TSTP Solution File: SET600+3 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET600+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.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 14:34:59 EDT 2024
% Result : Theorem 0.47s 1.16s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 14 unt; 0 def)
% Number of atoms : 193 ( 93 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 199 ( 74 ~; 85 |; 30 &)
% ( 6 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 11 sgn 55 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f4,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f9,conjecture,
! [X0,X1] :
( union(X0,X1) = empty_set
<=> ( empty_set = X1
& empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( union(X0,X1) = empty_set
<=> ( empty_set = X1
& empty_set = X0 ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f12,plain,
? [X0,X1] :
( union(X0,X1) = empty_set
<~> ( empty_set = X1
& empty_set = X0 ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f15]) ).
fof(f17,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,[],[f11]) ).
fof(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f20,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])],[f18,f19]) ).
fof(f25,plain,
? [X0,X1] :
( ( empty_set != X1
| empty_set != X0
| union(X0,X1) != empty_set )
& ( ( empty_set = X1
& empty_set = X0 )
| union(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f26,plain,
? [X0,X1] :
( ( empty_set != X1
| empty_set != X0
| union(X0,X1) != empty_set )
& ( ( empty_set = X1
& empty_set = X0 )
| union(X0,X1) = empty_set ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
( ? [X0,X1] :
( ( empty_set != X1
| empty_set != X0
| union(X0,X1) != empty_set )
& ( ( empty_set = X1
& empty_set = X0 )
| union(X0,X1) = empty_set ) )
=> ( ( empty_set != sK3
| empty_set != sK2
| empty_set != union(sK2,sK3) )
& ( ( empty_set = sK3
& empty_set = sK2 )
| empty_set = union(sK2,sK3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ( empty_set != sK3
| empty_set != sK2
| empty_set != union(sK2,sK3) )
& ( ( empty_set = sK3
& empty_set = sK2 )
| empty_set = union(sK2,sK3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f26,f27]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f32,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f36,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f38,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f45,plain,
( empty_set = sK2
| empty_set = union(sK2,sK3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f46,plain,
( empty_set = sK3
| empty_set = union(sK2,sK3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
( empty_set != sK3
| empty_set != sK2
| empty_set != union(sK2,sK3) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_49,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_50,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_51,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_52,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f32]) ).
cnf(c_53,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_56,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f36]) ).
cnf(c_58,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_63,negated_conjecture,
( union(sK2,sK3) != empty_set
| empty_set != sK3
| empty_set != sK2 ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_64,negated_conjecture,
( union(sK2,sK3) = empty_set
| empty_set = sK3 ),
inference(cnf_transformation,[],[f46]) ).
cnf(c_65,negated_conjecture,
( union(sK2,sK3) = empty_set
| empty_set = sK2 ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_153,plain,
( union(sK3,sK2) = empty_set
| empty_set = sK2 ),
inference(demodulation,[status(thm)],[c_65,c_56]) ).
cnf(c_160,plain,
( union(sK3,sK2) = empty_set
| empty_set = sK3 ),
inference(demodulation,[status(thm)],[c_64,c_56]) ).
cnf(c_197,plain,
( union(sK3,sK2) != empty_set
| empty_set != sK3
| empty_set != sK2 ),
inference(demodulation,[status(thm)],[c_63,c_56]) ).
cnf(c_544,plain,
subset(empty_set,X0),
inference(superposition,[status(thm)],[c_58,c_52]) ).
cnf(c_551,plain,
( ~ member(X0,sK2)
| empty_set = sK3
| member(X0,empty_set) ),
inference(superposition,[status(thm)],[c_160,c_49]) ).
cnf(c_552,plain,
( ~ member(X0,sK2)
| empty_set = sK2
| member(X0,empty_set) ),
inference(superposition,[status(thm)],[c_153,c_49]) ).
cnf(c_553,plain,
( ~ member(X0,sK2)
| empty_set = sK2 ),
inference(forward_subsumption_resolution,[status(thm)],[c_552,c_52]) ).
cnf(c_556,plain,
( ~ member(X0,sK2)
| empty_set = sK3 ),
inference(forward_subsumption_resolution,[status(thm)],[c_551,c_52]) ).
cnf(c_567,plain,
( ~ member(X0,sK3)
| empty_set = sK3
| member(X0,empty_set) ),
inference(superposition,[status(thm)],[c_160,c_50]) ).
cnf(c_572,plain,
( ~ member(X0,sK3)
| empty_set = sK3 ),
inference(forward_subsumption_resolution,[status(thm)],[c_567,c_52]) ).
cnf(c_615,plain,
( member(sK0(union(X0,X1),X2),X0)
| member(sK0(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_58,c_51]) ).
cnf(c_628,plain,
( empty_set = sK2
| subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_58,c_553]) ).
cnf(c_640,plain,
( empty_set = sK3
| subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_58,c_556]) ).
cnf(c_660,plain,
( empty_set = sK3
| subset(sK3,X0) ),
inference(superposition,[status(thm)],[c_58,c_572]) ).
cnf(c_679,plain,
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(superposition,[status(thm)],[c_544,c_53]) ).
cnf(c_680,plain,
( ~ subset(X0,sK2)
| X0 = sK2
| empty_set = sK3 ),
inference(superposition,[status(thm)],[c_640,c_53]) ).
cnf(c_710,plain,
( empty_set = sK3
| empty_set = sK2 ),
inference(superposition,[status(thm)],[c_544,c_680]) ).
cnf(c_713,plain,
( empty_set = sK3
| sK3 = sK2 ),
inference(superposition,[status(thm)],[c_660,c_680]) ).
cnf(c_749,plain,
empty_set = sK3,
inference(superposition,[status(thm)],[c_713,c_710]) ).
cnf(c_759,plain,
( union(sK3,sK2) != empty_set
| empty_set != sK2 ),
inference(backward_subsumption_resolution,[status(thm)],[c_197,c_749]) ).
cnf(c_836,plain,
empty_set = sK2,
inference(superposition,[status(thm)],[c_628,c_679]) ).
cnf(c_878,plain,
union(sK3,sK2) != empty_set,
inference(global_subsumption_just,[status(thm)],[c_759,c_197,c_749,c_836]) ).
cnf(c_880,plain,
union(empty_set,empty_set) != empty_set,
inference(light_normalisation,[status(thm)],[c_878,c_749,c_836]) ).
cnf(c_1301,plain,
( member(sK0(union(X0,empty_set),X1),X0)
| subset(union(X0,empty_set),X1) ),
inference(superposition,[status(thm)],[c_615,c_52]) ).
cnf(c_1446,plain,
subset(union(empty_set,empty_set),X0),
inference(superposition,[status(thm)],[c_1301,c_52]) ).
cnf(c_1474,plain,
union(empty_set,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_1446,c_679]) ).
cnf(c_1479,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1474,c_880]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET600+3 : TPTP v8.2.0. Released v2.2.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Jun 23 12:21:09 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 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
% 0.47/1.16 % SZS status Started for theBenchmark.p
% 0.47/1.16 % SZS status Theorem for theBenchmark.p
% 0.47/1.16
% 0.47/1.16 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.47/1.16
% 0.47/1.16 ------ iProver source info
% 0.47/1.16
% 0.47/1.16 git: date: 2024-06-12 09:56:46 +0000
% 0.47/1.16 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 0.47/1.16 git: non_committed_changes: false
% 0.47/1.16
% 0.47/1.16 ------ Parsing...
% 0.47/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.47/1.16
% 0.47/1.16 ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.47/1.16
% 0.47/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.47/1.16
% 0.47/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.47/1.16 ------ Proving...
% 0.47/1.16 ------ Problem Properties
% 0.47/1.16
% 0.47/1.16
% 0.47/1.16 clauses 15
% 0.47/1.16 conjectures 0
% 0.47/1.16 EPR 4
% 0.47/1.16 Horn 10
% 0.47/1.16 unary 3
% 0.47/1.16 binary 6
% 0.47/1.16 lits 33
% 0.47/1.16 lits eq 11
% 0.47/1.16 fd_pure 0
% 0.47/1.16 fd_pseudo 0
% 0.47/1.16 fd_cond 0
% 0.47/1.16 fd_pseudo_cond 3
% 0.47/1.16 AC symbols 0
% 0.47/1.16
% 0.47/1.16 ------ Schedule dynamic 5 is on
% 0.47/1.16
% 0.47/1.16 ------ no conjectures: strip conj schedule
% 0.47/1.16
% 0.47/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.47/1.16
% 0.47/1.16
% 0.47/1.16 ------
% 0.47/1.16 Current options:
% 0.47/1.16 ------
% 0.47/1.16
% 0.47/1.16
% 0.47/1.16
% 0.47/1.16
% 0.47/1.16 ------ Proving...
% 0.47/1.16
% 0.47/1.16
% 0.47/1.16 % SZS status Theorem for theBenchmark.p
% 0.47/1.16
% 0.47/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.47/1.16
% 0.47/1.17
%------------------------------------------------------------------------------