TSTP Solution File: SET015+4 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET015+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n029.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 15:05:30 EDT 2023
% Result : Theorem 4.01s 1.18s
% Output : CNFRefutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 7 unt; 0 def)
% Number of atoms : 123 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 132 ( 55 ~; 54 |; 14 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 2 sgn; 56 !; 7 ?)
% 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(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f5,axiom,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f12,conjecture,
! [X0,X1] : equal_set(union(X0,X1),union(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI07) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : equal_set(union(X0,X1),union(X1,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] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f28,plain,
? [X0,X1] : ~ equal_set(union(X0,X1),union(X1,X0)),
inference(ennf_transformation,[],[f13]) ).
fof(f29,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(f30,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,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f32,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])],[f30,f31]) ).
fof(f36,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(f37,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,[],[f36]) ).
fof(f51,plain,
( ? [X0,X1] : ~ equal_set(union(X0,X1),union(X1,X0))
=> ~ equal_set(union(sK3,sK4),union(sK4,sK3)) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
~ equal_set(union(sK3,sK4),union(sK4,sK3)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f28,f51]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f62,plain,
! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f63,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f64,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f80,plain,
~ equal_set(union(sK3,sK4),union(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_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_58,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_59,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_60,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_76,negated_conjecture,
~ equal_set(union(sK3,sK4),union(sK4,sK3)),
inference(cnf_transformation,[],[f80]) ).
cnf(c_426,plain,
( union(sK3,sK4) != X0
| union(sK4,sK3) != X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).
cnf(c_427,plain,
( ~ subset(union(sK3,sK4),union(sK4,sK3))
| ~ subset(union(sK4,sK3),union(sK3,sK4)) ),
inference(unflattening,[status(thm)],[c_426]) ).
cnf(c_1442,plain,
( ~ member(sK0(union(sK3,sK4),union(sK4,sK3)),union(sK4,sK3))
| subset(union(sK3,sK4),union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_1498,plain,
( member(sK0(union(sK3,sK4),union(sK4,sK3)),union(sK3,sK4))
| subset(union(sK3,sK4),union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2074,plain,
( member(sK0(union(sK4,sK3),union(sK3,sK4)),union(sK4,sK3))
| subset(union(sK4,sK3),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2075,plain,
( ~ member(sK0(union(sK4,sK3),union(sK3,sK4)),union(sK3,sK4))
| subset(union(sK4,sK3),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_3943,plain,
( ~ member(sK0(union(sK4,sK3),union(sK3,sK4)),union(sK4,sK3))
| member(sK0(union(sK4,sK3),union(sK3,sK4)),sK3)
| member(sK0(union(sK4,sK3),union(sK3,sK4)),sK4) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_4338,plain,
( ~ member(sK0(union(sK3,sK4),union(sK4,sK3)),sK3)
| member(sK0(union(sK3,sK4),union(sK4,sK3)),union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_4353,plain,
( ~ member(sK0(union(sK4,sK3),union(sK3,sK4)),sK4)
| member(sK0(union(sK4,sK3),union(sK3,sK4)),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_4435,plain,
( ~ member(sK0(union(sK3,sK4),union(sK4,sK3)),sK4)
| member(sK0(union(sK3,sK4),union(sK4,sK3)),union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_4443,plain,
( ~ member(sK0(union(sK4,sK3),union(sK3,sK4)),sK3)
| member(sK0(union(sK4,sK3),union(sK3,sK4)),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_8864,plain,
( ~ member(sK0(union(sK3,sK4),union(sK4,sK3)),union(sK3,sK4))
| member(sK0(union(sK3,sK4),union(sK4,sK3)),sK3)
| member(sK0(union(sK3,sK4),union(sK4,sK3)),sK4) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_11572,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8864,c_4443,c_4435,c_4353,c_4338,c_3943,c_2074,c_2075,c_1498,c_1442,c_427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET015+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n029.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 11:33:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.01/1.18 % SZS status Started for theBenchmark.p
% 4.01/1.18 % SZS status Theorem for theBenchmark.p
% 4.01/1.18
% 4.01/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 4.01/1.18
% 4.01/1.18 ------ iProver source info
% 4.01/1.18
% 4.01/1.18 git: date: 2023-05-31 18:12:56 +0000
% 4.01/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 4.01/1.18 git: non_committed_changes: false
% 4.01/1.18 git: last_make_outside_of_git: false
% 4.01/1.18
% 4.01/1.18 ------ Parsing...
% 4.01/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.01/1.18
% 4.01/1.18 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 4.01/1.18
% 4.01/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.01/1.18
% 4.01/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.01/1.18 ------ Proving...
% 4.01/1.18 ------ Problem Properties
% 4.01/1.18
% 4.01/1.18
% 4.01/1.18 clauses 27
% 4.01/1.18 conjectures 0
% 4.01/1.18 EPR 2
% 4.01/1.18 Horn 22
% 4.01/1.18 unary 4
% 4.01/1.18 binary 16
% 4.01/1.18 lits 57
% 4.01/1.18 lits eq 3
% 4.01/1.18 fd_pure 0
% 4.01/1.18 fd_pseudo 0
% 4.01/1.18 fd_cond 0
% 4.01/1.18 fd_pseudo_cond 2
% 4.01/1.18 AC symbols 0
% 4.01/1.18
% 4.01/1.18 ------ Schedule dynamic 5 is on
% 4.01/1.18
% 4.01/1.18 ------ no conjectures: strip conj schedule
% 4.01/1.18
% 4.01/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.01/1.18
% 4.01/1.18
% 4.01/1.18 ------
% 4.01/1.18 Current options:
% 4.01/1.18 ------
% 4.01/1.18
% 4.01/1.18
% 4.01/1.18
% 4.01/1.18
% 4.01/1.18 ------ Proving...
% 4.01/1.18
% 4.01/1.18
% 4.01/1.18 % SZS status Theorem for theBenchmark.p
% 4.01/1.18
% 4.01/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.01/1.18
% 4.01/1.18
%------------------------------------------------------------------------------