TSTP Solution File: KLE002+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : KLE002+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n031.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 05:31:34 EDT 2023
% Result : Theorem 0.49s 1.15s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 19 unt; 0 def)
% Number of atoms : 59 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 25 ~; 13 |; 5 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn; 36 !; 6 ?)
% 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(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f13,conjecture,
! [X3,X4,X5] :
( leq(X3,X4)
=> leq(multiplication(X3,X5),multiplication(X4,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f14,negated_conjecture,
~ ! [X3,X4,X5] :
( leq(X3,X4)
=> leq(multiplication(X3,X5),multiplication(X4,X5)) ),
inference(negated_conjecture,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f16,plain,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
inference(rectify,[],[f14]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X0,X2),multiplication(X1,X2))
& leq(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f19,plain,
( ? [X0,X1,X2] :
( ~ leq(multiplication(X0,X2),multiplication(X1,X2))
& leq(X0,X1) )
=> ( ~ leq(multiplication(sK0,sK2),multiplication(sK1,sK2))
& leq(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
( ~ leq(multiplication(sK0,sK2),multiplication(sK1,sK2))
& leq(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f22,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f32,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
leq(sK0,sK1),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
~ leq(multiplication(sK0,sK2),multiplication(sK1,sK2)),
inference(cnf_transformation,[],[f20]) ).
cnf(c_49,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f21]) ).
cnf(c_50,plain,
addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f22]) ).
cnf(c_57,plain,
addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f29]) ).
cnf(c_60,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_61,plain,
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_62,negated_conjecture,
~ leq(multiplication(sK0,sK2),multiplication(sK1,sK2)),
inference(cnf_transformation,[],[f35]) ).
cnf(c_63,negated_conjecture,
leq(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
cnf(c_74,plain,
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
cnf(c_75,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(renaming,[status(thm)],[c_74]) ).
cnf(c_76,plain,
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
cnf(c_145,plain,
( addition(X0,X1) != X1
| multiplication(sK0,sK2) != X0
| multiplication(sK1,sK2) != X1 ),
inference(resolution_lifted,[status(thm)],[c_75,c_62]) ).
cnf(c_146,plain,
addition(multiplication(sK0,sK2),multiplication(sK1,sK2)) != multiplication(sK1,sK2),
inference(unflattening,[status(thm)],[c_145]) ).
cnf(c_150,plain,
( X0 != sK0
| X1 != sK1
| addition(X0,X1) = X1 ),
inference(resolution_lifted,[status(thm)],[c_76,c_63]) ).
cnf(c_151,plain,
addition(sK0,sK1) = sK1,
inference(unflattening,[status(thm)],[c_150]) ).
cnf(c_198,plain,
multiplication(addition(sK0,sK1),sK2) != multiplication(sK1,sK2),
inference(ac_demodulation,[status(thm)],[c_146,c_57,c_50,c_49]) ).
cnf(c_200,plain,
multiplication(sK1,sK2) != multiplication(sK1,sK2),
inference(light_normalisation,[status(thm)],[c_198,c_151]) ).
cnf(c_201,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE002+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n031.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 12:24:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.49/1.15 % SZS status Started for theBenchmark.p
% 0.49/1.15 % SZS status Theorem for theBenchmark.p
% 0.49/1.15
% 0.49/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.49/1.15
% 0.49/1.15 ------ iProver source info
% 0.49/1.15
% 0.49/1.15 git: date: 2023-05-31 18:12:56 +0000
% 0.49/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.49/1.15 git: non_committed_changes: false
% 0.49/1.15 git: last_make_outside_of_git: false
% 0.49/1.15
% 0.49/1.15 ------ Parsing...
% 0.49/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.49/1.15
% 0.49/1.15 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e
% 0.49/1.15
% 0.49/1.15 % SZS status Theorem for theBenchmark.p
% 0.49/1.15
% 0.49/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.49/1.15
% 0.49/1.15
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