TSTP Solution File: SET355+4 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET355+4 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 : Mon Jun 24 14:34:26 EDT 2024
% Result : Theorem 3.92s 1.14s
% Output : CNFRefutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 7 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 99 ( 37 ~; 29 |; 22 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 45 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f10,axiom,
! [X2,X0] :
( member(X2,sum(X0))
<=> ? [X4] :
( member(X2,X4)
& member(X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
fof(f12,conjecture,
! [X0,X2] :
( member(X2,X0)
=> subset(X2,sum(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI43) ).
fof(f13,negated_conjecture,
~ ! [X0,X2] :
( member(X2,X0)
=> subset(X2,sum(X0)) ),
inference(negated_conjecture,[],[f12]) ).
fof(f21,plain,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f23,plain,
~ ! [X0,X1] :
( member(X1,X0)
=> subset(X1,sum(X0)) ),
inference(rectify,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
? [X0,X1] :
( ~ subset(X1,sum(X0))
& member(X1,X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f27,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,[],[f24]) ).
fof(f28,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,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f30,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])],[f28,f29]) ).
fof(f41,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X0,X2)
& member(X2,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f42,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
=> ( member(X0,sK1(X0,X1))
& member(sK1(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ( member(X0,sK1(X0,X1))
& member(sK1(X0,X1),X1) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f42,f43]) ).
fof(f49,plain,
( ? [X0,X1] :
( ~ subset(X1,sum(X0))
& member(X1,X0) )
=> ( ~ subset(sK4,sum(sK3))
& member(sK4,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
( ~ subset(sK4,sum(sK3))
& member(sK4,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f26,f49]) ).
fof(f52,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f73,plain,
! [X2,X0,X1] :
( member(X0,sum(X1))
| ~ member(X0,X2)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f77,plain,
member(sK4,sK3),
inference(cnf_transformation,[],[f50]) ).
fof(f78,plain,
~ subset(sK4,sum(sK3)),
inference(cnf_transformation,[],[f50]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_69,plain,
( ~ member(X0,X1)
| ~ member(X1,X2)
| member(X0,sum(X2)) ),
inference(cnf_transformation,[],[f73]) ).
cnf(c_75,negated_conjecture,
~ subset(sK4,sum(sK3)),
inference(cnf_transformation,[],[f78]) ).
cnf(c_76,negated_conjecture,
member(sK4,sK3),
inference(cnf_transformation,[],[f77]) ).
cnf(c_399,negated_conjecture,
member(sK4,sK3),
inference(demodulation,[status(thm)],[c_76]) ).
cnf(c_3472,plain,
( ~ member(X0,sK4)
| member(X0,sum(sK3)) ),
inference(resolution,[status(thm)],[c_69,c_399]) ).
cnf(c_4005,plain,
( ~ member(sK0(X0,sum(sK3)),sK4)
| subset(X0,sum(sK3)) ),
inference(resolution,[status(thm)],[c_3472,c_49]) ).
cnf(c_4085,plain,
subset(sK4,sum(sK3)),
inference(resolution,[status(thm)],[c_4005,c_50]) ).
cnf(c_4086,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4085,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET355+4 : TPTP v8.2.0. Released v2.2.0.
% 0.07/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jun 23 12:59:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.92/1.14 % SZS status Started for theBenchmark.p
% 3.92/1.14 % SZS status Theorem for theBenchmark.p
% 3.92/1.14
% 3.92/1.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.92/1.14
% 3.92/1.14 ------ iProver source info
% 3.92/1.14
% 3.92/1.14 git: date: 2024-06-12 09:56:46 +0000
% 3.92/1.14 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 3.92/1.14 git: non_committed_changes: false
% 3.92/1.14
% 3.92/1.14 ------ Parsing...
% 3.92/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.92/1.14
% 3.92/1.14 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.92/1.14
% 3.92/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.92/1.14
% 3.92/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.92/1.14 ------ Proving...
% 3.92/1.14 ------ Problem Properties
% 3.92/1.14
% 3.92/1.14
% 3.92/1.14 clauses 29
% 3.92/1.14 conjectures 2
% 3.92/1.14 EPR 4
% 3.92/1.14 Horn 24
% 3.92/1.14 unary 7
% 3.92/1.14 binary 15
% 3.92/1.14 lits 58
% 3.92/1.14 lits eq 4
% 3.92/1.14 fd_pure 0
% 3.92/1.14 fd_pseudo 0
% 3.92/1.14 fd_cond 0
% 3.92/1.14 fd_pseudo_cond 2
% 3.92/1.14 AC symbols 0
% 3.92/1.14
% 3.92/1.14 ------ Input Options Time Limit: Unbounded
% 3.92/1.14
% 3.92/1.14
% 3.92/1.14 ------
% 3.92/1.14 Current options:
% 3.92/1.14 ------
% 3.92/1.14
% 3.92/1.14
% 3.92/1.14
% 3.92/1.14
% 3.92/1.14 ------ Proving...
% 3.92/1.14
% 3.92/1.14
% 3.92/1.14 % SZS status Theorem for theBenchmark.p
% 3.92/1.14
% 3.92/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.92/1.14
% 3.92/1.14
%------------------------------------------------------------------------------