TSTP Solution File: SET009+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET009+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.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 15:05:22 EDT 2023
% Result : Theorem 0.75s 1.13s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 7 unt; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 124 ( 54 ~; 45 |; 17 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 3 sgn; 48 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_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(f4,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_difference) ).
fof(f5,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ),
inference(negated_conjecture,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f7,plain,
? [X0,X1,X2] :
( ~ subset(difference(X2,X1),difference(X2,X0))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f8,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f8]) ).
fof(f10,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,[],[f6]) ).
fof(f11,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,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f13,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])],[f11,f12]) ).
fof(f14,plain,
( ? [X0,X1,X2] :
( ~ subset(difference(X2,X1),difference(X2,X0))
& subset(X0,X1) )
=> ( ~ subset(difference(sK3,sK2),difference(sK3,sK1))
& subset(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ~ subset(difference(sK3,sK2),difference(sK3,sK1))
& subset(sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f7,f14]) ).
fof(f16,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
~ subset(difference(sK3,sK2),difference(sK3,sK1)),
inference(cnf_transformation,[],[f15]) ).
cnf(c_49,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
cnf(c_50,plain,
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f17]) ).
cnf(c_51,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
cnf(c_52,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
cnf(c_53,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
cnf(c_54,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf_transformation,[],[f19]) ).
cnf(c_56,negated_conjecture,
~ subset(difference(sK3,sK2),difference(sK3,sK1)),
inference(cnf_transformation,[],[f24]) ).
cnf(c_57,negated_conjecture,
subset(sK1,sK2),
inference(cnf_transformation,[],[f23]) ).
cnf(c_124,plain,
member(sK0(difference(sK3,sK2),difference(sK3,sK1)),difference(sK3,sK2)),
inference(resolution,[status(thm)],[c_53,c_56]) ).
cnf(c_128,plain,
~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),difference(sK3,sK1)),
inference(resolution,[status(thm)],[c_52,c_56]) ).
cnf(c_150,plain,
( ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),difference(sK3,sK2))
| member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK3) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_151,plain,
( ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK3)
| member(sK0(difference(sK3,sK2),difference(sK3,sK1)),difference(sK3,X0))
| member(sK0(difference(sK3,sK2),difference(sK3,sK1)),X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_154,plain,
( ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK3)
| member(sK0(difference(sK3,sK2),difference(sK3,sK1)),difference(sK3,sK1))
| member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK1) ),
inference(instantiation,[status(thm)],[c_151]) ).
cnf(c_158,plain,
( ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),X0)
| ~ subset(X0,X1)
| member(sK0(difference(sK3,sK2),difference(sK3,sK1)),X1) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_159,plain,
( ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),difference(X0,X1))
| ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),X1) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_202,plain,
( ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),difference(sK3,sK2))
| ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK2) ),
inference(instantiation,[status(thm)],[c_159]) ).
cnf(c_339,plain,
( ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),X0)
| ~ subset(X0,sK2)
| member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK2) ),
inference(instantiation,[status(thm)],[c_158]) ).
cnf(c_342,plain,
( ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK1)
| ~ subset(sK1,sK2)
| member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK2) ),
inference(instantiation,[status(thm)],[c_339]) ).
cnf(c_343,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_342,c_202,c_154,c_150,c_128,c_124,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET009+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.12 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 15:55:56 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.45 Running first-order theorem proving
% 0.19/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.75/1.13 % SZS status Started for theBenchmark.p
% 0.75/1.13 % SZS status Theorem for theBenchmark.p
% 0.75/1.13
% 0.75/1.13 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.75/1.13
% 0.75/1.13 ------ iProver source info
% 0.75/1.13
% 0.75/1.13 git: date: 2023-05-31 18:12:56 +0000
% 0.75/1.13 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.75/1.13 git: non_committed_changes: false
% 0.75/1.13 git: last_make_outside_of_git: false
% 0.75/1.13
% 0.75/1.13 ------ Parsing...
% 0.75/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.75/1.13
% 0.75/1.13 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e
% 0.75/1.13
% 0.75/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.75/1.13 ------ Proving...
% 0.75/1.13 ------ Problem Properties
% 0.75/1.13
% 0.75/1.13
% 0.75/1.13 clauses 9
% 0.75/1.13 conjectures 2
% 0.75/1.13 EPR 3
% 0.75/1.13 Horn 7
% 0.75/1.13 unary 3
% 0.75/1.13 binary 4
% 0.75/1.13 lits 17
% 0.75/1.13 lits eq 0
% 0.75/1.13 fd_pure 0
% 0.75/1.13 fd_pseudo 0
% 0.75/1.13 fd_cond 0
% 0.75/1.13 fd_pseudo_cond 0
% 0.75/1.13 AC symbols 0
% 0.75/1.13
% 0.75/1.13 ------ Schedule dynamic 5 is on
% 0.75/1.13
% 0.75/1.13 ------ no equalities: superposition off
% 0.75/1.13
% 0.75/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.75/1.13
% 0.75/1.13
% 0.75/1.13 ------
% 0.75/1.13 Current options:
% 0.75/1.13 ------
% 0.75/1.13
% 0.75/1.13
% 0.75/1.13
% 0.75/1.13
% 0.75/1.13 ------ Proving...
% 0.75/1.13
% 0.75/1.13
% 0.75/1.13 % SZS status Theorem for theBenchmark.p
% 0.75/1.13
% 0.75/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.75/1.13
% 0.75/1.13
%------------------------------------------------------------------------------