TSTP Solution File: SET002+4 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET002+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.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 02:59:12 EDT 2024
% Result : Theorem 3.31s 1.14s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 113 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 122 ( 51 ~; 48 |; 14 &)
% ( 5 <=>; 4 =>; 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 : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 76 ( 1 sgn 51 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f5,axiom,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f12,conjecture,
! [X0] : equal_set(union(X0,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI14) ).
fof(f13,negated_conjecture,
~ ! [X0] : equal_set(union(X0,X0),X0),
inference(negated_conjecture,[],[f12]) ).
fof(f16,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f23,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f28,plain,
? [X0] : ~ equal_set(union(X0,X0),X0),
inference(ennf_transformation,[],[f13]) ).
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,[],[f24]) ).
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(f36,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f36]) ).
fof(f51,plain,
( ? [X0] : ~ equal_set(union(X0,X0),X0)
=> ~ equal_set(union(sK3,sK3),sK3) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
~ equal_set(union(sK3,sK3),sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f28,f51]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f62,plain,
! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f64,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f80,plain,
~ equal_set(union(sK3,sK3),sK3),
inference(cnf_transformation,[],[f52]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_58,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_60,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_76,negated_conjecture,
~ equal_set(union(sK3,sK3),sK3),
inference(cnf_transformation,[],[f80]) ).
cnf(c_426,plain,
( union(sK3,sK3) != X0
| X1 != sK3
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).
cnf(c_427,plain,
( ~ subset(union(sK3,sK3),sK3)
| ~ subset(sK3,union(sK3,sK3)) ),
inference(unflattening,[status(thm)],[c_426]) ).
cnf(c_492,plain,
( ~ subset(union(sK3,sK3),sK3)
| ~ subset(sK3,union(sK3,sK3)) ),
inference(prop_impl_just,[status(thm)],[c_427]) ).
cnf(c_1331,plain,
( ~ member(sK0(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ),
inference(superposition,[status(thm)],[c_58,c_49]) ).
cnf(c_1334,plain,
( ~ member(sK0(sK3,union(sK3,sK3)),sK3)
| subset(sK3,union(sK3,sK3)) ),
inference(instantiation,[status(thm)],[c_1331]) ).
cnf(c_1442,plain,
( ~ member(sK0(union(sK3,sK3),sK3),sK3)
| subset(union(sK3,sK3),sK3) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_1519,plain,
( member(sK0(union(X0,X1),X2),X0)
| member(sK0(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50,c_60]) ).
cnf(c_1533,plain,
( member(sK0(union(sK3,sK3),sK3),sK3)
| subset(union(sK3,sK3),sK3) ),
inference(instantiation,[status(thm)],[c_1519]) ).
cnf(c_1833,plain,
~ subset(sK3,union(sK3,sK3)),
inference(global_subsumption_just,[status(thm)],[c_492,c_427,c_1442,c_1533]) ).
cnf(c_2047,plain,
( member(sK0(sK3,union(sK3,sK3)),sK3)
| subset(sK3,union(sK3,sK3)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2050,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2047,c_1833,c_1334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET002+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 2 20:56:03 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 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
% 3.31/1.14 % SZS status Started for theBenchmark.p
% 3.31/1.14 % SZS status Theorem for theBenchmark.p
% 3.31/1.14
% 3.31/1.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.31/1.14
% 3.31/1.14 ------ iProver source info
% 3.31/1.14
% 3.31/1.14 git: date: 2024-05-02 19:28:25 +0000
% 3.31/1.14 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.31/1.14 git: non_committed_changes: false
% 3.31/1.14
% 3.31/1.14 ------ Parsing...
% 3.31/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.31/1.14
% 3.31/1.14 ------ 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
% 3.31/1.14
% 3.31/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.31/1.14
% 3.31/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.31/1.14 ------ Proving...
% 3.31/1.14 ------ Problem Properties
% 3.31/1.14
% 3.31/1.14
% 3.31/1.14 clauses 27
% 3.31/1.14 conjectures 0
% 3.31/1.14 EPR 2
% 3.31/1.14 Horn 22
% 3.31/1.14 unary 4
% 3.31/1.14 binary 16
% 3.31/1.14 lits 57
% 3.31/1.14 lits eq 3
% 3.31/1.14 fd_pure 0
% 3.31/1.14 fd_pseudo 0
% 3.31/1.14 fd_cond 0
% 3.31/1.14 fd_pseudo_cond 2
% 3.31/1.14 AC symbols 0
% 3.31/1.14
% 3.31/1.14 ------ Schedule dynamic 5 is on
% 3.31/1.14
% 3.31/1.14 ------ no conjectures: strip conj schedule
% 3.31/1.14
% 3.31/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.31/1.14
% 3.31/1.14
% 3.31/1.14 ------
% 3.31/1.14 Current options:
% 3.31/1.14 ------
% 3.31/1.14
% 3.31/1.14
% 3.31/1.14
% 3.31/1.14
% 3.31/1.14 ------ Proving...
% 3.31/1.14
% 3.31/1.14
% 3.31/1.14 % SZS status Theorem for theBenchmark.p
% 3.31/1.14
% 3.31/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.31/1.14
% 3.31/1.14
%------------------------------------------------------------------------------