TSTP Solution File: REL012+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : REL012+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 13:40:42 EDT 2023
% Result : Theorem 166.07s 22.81s
% Output : CNFRefutation 166.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 14
% Syntax : Number of formulae : 104 ( 103 unt; 0 def)
% Number of atoms : 105 ( 104 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 155 ( 6 sgn; 49 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f3,axiom,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f4,axiom,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f14,conjecture,
! [X0,X1] : complement(X0) = join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] : complement(X0) = join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0)),
inference(negated_conjecture,[],[f14]) ).
fof(f16,plain,
? [X0,X1] : complement(X0) != join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0)),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( ? [X0,X1] : complement(X0) != join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0))
=> complement(sK0) != join(composition(complement(composition(sK0,sK1)),converse(sK1)),complement(sK0)) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
complement(sK0) != join(composition(complement(composition(sK0,sK1)),converse(sK1)),complement(sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17]) ).
fof(f19,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f23,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f26,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f28,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f29,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f32,plain,
complement(sK0) != join(composition(complement(composition(sK0,sK1)),converse(sK1)),complement(sK0)),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f31,f22]) ).
cnf(c_49,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f19]) ).
cnf(c_50,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f20]) ).
cnf(c_51,plain,
join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f21]) ).
cnf(c_52,plain,
composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f23]) ).
cnf(c_53,plain,
composition(X0,one) = X0,
inference(cnf_transformation,[],[f24]) ).
cnf(c_55,plain,
converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f26]) ).
cnf(c_56,plain,
join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
cnf(c_57,plain,
composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f28]) ).
cnf(c_58,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f29]) ).
cnf(c_59,plain,
join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f30]) ).
cnf(c_60,plain,
complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f33]) ).
cnf(c_61,negated_conjecture,
join(composition(complement(composition(sK0,sK1)),converse(sK1)),complement(sK0)) != complement(sK0),
inference(cnf_transformation,[],[f32]) ).
cnf(c_74,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(theory_normalisation,[status(thm)],[c_51,c_50,c_49]) ).
cnf(c_75,plain,
join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_58,c_50,c_49]) ).
cnf(c_76,negated_conjecture,
join(complement(sK0),composition(complement(composition(sK0,sK1)),converse(sK1))) != complement(sK0),
inference(theory_normalisation,[status(thm)],[c_61,c_50,c_49]) ).
cnf(c_105,plain,
complement(top) = zero,
inference(demodulation,[status(thm)],[c_60,c_59]) ).
cnf(c_176,plain,
join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_188,plain,
converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
cnf(c_216,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X1),complement(X0)))) = X0,
inference(superposition,[status(thm)],[c_49,c_74]) ).
cnf(c_218,plain,
join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_74]) ).
cnf(c_223,plain,
join(complement(X0),complement(join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1))))))) = join(complement(X0),X1),
inference(superposition,[status(thm)],[c_74,c_74]) ).
cnf(c_224,plain,
join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_218,c_50,c_49]) ).
cnf(c_225,plain,
join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_224,c_105]) ).
cnf(c_233,plain,
converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
cnf(c_251,plain,
composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
cnf(c_376,plain,
join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_188]) ).
cnf(c_493,plain,
join(complement(X0),composition(X1,complement(composition(converse(X1),X0)))) = complement(X0),
inference(superposition,[status(thm)],[c_55,c_75]) ).
cnf(c_679,plain,
composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_233]) ).
cnf(c_701,plain,
composition(converse(one),X0) = X0,
inference(demodulation,[status(thm)],[c_679,c_55]) ).
cnf(c_773,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_701,c_53]) ).
cnf(c_780,plain,
composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_701,c_251]) ).
cnf(c_781,plain,
composition(one,X0) = X0,
inference(demodulation,[status(thm)],[c_780,c_701]) ).
cnf(c_862,plain,
join(complement(X0),composition(one,complement(composition(one,X0)))) = complement(X0),
inference(superposition,[status(thm)],[c_773,c_75]) ).
cnf(c_869,plain,
join(complement(X0),complement(X0)) = complement(X0),
inference(demodulation,[status(thm)],[c_862,c_781]) ).
cnf(c_870,plain,
join(zero,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_225,c_869]) ).
cnf(c_1283,plain,
join(zero,zero) = zero,
inference(superposition,[status(thm)],[c_105,c_869]) ).
cnf(c_1431,plain,
join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_1283,c_50]) ).
cnf(c_1620,plain,
join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_870,c_1431]) ).
cnf(c_1627,plain,
complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_870,c_1620]) ).
cnf(c_1635,plain,
join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_1620,c_49]) ).
cnf(c_1685,plain,
join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_1627,c_869]) ).
cnf(c_1713,plain,
join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_1685,c_50]) ).
cnf(c_1718,plain,
join(X0,join(X1,X0)) = join(X1,X0),
inference(superposition,[status(thm)],[c_1685,c_176]) ).
cnf(c_1963,plain,
join(X0,top) = top,
inference(superposition,[status(thm)],[c_59,c_1713]) ).
cnf(c_2009,plain,
join(top,X0) = top,
inference(superposition,[status(thm)],[c_1963,c_49]) ).
cnf(c_2030,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_2009,c_376]) ).
cnf(c_2034,plain,
join(X0,converse(complement(converse(X0)))) = top,
inference(demodulation,[status(thm)],[c_376,c_2030]) ).
cnf(c_2189,plain,
join(complement(join(complement(X0),X1)),X0) = X0,
inference(superposition,[status(thm)],[c_216,c_1713]) ).
cnf(c_2195,plain,
join(X0,complement(join(complement(X0),X1))) = X0,
inference(theory_normalisation,[status(thm)],[c_2189,c_50,c_49]) ).
cnf(c_3185,plain,
join(X0,complement(join(X1,complement(X0)))) = X0,
inference(superposition,[status(thm)],[c_1718,c_2195]) ).
cnf(c_3251,plain,
join(complement(X0),complement(join(X1,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_1627,c_3185]) ).
cnf(c_3381,plain,
join(complement(X0),complement(join(complement(join(complement(X0),X1)),join(complement(X0),complement(X1))))) = join(complement(X0),X1),
inference(demodulation,[status(thm)],[c_223,c_1627]) ).
cnf(c_3382,plain,
join(complement(X0),complement(join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))))) = join(complement(X0),X1),
inference(theory_normalisation,[status(thm)],[c_3381,c_50,c_49]) ).
cnf(c_3383,plain,
join(complement(X0),complement(join(complement(X0),complement(X1)))) = join(complement(X0),X1),
inference(demodulation,[status(thm)],[c_3382,c_3251]) ).
cnf(c_3395,plain,
join(X0,complement(join(X0,complement(X1)))) = join(X0,X1),
inference(superposition,[status(thm)],[c_1627,c_3383]) ).
cnf(c_22837,plain,
join(X0,complement(join(complement(X1),X0))) = join(X0,X1),
inference(superposition,[status(thm)],[c_49,c_3395]) ).
cnf(c_22855,plain,
join(X0,complement(join(X0,X1))) = join(X0,complement(X1)),
inference(superposition,[status(thm)],[c_1627,c_3395]) ).
cnf(c_24554,plain,
join(converse(complement(converse(complement(X0)))),complement(top)) = join(converse(complement(converse(complement(X0)))),X0),
inference(superposition,[status(thm)],[c_2034,c_22837]) ).
cnf(c_24711,plain,
join(complement(top),converse(complement(converse(complement(X0))))) = join(X0,converse(complement(converse(complement(X0))))),
inference(theory_normalisation,[status(thm)],[c_24554,c_50,c_49]) ).
cnf(c_24712,plain,
join(X0,converse(complement(converse(complement(X0))))) = converse(complement(converse(complement(X0)))),
inference(demodulation,[status(thm)],[c_24711,c_105,c_1620]) ).
cnf(c_44980,plain,
join(X0,complement(converse(complement(converse(X0))))) = join(X0,complement(top)),
inference(superposition,[status(thm)],[c_2034,c_22855]) ).
cnf(c_45183,plain,
join(X0,complement(converse(complement(converse(X0))))) = X0,
inference(demodulation,[status(thm)],[c_44980,c_105,c_1635]) ).
cnf(c_46407,plain,
join(X0,converse(complement(converse(complement(converse(converse(X0))))))) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_45183,c_188]) ).
cnf(c_46473,plain,
converse(complement(converse(complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_46407,c_55,c_24712]) ).
cnf(c_46983,plain,
converse(complement(converse(X0))) = complement(X0),
inference(superposition,[status(thm)],[c_1627,c_46473]) ).
cnf(c_47255,plain,
converse(composition(X0,complement(converse(X1)))) = composition(complement(X1),converse(X0)),
inference(superposition,[status(thm)],[c_46983,c_57]) ).
cnf(c_47256,plain,
converse(join(complement(converse(X0)),X1)) = join(complement(X0),converse(X1)),
inference(superposition,[status(thm)],[c_46983,c_56]) ).
cnf(c_47257,plain,
complement(converse(X0)) = converse(complement(X0)),
inference(superposition,[status(thm)],[c_46983,c_55]) ).
cnf(c_94298,plain,
composition(complement(composition(converse(X0),X1)),converse(X2)) = converse(composition(X2,complement(composition(converse(X1),X0)))),
inference(superposition,[status(thm)],[c_233,c_47255]) ).
cnf(c_95160,plain,
join(complement(X0),converse(composition(X1,complement(composition(converse(X1),converse(X0)))))) = converse(complement(converse(X0))),
inference(superposition,[status(thm)],[c_493,c_47256]) ).
cnf(c_95400,plain,
join(complement(X0),composition(complement(composition(X0,X1)),converse(X1))) = complement(X0),
inference(demodulation,[status(thm)],[c_95160,c_55,c_47257,c_94298]) ).
cnf(c_95430,plain,
complement(sK0) != complement(sK0),
inference(demodulation,[status(thm)],[c_76,c_95400]) ).
cnf(c_95431,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_95430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL012+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 19:36:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 166.07/22.81 % SZS status Started for theBenchmark.p
% 166.07/22.81 % SZS status Theorem for theBenchmark.p
% 166.07/22.81
% 166.07/22.81 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 166.07/22.81
% 166.07/22.81 ------ iProver source info
% 166.07/22.81
% 166.07/22.81 git: date: 2023-05-31 18:12:56 +0000
% 166.07/22.81 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 166.07/22.81 git: non_committed_changes: false
% 166.07/22.81 git: last_make_outside_of_git: false
% 166.07/22.81
% 166.07/22.81 ------ Parsing...
% 166.07/22.81 ------ Clausification by vclausify_rel & Parsing by iProver...
% 166.07/22.81
% 166.07/22.81 ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e
% 166.07/22.81
% 166.07/22.81 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 166.07/22.81
% 166.07/22.81 ------ Preprocessing... sf_s rm: 0 0s sf_e
% 166.07/22.81 ------ Proving...
% 166.07/22.81 ------ Problem Properties
% 166.07/22.81
% 166.07/22.81
% 166.07/22.81 clauses 13
% 166.07/22.81 conjectures 1
% 166.07/22.81 EPR 0
% 166.07/22.81 Horn 13
% 166.07/22.81 unary 13
% 166.07/22.81 binary 0
% 166.07/22.81 lits 13
% 166.07/22.81 lits eq 13
% 166.07/22.81 fd_pure 0
% 166.07/22.81 fd_pseudo 0
% 166.07/22.81 fd_cond 0
% 166.07/22.81 fd_pseudo_cond 0
% 166.07/22.81 AC symbols 1
% 166.07/22.81
% 166.07/22.81 ------ Input Options Time Limit: Unbounded
% 166.07/22.81
% 166.07/22.81
% 166.07/22.81 ------
% 166.07/22.81 Current options:
% 166.07/22.81 ------
% 166.07/22.81
% 166.07/22.81
% 166.07/22.81
% 166.07/22.81
% 166.07/22.81 ------ Proving...
% 166.07/22.81
% 166.07/22.81
% 166.07/22.81 % SZS status Theorem for theBenchmark.p
% 166.07/22.81
% 166.07/22.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 166.07/22.81
% 166.07/22.82
%------------------------------------------------------------------------------