TSTP Solution File: SET012+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET012+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.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 15:05:25 EDT 2023
% Result : Theorem 56.79s 8.72s
% Output : CNFRefutation 56.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 6 unt; 0 def)
% Number of atoms : 160 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 177 ( 77 ~; 68 |; 20 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 110 ( 4 sgn; 61 !; 7 ?)
% 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(f7,axiom,
! [X1,X0,X3] :
( member(X1,difference(X3,X0))
<=> ( ~ member(X1,X0)
& member(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
fof(f12,conjecture,
! [X0,X3] :
( subset(X0,X3)
=> equal_set(difference(X3,difference(X3,X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI23) ).
fof(f13,negated_conjecture,
~ ! [X0,X3] :
( subset(X0,X3)
=> equal_set(difference(X3,difference(X3,X0)),X0) ),
inference(negated_conjecture,[],[f12]) ).
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(difference(X1,difference(X1,X0)),X0) ),
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(difference(X1,difference(X1,X0)),X0)
& 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(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(difference(X1,difference(X1,X0)),X0)
& subset(X0,X1) )
=> ( ~ equal_set(difference(sK4,difference(sK4,sK3)),sK3)
& subset(sK3,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
( ~ equal_set(difference(sK4,difference(sK4,sK3)),sK3)
& 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(f67,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ 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(difference(sK4,difference(sK4,sK3)),sK3),
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_62,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f69]) ).
cnf(c_63,plain,
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
cnf(c_64,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
cnf(c_76,negated_conjecture,
~ equal_set(difference(sK4,difference(sK4,sK3)),sK3),
inference(cnf_transformation,[],[f82]) ).
cnf(c_77,negated_conjecture,
subset(sK3,sK4),
inference(cnf_transformation,[],[f81]) ).
cnf(c_431,plain,
( difference(sK4,difference(sK4,sK3)) != X0
| X1 != sK3
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).
cnf(c_432,plain,
( ~ subset(difference(sK4,difference(sK4,sK3)),sK3)
| ~ subset(sK3,difference(sK4,difference(sK4,sK3))) ),
inference(unflattening,[status(thm)],[c_431]) ).
cnf(c_497,plain,
( ~ subset(difference(sK4,difference(sK4,sK3)),sK3)
| ~ subset(sK3,difference(sK4,difference(sK4,sK3))) ),
inference(prop_impl_just,[status(thm)],[c_432]) ).
cnf(c_1296,plain,
( ~ member(sK0(sK3,difference(sK4,difference(sK4,sK3))),difference(sK4,difference(sK4,sK3)))
| subset(sK3,difference(sK4,difference(sK4,sK3))) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_1298,plain,
( member(sK0(difference(X0,X1),X2),difference(X0,X1))
| subset(difference(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1303,plain,
( ~ member(sK0(X0,X1),X0)
| ~ subset(X0,X2)
| member(sK0(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_1434,plain,
( ~ member(sK0(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50,c_63]) ).
cnf(c_1475,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,difference(X2,X3)))
| member(X0,difference(X2,X3)) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_1922,plain,
( ~ member(sK0(X0,X1),difference(X2,X3))
| member(sK0(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_1923,plain,
( ~ member(sK0(X0,X1),difference(X2,X3))
| ~ member(sK0(X0,X1),X3) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_2276,plain,
( ~ member(sK0(difference(sK4,difference(sK4,sK3)),sK3),sK3)
| subset(difference(sK4,difference(sK4,sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_2280,plain,
( member(sK0(difference(sK4,difference(sK4,sK3)),sK3),difference(sK4,difference(sK4,sK3)))
| subset(difference(sK4,difference(sK4,sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_1298]) ).
cnf(c_2789,plain,
( ~ member(sK0(sK3,difference(sK4,difference(sK4,sK3))),sK4)
| member(sK0(sK3,difference(sK4,difference(sK4,sK3))),difference(sK4,difference(sK4,sK3)))
| member(sK0(sK3,difference(sK4,difference(sK4,sK3))),difference(sK4,sK3)) ),
inference(instantiation,[status(thm)],[c_1475]) ).
cnf(c_6397,plain,
( ~ member(sK0(sK3,difference(sK4,difference(sK4,sK3))),sK3)
| ~ subset(sK3,sK4)
| member(sK0(sK3,difference(sK4,difference(sK4,sK3))),sK4) ),
inference(instantiation,[status(thm)],[c_1303]) ).
cnf(c_6412,plain,
( member(sK0(sK3,difference(sK4,difference(sK4,sK3))),sK3)
| subset(sK3,difference(sK4,difference(sK4,sK3))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_11383,plain,
( ~ member(sK0(difference(sK4,difference(sK4,sK3)),sK3),difference(sK4,difference(sK4,sK3)))
| member(sK0(difference(sK4,difference(sK4,sK3)),sK3),sK4) ),
inference(instantiation,[status(thm)],[c_1922]) ).
cnf(c_15169,plain,
( ~ member(sK0(sK3,difference(sK4,difference(sK4,sK3))),difference(sK4,sK3))
| ~ member(sK0(sK3,difference(sK4,difference(sK4,sK3))),sK3) ),
inference(instantiation,[status(thm)],[c_1923]) ).
cnf(c_24581,plain,
~ subset(difference(sK4,difference(sK4,sK3)),sK3),
inference(global_subsumption_just,[status(thm)],[c_497,c_77,c_432,c_1296,c_2789,c_6397,c_6412,c_15169]) ).
cnf(c_120357,plain,
( ~ member(sK0(difference(sK4,difference(sK4,sK3)),sK3),difference(sK4,sK3))
| subset(difference(sK4,difference(sK4,sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_1434]) ).
cnf(c_122671,plain,
( ~ member(sK0(difference(sK4,difference(sK4,sK3)),sK3),X0)
| member(sK0(difference(sK4,difference(sK4,sK3)),sK3),difference(X0,sK3))
| member(sK0(difference(sK4,difference(sK4,sK3)),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_151214,plain,
( ~ member(sK0(difference(sK4,difference(sK4,sK3)),sK3),sK4)
| member(sK0(difference(sK4,difference(sK4,sK3)),sK3),difference(sK4,sK3))
| member(sK0(difference(sK4,difference(sK4,sK3)),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_122671]) ).
cnf(c_151215,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_151214,c_120357,c_24581,c_11383,c_2280,c_2276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET012+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n003.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 08:54:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 56.79/8.72 % SZS status Started for theBenchmark.p
% 56.79/8.72 % SZS status Theorem for theBenchmark.p
% 56.79/8.72
% 56.79/8.72 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 56.79/8.72
% 56.79/8.72 ------ iProver source info
% 56.79/8.72
% 56.79/8.72 git: date: 2023-05-31 18:12:56 +0000
% 56.79/8.72 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 56.79/8.72 git: non_committed_changes: false
% 56.79/8.72 git: last_make_outside_of_git: false
% 56.79/8.72
% 56.79/8.72 ------ Parsing...
% 56.79/8.72 ------ Clausification by vclausify_rel & Parsing by iProver...
% 56.79/8.72
% 56.79/8.72 ------ 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
% 56.79/8.72
% 56.79/8.72 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 56.79/8.72
% 56.79/8.72 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 56.79/8.72 ------ Proving...
% 56.79/8.72 ------ Problem Properties
% 56.79/8.72
% 56.79/8.72
% 56.79/8.72 clauses 28
% 56.79/8.72 conjectures 1
% 56.79/8.72 EPR 3
% 56.79/8.72 Horn 23
% 56.79/8.72 unary 5
% 56.79/8.72 binary 16
% 56.79/8.72 lits 58
% 56.79/8.72 lits eq 3
% 56.79/8.72 fd_pure 0
% 56.79/8.72 fd_pseudo 0
% 56.79/8.72 fd_cond 0
% 56.79/8.72 fd_pseudo_cond 2
% 56.79/8.72 AC symbols 0
% 56.79/8.72
% 56.79/8.72 ------ Input Options Time Limit: Unbounded
% 56.79/8.72
% 56.79/8.72
% 56.79/8.72 ------
% 56.79/8.72 Current options:
% 56.79/8.72 ------
% 56.79/8.72
% 56.79/8.72
% 56.79/8.72
% 56.79/8.72
% 56.79/8.72 ------ Proving...
% 56.79/8.72
% 56.79/8.72
% 56.79/8.72 % SZS status Theorem for theBenchmark.p
% 56.79/8.72
% 56.79/8.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 56.79/8.72
% 56.79/8.73
%------------------------------------------------------------------------------