TSTP Solution File: SET014+4 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET014+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.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 : Fri May 3 02:59:17 EDT 2024
% Result : Theorem 38.89s 6.24s
% Output : CNFRefutation 38.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 62 ( 3 unt; 0 def)
% Number of atoms : 192 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 213 ( 83 ~; 93 |; 26 &)
% ( 7 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 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 : 115 ( 6 sgn 54 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f5,axiom,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f12,conjecture,
! [X0,X2,X4] :
( ( subset(X4,X0)
& subset(X2,X0) )
<=> subset(union(X2,X4),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI45) ).
fof(f13,negated_conjecture,
~ ! [X0,X2,X4] :
( ( subset(X4,X0)
& subset(X2,X0) )
<=> subset(union(X2,X4),X0) ),
inference(negated_conjecture,[],[f12]) ).
fof(f16,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f23,plain,
~ ! [X0,X1,X2] :
( ( subset(X2,X0)
& subset(X1,X0) )
<=> subset(union(X1,X2),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,X2] :
( ( subset(X2,X0)
& subset(X1,X0) )
<~> subset(union(X1,X2),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(f34,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f34]) ).
fof(f49,plain,
? [X0,X1,X2] :
( ( ~ subset(union(X1,X2),X0)
| ~ subset(X2,X0)
| ~ subset(X1,X0) )
& ( subset(union(X1,X2),X0)
| ( subset(X2,X0)
& subset(X1,X0) ) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f50,plain,
? [X0,X1,X2] :
( ( ~ subset(union(X1,X2),X0)
| ~ subset(X2,X0)
| ~ subset(X1,X0) )
& ( subset(union(X1,X2),X0)
| ( subset(X2,X0)
& subset(X1,X0) ) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
( ? [X0,X1,X2] :
( ( ~ subset(union(X1,X2),X0)
| ~ subset(X2,X0)
| ~ subset(X1,X0) )
& ( subset(union(X1,X2),X0)
| ( subset(X2,X0)
& subset(X1,X0) ) ) )
=> ( ( ~ subset(union(sK4,sK5),sK3)
| ~ subset(sK5,sK3)
| ~ subset(sK4,sK3) )
& ( subset(union(sK4,sK5),sK3)
| ( subset(sK5,sK3)
& subset(sK4,sK3) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
( ( ~ subset(union(sK4,sK5),sK3)
| ~ subset(sK5,sK3)
| ~ subset(sK4,sK3) )
& ( subset(union(sK4,sK5),sK3)
| ( subset(sK5,sK3)
& subset(sK4,sK3) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f50,f51]) ).
fof(f53,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f61,plain,
! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f62,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f63,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f79,plain,
( subset(union(sK4,sK5),sK3)
| subset(sK4,sK3) ),
inference(cnf_transformation,[],[f52]) ).
fof(f80,plain,
( subset(union(sK4,sK5),sK3)
| subset(sK5,sK3) ),
inference(cnf_transformation,[],[f52]) ).
fof(f81,plain,
( ~ subset(union(sK4,sK5),sK3)
| ~ subset(sK5,sK3)
| ~ subset(sK4,sK3) ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_57,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_58,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_59,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_75,negated_conjecture,
( ~ subset(union(sK4,sK5),sK3)
| ~ subset(sK4,sK3)
| ~ subset(sK5,sK3) ),
inference(cnf_transformation,[],[f81]) ).
cnf(c_76,negated_conjecture,
( subset(union(sK4,sK5),sK3)
| subset(sK5,sK3) ),
inference(cnf_transformation,[],[f80]) ).
cnf(c_77,negated_conjecture,
( subset(union(sK4,sK5),sK3)
| subset(sK4,sK3) ),
inference(cnf_transformation,[],[f79]) ).
cnf(c_233,plain,
( ~ member(sK0(union(sK4,sK5),sK3),sK3)
| subset(union(sK4,sK5),sK3) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_234,plain,
( member(sK0(union(sK4,sK5),sK3),union(sK4,sK5))
| subset(union(sK4,sK5),sK3) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_718,plain,
( ~ subset(union(X0,X1),X2)
| ~ member(X3,X1)
| member(X3,X2) ),
inference(resolution,[status(thm)],[c_51,c_57]) ).
cnf(c_719,plain,
( ~ subset(union(X0,X1),X2)
| ~ member(X3,X0)
| member(X3,X2) ),
inference(resolution,[status(thm)],[c_51,c_58]) ).
cnf(c_1773,plain,
( ~ subset(union(X0,X1),X2)
| ~ member(X3,X1)
| member(X3,X2) ),
inference(superposition,[status(thm)],[c_57,c_51]) ).
cnf(c_1802,plain,
( ~ subset(union(X0,X1),X2)
| ~ member(X3,X0)
| member(X3,X2) ),
inference(superposition,[status(thm)],[c_58,c_51]) ).
cnf(c_1958,plain,
( ~ member(X0,sK5)
| member(X0,sK3)
| subset(sK5,sK3) ),
inference(superposition,[status(thm)],[c_76,c_1773]) ).
cnf(c_1963,plain,
( ~ member(X0,sK5)
| member(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1958,c_51]) ).
cnf(c_2115,plain,
( ~ member(X0,sK4)
| member(X0,sK3)
| subset(sK4,sK3) ),
inference(superposition,[status(thm)],[c_77,c_1802]) ).
cnf(c_2125,plain,
( ~ member(X0,sK4)
| member(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2115,c_51]) ).
cnf(c_5537,plain,
( ~ member(X0,sK5)
| member(X0,sK3)
| subset(sK5,sK3) ),
inference(resolution,[status(thm)],[c_718,c_76]) ).
cnf(c_5690,plain,
( ~ member(sK0(union(sK4,sK5),sK3),union(sK4,sK5))
| member(sK0(union(sK4,sK5),sK3),sK4)
| member(sK0(union(sK4,sK5),sK3),sK5) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_5722,plain,
( ~ member(X0,sK4)
| member(X0,sK3)
| subset(sK5,sK3) ),
inference(resolution,[status(thm)],[c_719,c_76]) ).
cnf(c_6074,plain,
( member(X0,sK3)
| ~ member(X0,sK5) ),
inference(global_subsumption_just,[status(thm)],[c_5537,c_1963]) ).
cnf(c_6075,plain,
( ~ member(X0,sK5)
| member(X0,sK3) ),
inference(renaming,[status(thm)],[c_6074]) ).
cnf(c_6084,plain,
( ~ member(sK0(X0,sK3),sK5)
| subset(X0,sK3) ),
inference(resolution,[status(thm)],[c_6075,c_49]) ).
cnf(c_6116,plain,
( member(X0,sK3)
| ~ member(X0,sK4) ),
inference(global_subsumption_just,[status(thm)],[c_5722,c_2125]) ).
cnf(c_6117,plain,
( ~ member(X0,sK4)
| member(X0,sK3) ),
inference(renaming,[status(thm)],[c_6116]) ).
cnf(c_6126,plain,
( ~ member(sK0(X0,sK3),sK4)
| subset(X0,sK3) ),
inference(resolution,[status(thm)],[c_6117,c_49]) ).
cnf(c_6190,plain,
subset(sK5,sK3),
inference(resolution,[status(thm)],[c_6084,c_50]) ).
cnf(c_6316,plain,
subset(sK4,sK3),
inference(resolution,[status(thm)],[c_6126,c_50]) ).
cnf(c_7074,plain,
( ~ member(sK0(union(sK4,sK5),sK3),sK5)
| ~ subset(sK5,X0)
| member(sK0(union(sK4,sK5),sK3),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_7075,plain,
( ~ member(sK0(union(sK4,sK5),sK3),sK5)
| ~ subset(sK5,sK3)
| member(sK0(union(sK4,sK5),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_7074]) ).
cnf(c_8558,plain,
( ~ member(sK0(union(sK4,sK5),sK3),X0)
| ~ subset(X0,sK3)
| member(sK0(union(sK4,sK5),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_13098,plain,
( ~ member(sK0(union(sK4,sK5),sK3),sK4)
| ~ subset(sK4,sK3)
| member(sK0(union(sK4,sK5),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_8558]) ).
cnf(c_13099,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13098,c_7075,c_6316,c_6190,c_5690,c_233,c_234,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET014+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 2 20:46:50 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 38.89/6.24 % SZS status Started for theBenchmark.p
% 38.89/6.24 % SZS status Theorem for theBenchmark.p
% 38.89/6.24
% 38.89/6.24 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 38.89/6.24
% 38.89/6.24 ------ iProver source info
% 38.89/6.24
% 38.89/6.24 git: date: 2024-05-02 19:28:25 +0000
% 38.89/6.24 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 38.89/6.24 git: non_committed_changes: false
% 38.89/6.24
% 38.89/6.24 ------ Parsing...
% 38.89/6.24 ------ Clausification by vclausify_rel & Parsing by iProver...
% 38.89/6.24
% 38.89/6.24 ------ Preprocessing... sf_s rm: 1 0s sf_e
% 38.89/6.24
% 38.89/6.24 ------ Preprocessing...
% 38.89/6.24
% 38.89/6.24 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 38.89/6.24 ------ Proving...
% 38.89/6.24 ------ Problem Properties
% 38.89/6.24
% 38.89/6.24
% 38.89/6.24 clauses 29
% 38.89/6.24 conjectures 3
% 38.89/6.24 EPR 2
% 38.89/6.24 Horn 22
% 38.89/6.24 unary 4
% 38.89/6.24 binary 17
% 38.89/6.24 lits 62
% 38.89/6.24 lits eq 3
% 38.89/6.24 fd_pure 0
% 38.89/6.24 fd_pseudo 0
% 38.89/6.24 fd_cond 0
% 38.89/6.24 fd_pseudo_cond 2
% 38.89/6.24 AC symbols 0
% 38.89/6.24
% 38.89/6.24 ------ Input Options Time Limit: Unbounded
% 38.89/6.24
% 38.89/6.24
% 38.89/6.24 ------
% 38.89/6.24 Current options:
% 38.89/6.24 ------
% 38.89/6.24
% 38.89/6.24
% 38.89/6.24
% 38.89/6.24
% 38.89/6.24 ------ Proving...
% 38.89/6.24
% 38.89/6.24
% 38.89/6.24 % SZS status Theorem for theBenchmark.p
% 38.89/6.24
% 38.89/6.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 38.89/6.24
% 38.89/6.24
%------------------------------------------------------------------------------