TSTP Solution File: SET664+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 : Thu Aug 31 15:09:00 EDT 2023
% Result : Theorem 2.72s 1.18s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f189)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( subset(X0,empty_set)
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ( ( empty_set = range_of(X0)
| empty_set = domain_of(X0) )
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f7,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(f29,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',p28) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(f35,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( ilf_type(X2,relation_type(X1,empty_set))
=> empty_set = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_27) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( ilf_type(X2,relation_type(X1,empty_set))
=> empty_set = X2 ) ) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f37,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,[],[f7]) ).
fof(f39,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f40,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0] :
( empty_set = X0
| ( empty_set != range_of(X0)
& empty_set != domain_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f42,plain,
! [X0] :
( empty_set = X0
| ( empty_set != range_of(X0)
& empty_set != domain_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f45,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,[],[f37]) ).
fof(f73,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,[],[f29]) ).
fof(f78,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f79,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f78]) ).
fof(f116,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,sK12)) )
& ilf_type(X1,set_type) )
& ilf_type(sK12,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,sK12)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(sK13,empty_set))
& ilf_type(X2,relation_type(sK13,sK12)) )
& ilf_type(sK13,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(sK13,empty_set))
& ilf_type(X2,relation_type(sK13,sK12)) )
=> ( empty_set != sK14
& ilf_type(sK14,relation_type(sK13,empty_set))
& ilf_type(sK14,relation_type(sK13,sK12)) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
( empty_set != sK14
& ilf_type(sK14,relation_type(sK13,empty_set))
& ilf_type(sK14,relation_type(sK13,sK12))
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f79,f118,f117,f116]) ).
fof(f120,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f40]) ).
fof(f122,plain,
! [X0] :
( empty_set = X0
| empty_set != range_of(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f42]) ).
fof(f124,plain,
! [X2,X0,X1] :
( subset(range_of(X2),X1)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f43]) ).
fof(f128,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,[],[f45]) ).
fof(f173,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,[],[f73]) ).
fof(f178,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f182,plain,
ilf_type(sK14,relation_type(sK13,empty_set)),
inference(cnf_transformation,[],[f119]) ).
fof(f183,plain,
empty_set != sK14,
inference(cnf_transformation,[],[f119]) ).
cnf(c_49,plain,
( ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type)
| X0 = empty_set ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_50,plain,
( range_of(X0) != empty_set
| ~ ilf_type(X0,binary_relation_type)
| X0 = empty_set ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_52,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(range_of(X0),X2) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_56,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,[],[f128]) ).
cnf(c_69,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f189]) ).
cnf(c_100,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,[],[f173]) ).
cnf(c_105,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f178]) ).
cnf(c_106,negated_conjecture,
empty_set != sK14,
inference(cnf_transformation,[],[f183]) ).
cnf(c_107,negated_conjecture,
ilf_type(sK14,relation_type(sK13,empty_set)),
inference(cnf_transformation,[],[f182]) ).
cnf(c_188,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_105,c_69]) ).
cnf(c_259,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_188]) ).
cnf(c_396,plain,
( range_of(X0) != empty_set
| ~ relation_like(X0)
| X0 = empty_set ),
inference(bin_hyper_res,[status(thm)],[c_50,c_259]) ).
cnf(c_416,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| subset(range_of(X0),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_105]) ).
cnf(c_421,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_100,c_105]) ).
cnf(c_428,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_56,c_105]) ).
cnf(c_536,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_421,c_105]) ).
cnf(c_547,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| subset(range_of(X0),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_416,c_105]) ).
cnf(c_597,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_428,c_105]) ).
cnf(c_1539,plain,
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(prop_impl_just,[status(thm)],[c_105,c_49]) ).
cnf(c_1541,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| subset(range_of(X0),X2) ),
inference(prop_impl_just,[status(thm)],[c_547]) ).
cnf(c_1545,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_536,c_597]) ).
cnf(c_3126,plain,
relation_like(sK14),
inference(superposition,[status(thm)],[c_107,c_1545]) ).
cnf(c_3248,plain,
subset(range_of(sK14),empty_set),
inference(superposition,[status(thm)],[c_107,c_1541]) ).
cnf(c_3277,plain,
range_of(sK14) = empty_set,
inference(superposition,[status(thm)],[c_3248,c_1539]) ).
cnf(c_4726,plain,
( ~ relation_like(sK14)
| empty_set = sK14 ),
inference(superposition,[status(thm)],[c_3277,c_396]) ).
cnf(c_4731,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4726,c_106,c_3126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:15:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.72/1.18 % SZS status Started for theBenchmark.p
% 2.72/1.18 % SZS status Theorem for theBenchmark.p
% 2.72/1.18
% 2.72/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.72/1.18
% 2.72/1.18 ------ iProver source info
% 2.72/1.18
% 2.72/1.18 git: date: 2023-05-31 18:12:56 +0000
% 2.72/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.72/1.18 git: non_committed_changes: false
% 2.72/1.18 git: last_make_outside_of_git: false
% 2.72/1.18
% 2.72/1.18 ------ Parsing...
% 2.72/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.72/1.18
% 2.72/1.18 ------ 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
% 2.72/1.18
% 2.72/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.72/1.18
% 2.72/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.72/1.18 ------ Proving...
% 2.72/1.18 ------ Problem Properties
% 2.72/1.18
% 2.72/1.18
% 2.72/1.18 clauses 44
% 2.72/1.18 conjectures 3
% 2.72/1.18 EPR 12
% 2.72/1.18 Horn 37
% 2.72/1.18 unary 11
% 2.72/1.18 binary 25
% 2.72/1.18 lits 89
% 2.72/1.18 lits eq 12
% 2.72/1.18 fd_pure 0
% 2.72/1.18 fd_pseudo 0
% 2.72/1.18 fd_cond 3
% 2.72/1.18 fd_pseudo_cond 2
% 2.72/1.18 AC symbols 0
% 2.72/1.18
% 2.72/1.18 ------ Schedule dynamic 5 is on
% 2.72/1.18
% 2.72/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.72/1.18
% 2.72/1.18
% 2.72/1.18 ------
% 2.72/1.18 Current options:
% 2.72/1.18 ------
% 2.72/1.18
% 2.72/1.18
% 2.72/1.18
% 2.72/1.18
% 2.72/1.18 ------ Proving...
% 2.72/1.18
% 2.72/1.18
% 2.72/1.18 % SZS status Theorem for theBenchmark.p
% 2.72/1.18
% 2.72/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.72/1.18
% 2.72/1.18
%------------------------------------------------------------------------------