TSTP Solution File: KLE041+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : KLE041+1 : TPTP v8.1.2. Released v4.0.0.
% 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 05:31:52 EDT 2023
% Result : Theorem 18.40s 3.19s
% Output : CNFRefutation 18.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 53 unt; 0 def)
% Number of atoms : 91 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 18 ~; 10 |; 5 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 10 sgn; 56 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_left) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X0)
=> leq(multiplication(X2,star(X1)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_right) ).
fof(f17,conjecture,
! [X3,X4] :
( leq(X3,X4)
=> leq(star(X3),star(X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X3,X4] :
( leq(X3,X4)
=> leq(star(X3),star(X4)) ),
inference(negated_conjecture,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f20,plain,
~ ! [X0,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
inference(rectify,[],[f18]) ).
fof(f22,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f23,plain,
? [X0,X1] :
( ~ leq(star(X0),star(X1))
& leq(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f24,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f25,plain,
( ? [X0,X1] :
( ~ leq(star(X0),star(X1))
& leq(X0,X1) )
=> ( ~ leq(star(sK0),star(sK1))
& leq(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( ~ leq(star(sK0),star(sK1))
& leq(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f23,f25]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f38,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f43,plain,
! [X2,X0,X1] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
leq(sK0,sK1),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
~ leq(star(sK0),star(sK1)),
inference(cnf_transformation,[],[f26]) ).
cnf(c_49,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f27]) ).
cnf(c_50,plain,
addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f28]) ).
cnf(c_52,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[],[f30]) ).
cnf(c_54,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f32]) ).
cnf(c_55,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f33]) ).
cnf(c_56,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
cnf(c_57,plain,
addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f35]) ).
cnf(c_60,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_61,plain,
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_63,plain,
leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f41]) ).
cnf(c_65,plain,
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_66,negated_conjecture,
~ leq(star(sK0),star(sK1)),
inference(cnf_transformation,[],[f45]) ).
cnf(c_67,negated_conjecture,
leq(sK0,sK1),
inference(cnf_transformation,[],[f44]) ).
cnf(c_487,plain,
addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_63,c_61]) ).
cnf(c_488,plain,
addition(sK0,sK1) = sK1,
inference(superposition,[status(thm)],[c_67,c_61]) ).
cnf(c_489,plain,
addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(theory_normalisation,[status(thm)],[c_487,c_50,c_49]) ).
cnf(c_544,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
cnf(c_600,plain,
addition(multiplication(X0,sK0),multiplication(X0,sK1)) = multiplication(X0,sK1),
inference(superposition,[status(thm)],[c_488,c_56]) ).
cnf(c_694,plain,
leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_544,c_60]) ).
cnf(c_1077,plain,
( ~ leq(addition(X0,multiplication(X1,X2)),X1)
| leq(multiplication(X0,star(X2)),X1) ),
inference(superposition,[status(thm)],[c_49,c_65]) ).
cnf(c_1206,plain,
leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_694]) ).
cnf(c_1509,plain,
leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_1206]) ).
cnf(c_1549,plain,
leq(X0,addition(X1,addition(X0,X2))),
inference(superposition,[status(thm)],[c_49,c_1509]) ).
cnf(c_1599,plain,
leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(superposition,[status(thm)],[c_50,c_1549]) ).
cnf(c_14813,plain,
leq(addition(X0,multiplication(X1,sK0)),addition(X2,addition(X0,multiplication(X1,sK1)))),
inference(superposition,[status(thm)],[c_600,c_1599]) ).
cnf(c_47086,plain,
addition(one,star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_489,c_544]) ).
cnf(c_47185,plain,
leq(addition(star(sK1),multiplication(star(sK1),sK0)),star(sK1)),
inference(superposition,[status(thm)],[c_489,c_14813]) ).
cnf(c_47647,plain,
leq(multiplication(star(sK1),star(sK0)),star(sK1)),
inference(superposition,[status(thm)],[c_47185,c_1077]) ).
cnf(c_51113,plain,
addition(multiplication(X0,one),multiplication(X0,star(X1))) = multiplication(X0,star(X1)),
inference(superposition,[status(thm)],[c_47086,c_56]) ).
cnf(c_51123,plain,
addition(multiplication(one,X0),multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(superposition,[status(thm)],[c_47086,c_57]) ).
cnf(c_51197,plain,
addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(light_normalisation,[status(thm)],[c_51123,c_55]) ).
cnf(c_51198,plain,
addition(X0,multiplication(X0,star(X1))) = multiplication(X0,star(X1)),
inference(light_normalisation,[status(thm)],[c_51113,c_54]) ).
cnf(c_51709,plain,
leq(X0,multiplication(star(X1),X0)),
inference(superposition,[status(thm)],[c_51197,c_60]) ).
cnf(c_60398,plain,
addition(multiplication(star(sK1),star(sK0)),star(sK1)) = star(sK1),
inference(superposition,[status(thm)],[c_47647,c_61]) ).
cnf(c_60399,plain,
addition(star(sK1),multiplication(star(sK1),star(sK0))) = star(sK1),
inference(theory_normalisation,[status(thm)],[c_60398,c_50,c_49]) ).
cnf(c_90977,plain,
multiplication(star(sK1),star(sK0)) = star(sK1),
inference(demodulation,[status(thm)],[c_60399,c_51198]) ).
cnf(c_91022,plain,
leq(star(sK0),star(sK1)),
inference(superposition,[status(thm)],[c_90977,c_51709]) ).
cnf(c_91039,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_91022,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE041+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 12:27:57 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 18.40/3.19 % SZS status Started for theBenchmark.p
% 18.40/3.19 % SZS status Theorem for theBenchmark.p
% 18.40/3.19
% 18.40/3.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 18.40/3.19
% 18.40/3.19 ------ iProver source info
% 18.40/3.19
% 18.40/3.19 git: date: 2023-05-31 18:12:56 +0000
% 18.40/3.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 18.40/3.19 git: non_committed_changes: false
% 18.40/3.19 git: last_make_outside_of_git: false
% 18.40/3.19
% 18.40/3.19 ------ Parsing...
% 18.40/3.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 18.40/3.19
% 18.40/3.19 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 18.40/3.19
% 18.40/3.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 18.40/3.19
% 18.40/3.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.40/3.19 ------ Proving...
% 18.40/3.19 ------ Problem Properties
% 18.40/3.19
% 18.40/3.19
% 18.40/3.19 clauses 19
% 18.40/3.19 conjectures 2
% 18.40/3.19 EPR 1
% 18.40/3.19 Horn 19
% 18.40/3.19 unary 15
% 18.40/3.19 binary 4
% 18.40/3.19 lits 23
% 18.40/3.19 lits eq 13
% 18.40/3.19 fd_pure 0
% 18.40/3.19 fd_pseudo 0
% 18.40/3.19 fd_cond 0
% 18.40/3.19 fd_pseudo_cond 0
% 18.40/3.19 AC symbols 1
% 18.40/3.19
% 18.40/3.19 ------ Schedule dynamic 5 is on
% 18.40/3.19
% 18.40/3.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.40/3.19
% 18.40/3.19
% 18.40/3.19 ------
% 18.40/3.19 Current options:
% 18.40/3.19 ------
% 18.40/3.19
% 18.40/3.19
% 18.40/3.19
% 18.40/3.19
% 18.40/3.19 ------ Proving...
% 18.40/3.19
% 18.40/3.19
% 18.40/3.19 % SZS status Theorem for theBenchmark.p
% 18.40/3.19
% 18.40/3.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.40/3.19
% 18.40/3.20
%------------------------------------------------------------------------------