TSTP Solution File: SEU180+2 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU180+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : Fri May 3 03:04:52 EDT 2024
% Result : Theorem 158.72s 21.76s
% Output : CNFRefutation 158.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 21 unt; 0 def)
% Number of atoms : 234 ( 24 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 260 ( 101 ~; 95 |; 49 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 161 ( 10 sgn 109 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f14,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f16,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f24,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f25,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f87,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f100,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f108,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f109,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
inference(negated_conjecture,[],[f108]) ).
fof(f139,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f168,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f172,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f218,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f100]) ).
fof(f226,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_field(X2))
| ~ in(X0,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f109]) ).
fof(f227,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_field(X2))
| ~ in(X0,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f226]) ).
fof(f294,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f295,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f294]) ).
fof(f296,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f295]) ).
fof(f297,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK10(X0,X1,X2),X1)
& ~ in(sK10(X0,X1,X2),X0) )
| ~ in(sK10(X0,X1,X2),X2) )
& ( in(sK10(X0,X1,X2),X1)
| in(sK10(X0,X1,X2),X0)
| in(sK10(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f298,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK10(X0,X1,X2),X1)
& ~ in(sK10(X0,X1,X2),X0) )
| ~ in(sK10(X0,X1,X2),X2) )
& ( in(sK10(X0,X1,X2),X1)
| in(sK10(X0,X1,X2),X0)
| in(sK10(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f296,f297]) ).
fof(f305,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f168]) ).
fof(f306,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f305]) ).
fof(f307,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK16(X0,X1),X1)
& in(sK16(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f308,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK16(X0,X1),X1)
& in(sK16(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f306,f307]) ).
fof(f363,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f87]) ).
fof(f364,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f363]) ).
fof(f371,plain,
( ? [X0,X1,X2] :
( ( ~ in(X1,relation_field(X2))
| ~ in(X0,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) )
=> ( ( ~ in(sK39,relation_field(sK40))
| ~ in(sK38,relation_field(sK40)) )
& in(ordered_pair(sK38,sK39),sK40)
& relation(sK40) ) ),
introduced(choice_axiom,[]) ).
fof(f372,plain,
( ( ~ in(sK39,relation_field(sK40))
| ~ in(sK38,relation_field(sK40)) )
& in(ordered_pair(sK38,sK39),sK40)
& relation(sK40) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39,sK40])],[f227,f371]) ).
fof(f393,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f431,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f298]) ).
fof(f432,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f298]) ).
fof(f444,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f308]) ).
fof(f475,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f476,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f538,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f364]) ).
fof(f539,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f364]) ).
fof(f557,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f567,plain,
relation(sK40),
inference(cnf_transformation,[],[f372]) ).
fof(f568,plain,
in(ordered_pair(sK38,sK39),sK40),
inference(cnf_transformation,[],[f372]) ).
fof(f569,plain,
( ~ in(sK39,relation_field(sK40))
| ~ in(sK38,relation_field(sK40)) ),
inference(cnf_transformation,[],[f372]) ).
fof(f612,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f139]) ).
fof(f629,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f475,f612]) ).
fof(f674,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f539,f629]) ).
fof(f675,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f538,f629]) ).
fof(f684,plain,
in(unordered_pair(unordered_pair(sK38,sK39),unordered_pair(sK38,sK38)),sK40),
inference(definition_unfolding,[],[f568,f629]) ).
fof(f720,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f432]) ).
fof(f721,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f431]) ).
cnf(c_51,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f393]) ).
cnf(c_91,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ),
inference(cnf_transformation,[],[f720]) ).
cnf(c_92,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f721]) ).
cnf(c_104,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f444]) ).
cnf(c_133,plain,
( ~ relation(X0)
| set_union2(relation_dom(X0),relation_rng(X0)) = relation_field(X0) ),
inference(cnf_transformation,[],[f476]) ).
cnf(c_196,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f674]) ).
cnf(c_197,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f675]) ).
cnf(c_214,plain,
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(cnf_transformation,[],[f557]) ).
cnf(c_224,negated_conjecture,
( ~ in(sK39,relation_field(sK40))
| ~ in(sK38,relation_field(sK40)) ),
inference(cnf_transformation,[],[f569]) ).
cnf(c_225,negated_conjecture,
in(unordered_pair(unordered_pair(sK38,sK39),unordered_pair(sK38,sK38)),sK40),
inference(cnf_transformation,[],[f684]) ).
cnf(c_226,negated_conjecture,
relation(sK40),
inference(cnf_transformation,[],[f567]) ).
cnf(c_2027,plain,
in(unordered_pair(unordered_pair(sK38,sK38),unordered_pair(sK38,sK39)),sK40),
inference(demodulation,[status(thm)],[c_225,c_51]) ).
cnf(c_36047,plain,
( ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(superposition,[status(thm)],[c_51,c_196]) ).
cnf(c_36054,plain,
( ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(superposition,[status(thm)],[c_51,c_197]) ).
cnf(c_36451,plain,
set_union2(relation_dom(sK40),relation_rng(sK40)) = relation_field(sK40),
inference(superposition,[status(thm)],[c_226,c_133]) ).
cnf(c_36487,plain,
( ~ in(X0,relation_rng(sK40))
| in(X0,relation_field(sK40)) ),
inference(superposition,[status(thm)],[c_36451,c_91]) ).
cnf(c_36516,plain,
( ~ in(X0,relation_dom(sK40))
| in(X0,relation_field(sK40)) ),
inference(superposition,[status(thm)],[c_36451,c_92]) ).
cnf(c_39640,plain,
( ~ subset(sK40,X0)
| in(unordered_pair(unordered_pair(sK38,sK38),unordered_pair(sK38,sK39)),X0) ),
inference(superposition,[status(thm)],[c_2027,c_104]) ).
cnf(c_40131,plain,
( ~ subset(sK40,cartesian_product2(X0,X1))
| in(sK38,X0) ),
inference(superposition,[status(thm)],[c_39640,c_36054]) ).
cnf(c_40132,plain,
( ~ subset(sK40,cartesian_product2(X0,X1))
| in(sK39,X1) ),
inference(superposition,[status(thm)],[c_39640,c_36047]) ).
cnf(c_41467,plain,
( ~ relation(sK40)
| in(sK38,relation_dom(sK40)) ),
inference(superposition,[status(thm)],[c_214,c_40131]) ).
cnf(c_41468,plain,
in(sK38,relation_dom(sK40)),
inference(forward_subsumption_resolution,[status(thm)],[c_41467,c_226]) ).
cnf(c_41477,plain,
in(sK38,relation_field(sK40)),
inference(superposition,[status(thm)],[c_41468,c_36516]) ).
cnf(c_41483,plain,
~ in(sK39,relation_field(sK40)),
inference(backward_subsumption_resolution,[status(thm)],[c_224,c_41477]) ).
cnf(c_42753,plain,
( ~ relation(sK40)
| in(sK39,relation_rng(sK40)) ),
inference(superposition,[status(thm)],[c_214,c_40132]) ).
cnf(c_42754,plain,
in(sK39,relation_rng(sK40)),
inference(forward_subsumption_resolution,[status(thm)],[c_42753,c_226]) ).
cnf(c_42774,plain,
in(sK39,relation_field(sK40)),
inference(superposition,[status(thm)],[c_42754,c_36487]) ).
cnf(c_42775,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_42774,c_41483]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU180+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n029.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 : Thu May 2 18:00:07 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 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
% 158.72/21.76 % SZS status Started for theBenchmark.p
% 158.72/21.76 % SZS status Theorem for theBenchmark.p
% 158.72/21.76
% 158.72/21.76 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 158.72/21.76
% 158.72/21.76 ------ iProver source info
% 158.72/21.76
% 158.72/21.76 git: date: 2024-05-02 19:28:25 +0000
% 158.72/21.76 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 158.72/21.76 git: non_committed_changes: false
% 158.72/21.76
% 158.72/21.76 ------ Parsing...
% 158.72/21.76 ------ Clausification by vclausify_rel & Parsing by iProver...
% 158.72/21.76
% 158.72/21.76 ------ Preprocessing... sup_sim: 14 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
% 158.72/21.76
% 158.72/21.76 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 158.72/21.76
% 158.72/21.76 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 158.72/21.76 ------ Proving...
% 158.72/21.76 ------ Problem Properties
% 158.72/21.76
% 158.72/21.76
% 158.72/21.76 clauses 204
% 158.72/21.76 conjectures 2
% 158.72/21.76 EPR 30
% 158.72/21.76 Horn 157
% 158.72/21.76 unary 38
% 158.72/21.76 binary 80
% 158.72/21.76 lits 485
% 158.72/21.76 lits eq 115
% 158.72/21.76 fd_pure 0
% 158.72/21.76 fd_pseudo 0
% 158.72/21.76 fd_cond 10
% 158.72/21.76 fd_pseudo_cond 45
% 158.72/21.76 AC symbols 0
% 158.72/21.76
% 158.72/21.76 ------ Input Options Time Limit: Unbounded
% 158.72/21.76
% 158.72/21.76
% 158.72/21.76 ------
% 158.72/21.76 Current options:
% 158.72/21.76 ------
% 158.72/21.76
% 158.72/21.76
% 158.72/21.76
% 158.72/21.76
% 158.72/21.76 ------ Proving...
% 158.72/21.76
% 158.72/21.76
% 158.72/21.76 % SZS status Theorem for theBenchmark.p
% 158.72/21.76
% 158.72/21.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 158.72/21.76
% 158.72/21.78
%------------------------------------------------------------------------------