TSTP Solution File: REL046+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL046+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 : 600s
% DateTime : Mon Jul 18 19:54:30 EDT 2022
% Result : Theorem 0.97s 1.27s
% Output : Refutation 0.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL046+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 10:39:13 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.44/1.00 ============================== Prover9 ===============================
% 0.44/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.00 Process 29002 was started by sandbox2 on n020.cluster.edu,
% 0.44/1.00 Fri Jul 8 10:39:14 2022
% 0.44/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28833_n020.cluster.edu".
% 0.44/1.00 ============================== end of head ===========================
% 0.44/1.00
% 0.44/1.00 ============================== INPUT =================================
% 0.44/1.00
% 0.44/1.00 % Reading from file /tmp/Prover9_28833_n020.cluster.edu
% 0.44/1.00
% 0.44/1.00 set(prolog_style_variables).
% 0.44/1.00 set(auto2).
% 0.44/1.00 % set(auto2) -> set(auto).
% 0.44/1.00 % set(auto) -> set(auto_inference).
% 0.44/1.00 % set(auto) -> set(auto_setup).
% 0.44/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.00 % set(auto) -> set(auto_limits).
% 0.44/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.00 % set(auto) -> set(auto_denials).
% 0.44/1.00 % set(auto) -> set(auto_process).
% 0.44/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.00 % set(auto2) -> assign(stats, some).
% 0.44/1.00 % set(auto2) -> clear(echo_input).
% 0.44/1.00 % set(auto2) -> set(quiet).
% 0.44/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.00 % set(auto2) -> clear(print_given).
% 0.44/1.00 assign(lrs_ticks,-1).
% 0.44/1.00 assign(sos_limit,10000).
% 0.44/1.00 assign(order,kbo).
% 0.44/1.00 set(lex_order_vars).
% 0.44/1.00 clear(print_given).
% 0.44/1.00
% 0.44/1.00 % formulas(sos). % not echoed (14 formulas)
% 0.44/1.00
% 0.44/1.00 ============================== end of input ==========================
% 0.44/1.00
% 0.44/1.00 % From the command line: assign(max_seconds, 300).
% 0.44/1.00
% 0.44/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.00
% 0.44/1.00 % Formulas that are not ordinary clauses:
% 0.44/1.00 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 14 -(all X0 all X1 all X2 (join(X0,meet(X1,X2)) = meet(X1,X2) -> join(X0,X1) = X1 & join(X0,X2) = X2)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.97/1.27
% 0.97/1.27 ============================== end of process non-clausal formulas ===
% 0.97/1.27
% 0.97/1.27 ============================== PROCESS INITIAL CLAUSES ===============
% 0.97/1.27
% 0.97/1.27 ============================== PREDICATE ELIMINATION =================
% 0.97/1.27
% 0.97/1.27 ============================== end predicate elimination =============
% 0.97/1.27
% 0.97/1.27 Auto_denials:
% 0.97/1.27 % copying label goals to answer in negative clause
% 0.97/1.27
% 0.97/1.27 Term ordering decisions:
% 0.97/1.27 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. c3=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 0.97/1.27
% 0.97/1.27 ============================== end of process initial clauses ========
% 0.97/1.27
% 0.97/1.27 ============================== CLAUSES FOR SEARCH ====================
% 0.97/1.27
% 0.97/1.27 ============================== end of clauses for search =============
% 0.97/1.27
% 0.97/1.27 ============================== SEARCH ================================
% 0.97/1.27
% 0.97/1.27 % Starting search at 0.01 seconds.
% 0.97/1.27
% 0.97/1.27 ============================== PROOF =================================
% 0.97/1.27 % SZS status Theorem
% 0.97/1.27 % SZS output start Refutation
% 0.97/1.27
% 0.97/1.27 % Proof 1 at 0.27 (+ 0.01) seconds: goals.
% 0.97/1.27 % Length of proof is 76.
% 0.97/1.27 % Level of proof is 22.
% 0.97/1.27 % Maximum clause weight is 21.000.
% 0.97/1.27 % Given clauses 243.
% 0.97/1.27
% 0.97/1.27 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 14 -(all X0 all X1 all X2 (join(X0,meet(X1,X2)) = meet(X1,X2) -> join(X0,X1) = X1 & join(X0,X2) = X2)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.97/1.27 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 0.97/1.27 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 0.97/1.27 17 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 0.97/1.27 18 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 0.97/1.27 19 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 0.97/1.27 20 meet(c2,c3) = join(c1,meet(c2,c3)) # label(goals) # label(negated_conjecture). [clausify(14)].
% 0.97/1.27 21 join(c1,meet(c2,c3)) = meet(c2,c3). [copy(20),flip(a)].
% 0.97/1.27 22 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 0.97/1.27 25 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 0.97/1.27 26 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(25),flip(a)].
% 0.97/1.27 27 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 0.97/1.27 28 join(A,join(B,C)) = join(C,join(A,B)). [copy(27),rewrite([19(2)]),flip(a)].
% 0.97/1.27 29 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 0.97/1.27 32 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 0.97/1.27 33 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(32),rewrite([19(7)]),flip(a)].
% 0.97/1.27 34 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 0.97/1.27 35 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(34),rewrite([19(6),19(8)]),rewrite([19(6)])].
% 0.97/1.27 36 join(c1,c2) != c2 | join(c1,c3) != c3 # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 0.97/1.27 37 join(c1,complement(join(complement(c2),complement(c3)))) = complement(join(complement(c2),complement(c3))). [back_rewrite(21),rewrite([22(4),22(11)])].
% 0.97/1.27 38 complement(top) = zero. [back_rewrite(18),rewrite([22(2),17(4)])].
% 0.97/1.27 41 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),26(a,1,2)),flip(a)].
% 0.97/1.27 42 join(A,join(B,complement(A))) = join(B,top). [para(17(a,1),28(a,2,2)),rewrite([19(2)])].
% 0.97/1.27 43 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),29(a,1,1)),flip(a)].
% 0.97/1.27 54 join(zero,complement(join(complement(A),complement(A)))) = A. [para(17(a,1),35(a,1,1,1)),rewrite([38(2)])].
% 0.97/1.27 58 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(35(a,1),35(a,1,2,1)),rewrite([19(10)])].
% 0.97/1.27 63 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(38(a,1),35(a,1,2,1,1))].
% 0.97/1.27 76 composition(converse(one),A) = A. [para(15(a,1),41(a,1,1)),rewrite([16(2)]),flip(a)].
% 0.97/1.27 80 join(A,join(B,join(C,complement(A)))) = join(B,join(C,top)). [para(42(a,1),28(a,2,2)),rewrite([19(3),28(3,R),19(2),28(7,R),19(6)])].
% 0.97/1.27 82 join(top,c1) = top. [para(37(a,1),42(a,1,2)),rewrite([17(12),19(4)]),flip(a)].
% 0.97/1.27 83 converse(one) = one. [para(76(a,1),15(a,1)),flip(a)].
% 0.97/1.27 87 join(complement(A),complement(composition(one,A))) = complement(A). [para(76(a,1),33(a,1,2))].
% 0.97/1.27 88 composition(one,A) = A. [para(76(a,1),43(a,2)),rewrite([83(2),43(4)])].
% 0.97/1.27 89 join(complement(A),complement(A)) = complement(A). [back_rewrite(87),rewrite([88(3)])].
% 0.97/1.27 90 join(zero,complement(complement(A))) = A. [back_rewrite(54),rewrite([89(4)])].
% 0.97/1.27 95 join(top,complement(A)) = top. [para(89(a,1),42(a,1,2)),rewrite([17(2),19(4)]),flip(a)].
% 0.97/1.27 96 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(63),rewrite([95(3),38(2)])].
% 0.97/1.27 97 join(top,top) = join(A,top). [para(95(a,1),42(a,1,2)),flip(a)].
% 0.97/1.27 108 join(A,top) = join(B,top). [para(97(a,1),42(a,2)),rewrite([95(3)])].
% 0.97/1.27 109 join(A,top) = c_0. [new_symbol(108)].
% 0.97/1.27 111 join(A,join(B,join(C,complement(A)))) = join(B,c_0). [back_rewrite(80),rewrite([109(6)])].
% 0.97/1.27 112 join(A,join(B,complement(A))) = c_0. [back_rewrite(42),rewrite([109(5)])].
% 0.97/1.27 117 c_0 = top. [para(37(a,1),112(a,1,2)),rewrite([17(12)]),flip(a)].
% 0.97/1.27 118 join(A,join(B,complement(A))) = top. [back_rewrite(112),rewrite([117(4)])].
% 0.97/1.27 119 join(A,join(B,join(C,complement(A)))) = top. [back_rewrite(111),rewrite([117(5),109(6),117(5)])].
% 0.97/1.27 120 join(A,top) = top. [back_rewrite(109),rewrite([117(3)])].
% 0.97/1.27 145 join(zero,complement(A)) = complement(A). [para(90(a,1),96(a,1,2,1))].
% 0.97/1.27 146 complement(complement(A)) = A. [back_rewrite(96),rewrite([145(4),145(4)])].
% 0.97/1.27 153 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(146(a,1),35(a,1,1,1,2)),rewrite([146(5),19(4)])].
% 0.97/1.27 155 join(A,A) = A. [para(146(a,1),89(a,1,1)),rewrite([146(2),146(3)])].
% 0.97/1.27 159 join(A,join(A,B)) = join(A,B). [para(155(a,1),28(a,1)),rewrite([19(3),28(4,R),19(3),28(3,R),155(2)]),flip(a)].
% 0.97/1.27 160 join(A,complement(join(B,complement(A)))) = A. [para(35(a,1),159(a,1,2)),rewrite([19(4),35(12)])].
% 0.97/1.27 174 join(complement(A),complement(join(A,B))) = complement(A). [para(146(a,1),160(a,1,2,1,2)),rewrite([19(2)])].
% 0.97/1.27 185 join(complement(c1),join(complement(c2),complement(c3))) = complement(c1). [para(37(a,1),174(a,1,2,1)),rewrite([146(9)])].
% 0.97/1.27 298 join(A,complement(join(complement(A),complement(B)))) = A. [para(58(a,1),174(a,1,2,1)),rewrite([146(2),19(3),146(7)])].
% 0.97/1.27 593 join(A,join(complement(A),complement(B))) = top. [para(298(a,1),118(a,1,2)),rewrite([19(4)])].
% 0.97/1.27 595 join(A,join(B,join(complement(A),complement(C)))) = top. [para(593(a,1),28(a,2,2)),rewrite([19(4),120(7)])].
% 0.97/1.27 985 join(c3,complement(c1)) = top. [para(185(a,1),119(a,1,2))].
% 0.97/1.27 987 complement(join(complement(c1),complement(c3))) = c1. [para(985(a,1),35(a,1,1,1)),rewrite([38(2),19(6),145(8)])].
% 0.97/1.27 990 join(complement(c1),complement(c3)) = complement(c1). [para(985(a,1),58(a,1,2,1,1)),rewrite([19(8),987(9),82(5),38(4),19(4),145(4),19(7)]),flip(a)].
% 0.97/1.27 1029 join(c1,c3) = c3. [para(990(a,1),160(a,1,2,1)),rewrite([146(4),19(3)])].
% 0.97/1.27 1034 join(c1,c2) != c2 # answer(goals). [back_rewrite(36),rewrite([1029(8)]),xx(b)].
% 0.97/1.27 1883 join(c2,complement(c1)) = top. [para(185(a,1),595(a,1,2))].
% 0.97/1.27 1954 complement(join(c1,c2)) = complement(c2). [para(1883(a,1),153(a,1,2,1)),rewrite([38(6),19(6),145(6)])].
% 0.97/1.27 1969 $F # answer(goals). [para(1954(a,1),35(a,1,1,1,2)),rewrite([1954(9),35(10)]),flip(a),unit_del(a,1034)].
% 0.97/1.27
% 0.97/1.27 % SZS output end Refutation
% 0.97/1.27 ============================== end of proof ==========================
% 0.97/1.27
% 0.97/1.27 ============================== STATISTICS ============================
% 0.97/1.27
% 0.97/1.27 Given=243. Generated=13350. Kept=1947. proofs=1.
% 0.97/1.27 Usable=191. Sos=1480. Demods=1573. Limbo=1, Disabled=290. Hints=0.
% 0.97/1.27 Megabytes=2.64.
% 0.97/1.27 User_CPU=0.27, System_CPU=0.01, Wall_clock=0.
% 0.97/1.27
% 0.97/1.27 ============================== end of statistics =====================
% 0.97/1.27
% 0.97/1.27 ============================== end of search =========================
% 0.97/1.27
% 0.97/1.27 THEOREM PROVED
% 0.97/1.27 % SZS status Theorem
% 0.97/1.27
% 0.97/1.27 Exiting with 1 proof.
% 0.97/1.27
% 0.97/1.27 Process 29002 exit (max_proofs) Fri Jul 8 10:39:14 2022
% 0.97/1.27 Prover9 interrupted
%------------------------------------------------------------------------------