TSTP Solution File: SET791+4 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET791+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n009.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 15:09:52 EDT 2023
% Result : Theorem 0.48s 1.17s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 13 unt; 0 def)
% Number of atoms : 247 ( 40 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 293 ( 106 ~; 94 |; 58 &)
% ( 6 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 164 ( 2 sgn; 109 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X2,X3] :
( ( member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X2)
& apply(X0,X2,X3) )
=> X2 = X3 ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f5,axiom,
! [X0,X1,X5] :
( greatest(X5,X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X5) )
& member(X5,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greatest) ).
fof(f7,axiom,
! [X0,X1,X5] :
( max(X5,X0,X1)
<=> ( ! [X2] :
( ( apply(X0,X5,X2)
& member(X2,X1) )
=> X2 = X5 )
& member(X5,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max) ).
fof(f11,conjecture,
! [X0,X1,X5] :
( ( greatest(X5,X0,X1)
& order(X0,X1) )
=> max(X5,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV3) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X5] :
( ( greatest(X5,X0,X1)
& order(X0,X1) )
=> max(X5,X0,X1) ),
inference(negated_conjecture,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X1)
& member(X5,X1) )
=> ( ( apply(X0,X6,X5)
& apply(X0,X5,X6) )
=> X5 = X6 ) )
& ! [X7] :
( member(X7,X1)
=> apply(X0,X7,X7) ) ) ),
inference(rectify,[],[f1]) ).
fof(f16,plain,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) )
& member(X2,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f18,plain,
! [X0,X1,X2] :
( max(X2,X0,X1)
<=> ( ! [X3] :
( ( apply(X0,X2,X3)
& member(X3,X1) )
=> X2 = X3 )
& member(X2,X1) ) ),
inference(rectify,[],[f7]) ).
fof(f22,plain,
~ ! [X0,X1,X2] :
( ( greatest(X2,X0,X1)
& order(X0,X1) )
=> max(X2,X0,X1) ),
inference(rectify,[],[f12]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( apply(X0,X2,X3)
& member(X3,X1) )
=> X2 = X3 )
& member(X2,X1) )
=> max(X2,X0,X1) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f24,plain,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
=> ( ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) )
& member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f25,plain,
! [X0,X1] :
( order(X0,X1)
=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X1)
& member(X5,X1) )
=> ( ( apply(X0,X6,X5)
& apply(X0,X5,X6) )
=> X5 = X6 ) )
& ! [X7] :
( member(X7,X1)
=> apply(X0,X7,X7) ) ) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f26,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1) )
& ! [X5,X6] :
( X5 = X6
| ~ apply(X0,X6,X5)
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1) )
& ! [X7] :
( apply(X0,X7,X7)
| ~ member(X7,X1) ) )
| ~ order(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1) )
& ! [X5,X6] :
( X5 = X6
| ~ apply(X0,X6,X5)
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1) )
& ! [X7] :
( apply(X0,X7,X7)
| ~ member(X7,X1) ) )
| ~ order(X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) )
& member(X2,X1) )
| ~ greatest(X2,X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f29,plain,
! [X0,X1,X2] :
( max(X2,X0,X1)
| ? [X3] :
( X2 != X3
& apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X2,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f30,plain,
! [X0,X1,X2] :
( max(X2,X0,X1)
| ? [X3] :
( X2 != X3
& apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X2,X1) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
? [X0,X1,X2] :
( ~ max(X2,X0,X1)
& greatest(X2,X0,X1)
& order(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ~ max(X2,X0,X1)
& greatest(X2,X0,X1)
& order(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ? [X3] :
( X2 != X3
& apply(X0,X2,X3)
& member(X3,X1) )
=> ( sK0(X0,X1,X2) != X2
& apply(X0,X2,sK0(X0,X1,X2))
& member(sK0(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0,X1,X2] :
( max(X2,X0,X1)
| ( sK0(X0,X1,X2) != X2
& apply(X0,X2,sK0(X0,X1,X2))
& member(sK0(X0,X1,X2),X1) )
| ~ member(X2,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f30,f33]) ).
fof(f35,plain,
( ? [X0,X1,X2] :
( ~ max(X2,X0,X1)
& greatest(X2,X0,X1)
& order(X0,X1) )
=> ( ~ max(sK3,sK1,sK2)
& greatest(sK3,sK1,sK2)
& order(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
( ~ max(sK3,sK1,sK2)
& greatest(sK3,sK1,sK2)
& order(sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f32,f35]) ).
fof(f38,plain,
! [X0,X1,X6,X5] :
( X5 = X6
| ~ apply(X0,X6,X5)
| ~ apply(X0,X5,X6)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f40,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ greatest(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
! [X2,X3,X0,X1] :
( apply(X0,X3,X2)
| ~ member(X3,X1)
| ~ greatest(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
! [X2,X0,X1] :
( max(X2,X0,X1)
| member(sK0(X0,X1,X2),X1)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f43,plain,
! [X2,X0,X1] :
( max(X2,X0,X1)
| apply(X0,X2,sK0(X0,X1,X2))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f44,plain,
! [X2,X0,X1] :
( max(X2,X0,X1)
| sK0(X0,X1,X2) != X2
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f45,plain,
order(sK1,sK2),
inference(cnf_transformation,[],[f36]) ).
fof(f46,plain,
greatest(sK3,sK1,sK2),
inference(cnf_transformation,[],[f36]) ).
fof(f47,plain,
~ max(sK3,sK1,sK2),
inference(cnf_transformation,[],[f36]) ).
cnf(c_50,plain,
( ~ apply(X0,X1,X2)
| ~ apply(X0,X2,X1)
| ~ member(X1,X3)
| ~ member(X2,X3)
| ~ order(X0,X3)
| X1 = X2 ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_52,plain,
( ~ greatest(X0,X1,X2)
| ~ member(X3,X2)
| apply(X1,X3,X0) ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_53,plain,
( ~ greatest(X0,X1,X2)
| member(X0,X2) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_54,plain,
( sK0(X0,X1,X2) != X2
| ~ member(X2,X1)
| max(X2,X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_55,plain,
( ~ member(X0,X1)
| apply(X2,X0,sK0(X2,X1,X0))
| max(X0,X2,X1) ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_56,plain,
( ~ member(X0,X1)
| member(sK0(X2,X1,X0),X1)
| max(X0,X2,X1) ),
inference(cnf_transformation,[],[f42]) ).
cnf(c_57,negated_conjecture,
~ max(sK3,sK1,sK2),
inference(cnf_transformation,[],[f47]) ).
cnf(c_58,negated_conjecture,
greatest(sK3,sK1,sK2),
inference(cnf_transformation,[],[f46]) ).
cnf(c_59,negated_conjecture,
order(sK1,sK2),
inference(cnf_transformation,[],[f45]) ).
cnf(c_199,plain,
( X0 != sK3
| X1 != sK1
| X2 != sK2
| member(X0,X2) ),
inference(resolution_lifted,[status(thm)],[c_53,c_58]) ).
cnf(c_200,plain,
member(sK3,sK2),
inference(unflattening,[status(thm)],[c_199]) ).
cnf(c_204,plain,
( X0 != sK3
| X1 != sK1
| X2 != sK2
| ~ member(X3,X2)
| apply(X1,X3,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_58]) ).
cnf(c_205,plain,
( ~ member(X0,sK2)
| apply(sK1,X0,sK3) ),
inference(unflattening,[status(thm)],[c_204]) ).
cnf(c_216,plain,
( sK0(X0,X1,X2) != X2
| X0 != sK1
| X1 != sK2
| X2 != sK3
| ~ member(X2,X1) ),
inference(resolution_lifted,[status(thm)],[c_54,c_57]) ).
cnf(c_217,plain,
( sK0(sK1,sK2,sK3) != sK3
| ~ member(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_216]) ).
cnf(c_218,plain,
sK0(sK1,sK2,sK3) != sK3,
inference(global_subsumption_just,[status(thm)],[c_217,c_200,c_217]) ).
cnf(c_223,plain,
( X0 != sK3
| X1 != sK2
| X2 != sK1
| ~ member(X0,X1)
| member(sK0(X2,X1,X0),X1) ),
inference(resolution_lifted,[status(thm)],[c_56,c_57]) ).
cnf(c_224,plain,
( ~ member(sK3,sK2)
| member(sK0(sK1,sK2,sK3),sK2) ),
inference(unflattening,[status(thm)],[c_223]) ).
cnf(c_225,plain,
member(sK0(sK1,sK2,sK3),sK2),
inference(global_subsumption_just,[status(thm)],[c_224,c_200,c_224]) ).
cnf(c_230,plain,
( X0 != sK3
| X1 != sK2
| X2 != sK1
| ~ member(X0,X1)
| apply(X2,X0,sK0(X2,X1,X0)) ),
inference(resolution_lifted,[status(thm)],[c_55,c_57]) ).
cnf(c_231,plain,
( ~ member(sK3,sK2)
| apply(sK1,sK3,sK0(sK1,sK2,sK3)) ),
inference(unflattening,[status(thm)],[c_230]) ).
cnf(c_232,plain,
apply(sK1,sK3,sK0(sK1,sK2,sK3)),
inference(global_subsumption_just,[status(thm)],[c_231,c_200,c_231]) ).
cnf(c_260,plain,
( X0 != sK1
| X1 != sK2
| ~ apply(X0,X2,X3)
| ~ apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1)
| X2 = X3 ),
inference(resolution_lifted,[status(thm)],[c_50,c_59]) ).
cnf(c_261,plain,
( ~ apply(sK1,X0,X1)
| ~ apply(sK1,X1,X0)
| ~ member(X0,sK2)
| ~ member(X1,sK2)
| X0 = X1 ),
inference(unflattening,[status(thm)],[c_260]) ).
cnf(c_544,plain,
( ~ apply(sK1,sK0(sK1,sK2,sK3),sK3)
| ~ member(sK0(sK1,sK2,sK3),sK2)
| ~ member(sK3,sK2)
| sK0(sK1,sK2,sK3) = sK3 ),
inference(superposition,[status(thm)],[c_232,c_261]) ).
cnf(c_550,plain,
~ apply(sK1,sK0(sK1,sK2,sK3),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_544,c_218,c_200,c_225]) ).
cnf(c_577,plain,
~ member(sK0(sK1,sK2,sK3),sK2),
inference(superposition,[status(thm)],[c_205,c_550]) ).
cnf(c_578,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_577,c_225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET791+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:05:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.48/1.17 % SZS status Started for theBenchmark.p
% 0.48/1.17 % SZS status Theorem for theBenchmark.p
% 0.48/1.17
% 0.48/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.48/1.17
% 0.48/1.17 ------ iProver source info
% 0.48/1.17
% 0.48/1.17 git: date: 2023-05-31 18:12:56 +0000
% 0.48/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.48/1.17 git: non_committed_changes: false
% 0.48/1.17 git: last_make_outside_of_git: false
% 0.48/1.17
% 0.48/1.17 ------ Parsing...
% 0.48/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.48/1.17
% 0.48/1.17 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 0.48/1.17
% 0.48/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.48/1.17
% 0.48/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.48/1.17 ------ Proving...
% 0.48/1.17 ------ Problem Properties
% 0.48/1.17
% 0.48/1.17
% 0.48/1.17 clauses 8
% 0.48/1.17 conjectures 0
% 0.48/1.17 EPR 5
% 0.48/1.17 Horn 8
% 0.48/1.17 unary 4
% 0.48/1.17 binary 2
% 0.48/1.17 lits 19
% 0.48/1.18 lits eq 2
% 0.48/1.18 fd_pure 0
% 0.48/1.18 fd_pseudo 0
% 0.48/1.18 fd_cond 0
% 0.48/1.18 fd_pseudo_cond 1
% 0.48/1.18 AC symbols 0
% 0.48/1.18
% 0.48/1.18 ------ Schedule dynamic 5 is on
% 0.48/1.18
% 0.48/1.18 ------ no conjectures: strip conj schedule
% 0.48/1.18
% 0.48/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.48/1.18
% 0.48/1.18
% 0.48/1.18 ------
% 0.48/1.18 Current options:
% 0.48/1.18 ------
% 0.48/1.18
% 0.48/1.18
% 0.48/1.18
% 0.48/1.18
% 0.48/1.18 ------ Proving...
% 0.48/1.18
% 0.48/1.18
% 0.48/1.18 % SZS status Theorem for theBenchmark.p
% 0.48/1.18
% 0.48/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.66/1.18
% 1.66/1.18
%------------------------------------------------------------------------------