TSTP Solution File: SET588+3 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET588+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.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 15:08:26 EDT 2023
% Result : Theorem 2.16s 1.17s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% 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 : 123 ( 53 ~; 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(X0,X2),difference(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_subset1) ).
fof(f5,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X0,X2),difference(X1,X2)) ),
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(X0,X2),difference(X1,X2))
& 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(X0,X2),difference(X1,X2))
& subset(X0,X1) )
=> ( ~ subset(difference(sK1,sK3),difference(sK2,sK3))
& subset(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ~ subset(difference(sK1,sK3),difference(sK2,sK3))
& 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(sK1,sK3),difference(sK2,sK3)),
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(sK1,sK3),difference(sK2,sK3)),
inference(cnf_transformation,[],[f24]) ).
cnf(c_57,negated_conjecture,
subset(sK1,sK2),
inference(cnf_transformation,[],[f23]) ).
cnf(c_124,plain,
member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(sK1,sK3)),
inference(resolution,[status(thm)],[c_53,c_56]) ).
cnf(c_128,plain,
~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(sK2,sK3)),
inference(resolution,[status(thm)],[c_52,c_56]) ).
cnf(c_150,plain,
( ~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(sK1,sK3))
| member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK1) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_152,plain,
( ~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK1)
| ~ subset(sK1,X0)
| member(sK0(difference(sK1,sK3),difference(sK2,sK3)),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_155,plain,
( ~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),X0)
| member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(X0,X1))
| member(sK0(difference(sK1,sK3),difference(sK2,sK3)),X1) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_157,plain,
( ~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(X0,X1))
| ~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),X1) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_199,plain,
( ~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(sK1,sK3))
| ~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_157]) ).
cnf(c_325,plain,
( ~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),X0)
| member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(X0,sK3))
| member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_155]) ).
cnf(c_878,plain,
( ~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK2)
| member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(sK2,sK3))
| member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_325]) ).
cnf(c_1602,plain,
( ~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK1)
| ~ subset(sK1,sK2)
| member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK2) ),
inference(instantiation,[status(thm)],[c_152]) ).
cnf(c_1606,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1602,c_878,c_199,c_150,c_128,c_124,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET588+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 09:29:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.16/1.17 % SZS status Started for theBenchmark.p
% 2.16/1.17 % SZS status Theorem for theBenchmark.p
% 2.16/1.17
% 2.16/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.16/1.17
% 2.16/1.17 ------ iProver source info
% 2.16/1.17
% 2.16/1.17 git: date: 2023-05-31 18:12:56 +0000
% 2.16/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.16/1.17 git: non_committed_changes: false
% 2.16/1.17 git: last_make_outside_of_git: false
% 2.16/1.17
% 2.16/1.17 ------ Parsing...
% 2.16/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.16/1.17
% 2.16/1.17 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e
% 2.16/1.17
% 2.16/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.16/1.17 ------ Proving...
% 2.16/1.17 ------ Problem Properties
% 2.16/1.17
% 2.16/1.17
% 2.16/1.17 clauses 9
% 2.16/1.17 conjectures 2
% 2.16/1.17 EPR 3
% 2.16/1.17 Horn 7
% 2.16/1.17 unary 3
% 2.16/1.17 binary 4
% 2.16/1.17 lits 17
% 2.16/1.17 lits eq 0
% 2.16/1.17 fd_pure 0
% 2.16/1.17 fd_pseudo 0
% 2.16/1.17 fd_cond 0
% 2.16/1.17 fd_pseudo_cond 0
% 2.16/1.17 AC symbols 0
% 2.16/1.17
% 2.16/1.17 ------ Schedule dynamic 5 is on
% 2.16/1.17
% 2.16/1.17 ------ no equalities: superposition off
% 2.16/1.17
% 2.16/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.16/1.17
% 2.16/1.17
% 2.16/1.17 ------
% 2.16/1.17 Current options:
% 2.16/1.17 ------
% 2.16/1.17
% 2.16/1.17
% 2.16/1.17
% 2.16/1.17
% 2.16/1.17 ------ Proving...
% 2.16/1.17
% 2.16/1.17
% 2.16/1.17 % SZS status Theorem for theBenchmark.p
% 2.16/1.17
% 2.16/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.16/1.17
% 2.16/1.17
%------------------------------------------------------------------------------