TSTP Solution File: SET016+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n016.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 15:05:31 EDT 2023
% Result : Theorem 3.55s 1.17s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 15 unt; 0 def)
% Number of atoms : 155 ( 54 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 151 ( 60 ~; 57 |; 20 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 117 ( 2 sgn; 73 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f8,axiom,
! [X2,X0] :
( member(X2,singleton(X0))
<=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
fof(f9,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( X1 = X2
| X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
fof(f12,conjecture,
! [X0,X1,X5,X6] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X5),unordered_pair(X5,X6)))
=> X0 = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI50a) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X5,X6] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X5),unordered_pair(X5,X6)))
=> X0 = X5 ),
inference(negated_conjecture,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f20,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( X0 = X2
| X0 = X1 ) ),
inference(rectify,[],[f9]) ).
fof(f23,plain,
~ ! [X0,X1,X2,X3] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3)))
=> X0 = X2 ),
inference(rectify,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( equal_set(X0,X1)
=> ( subset(X1,X0)
& subset(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f28,plain,
? [X0,X1,X2,X3] :
( X0 != X2
& equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3))) ),
inference(ennf_transformation,[],[f23]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f30,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f30,f31]) ).
fof(f40,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 ) )
& ( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 ) )
& ( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f41]) ).
fof(f51,plain,
( ? [X0,X1,X2,X3] :
( X0 != X2
& equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3))) )
=> ( sK3 != sK5
& equal_set(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),unordered_pair(singleton(sK5),unordered_pair(sK5,sK6))) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
( sK3 != sK5
& equal_set(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),unordered_pair(singleton(sK5),unordered_pair(sK5,sK6))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f28,f51]) ).
fof(f53,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f57,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f70,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f71,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f40]) ).
fof(f72,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f73,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1 ),
inference(cnf_transformation,[],[f42]) ).
fof(f81,plain,
equal_set(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),unordered_pair(singleton(sK5),unordered_pair(sK5,sK6))),
inference(cnf_transformation,[],[f52]) ).
fof(f82,plain,
sK3 != sK5,
inference(cnf_transformation,[],[f52]) ).
fof(f83,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f71]) ).
fof(f85,plain,
! [X2,X1] : member(X1,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f73]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_52,plain,
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_53,plain,
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_66,plain,
member(X0,singleton(X0)),
inference(cnf_transformation,[],[f83]) ).
cnf(c_67,plain,
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f70]) ).
cnf(c_69,plain,
member(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f85]) ).
cnf(c_70,plain,
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f72]) ).
cnf(c_77,negated_conjecture,
sK3 != sK5,
inference(cnf_transformation,[],[f82]) ).
cnf(c_78,negated_conjecture,
equal_set(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),unordered_pair(singleton(sK5),unordered_pair(sK5,sK6))),
inference(cnf_transformation,[],[f81]) ).
cnf(c_79,plain,
member(sK3,singleton(sK3)),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_87,plain,
( ~ member(sK3,singleton(sK3))
| sK3 = sK3 ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_110,plain,
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_53]) ).
cnf(c_111,plain,
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_110]) ).
cnf(c_114,plain,
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
cnf(c_444,plain,
( unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)) != X0
| unordered_pair(singleton(sK5),unordered_pair(sK5,sK6)) != X1
| subset(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_111,c_78]) ).
cnf(c_445,plain,
subset(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),unordered_pair(singleton(sK5),unordered_pair(sK5,sK6))),
inference(unflattening,[status(thm)],[c_444]) ).
cnf(c_449,plain,
( unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)) != X0
| unordered_pair(singleton(sK5),unordered_pair(sK5,sK6)) != X1
| subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_114,c_78]) ).
cnf(c_450,plain,
subset(unordered_pair(singleton(sK5),unordered_pair(sK5,sK6)),unordered_pair(singleton(sK3),unordered_pair(sK3,sK4))),
inference(unflattening,[status(thm)],[c_449]) ).
cnf(c_975,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_1677,plain,
( ~ subset(unordered_pair(X0,X1),X2)
| member(X0,X2) ),
inference(superposition,[status(thm)],[c_69,c_51]) ).
cnf(c_1717,plain,
( sK3 != X0
| sK5 != X0
| sK3 = sK5 ),
inference(instantiation,[status(thm)],[c_975]) ).
cnf(c_1718,plain,
( sK3 != sK3
| sK5 != sK3
| sK3 = sK5 ),
inference(instantiation,[status(thm)],[c_1717]) ).
cnf(c_2270,plain,
member(singleton(sK3),unordered_pair(singleton(sK5),unordered_pair(sK5,sK6))),
inference(superposition,[status(thm)],[c_445,c_1677]) ).
cnf(c_2423,plain,
( ~ member(sK5,singleton(X0))
| sK5 = X0 ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_2424,plain,
( ~ member(sK5,singleton(sK3))
| sK5 = sK3 ),
inference(instantiation,[status(thm)],[c_2423]) ).
cnf(c_2481,plain,
( unordered_pair(sK5,sK6) = singleton(sK3)
| singleton(sK3) = singleton(sK5) ),
inference(superposition,[status(thm)],[c_2270,c_70]) ).
cnf(c_2625,plain,
( singleton(sK3) = singleton(sK5)
| member(sK5,singleton(sK3)) ),
inference(superposition,[status(thm)],[c_2481,c_69]) ).
cnf(c_2635,plain,
( singleton(sK3) = singleton(sK5)
| subset(unordered_pair(singleton(sK5),singleton(sK3)),unordered_pair(singleton(sK3),unordered_pair(sK3,sK4))) ),
inference(superposition,[status(thm)],[c_2481,c_450]) ).
cnf(c_2920,plain,
singleton(sK3) = singleton(sK5),
inference(global_subsumption_just,[status(thm)],[c_2635,c_79,c_77,c_87,c_1718,c_2424,c_2625]) ).
cnf(c_2953,plain,
member(sK5,singleton(sK3)),
inference(superposition,[status(thm)],[c_2920,c_66]) ).
cnf(c_2963,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2953,c_2424,c_1718,c_87,c_77,c_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sat Aug 26 11:42:27 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.55/1.17 % SZS status Started for theBenchmark.p
% 3.55/1.17 % SZS status Theorem for theBenchmark.p
% 3.55/1.17
% 3.55/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.55/1.17
% 3.55/1.17 ------ iProver source info
% 3.55/1.17
% 3.55/1.17 git: date: 2023-05-31 18:12:56 +0000
% 3.55/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.55/1.17 git: non_committed_changes: false
% 3.55/1.17 git: last_make_outside_of_git: false
% 3.55/1.17
% 3.55/1.17 ------ Parsing...
% 3.55/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.55/1.17
% 3.55/1.17 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 3.55/1.17
% 3.55/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.55/1.17
% 3.55/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.55/1.17 ------ Proving...
% 3.55/1.17 ------ Problem Properties
% 3.55/1.17
% 3.55/1.17
% 3.55/1.17 clauses 29
% 3.55/1.17 conjectures 1
% 3.55/1.17 EPR 3
% 3.55/1.17 Horn 24
% 3.55/1.17 unary 7
% 3.55/1.17 binary 15
% 3.55/1.17 lits 58
% 3.55/1.17 lits eq 4
% 3.55/1.17 fd_pure 0
% 3.55/1.17 fd_pseudo 0
% 3.55/1.17 fd_cond 0
% 3.55/1.17 fd_pseudo_cond 2
% 3.55/1.17 AC symbols 0
% 3.55/1.17
% 3.55/1.17 ------ Schedule dynamic 5 is on
% 3.55/1.17
% 3.55/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.55/1.17
% 3.55/1.17
% 3.55/1.17 ------
% 3.55/1.17 Current options:
% 3.55/1.17 ------
% 3.55/1.17
% 3.55/1.17
% 3.55/1.17
% 3.55/1.17
% 3.55/1.17 ------ Proving...
% 3.55/1.17
% 3.55/1.17
% 3.55/1.17 % SZS status Theorem for theBenchmark.p
% 3.55/1.17
% 3.55/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.55/1.17
% 3.55/1.18
%------------------------------------------------------------------------------