TSTP Solution File: SET185+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET185+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 15:07:02 EDT 2023
% Result : Theorem 0.52s 1.20s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 9 unt; 0 def)
% Number of atoms : 170 ( 25 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 190 ( 73 ~; 79 |; 27 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 97 ( 2 sgn; 65 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f4,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f7,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> union(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_union) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> union(X0,X1) = X1 ),
inference(negated_conjecture,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f10,plain,
? [X0,X1] :
( union(X0,X1) != X1
& subset(X0,X1) ),
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(f13,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,[],[f9]) ).
fof(f14,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,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f16,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])],[f14,f15]) ).
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] :
( union(X0,X1) != X1
& subset(X0,X1) )
=> ( sK3 != union(sK2,sK3)
& subset(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
( sK3 != union(sK2,sK3)
& subset(sK2,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[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(f28,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f4]) ).
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,
subset(sK2,sK3),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
sK3 != union(sK2,sK3),
inference(cnf_transformation,[],[f24]) ).
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_52,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_53,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_54,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_58,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f34]) ).
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(sK2,sK3) != sK3,
inference(cnf_transformation,[],[f41]) ).
cnf(c_63,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f40]) ).
cnf(c_125,plain,
union(sK3,sK2) != sK3,
inference(demodulation,[status(thm)],[c_62,c_58]) ).
cnf(c_623,plain,
( ~ member(sK1(union(sK3,sK2),sK3),union(sK3,sK2))
| ~ member(sK1(union(sK3,sK2),sK3),sK3)
| union(sK3,sK2) = sK3 ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_624,plain,
( union(sK3,sK2) = sK3
| member(sK1(union(sK3,sK2),sK3),union(sK3,sK2))
| member(sK1(union(sK3,sK2),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_642,plain,
( member(sK0(union(sK3,sK2),sK3),union(sK3,sK2))
| subset(union(sK3,sK2),sK3) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_643,plain,
( ~ member(sK0(union(sK3,sK2),sK3),sK3)
| subset(union(sK3,sK2),sK3) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_670,plain,
( ~ member(sK1(union(sK3,sK2),sK3),union(sK3,sK2))
| ~ subset(union(sK3,sK2),X0)
| member(sK1(union(sK3,sK2),sK3),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_675,plain,
( ~ member(sK1(union(sK3,sK2),sK3),union(sK3,sK2))
| ~ subset(union(sK3,sK2),sK3)
| member(sK1(union(sK3,sK2),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_670]) ).
cnf(c_947,plain,
( ~ member(sK1(union(sK3,sK2),sK3),sK3)
| member(sK1(union(sK3,sK2),sK3),union(sK3,X0)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1466,plain,
( ~ member(sK0(union(sK3,sK2),sK3),union(sK3,sK2))
| member(sK0(union(sK3,sK2),sK3),sK3)
| member(sK0(union(sK3,sK2),sK3),sK2) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_2616,plain,
( ~ member(sK0(union(sK3,sK2),sK3),sK2)
| ~ subset(sK2,X0)
| member(sK0(union(sK3,sK2),sK3),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_2621,plain,
( ~ member(sK0(union(sK3,sK2),sK3),sK2)
| ~ subset(sK2,sK3)
| member(sK0(union(sK3,sK2),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_2616]) ).
cnf(c_2940,plain,
( ~ member(sK1(union(sK3,sK2),sK3),sK3)
| member(sK1(union(sK3,sK2),sK3),union(sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_947]) ).
cnf(c_5385,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2940,c_2621,c_1466,c_675,c_642,c_643,c_624,c_623,c_125,c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET185+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n020.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 11:54:14 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.52/1.20 % SZS status Started for theBenchmark.p
% 0.52/1.20 % SZS status Theorem for theBenchmark.p
% 0.52/1.20
% 0.52/1.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.52/1.20
% 0.52/1.20 ------ iProver source info
% 0.52/1.20
% 0.52/1.20 git: date: 2023-05-31 18:12:56 +0000
% 0.52/1.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.52/1.20 git: non_committed_changes: false
% 0.52/1.20 git: last_make_outside_of_git: false
% 0.52/1.20
% 0.52/1.20 ------ Parsing...
% 0.52/1.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.52/1.20
% 0.52/1.20 ------ 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
% 0.52/1.20
% 0.52/1.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.52/1.20
% 0.52/1.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.52/1.20 ------ Proving...
% 0.52/1.20 ------ Problem Properties
% 0.52/1.20
% 0.52/1.20
% 0.52/1.20 clauses 13
% 0.52/1.20 conjectures 1
% 0.52/1.20 EPR 4
% 0.52/1.20 Horn 10
% 0.52/1.20 unary 4
% 0.52/1.20 binary 4
% 0.52/1.20 lits 27
% 0.52/1.20 lits eq 5
% 0.52/1.20 fd_pure 0
% 0.52/1.20 fd_pseudo 0
% 0.52/1.20 fd_cond 0
% 0.52/1.20 fd_pseudo_cond 3
% 0.52/1.20 AC symbols 0
% 0.52/1.20
% 0.52/1.20 ------ Schedule dynamic 5 is on
% 0.52/1.20
% 0.52/1.20 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.52/1.20
% 0.52/1.20
% 0.52/1.20 ------
% 0.52/1.20 Current options:
% 0.52/1.20 ------
% 0.52/1.20
% 0.52/1.20
% 0.52/1.20
% 0.52/1.20
% 0.52/1.20 ------ Proving...
% 0.52/1.20
% 0.52/1.20
% 0.52/1.20 % SZS status Theorem for theBenchmark.p
% 0.52/1.20
% 0.52/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.52/1.20
% 0.52/1.20
%------------------------------------------------------------------------------