TSTP Solution File: KLE167+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : KLE167+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : Thu Aug 31 05:32:22 EDT 2023
% Result : Theorem 7.61s 1.68s
% Output : CNFRefutation 7.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 32 unt; 0 def)
% Number of atoms : 87 ( 43 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 61 ( 28 ~; 19 |; 8 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 2 sgn; 48 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f12,axiom,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold2) ).
fof(f14,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X2,X0),X1),X2)
=> leq(multiplication(X1,star(X0)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction2) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f19,conjecture,
! [X3,X4] :
( leq(X3,multiplication(X3,star(X4)))
& ( zero = multiplication(X3,X4)
=> leq(multiplication(X3,star(X4)),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X3,X4] :
( leq(X3,multiplication(X3,star(X4)))
& ( zero = multiplication(X3,X4)
=> leq(multiplication(X3,star(X4)),X3) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f22,plain,
~ ! [X0,X1] :
( leq(X0,multiplication(X0,star(X1)))
& ( zero = multiplication(X0,X1)
=> leq(multiplication(X0,star(X1)),X0) ) ),
inference(rectify,[],[f20]) ).
fof(f24,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X0)),X2)
| ~ leq(addition(multiplication(X2,X0),X1),X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f26,plain,
? [X0,X1] :
( ~ leq(X0,multiplication(X0,star(X1)))
| ( ~ leq(multiplication(X0,star(X1)),X0)
& zero = multiplication(X0,X1) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f27,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f28,plain,
( ? [X0,X1] :
( ~ leq(X0,multiplication(X0,star(X1)))
| ( ~ leq(multiplication(X0,star(X1)),X0)
& zero = multiplication(X0,X1) ) )
=> ( ~ leq(sK0,multiplication(sK0,star(sK1)))
| ( ~ leq(multiplication(sK0,star(sK1)),sK0)
& zero = multiplication(sK0,sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| ( ~ leq(multiplication(sK0,star(sK1)),sK0)
& zero = multiplication(sK0,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f26,f28]) ).
fof(f30,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f21]) ).
fof(f32,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f41,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f43,plain,
! [X2,X0,X1] :
( leq(multiplication(X1,star(X0)),X2)
| ~ leq(addition(multiplication(X2,X0),X1),X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| zero = multiplication(sK0,sK1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f50,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| ~ leq(multiplication(sK0,star(sK1)),sK0) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_49,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f30]) ).
cnf(c_50,plain,
addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f31]) ).
cnf(c_51,plain,
addition(X0,zero) = X0,
inference(cnf_transformation,[],[f32]) ).
cnf(c_52,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[],[f33]) ).
cnf(c_54,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f35]) ).
cnf(c_56,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f37]) ).
cnf(c_60,plain,
addition(one,multiplication(star(X0),X0)) = star(X0),
inference(cnf_transformation,[],[f41]) ).
cnf(c_62,plain,
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_66,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_68,negated_conjecture,
( ~ leq(multiplication(sK0,star(sK1)),sK0)
| ~ leq(sK0,multiplication(sK0,star(sK1))) ),
inference(cnf_transformation,[],[f50]) ).
cnf(c_69,negated_conjecture,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| multiplication(sK0,sK1) = zero ),
inference(cnf_transformation,[],[f49]) ).
cnf(c_73,plain,
addition(sK0,sK0) = sK0,
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_76,plain,
( addition(sK0,sK0) != sK0
| leq(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_565,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
cnf(c_691,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
cnf(c_750,plain,
addition(multiplication(X0,one),multiplication(X0,multiplication(star(X1),X1))) = multiplication(X0,star(X1)),
inference(superposition,[status(thm)],[c_60,c_56]) ).
cnf(c_771,plain,
addition(X0,multiplication(X0,multiplication(star(X1),X1))) = multiplication(X0,star(X1)),
inference(light_normalisation,[status(thm)],[c_750,c_54]) ).
cnf(c_872,plain,
leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_691,c_66]) ).
cnf(c_19261,plain,
leq(X0,multiplication(X0,star(X1))),
inference(superposition,[status(thm)],[c_771,c_872]) ).
cnf(c_19415,plain,
multiplication(sK0,sK1) = zero,
inference(backward_subsumption_resolution,[status(thm)],[c_69,c_19261]) ).
cnf(c_19416,plain,
~ leq(multiplication(sK0,star(sK1)),sK0),
inference(backward_subsumption_resolution,[status(thm)],[c_68,c_19261]) ).
cnf(c_19915,plain,
( ~ leq(addition(zero,X0),sK0)
| leq(multiplication(X0,star(sK1)),sK0) ),
inference(superposition,[status(thm)],[c_19415,c_62]) ).
cnf(c_19934,plain,
( ~ leq(X0,sK0)
| leq(multiplication(X0,star(sK1)),sK0) ),
inference(light_normalisation,[status(thm)],[c_19915,c_565]) ).
cnf(c_19940,plain,
( ~ leq(sK0,sK0)
| leq(multiplication(sK0,star(sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_19934]) ).
cnf(c_19941,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_19940,c_19416,c_76,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE167+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n018.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 : Tue Aug 29 12:27:18 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.61/1.68 % SZS status Started for theBenchmark.p
% 7.61/1.68 % SZS status Theorem for theBenchmark.p
% 7.61/1.68
% 7.61/1.68 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.61/1.68
% 7.61/1.68 ------ iProver source info
% 7.61/1.68
% 7.61/1.68 git: date: 2023-05-31 18:12:56 +0000
% 7.61/1.68 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.61/1.68 git: non_committed_changes: false
% 7.61/1.68 git: last_make_outside_of_git: false
% 7.61/1.68
% 7.61/1.68 ------ Parsing...
% 7.61/1.68 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.61/1.68
% 7.61/1.68 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 7.61/1.68
% 7.61/1.68 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.61/1.68
% 7.61/1.68 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.61/1.68 ------ Proving...
% 7.61/1.68 ------ Problem Properties
% 7.61/1.68
% 7.61/1.68
% 7.61/1.68 clauses 21
% 7.61/1.68 conjectures 2
% 7.61/1.68 EPR 0
% 7.61/1.68 Horn 21
% 7.61/1.68 unary 14
% 7.61/1.68 binary 7
% 7.61/1.68 lits 28
% 7.61/1.68 lits eq 17
% 7.61/1.68 fd_pure 0
% 7.61/1.68 fd_pseudo 0
% 7.61/1.68 fd_cond 0
% 7.61/1.68 fd_pseudo_cond 0
% 7.61/1.68 AC symbols 1
% 7.61/1.68
% 7.61/1.68 ------ Schedule dynamic 5 is on
% 7.61/1.68
% 7.61/1.68 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.61/1.68
% 7.61/1.68
% 7.61/1.68 ------
% 7.61/1.68 Current options:
% 7.61/1.68 ------
% 7.61/1.68
% 7.61/1.68
% 7.61/1.68
% 7.61/1.68
% 7.61/1.68 ------ Proving...
% 7.61/1.68
% 7.61/1.68
% 7.61/1.68 % SZS status Theorem for theBenchmark.p
% 7.61/1.68
% 7.61/1.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.61/1.68
% 7.61/1.68
%------------------------------------------------------------------------------