TSTP Solution File: SET688+4 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET688+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 03:01:15 EDT 2024
% Result : Theorem 3.77s 1.11s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 13 unt; 0 def)
% Number of atoms : 155 ( 8 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 181 ( 78 ~; 52 |; 42 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 43 !; 12 ?)
% 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(f12,conjecture,
! [X0,X1,X5] :
( ( ~ equal_set(X1,X5)
& subset(X1,X5)
& ~ equal_set(X0,X1)
& subset(X0,X1) )
=> ~ equal_set(X0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI04) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X5] :
( ( ~ equal_set(X1,X5)
& subset(X1,X5)
& ~ equal_set(X0,X1)
& subset(X0,X1) )
=> ~ equal_set(X0,X5) ),
inference(negated_conjecture,[],[f12]) ).
fof(f23,plain,
~ ! [X0,X1,X2] :
( ( ~ equal_set(X1,X2)
& subset(X1,X2)
& ~ equal_set(X0,X1)
& subset(X0,X1) )
=> ~ equal_set(X0,X2) ),
inference(rectify,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
? [X0,X1,X2] :
( equal_set(X0,X2)
& ~ equal_set(X1,X2)
& subset(X1,X2)
& ~ equal_set(X0,X1)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f27,plain,
? [X0,X1,X2] :
( equal_set(X0,X2)
& ~ equal_set(X1,X2)
& subset(X1,X2)
& ~ equal_set(X0,X1)
& subset(X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f28,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(f29,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,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f31,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])],[f29,f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(flattening,[],[f32]) ).
fof(f52,plain,
( ? [X0,X1,X2] :
( equal_set(X0,X2)
& ~ equal_set(X1,X2)
& subset(X1,X2)
& ~ equal_set(X0,X1)
& subset(X0,X1) )
=> ( equal_set(sK3,sK5)
& ~ equal_set(sK4,sK5)
& subset(sK4,sK5)
& ~ equal_set(sK3,sK4)
& subset(sK3,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
( equal_set(sK3,sK5)
& ~ equal_set(sK4,sK5)
& subset(sK4,sK5)
& ~ equal_set(sK3,sK4)
& subset(sK3,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f27,f52]) ).
fof(f54,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f58,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f59,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f83,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f53]) ).
fof(f84,plain,
~ equal_set(sK3,sK4),
inference(cnf_transformation,[],[f53]) ).
fof(f85,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f53]) ).
fof(f87,plain,
equal_set(sK3,sK5),
inference(cnf_transformation,[],[f53]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_53,plain,
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_78,negated_conjecture,
equal_set(sK3,sK5),
inference(cnf_transformation,[],[f87]) ).
cnf(c_80,negated_conjecture,
subset(sK4,sK5),
inference(cnf_transformation,[],[f85]) ).
cnf(c_81,negated_conjecture,
~ equal_set(sK3,sK4),
inference(cnf_transformation,[],[f84]) ).
cnf(c_82,negated_conjecture,
subset(sK3,sK4),
inference(cnf_transformation,[],[f83]) ).
cnf(c_109,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
cnf(c_113,plain,
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
cnf(c_114,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_113]) ).
cnf(c_119,plain,
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_53]) ).
cnf(c_366,plain,
( X0 != sK3
| X1 != sK5
| subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_119,c_78]) ).
cnf(c_367,plain,
subset(sK5,sK3),
inference(unflattening,[status(thm)],[c_366]) ).
cnf(c_378,plain,
( X0 != sK3
| X1 != sK4
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_81]) ).
cnf(c_379,plain,
( ~ subset(sK3,sK4)
| ~ subset(sK4,sK3) ),
inference(unflattening,[status(thm)],[c_378]) ).
cnf(c_380,plain,
~ subset(sK4,sK3),
inference(global_subsumption_just,[status(thm)],[c_379,c_82,c_379]) ).
cnf(c_536,plain,
( X0 != sK4
| X1 != sK3
| member(sK0(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_114,c_380]) ).
cnf(c_537,plain,
member(sK0(sK4,sK3),sK4),
inference(unflattening,[status(thm)],[c_536]) ).
cnf(c_541,plain,
( X0 != sK4
| X1 != sK3
| ~ member(sK0(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_109,c_380]) ).
cnf(c_542,plain,
~ member(sK0(sK4,sK3),sK3),
inference(unflattening,[status(thm)],[c_541]) ).
cnf(c_1215,plain,
( ~ member(sK0(sK4,sK3),X0)
| ~ subset(X0,sK3)
| member(sK0(sK4,sK3),sK3) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_1958,plain,
( ~ member(sK0(sK4,sK3),sK5)
| ~ subset(sK5,sK3)
| member(sK0(sK4,sK3),sK3) ),
inference(instantiation,[status(thm)],[c_1215]) ).
cnf(c_2478,plain,
( ~ member(sK0(sK4,sK3),X0)
| ~ subset(X0,sK5)
| member(sK0(sK4,sK3),sK5) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_2479,plain,
( ~ member(sK0(sK4,sK3),sK4)
| ~ subset(sK4,sK5)
| member(sK0(sK4,sK3),sK5) ),
inference(instantiation,[status(thm)],[c_2478]) ).
cnf(c_2480,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2479,c_1958,c_542,c_537,c_367,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SET688+4 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.11 % Command : run_iprover %s %d THM
% 0.11/0.31 % Computer : n022.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu May 2 20:28:57 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 3.77/1.11 % SZS status Started for theBenchmark.p
% 3.77/1.11 % SZS status Theorem for theBenchmark.p
% 3.77/1.11
% 3.77/1.11 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.77/1.11
% 3.77/1.11 ------ iProver source info
% 3.77/1.11
% 3.77/1.11 git: date: 2024-05-02 19:28:25 +0000
% 3.77/1.11 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.77/1.11 git: non_committed_changes: false
% 3.77/1.11
% 3.77/1.11 ------ Parsing...
% 3.77/1.11 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.77/1.11
% 3.77/1.11 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e
% 3.77/1.11
% 3.77/1.11 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.77/1.11
% 3.77/1.11 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.77/1.11 ------ Proving...
% 3.77/1.11 ------ Problem Properties
% 3.77/1.11
% 3.77/1.11
% 3.77/1.11 clauses 34
% 3.77/1.11 conjectures 2
% 3.77/1.11 EPR 10
% 3.77/1.11 Horn 29
% 3.77/1.11 unary 12
% 3.77/1.11 binary 15
% 3.77/1.11 lits 63
% 3.77/1.11 lits eq 5
% 3.77/1.11 fd_pure 0
% 3.77/1.11 fd_pseudo 0
% 3.77/1.11 fd_cond 0
% 3.77/1.11 fd_pseudo_cond 2
% 3.77/1.11 AC symbols 0
% 3.77/1.11
% 3.77/1.11 ------ Input Options Time Limit: Unbounded
% 3.77/1.11
% 3.77/1.11
% 3.77/1.11 ------
% 3.77/1.11 Current options:
% 3.77/1.11 ------
% 3.77/1.11
% 3.77/1.11
% 3.77/1.11
% 3.77/1.11
% 3.77/1.11 ------ Proving...
% 3.77/1.11
% 3.77/1.11
% 3.77/1.11 % SZS status Theorem for theBenchmark.p
% 3.77/1.11
% 3.77/1.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.77/1.11
% 3.77/1.11
%------------------------------------------------------------------------------