TSTP Solution File: KLE082+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : KLE082+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.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 05:32:02 EDT 2023
% Result : Theorem 9.97s 2.15s
% Output : CNFRefutation 9.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 65 unt; 0 def)
% Number of atoms : 86 ( 85 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 25 ( 10 ~; 0 |; 11 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 118 ( 3 sgn; 54 !; 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',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f14,axiom,
! [X3,X4] : domain(multiplication(X3,X4)) = domain(multiplication(X3,domain(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f18,conjecture,
! [X3,X4] :
( ! [X5] :
( zero = multiplication(domain(X5),antidomain(X5))
& one = addition(domain(X5),antidomain(X5)) )
=> antidomain(multiplication(X3,domain(X4))) = addition(antidomain(multiplication(X3,X4)),antidomain(multiplication(X3,domain(X4)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X3,X4] :
( ! [X5] :
( zero = multiplication(domain(X5),antidomain(X5))
& one = addition(domain(X5),antidomain(X5)) )
=> antidomain(multiplication(X3,domain(X4))) = addition(antidomain(multiplication(X3,X4)),antidomain(multiplication(X3,domain(X4)))) ),
inference(negated_conjecture,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f22,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(rectify,[],[f14]) ).
fof(f25,plain,
~ ! [X0,X1] :
( ! [X2] :
( zero = multiplication(domain(X2),antidomain(X2))
& one = addition(domain(X2),antidomain(X2)) )
=> antidomain(multiplication(X0,domain(X1))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) ),
inference(rectify,[],[f19]) ).
fof(f26,plain,
? [X0,X1] :
( antidomain(multiplication(X0,domain(X1))) != addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1))))
& ! [X2] :
( zero = multiplication(domain(X2),antidomain(X2))
& one = addition(domain(X2),antidomain(X2)) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f27,plain,
( ? [X0,X1] :
( antidomain(multiplication(X0,domain(X1))) != addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1))))
& ! [X2] :
( zero = multiplication(domain(X2),antidomain(X2))
& one = addition(domain(X2),antidomain(X2)) ) )
=> ( antidomain(multiplication(sK0,domain(sK1))) != addition(antidomain(multiplication(sK0,sK1)),antidomain(multiplication(sK0,domain(sK1))))
& ! [X2] :
( zero = multiplication(domain(X2),antidomain(X2))
& one = addition(domain(X2),antidomain(X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( antidomain(multiplication(sK0,domain(sK1))) != addition(antidomain(multiplication(sK0,sK1)),antidomain(multiplication(sK0,domain(sK1))))
& ! [X2] :
( zero = multiplication(domain(X2),antidomain(X2))
& one = addition(domain(X2),antidomain(X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f26,f27]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f30,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f32,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f34,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f35,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f36,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f37,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f41,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X2] : one = addition(domain(X2),antidomain(X2)),
inference(cnf_transformation,[],[f28]) ).
fof(f46,plain,
! [X2] : zero = multiplication(domain(X2),antidomain(X2)),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
antidomain(multiplication(sK0,domain(sK1))) != addition(antidomain(multiplication(sK0,sK1)),antidomain(multiplication(sK0,domain(sK1)))),
inference(cnf_transformation,[],[f28]) ).
cnf(c_49,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f29]) ).
cnf(c_50,plain,
addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f30]) ).
cnf(c_51,plain,
addition(X0,zero) = X0,
inference(cnf_transformation,[],[f31]) ).
cnf(c_52,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[],[f32]) ).
cnf(c_54,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f34]) ).
cnf(c_55,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f35]) ).
cnf(c_56,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f36]) ).
cnf(c_57,plain,
addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f37]) ).
cnf(c_61,plain,
domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(cnf_transformation,[],[f41]) ).
cnf(c_65,negated_conjecture,
addition(antidomain(multiplication(sK0,sK1)),antidomain(multiplication(sK0,domain(sK1)))) != antidomain(multiplication(sK0,domain(sK1))),
inference(cnf_transformation,[],[f47]) ).
cnf(c_66,negated_conjecture,
multiplication(domain(X0),antidomain(X0)) = zero,
inference(cnf_transformation,[],[f46]) ).
cnf(c_67,negated_conjecture,
addition(domain(X0),antidomain(X0)) = one,
inference(cnf_transformation,[],[f45]) ).
cnf(c_205,plain,
addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_210,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
cnf(c_224,plain,
domain(multiplication(one,X0)) = domain(domain(X0)),
inference(superposition,[status(thm)],[c_55,c_61]) ).
cnf(c_229,plain,
multiplication(domain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = zero,
inference(superposition,[status(thm)],[c_61,c_66]) ).
cnf(c_232,plain,
domain(domain(X0)) = domain(X0),
inference(light_normalisation,[status(thm)],[c_224,c_55]) ).
cnf(c_322,plain,
addition(domain(X0),addition(X1,antidomain(X0))) = addition(X1,one),
inference(superposition,[status(thm)],[c_67,c_205]) ).
cnf(c_467,plain,
addition(domain(X0),antidomain(X0)) = addition(antidomain(X0),one),
inference(superposition,[status(thm)],[c_52,c_322]) ).
cnf(c_484,plain,
addition(domain(X0),antidomain(X0)) = addition(one,antidomain(X0)),
inference(theory_normalisation,[status(thm)],[c_467,c_50,c_49]) ).
cnf(c_485,plain,
addition(one,antidomain(X0)) = one,
inference(light_normalisation,[status(thm)],[c_484,c_67]) ).
cnf(c_705,plain,
addition(multiplication(X0,one),multiplication(X0,antidomain(X1))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_485,c_56]) ).
cnf(c_723,plain,
addition(X0,multiplication(X0,antidomain(X1))) = X0,
inference(light_normalisation,[status(thm)],[c_705,c_54]) ).
cnf(c_742,plain,
addition(multiplication(domain(X0),X1),multiplication(antidomain(X0),X1)) = multiplication(one,X1),
inference(superposition,[status(thm)],[c_67,c_57]) ).
cnf(c_857,plain,
addition(multiplication(domain(X0),X1),multiplication(antidomain(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_742,c_55]) ).
cnf(c_863,plain,
addition(zero,multiplication(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1))))) = antidomain(multiplication(X0,domain(X1))),
inference(superposition,[status(thm)],[c_229,c_857]) ).
cnf(c_869,plain,
addition(multiplication(domain(X0),X1),multiplication(antidomain(domain(X0)),X1)) = X1,
inference(superposition,[status(thm)],[c_232,c_857]) ).
cnf(c_5977,plain,
multiplication(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))),
inference(demodulation,[status(thm)],[c_863,c_210]) ).
cnf(c_6011,plain,
multiplication(antidomain(multiplication(one,X0)),antidomain(domain(X0))) = antidomain(domain(X0)),
inference(superposition,[status(thm)],[c_55,c_5977]) ).
cnf(c_6051,plain,
addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,X1)),
inference(superposition,[status(thm)],[c_5977,c_723]) ).
cnf(c_6059,plain,
multiplication(antidomain(X0),antidomain(domain(X0))) = antidomain(domain(X0)),
inference(light_normalisation,[status(thm)],[c_6011,c_55]) ).
cnf(c_6089,plain,
antidomain(multiplication(sK0,domain(sK1))) != antidomain(multiplication(sK0,sK1)),
inference(demodulation,[status(thm)],[c_65,c_6051]) ).
cnf(c_6138,plain,
addition(antidomain(X0),antidomain(domain(X0))) = antidomain(X0),
inference(superposition,[status(thm)],[c_6059,c_723]) ).
cnf(c_24115,plain,
addition(zero,multiplication(antidomain(domain(X0)),antidomain(X0))) = antidomain(X0),
inference(superposition,[status(thm)],[c_66,c_869]) ).
cnf(c_24252,plain,
multiplication(antidomain(domain(X0)),antidomain(X0)) = antidomain(X0),
inference(demodulation,[status(thm)],[c_24115,c_210]) ).
cnf(c_24334,plain,
addition(antidomain(domain(X0)),antidomain(X0)) = antidomain(domain(X0)),
inference(superposition,[status(thm)],[c_24252,c_723]) ).
cnf(c_24366,plain,
addition(antidomain(X0),antidomain(domain(X0))) = antidomain(domain(X0)),
inference(theory_normalisation,[status(thm)],[c_24334,c_50,c_49]) ).
cnf(c_24367,plain,
antidomain(domain(X0)) = antidomain(X0),
inference(light_normalisation,[status(thm)],[c_24366,c_6138]) ).
cnf(c_24424,plain,
antidomain(multiplication(X0,domain(X1))) = antidomain(domain(multiplication(X0,X1))),
inference(superposition,[status(thm)],[c_61,c_24367]) ).
cnf(c_25314,plain,
antidomain(multiplication(X0,domain(X1))) = antidomain(multiplication(X0,X1)),
inference(demodulation,[status(thm)],[c_24424,c_24367]) ).
cnf(c_25330,plain,
antidomain(multiplication(sK0,sK1)) != antidomain(multiplication(sK0,sK1)),
inference(demodulation,[status(thm)],[c_6089,c_25314]) ).
cnf(c_25338,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_25330]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE082+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n005.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 12:23:23 EDT 2023
% 0.13/0.35 % 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
% 9.97/2.15 % SZS status Started for theBenchmark.p
% 9.97/2.15 % SZS status Theorem for theBenchmark.p
% 9.97/2.15
% 9.97/2.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 9.97/2.15
% 9.97/2.15 ------ iProver source info
% 9.97/2.15
% 9.97/2.15 git: date: 2023-05-31 18:12:56 +0000
% 9.97/2.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 9.97/2.15 git: non_committed_changes: false
% 9.97/2.15 git: last_make_outside_of_git: false
% 9.97/2.15
% 9.97/2.15 ------ Parsing...
% 9.97/2.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 9.97/2.15
% 9.97/2.15 ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e
% 9.97/2.15
% 9.97/2.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 9.97/2.15
% 9.97/2.15 ------ Preprocessing... sf_s rm: 0 0s sf_e
% 9.97/2.15 ------ Proving...
% 9.97/2.15 ------ Problem Properties
% 9.97/2.15
% 9.97/2.15
% 9.97/2.15 clauses 19
% 9.97/2.15 conjectures 3
% 9.97/2.15 EPR 0
% 9.97/2.15 Horn 19
% 9.97/2.15 unary 19
% 9.97/2.15 binary 0
% 9.97/2.15 lits 19
% 9.97/2.15 lits eq 19
% 9.97/2.15 fd_pure 0
% 9.97/2.15 fd_pseudo 0
% 9.97/2.15 fd_cond 0
% 9.97/2.15 fd_pseudo_cond 0
% 9.97/2.15 AC symbols 1
% 9.97/2.15
% 9.97/2.15 ------ Schedule UEQ
% 9.97/2.15
% 9.97/2.15 ------ Option_UEQ Time Limit: 10.
% 9.97/2.15
% 9.97/2.15
% 9.97/2.15 ------
% 9.97/2.15 Current options:
% 9.97/2.15 ------
% 9.97/2.15
% 9.97/2.15
% 9.97/2.15
% 9.97/2.15
% 9.97/2.15 ------ Proving...
% 9.97/2.15
% 9.97/2.15
% 9.97/2.15 % SZS status Theorem for theBenchmark.p
% 9.97/2.15
% 9.97/2.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.97/2.15
% 9.97/2.15
%------------------------------------------------------------------------------