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f182,plain,
! [X4] :
( ~ member(ordered_pair(X4,sK14),sK13)
| ~ ilf_type(X4,member_type(sK12))
| ~ member(sK14,range(sK12,sK11,sK13)) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_49,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(X1,range_of(X2)) ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_50,plain,
( ~ member(X0,range_of(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK0(X0,X1),X0),X1) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_52,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(X1,range_of(X2)) ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_53,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(X0,domain_of(X2)) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_59,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,[],[f129]) ).
cnf(c_62,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_63,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,[],[f131]) ).
cnf(c_67,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_74,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f187]) ).
cnf(c_78,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,[],[f147]) ).
cnf(c_88,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,[],[f155]) ).
cnf(c_90,plain,
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_98,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,[],[f168]) ).
cnf(c_99,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,[],[f169]) ).
cnf(c_100,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,[],[f170]) ).
cnf(c_101,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,[],[f171]) ).
cnf(c_103,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f173]) ).
cnf(c_104,negated_conjecture,
( ~ member(sK14,range(sK12,sK11,sK13))
| ~ member(ordered_pair(X0,sK14),sK13)
| ~ ilf_type(X0,member_type(sK12)) ),
inference(cnf_transformation,[],[f182]) ).
cnf(c_105,negated_conjecture,
( member(sK14,range(sK12,sK11,sK13))
| member(ordered_pair(sK15,sK14),sK13) ),
inference(cnf_transformation,[],[f181]) ).
cnf(c_108,negated_conjecture,
ilf_type(sK13,relation_type(sK12,sK11)),
inference(cnf_transformation,[],[f178]) ).
cnf(c_163,plain,
~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_90,c_103,c_90]) ).
cnf(c_187,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_74,c_103,c_74]) ).
cnf(c_243,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_78,c_103,c_78]) ).
cnf(c_247,plain,
( ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| empty(X1) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_103,c_63]) ).
cnf(c_249,plain,
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_62,c_103,c_67,c_62]) ).
cnf(c_250,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(renaming,[status(thm)],[c_249]) ).
cnf(c_259,plain,
( ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK0(X0,X1),X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_103,c_50]) ).
cnf(c_269,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(X0,domain_of(X2)) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_103,c_53]) ).
cnf(c_273,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(X1,range_of(X2)) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_103,c_52]) ).
cnf(c_277,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_88,c_103,c_88]) ).
cnf(c_278,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_277]) ).
cnf(c_451,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_59,c_103]) ).
cnf(c_452,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_100,c_103]) ).
cnf(c_453,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_99,c_103]) ).
cnf(c_455,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_101,c_103]) ).
cnf(c_458,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_278,c_103]) ).
cnf(c_459,plain,
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_247,c_103]) ).
cnf(c_460,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| member(X1,range_of(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_273,c_103]) ).
cnf(c_461,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| member(X0,domain_of(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_269,c_103]) ).
cnf(c_465,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_250,c_103]) ).
cnf(c_467,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_98,c_103]) ).
cnf(c_470,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_243,c_103]) ).
cnf(c_564,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_467,c_103]) ).
cnf(c_627,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_451,c_103]) ).
cnf(c_644,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_452,c_103]) ).
cnf(c_672,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| domain(X1,X2,X0) = domain_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_453,c_103]) ).
cnf(c_683,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| range(X1,X2,X0) = range_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_455,c_103]) ).
cnf(c_695,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_458,c_103]) ).
cnf(c_1160,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_187]) ).
cnf(c_1164,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_470]) ).
cnf(c_1166,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_564,c_627]) ).
cnf(c_1168,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| domain(X1,X2,X0) = domain_of(X0) ),
inference(prop_impl_just,[status(thm)],[c_672]) ).
cnf(c_1170,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_644]) ).
cnf(c_1172,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| range(X1,X2,X0) = range_of(X0) ),
inference(prop_impl_just,[status(thm)],[c_683]) ).
cnf(c_1176,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_465]) ).
cnf(c_1882,plain,
relation_type(sK12,sK11) = sP0_iProver_def,
definition ).
cnf(c_1884,plain,
range(sK12,sK11,sK13) = sP2_iProver_def,
definition ).
cnf(c_1885,plain,
member_type(sK12) = sP3_iProver_def,
definition ).
cnf(c_1886,plain,
ordered_pair(sK15,sK14) = sP4_iProver_def,
definition ).
cnf(c_1889,negated_conjecture,
ilf_type(sK13,sP0_iProver_def),
inference(demodulation,[status(thm)],[c_108,c_1882]) ).
cnf(c_1892,negated_conjecture,
( member(sK14,sP2_iProver_def)
| member(sP4_iProver_def,sK13) ),
inference(demodulation,[status(thm)],[c_105,c_1886]) ).
cnf(c_1893,negated_conjecture,
( ~ member(ordered_pair(X0,sK14),sK13)
| ~ ilf_type(X0,sP3_iProver_def)
| ~ member(sK14,sP2_iProver_def) ),
inference(demodulation,[status(thm)],[c_104]) ).
cnf(c_2857,plain,
( ~ ilf_type(X0,sP0_iProver_def)
| relation_like(X0) ),
inference(superposition,[status(thm)],[c_1882,c_1166]) ).
cnf(c_2866,plain,
( ~ member(X0,sK12)
| ilf_type(X0,sP3_iProver_def) ),
inference(superposition,[status(thm)],[c_1885,c_1176]) ).
cnf(c_2906,plain,
relation_like(sK13),
inference(superposition,[status(thm)],[c_1889,c_2857]) ).
cnf(c_2951,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1))
| empty(power_set(X1)) ),
inference(superposition,[status(thm)],[c_1164,c_459]) ).
cnf(c_2952,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2951,c_163]) ).
cnf(c_3057,plain,
( ~ member(sP4_iProver_def,X0)
| ~ ilf_type(X0,binary_relation_type)
| member(sK14,range_of(X0)) ),
inference(superposition,[status(thm)],[c_1886,c_460]) ).
cnf(c_3078,plain,
( ~ ilf_type(X0,sP0_iProver_def)
| domain(sK12,sK11,X0) = domain_of(X0) ),
inference(superposition,[status(thm)],[c_1882,c_1168]) ).
cnf(c_3228,plain,
( ~ ilf_type(X0,sP0_iProver_def)
| range(sK12,sK11,X0) = range_of(X0) ),
inference(superposition,[status(thm)],[c_1882,c_1172]) ).
cnf(c_3327,plain,
( ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| member(sK0(X0,X1),domain_of(X1)) ),
inference(superposition,[status(thm)],[c_259,c_461]) ).
cnf(c_3332,plain,
( ~ ilf_type(sK0(sK14,sK13),sP3_iProver_def)
| ~ member(sK14,range_of(sK13))
| ~ member(sK14,sP2_iProver_def)
| ~ ilf_type(sK13,binary_relation_type) ),
inference(superposition,[status(thm)],[c_259,c_1893]) ).
cnf(c_4425,plain,
domain(sK12,sK11,sK13) = domain_of(sK13),
inference(superposition,[status(thm)],[c_1889,c_3078]) ).
cnf(c_4439,plain,
( ~ ilf_type(sK13,relation_type(sK12,sK11))
| ilf_type(domain_of(sK13),subset_type(sK12)) ),
inference(superposition,[status(thm)],[c_4425,c_1170]) ).
cnf(c_4440,plain,
( ~ ilf_type(sK13,sP0_iProver_def)
| ilf_type(domain_of(sK13),subset_type(sK12)) ),
inference(light_normalisation,[status(thm)],[c_4439,c_1882]) ).
cnf(c_4441,plain,
ilf_type(domain_of(sK13),subset_type(sK12)),
inference(forward_subsumption_resolution,[status(thm)],[c_4440,c_1889]) ).
cnf(c_4443,plain,
member(domain_of(sK13),power_set(sK12)),
inference(superposition,[status(thm)],[c_4441,c_2952]) ).
cnf(c_4519,plain,
( ~ member(X0,domain_of(sK13))
| member(X0,sK12) ),
inference(superposition,[status(thm)],[c_4443,c_695]) ).
cnf(c_4907,plain,
range(sK12,sK11,sK13) = range_of(sK13),
inference(superposition,[status(thm)],[c_1889,c_3228]) ).
cnf(c_4911,plain,
range_of(sK13) = sP2_iProver_def,
inference(light_normalisation,[status(thm)],[c_4907,c_1884]) ).
cnf(c_4912,plain,
( ~ ilf_type(sK0(sK14,sK13),sP3_iProver_def)
| ~ member(sK14,sP2_iProver_def)
| ~ ilf_type(sK13,binary_relation_type) ),
inference(demodulation,[status(thm)],[c_3332,c_4911]) ).
cnf(c_4928,plain,
( ~ member(sP4_iProver_def,sK13)
| ~ ilf_type(sK13,binary_relation_type)
| member(sK14,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_4911,c_3057]) ).
cnf(c_5006,plain,
( ~ ilf_type(sK0(sK14,sK13),sP3_iProver_def)
| ~ ilf_type(sK13,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_4912,c_1892,c_4912,c_4928]) ).
cnf(c_5012,plain,
( ~ ilf_type(sK13,binary_relation_type)
| member(sK14,sP2_iProver_def) ),
inference(global_subsumption_just,[status(thm)],[c_4928,c_1892,c_4928]) ).
cnf(c_5018,plain,
( ~ relation_like(sK13)
| member(sK14,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_1160,c_5012]) ).
cnf(c_5019,plain,
member(sK14,sP2_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_5018,c_2906]) ).
cnf(c_12658,plain,
( ~ member(X0,range_of(sK13))
| ~ ilf_type(sK13,binary_relation_type)
| member(sK0(X0,sK13),sK12) ),
inference(superposition,[status(thm)],[c_3327,c_4519]) ).
cnf(c_12662,plain,
( ~ member(X0,sP2_iProver_def)
| ~ ilf_type(sK13,binary_relation_type)
| member(sK0(X0,sK13),sK12) ),
inference(light_normalisation,[status(thm)],[c_12658,c_4911]) ).
cnf(c_12739,plain,
( ~ member(X0,sP2_iProver_def)
| ~ ilf_type(sK13,binary_relation_type)
| ilf_type(sK0(X0,sK13),sP3_iProver_def) ),
inference(superposition,[status(thm)],[c_12662,c_2866]) ).
cnf(c_12770,plain,
( ~ member(sK14,sP2_iProver_def)
| ~ ilf_type(sK13,binary_relation_type) ),
inference(superposition,[status(thm)],[c_12739,c_5006]) ).
cnf(c_12771,plain,
~ ilf_type(sK13,binary_relation_type),
inference(forward_subsumption_resolution,[status(thm)],[c_12770,c_5019]) ).
cnf(c_12778,plain,
~ relation_like(sK13),
inference(superposition,[status(thm)],[c_1160,c_12771]) ).
cnf(c_12779,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12778,c_2906]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET681+3 : TPTP v8.2.0. Released v2.2.0.
% 0.04/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Jun 23 15:27:24 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.22/0.50 Running first-order theorem proving
% 0.22/0.50 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.94/1.69 % SZS status Started for theBenchmark.p
% 7.94/1.69 % SZS status Theorem for theBenchmark.p
% 7.94/1.69
% 7.94/1.69 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.94/1.69
% 7.94/1.69 ------ iProver source info
% 7.94/1.69
% 7.94/1.69 git: date: 2024-06-12 09:56:46 +0000
% 7.94/1.69 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 7.94/1.69 git: non_committed_changes: false
% 7.94/1.69
% 7.94/1.69 ------ Parsing...
% 7.94/1.69 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.94/1.69
% 7.94/1.69 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 7.94/1.69
% 7.94/1.69 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.94/1.69
% 7.94/1.69 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.94/1.69 ------ Proving...
% 7.94/1.69 ------ Problem Properties
% 7.94/1.69
% 7.94/1.69
% 7.94/1.69 clauses 49
% 7.94/1.69 conjectures 7
% 7.94/1.69 EPR 12
% 7.94/1.69 Horn 41
% 7.94/1.69 unary 16
% 7.94/1.69 binary 22
% 7.94/1.69 lits 93
% 7.94/1.69 lits eq 13
% 7.94/1.69 fd_pure 0
% 7.94/1.69 fd_pseudo 0
% 7.94/1.69 fd_cond 0
% 7.94/1.69 fd_pseudo_cond 2
% 7.94/1.69 AC symbols 0
% 7.94/1.69
% 7.94/1.69 ------ Schedule dynamic 5 is on
% 7.94/1.69
% 7.94/1.69 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.94/1.69
% 7.94/1.69
% 7.94/1.69 ------
% 7.94/1.69 Current options:
% 7.94/1.69 ------
% 7.94/1.69
% 7.94/1.69
% 7.94/1.69
% 7.94/1.69
% 7.94/1.69 ------ Proving...
% 7.94/1.69
% 7.94/1.69
% 7.94/1.69 % SZS status Theorem for theBenchmark.p
% 7.94/1.69
% 7.94/1.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.94/1.69
% 7.94/1.73
%------------------------------------------------------------------------------