TSTP Solution File: KLE040+2 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : KLE040+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 4.16s 1.20s
% Output : CNFRefutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 43 unt; 0 def)
% Number of atoms : 87 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 17 |; 4 &)
% ( 1 <=>; 2 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 104 ( 11 sgn; 47 !; 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',additive_idempotence) ).
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',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f13,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).
fof(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_left) ).
fof(f15,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X1)
=> leq(multiplication(star(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_left) ).
fof(f17,conjecture,
! [X3] :
( leq(star(X3),multiplication(star(X3),star(X3)))
& leq(multiplication(star(X3),star(X3)),star(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X3] :
( leq(star(X3),multiplication(star(X3),star(X3)))
& leq(multiplication(star(X3),star(X3)),star(X3)) ),
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] :
( leq(star(X0),multiplication(star(X0),star(X0)))
& leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(rectify,[],[f18]) ).
fof(f21,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
? [X0] :
( ~ leq(star(X0),multiplication(star(X0),star(X0)))
| ~ leq(multiplication(star(X0),star(X0)),star(X0)) ),
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] :
( ~ leq(star(X0),multiplication(star(X0),star(X0)))
| ~ leq(multiplication(star(X0),star(X0)),star(X0)) )
=> ( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
| ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
| ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[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(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
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(f40,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f41,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f42,plain,
! [X2,X0,X1] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f44,plain,
( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
| ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ),
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_55,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f33]) ).
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_62,plain,
leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f40]) ).
cnf(c_63,plain,
leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f41]) ).
cnf(c_64,plain,
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[],[f42]) ).
cnf(c_66,negated_conjecture,
( ~ leq(multiplication(star(sK0),star(sK0)),star(sK0))
| ~ leq(star(sK0),multiplication(star(sK0),star(sK0))) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_513,plain,
leq(X0,X0),
inference(superposition,[status(thm)],[c_52,c_60]) ).
cnf(c_524,plain,
addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_62,c_61]) ).
cnf(c_525,plain,
addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_63,c_61]) ).
cnf(c_526,plain,
addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(theory_normalisation,[status(thm)],[c_525,c_50,c_49]) ).
cnf(c_527,plain,
addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(theory_normalisation,[status(thm)],[c_524,c_50,c_49]) ).
cnf(c_583,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
cnf(c_698,plain,
( ~ leq(addition(X0,multiplication(X1,X2)),X2)
| leq(multiplication(star(X1),X0),X2) ),
inference(superposition,[status(thm)],[c_49,c_64]) ).
cnf(c_798,plain,
leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_583,c_60]) ).
cnf(c_817,plain,
leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_798]) ).
cnf(c_831,plain,
leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_817]) ).
cnf(c_845,plain,
leq(X0,addition(X1,addition(X0,X2))),
inference(superposition,[status(thm)],[c_49,c_831]) ).
cnf(c_5690,plain,
addition(one,star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_526,c_583]) ).
cnf(c_5720,plain,
leq(one,addition(X0,star(X1))),
inference(superposition,[status(thm)],[c_526,c_845]) ).
cnf(c_6818,plain,
leq(one,addition(star(X0),X1)),
inference(superposition,[status(thm)],[c_49,c_5720]) ).
cnf(c_6837,plain,
addition(one,addition(star(X0),X1)) = addition(star(X0),X1),
inference(superposition,[status(thm)],[c_6818,c_61]) ).
cnf(c_6838,plain,
addition(star(X0),multiplication(X0,star(X0))) = star(X0),
inference(demodulation,[status(thm)],[c_527,c_6837]) ).
cnf(c_6955,plain,
addition(multiplication(one,X0),multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(superposition,[status(thm)],[c_5690,c_57]) ).
cnf(c_7012,plain,
addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(light_normalisation,[status(thm)],[c_6955,c_55]) ).
cnf(c_7499,plain,
( ~ leq(star(X0),star(X0))
| leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(superposition,[status(thm)],[c_6838,c_698]) ).
cnf(c_7525,plain,
leq(multiplication(star(X0),star(X0)),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_7499,c_513]) ).
cnf(c_7546,plain,
~ leq(star(sK0),multiplication(star(sK0),star(sK0))),
inference(backward_subsumption_resolution,[status(thm)],[c_66,c_7525]) ).
cnf(c_8930,plain,
leq(X0,multiplication(star(X1),X0)),
inference(superposition,[status(thm)],[c_7012,c_60]) ).
cnf(c_9042,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_7546,c_8930]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE040+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n008.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 : Tue Aug 29 11:22:47 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
% 4.16/1.20 % SZS status Started for theBenchmark.p
% 4.16/1.20 % SZS status Theorem for theBenchmark.p
% 4.16/1.20
% 4.16/1.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 4.16/1.20
% 4.16/1.20 ------ iProver source info
% 4.16/1.20
% 4.16/1.20 git: date: 2023-05-31 18:12:56 +0000
% 4.16/1.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 4.16/1.20 git: non_committed_changes: false
% 4.16/1.20 git: last_make_outside_of_git: false
% 4.16/1.20
% 4.16/1.20 ------ Parsing...
% 4.16/1.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.16/1.20
% 4.16/1.20 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 4.16/1.20
% 4.16/1.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.16/1.20
% 4.16/1.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.16/1.20 ------ Proving...
% 4.16/1.20 ------ Problem Properties
% 4.16/1.20
% 4.16/1.20
% 4.16/1.20 clauses 18
% 4.16/1.20 conjectures 1
% 4.16/1.20 EPR 0
% 4.16/1.20 Horn 18
% 4.16/1.20 unary 13
% 4.16/1.20 binary 5
% 4.16/1.20 lits 23
% 4.16/1.20 lits eq 13
% 4.16/1.20 fd_pure 0
% 4.16/1.20 fd_pseudo 0
% 4.16/1.20 fd_cond 0
% 4.16/1.20 fd_pseudo_cond 0
% 4.16/1.20 AC symbols 1
% 4.16/1.20
% 4.16/1.20 ------ Schedule dynamic 5 is on
% 4.16/1.20
% 4.16/1.20 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.16/1.20
% 4.16/1.20
% 4.16/1.20 ------
% 4.16/1.20 Current options:
% 4.16/1.20 ------
% 4.16/1.20
% 4.16/1.20
% 4.16/1.20
% 4.16/1.20
% 4.16/1.20 ------ Proving...
% 4.16/1.20
% 4.16/1.20
% 4.16/1.20 % SZS status Theorem for theBenchmark.p
% 4.16/1.20
% 4.16/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.16/1.20
% 4.16/1.21
%------------------------------------------------------------------------------