TSTP Solution File: SET595+4 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET595+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.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 03:00:52 EDT 2024
% Result : Theorem 61.71s 9.27s
% Output : CNFRefutation 61.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 63 ( 5 unt; 0 def)
% Number of atoms : 179 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 194 ( 78 ~; 78 |; 24 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 124 ( 3 sgn 79 !; 7 ?)
% 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(f5,axiom,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f7,axiom,
! [X1,X0,X3] :
( member(X1,difference(X3,X0))
<=> ( ~ member(X1,X0)
& member(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
fof(f12,conjecture,
! [X0,X3] :
( subset(X0,X3)
=> equal_set(union(difference(X3,X0),X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI27) ).
fof(f13,negated_conjecture,
~ ! [X0,X3] :
( subset(X0,X3)
=> equal_set(union(difference(X3,X0),X0),X3) ),
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(f18,plain,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f7]) ).
fof(f23,plain,
~ ! [X0,X1] :
( subset(X0,X1)
=> equal_set(union(difference(X1,X0),X0),X1) ),
inference(rectify,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(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] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f29,plain,
? [X0,X1] :
( ~ equal_set(union(difference(X1,X0),X0),X1)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f30,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(f31,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,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f33,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])],[f31,f32]) ).
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(nnf_transformation,[],[f16]) ).
fof(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f39]) ).
fof(f52,plain,
( ? [X0,X1] :
( ~ equal_set(union(difference(X1,X0),X0),X1)
& subset(X0,X1) )
=> ( ~ equal_set(union(difference(sK4,sK3),sK3),sK4)
& subset(sK3,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
( ~ equal_set(union(difference(sK4,sK3),sK3),sK4)
& subset(sK3,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f29,f52]) ).
fof(f54,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f63,plain,
! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f64,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f65,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f38]) ).
fof(f67,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f69,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f81,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f53]) ).
fof(f82,plain,
~ equal_set(union(difference(sK4,sK3),sK3),sK4),
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,[],[f57]) ).
cnf(c_58,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_59,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_60,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_62,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f69]) ).
cnf(c_64,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
cnf(c_76,negated_conjecture,
~ equal_set(union(difference(sK4,sK3),sK3),sK4),
inference(cnf_transformation,[],[f82]) ).
cnf(c_77,negated_conjecture,
subset(sK3,sK4),
inference(cnf_transformation,[],[f81]) ).
cnf(c_432,plain,
( union(difference(sK4,sK3),sK3) != X0
| X1 != sK4
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).
cnf(c_433,plain,
( ~ subset(union(difference(sK4,sK3),sK3),sK4)
| ~ subset(sK4,union(difference(sK4,sK3),sK3)) ),
inference(unflattening,[status(thm)],[c_432]) ).
cnf(c_1530,plain,
( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),sK4)
| subset(union(difference(sK4,sK3),sK3),sK4) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_1531,plain,
( member(sK0(union(difference(sK4,sK3),sK3),sK4),union(difference(sK4,sK3),sK3))
| subset(union(difference(sK4,sK3),sK3),sK4) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1925,plain,
( ~ member(X0,union(difference(X1,X2),X3))
| member(X0,difference(X1,X2))
| member(X0,X3) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_1984,plain,
( ~ member(sK0(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ),
inference(superposition,[status(thm)],[c_58,c_49]) ).
cnf(c_2017,plain,
( ~ member(sK0(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(superposition,[status(thm)],[c_59,c_49]) ).
cnf(c_2064,plain,
( member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK4)
| subset(sK4,union(difference(sK4,sK3),sK3)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_8485,plain,
( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),union(difference(sK4,sK3),sK3))
| member(sK0(union(difference(sK4,sK3),sK3),sK4),difference(sK4,sK3))
| member(sK0(union(difference(sK4,sK3),sK3),sK4),sK3) ),
inference(instantiation,[status(thm)],[c_1925]) ).
cnf(c_21023,plain,
( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK4)
| member(sK0(sK4,union(difference(sK4,sK3),sK3)),difference(sK4,X0))
| member(sK0(sK4,union(difference(sK4,sK3),sK3)),X0) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_21029,plain,
( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK4)
| member(sK0(sK4,union(difference(sK4,sK3),sK3)),difference(sK4,sK3))
| member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_21023]) ).
cnf(c_22965,plain,
( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),X0)
| ~ subset(X0,sK4)
| member(sK0(union(difference(sK4,sK3),sK3),sK4),sK4) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_22966,plain,
( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),sK3)
| ~ subset(sK3,sK4)
| member(sK0(union(difference(sK4,sK3),sK3),sK4),sK4) ),
inference(instantiation,[status(thm)],[c_22965]) ).
cnf(c_35788,plain,
( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),difference(sK4,sK3))
| member(sK0(union(difference(sK4,sK3),sK3),sK4),sK4) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_305486,plain,
( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK3)
| subset(sK4,union(difference(sK4,sK3),sK3)) ),
inference(instantiation,[status(thm)],[c_1984]) ).
cnf(c_305614,plain,
( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),difference(sK4,sK3))
| subset(sK4,union(difference(sK4,sK3),sK3)) ),
inference(instantiation,[status(thm)],[c_2017]) ).
cnf(c_307102,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_305614,c_305486,c_35788,c_22966,c_21029,c_8485,c_2064,c_1531,c_1530,c_433,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET595+4 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 20:46:06 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 61.71/9.27 % SZS status Started for theBenchmark.p
% 61.71/9.27 % SZS status Theorem for theBenchmark.p
% 61.71/9.27
% 61.71/9.27 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 61.71/9.27
% 61.71/9.27 ------ iProver source info
% 61.71/9.27
% 61.71/9.27 git: date: 2024-05-02 19:28:25 +0000
% 61.71/9.27 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 61.71/9.27 git: non_committed_changes: false
% 61.71/9.27
% 61.71/9.27 ------ Parsing...
% 61.71/9.27 ------ Clausification by vclausify_rel & Parsing by iProver...
% 61.71/9.27
% 61.71/9.27 ------ 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
% 61.71/9.27
% 61.71/9.27 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 61.71/9.27
% 61.71/9.27 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 61.71/9.27 ------ Proving...
% 61.71/9.27 ------ Problem Properties
% 61.71/9.27
% 61.71/9.27
% 61.71/9.27 clauses 28
% 61.71/9.27 conjectures 1
% 61.71/9.27 EPR 3
% 61.71/9.27 Horn 23
% 61.71/9.27 unary 5
% 61.71/9.27 binary 16
% 61.71/9.27 lits 58
% 61.71/9.27 lits eq 3
% 61.71/9.27 fd_pure 0
% 61.71/9.27 fd_pseudo 0
% 61.71/9.27 fd_cond 0
% 61.71/9.27 fd_pseudo_cond 2
% 61.71/9.27 AC symbols 0
% 61.71/9.27
% 61.71/9.27 ------ Schedule dynamic 5 is on
% 61.71/9.27
% 61.71/9.27 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 61.71/9.27
% 61.71/9.27
% 61.71/9.27 ------
% 61.71/9.27 Current options:
% 61.71/9.27 ------
% 61.71/9.27
% 61.71/9.27
% 61.71/9.27
% 61.71/9.27
% 61.71/9.27 ------ Proving...
% 61.71/9.27
% 61.71/9.27
% 61.71/9.27 % SZS status Theorem for theBenchmark.p
% 61.71/9.27
% 61.71/9.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 61.71/9.27
% 61.71/9.28
%------------------------------------------------------------------------------