TSTP Solution File: KLE150+2 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.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 05:32:18 EDT 2023
% Result : Theorem 21.33s 3.73s
% Output : CNFRefutation 21.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 64 unt; 0 def)
% Number of atoms : 96 ( 53 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 12 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 119 ( 14 sgn; 50 !; 2 ?)
% 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',idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
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',distributivity2) ).
fof(f10,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f11,axiom,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).
fof(f12,axiom,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold2) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f17,axiom,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isolation) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f19,conjecture,
! [X3] :
( leq(addition(one,multiplication(X3,zero)),strong_iteration(multiplication(X3,zero)))
& leq(strong_iteration(multiplication(X3,zero)),addition(one,multiplication(X3,zero))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X3] :
( leq(addition(one,multiplication(X3,zero)),strong_iteration(multiplication(X3,zero)))
& leq(strong_iteration(multiplication(X3,zero)),addition(one,multiplication(X3,zero))) ),
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] :
( leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
& leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
inference(rectify,[],[f20]) ).
fof(f26,plain,
? [X0] :
( ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
| ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
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] :
( ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
| ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) )
=> ( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[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(f33,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f39,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f40,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f41,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f44,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f46,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[],[f17]) ).
fof(f47,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
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_52,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[],[f33]) ).
cnf(c_53,plain,
multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
cnf(c_55,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f36]) ).
cnf(c_57,plain,
addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f38]) ).
cnf(c_58,plain,
multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f39]) ).
cnf(c_59,plain,
addition(one,multiplication(X0,star(X0))) = star(X0),
inference(cnf_transformation,[],[f40]) ).
cnf(c_60,plain,
addition(one,multiplication(star(X0),X0)) = star(X0),
inference(cnf_transformation,[],[f41]) ).
cnf(c_63,plain,
addition(multiplication(X0,strong_iteration(X0)),one) = strong_iteration(X0),
inference(cnf_transformation,[],[f44]) ).
cnf(c_65,plain,
addition(star(X0),multiplication(strong_iteration(X0),zero)) = strong_iteration(X0),
inference(cnf_transformation,[],[f46]) ).
cnf(c_66,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_67,plain,
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_68,negated_conjecture,
( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
inference(cnf_transformation,[],[f49]) ).
cnf(c_86,plain,
addition(one,multiplication(X0,strong_iteration(X0))) = strong_iteration(X0),
inference(theory_normalisation,[status(thm)],[c_63,c_50,c_49]) ).
cnf(c_1079,plain,
leq(X0,X0),
inference(superposition,[status(thm)],[c_52,c_66]) ).
cnf(c_10311,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
cnf(c_10391,plain,
addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))) = strong_iteration(multiplication(X0,X1)),
inference(superposition,[status(thm)],[c_53,c_86]) ).
cnf(c_10512,plain,
addition(one,star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_59,c_10311]) ).
cnf(c_10514,plain,
addition(star(X0),strong_iteration(X0)) = strong_iteration(X0),
inference(superposition,[status(thm)],[c_65,c_10311]) ).
cnf(c_10517,plain,
leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_10311,c_66]) ).
cnf(c_10530,plain,
leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_10517]) ).
cnf(c_10532,plain,
leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[c_50,c_10517]) ).
cnf(c_10549,plain,
leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_10530]) ).
cnf(c_10553,plain,
leq(multiplication(star(X0),X0),star(X0)),
inference(superposition,[status(thm)],[c_60,c_10530]) ).
cnf(c_10770,plain,
leq(addition(X0,one),addition(X0,strong_iteration(X1))),
inference(superposition,[status(thm)],[c_86,c_10532]) ).
cnf(c_10812,plain,
leq(X0,addition(X1,addition(X0,X2))),
inference(superposition,[status(thm)],[c_49,c_10549]) ).
cnf(c_10843,plain,
addition(multiplication(star(X0),X0),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_10553,c_67]) ).
cnf(c_10844,plain,
addition(star(X0),multiplication(star(X0),X0)) = star(X0),
inference(theory_normalisation,[status(thm)],[c_10843,c_50,c_49]) ).
cnf(c_11569,plain,
addition(multiplication(one,X0),multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(superposition,[status(thm)],[c_10512,c_57]) ).
cnf(c_11581,plain,
addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(light_normalisation,[status(thm)],[c_11569,c_55]) ).
cnf(c_12432,plain,
leq(addition(one,X0),addition(X0,strong_iteration(X1))),
inference(superposition,[status(thm)],[c_49,c_10770]) ).
cnf(c_43229,plain,
leq(X0,addition(X1,multiplication(star(X2),X0))),
inference(superposition,[status(thm)],[c_11581,c_10812]) ).
cnf(c_49848,plain,
leq(X0,star(X0)),
inference(superposition,[status(thm)],[c_10844,c_43229]) ).
cnf(c_50222,plain,
addition(X0,star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_49848,c_67]) ).
cnf(c_50977,plain,
leq(X0,addition(X1,star(X0))),
inference(superposition,[status(thm)],[c_50222,c_10812]) ).
cnf(c_52976,plain,
leq(X0,addition(star(X0),X1)),
inference(superposition,[status(thm)],[c_49,c_50977]) ).
cnf(c_53589,plain,
leq(X0,strong_iteration(X0)),
inference(superposition,[status(thm)],[c_10514,c_52976]) ).
cnf(c_53639,plain,
addition(X0,strong_iteration(X0)) = strong_iteration(X0),
inference(superposition,[status(thm)],[c_53589,c_67]) ).
cnf(c_59967,plain,
leq(addition(one,X0),strong_iteration(X0)),
inference(superposition,[status(thm)],[c_53639,c_12432]) ).
cnf(c_60038,plain,
~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))),
inference(backward_subsumption_resolution,[status(thm)],[c_68,c_59967]) ).
cnf(c_115957,plain,
addition(one,multiplication(X0,zero)) = strong_iteration(multiplication(X0,zero)),
inference(superposition,[status(thm)],[c_58,c_10391]) ).
cnf(c_116074,plain,
~ leq(addition(one,multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))),
inference(demodulation,[status(thm)],[c_60038,c_115957]) ).
cnf(c_116075,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_116074,c_1079]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n014.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 11:06:45 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 21.33/3.73 % SZS status Started for theBenchmark.p
% 21.33/3.73 % SZS status Theorem for theBenchmark.p
% 21.33/3.73
% 21.33/3.73 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 21.33/3.73
% 21.33/3.73 ------ iProver source info
% 21.33/3.73
% 21.33/3.73 git: date: 2023-05-31 18:12:56 +0000
% 21.33/3.73 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 21.33/3.73 git: non_committed_changes: false
% 21.33/3.73 git: last_make_outside_of_git: false
% 21.33/3.73
% 21.33/3.73 ------ Parsing...
% 21.33/3.73 ------ Clausification by vclausify_rel & Parsing by iProver...
% 21.33/3.73
% 21.33/3.73 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 21.33/3.73
% 21.33/3.73 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 21.33/3.73
% 21.33/3.73 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 21.33/3.73 ------ Proving...
% 21.33/3.73 ------ Problem Properties
% 21.33/3.73
% 21.33/3.73
% 21.33/3.73 clauses 20
% 21.33/3.73 conjectures 1
% 21.33/3.73 EPR 0
% 21.33/3.73 Horn 20
% 21.33/3.73 unary 14
% 21.33/3.73 binary 6
% 21.33/3.73 lits 26
% 21.33/3.73 lits eq 16
% 21.33/3.73 fd_pure 0
% 21.33/3.73 fd_pseudo 0
% 21.33/3.73 fd_cond 0
% 21.33/3.73 fd_pseudo_cond 0
% 21.33/3.73 AC symbols 1
% 21.33/3.73
% 21.33/3.73 ------ Schedule dynamic 5 is on
% 21.33/3.73
% 21.33/3.73 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 21.33/3.73
% 21.33/3.73
% 21.33/3.73 ------
% 21.33/3.73 Current options:
% 21.33/3.73 ------
% 21.33/3.73
% 21.33/3.73
% 21.33/3.73
% 21.33/3.73
% 21.33/3.73 ------ Proving...
% 21.33/3.73
% 21.33/3.73
% 21.33/3.73 % SZS status Theorem for theBenchmark.p
% 21.33/3.73
% 21.33/3.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.33/3.73
% 21.33/3.73
%------------------------------------------------------------------------------