TSTP Solution File: SET014+3 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 15:05:27 EDT 2023
% Result : Theorem 2.52s 1.16s
% Output : CNFRefutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 9 unt; 0 def)
% Number of atoms : 114 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 124 ( 49 ~; 43 |; 24 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn; 42 !; 12 ?)
% 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(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(union(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_subset) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(union(X0,X2),X1) ),
inference(negated_conjecture,[],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
? [X0,X1,X2] :
( ~ subset(union(X0,X2),X1)
& subset(X2,X1)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
? [X0,X1,X2] :
( ~ subset(union(X0,X2),X1)
& subset(X2,X1)
& subset(X0,X1) ),
inference(flattening,[],[f9]) ).
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,[],[f8]) ).
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(f21,plain,
( ? [X0,X1,X2] :
( ~ subset(union(X0,X2),X1)
& subset(X2,X1)
& subset(X0,X1) )
=> ( ~ subset(union(sK2,sK4),sK3)
& subset(sK4,sK3)
& subset(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
( ~ subset(union(sK2,sK4),sK3)
& subset(sK4,sK3)
& subset(sK2,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f10,f21]) ).
fof(f23,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
subset(sK4,sK3),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
~ subset(union(sK2,sK4),sK3),
inference(cnf_transformation,[],[f22]) ).
cnf(c_51,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
cnf(c_52,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_53,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
cnf(c_54,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
cnf(c_59,negated_conjecture,
~ subset(union(sK2,sK4),sK3),
inference(cnf_transformation,[],[f37]) ).
cnf(c_60,negated_conjecture,
subset(sK4,sK3),
inference(cnf_transformation,[],[f36]) ).
cnf(c_61,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f35]) ).
cnf(c_204,plain,
( union(sK2,sK4) != X0
| X1 != sK3
| member(sK0(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_53,c_59]) ).
cnf(c_205,plain,
member(sK0(union(sK2,sK4),sK3),union(sK2,sK4)),
inference(unflattening,[status(thm)],[c_204]) ).
cnf(c_209,plain,
( union(sK2,sK4) != X0
| X1 != sK3
| ~ member(sK0(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_52,c_59]) ).
cnf(c_210,plain,
~ member(sK0(union(sK2,sK4),sK3),sK3),
inference(unflattening,[status(thm)],[c_209]) ).
cnf(c_602,plain,
( ~ member(sK0(union(sK2,sK4),sK3),union(sK2,sK4))
| member(sK0(union(sK2,sK4),sK3),sK2)
| member(sK0(union(sK2,sK4),sK3),sK4) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_778,plain,
( ~ member(sK0(union(sK2,sK4),sK3),sK2)
| ~ subset(sK2,X0)
| member(sK0(union(sK2,sK4),sK3),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_783,plain,
( ~ member(sK0(union(sK2,sK4),sK3),sK2)
| ~ subset(sK2,sK3)
| member(sK0(union(sK2,sK4),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_778]) ).
cnf(c_1469,plain,
( ~ member(sK0(union(sK2,sK4),sK3),sK4)
| ~ subset(sK4,X0)
| member(sK0(union(sK2,sK4),sK3),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_1474,plain,
( ~ member(sK0(union(sK2,sK4),sK3),sK4)
| ~ subset(sK4,sK3)
| member(sK0(union(sK2,sK4),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_1469]) ).
cnf(c_1475,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1474,c_783,c_602,c_210,c_205,c_60,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 12:36:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.52/1.16 % SZS status Started for theBenchmark.p
% 2.52/1.16 % SZS status Theorem for theBenchmark.p
% 2.52/1.16
% 2.52/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.52/1.16
% 2.52/1.16 ------ iProver source info
% 2.52/1.16
% 2.52/1.16 git: date: 2023-05-31 18:12:56 +0000
% 2.52/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.52/1.16 git: non_committed_changes: false
% 2.52/1.16 git: last_make_outside_of_git: false
% 2.52/1.16
% 2.52/1.16 ------ Parsing...
% 2.52/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.52/1.16
% 2.52/1.16 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 2.52/1.16
% 2.52/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.52/1.16
% 2.52/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.52/1.16 ------ Proving...
% 2.52/1.16 ------ Problem Properties
% 2.52/1.16
% 2.52/1.16
% 2.52/1.16 clauses 13
% 2.52/1.16 conjectures 3
% 2.52/1.16 EPR 4
% 2.52/1.16 Horn 10
% 2.52/1.16 unary 5
% 2.52/1.16 binary 4
% 2.52/1.16 lits 25
% 2.52/1.16 lits eq 3
% 2.52/1.16 fd_pure 0
% 2.52/1.16 fd_pseudo 0
% 2.52/1.16 fd_cond 0
% 2.52/1.16 fd_pseudo_cond 2
% 2.52/1.16 AC symbols 0
% 2.52/1.16
% 2.52/1.16 ------ Schedule dynamic 5 is on
% 2.52/1.16
% 2.52/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.52/1.16
% 2.52/1.16
% 2.52/1.16 ------
% 2.52/1.16 Current options:
% 2.52/1.16 ------
% 2.52/1.16
% 2.52/1.16
% 2.52/1.16
% 2.52/1.16
% 2.52/1.16 ------ Proving...
% 2.52/1.16
% 2.52/1.16
% 2.52/1.16 % SZS status Theorem for theBenchmark.p
% 2.52/1.16
% 2.52/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.52/1.16
% 2.52/1.16
%------------------------------------------------------------------------------