TSTP Solution File: SET159+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET159+3 : 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 : Thu Aug 31 15:06:53 EDT 2023
% Result : Theorem 3.46s 1.14s
% Output : CNFRefutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 14 unt; 0 def)
% Number of atoms : 154 ( 26 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 166 ( 69 ~; 77 |; 15 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 7 sgn; 46 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f3,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_union) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(negated_conjecture,[],[f7]) ).
fof(f10,plain,
? [X0,X1,X2] : union(union(X0,X1),X2) != union(X0,union(X1,X2)),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f11]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f20,f21]) ).
fof(f23,plain,
( ? [X0,X1,X2] : union(union(X0,X1),X2) != union(X0,union(X1,X2))
=> union(union(sK2,sK3),sK4) != union(sK2,union(sK3,sK4)) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
union(union(sK2,sK3),sK4) != union(sK2,union(sK3,sK4)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f10,f23]) ).
fof(f25,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X0,X1] :
( X0 = X1
| member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
union(union(sK2,sK3),sK4) != union(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f24]) ).
cnf(c_49,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f27]) ).
cnf(c_50,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f26]) ).
cnf(c_51,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
cnf(c_55,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f31]) ).
cnf(c_60,plain,
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_61,plain,
( X0 = X1
| member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_62,negated_conjecture,
union(union(sK2,sK3),sK4) != union(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f40]) ).
cnf(c_122,plain,
union(sK2,union(sK3,sK4)) != union(sK4,union(sK2,sK3)),
inference(demodulation,[status(thm)],[c_62,c_55]) ).
cnf(c_342,plain,
( union(sK2,union(sK3,sK4)) = union(sK4,union(sK2,sK3))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4)))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_343,plain,
( union(sK2,union(sK3,sK4)) = union(sK4,union(sK2,sK3))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4)))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_344,plain,
( member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4)))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3))) ),
inference(global_subsumption_just,[status(thm)],[c_343,c_122,c_342]) ).
cnf(c_352,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4)))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK2) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_353,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4)))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3)))
| union(sK2,union(sK3,sK4)) = union(sK4,union(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_354,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3)))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4))) ),
inference(global_subsumption_just,[status(thm)],[c_353,c_122,c_353]) ).
cnf(c_355,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4)))
| ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3))) ),
inference(renaming,[status(thm)],[c_354]) ).
cnf(c_368,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3)))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK4) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_387,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X0)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X1,X0)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_388,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X0)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X0,X1)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_434,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK3)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK4) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_441,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X0,union(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_387]) ).
cnf(c_442,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_441]) ).
cnf(c_624,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_387]) ).
cnf(c_625,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK4)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_387]) ).
cnf(c_633,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK4)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK4,union(sK2,sK3))) ),
inference(instantiation,[status(thm)],[c_388]) ).
cnf(c_634,plain,
~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK4),
inference(global_subsumption_just,[status(thm)],[c_633,c_355,c_442,c_625,c_633]) ).
cnf(c_636,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK3)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_388]) ).
cnf(c_641,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK2)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,union(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_388]) ).
cnf(c_694,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X0)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X1,X0)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_695,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X0)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X0,X1)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_730,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(X0,X1))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X0)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),X1) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_799,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK3)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_694]) ).
cnf(c_800,plain,
~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK3),
inference(global_subsumption_just,[status(thm)],[c_799,c_122,c_353,c_442,c_624,c_636,c_799]) ).
cnf(c_803,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK2)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_695]) ).
cnf(c_804,plain,
member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3)),
inference(global_subsumption_just,[status(thm)],[c_803,c_344,c_352,c_368,c_434,c_634,c_800,c_803]) ).
cnf(c_985,plain,
( ~ member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),union(sK2,sK3))
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK2)
| member(sK1(union(sK2,union(sK3,sK4)),union(sK4,union(sK2,sK3))),sK3) ),
inference(instantiation,[status(thm)],[c_730]) ).
cnf(c_986,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_985,c_804,c_800,c_641,c_624,c_355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET159+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.16/0.35 % Computer : n028.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sat Aug 26 15:10:52 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.46/1.14 % SZS status Started for theBenchmark.p
% 3.46/1.14 % SZS status Theorem for theBenchmark.p
% 3.46/1.14
% 3.46/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.46/1.14
% 3.46/1.14 ------ iProver source info
% 3.46/1.14
% 3.46/1.14 git: date: 2023-05-31 18:12:56 +0000
% 3.46/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.46/1.14 git: non_committed_changes: false
% 3.46/1.14 git: last_make_outside_of_git: false
% 3.46/1.14
% 3.46/1.14 ------ Parsing...
% 3.46/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.46/1.14
% 3.46/1.14 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.46/1.14
% 3.46/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.46/1.14
% 3.46/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.46/1.14 ------ Proving...
% 3.46/1.14 ------ Problem Properties
% 3.46/1.14
% 3.46/1.14
% 3.46/1.14 clauses 12
% 3.46/1.14 conjectures 0
% 3.46/1.14 EPR 3
% 3.46/1.14 Horn 9
% 3.46/1.14 unary 3
% 3.46/1.14 binary 4
% 3.46/1.14 lits 26
% 3.46/1.14 lits eq 5
% 3.46/1.14 fd_pure 0
% 3.46/1.14 fd_pseudo 0
% 3.46/1.14 fd_cond 0
% 3.46/1.14 fd_pseudo_cond 3
% 3.46/1.14 AC symbols 0
% 3.46/1.14
% 3.46/1.14 ------ Input Options Time Limit: Unbounded
% 3.46/1.14
% 3.46/1.14
% 3.46/1.14 ------
% 3.46/1.14 Current options:
% 3.46/1.14 ------
% 3.46/1.14
% 3.46/1.14
% 3.46/1.14
% 3.46/1.14
% 3.46/1.14 ------ Proving...
% 3.46/1.14
% 3.46/1.14
% 3.46/1.14 % SZS status Theorem for theBenchmark.p
% 3.46/1.14
% 3.46/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.08/1.14
% 4.08/1.15
%------------------------------------------------------------------------------