TSTP Solution File: REL008+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL008+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 19:53:30 EDT 2022
% Result : Theorem 0.86s 1.13s
% Output : Refutation 0.86s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL008+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 12:06:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.00 ============================== Prover9 ===============================
% 0.71/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.00 Process 31979 was started by sandbox2 on n012.cluster.edu,
% 0.71/1.00 Fri Jul 8 12:07:00 2022
% 0.71/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31826_n012.cluster.edu".
% 0.71/1.00 ============================== end of head ===========================
% 0.71/1.00
% 0.71/1.00 ============================== INPUT =================================
% 0.71/1.00
% 0.71/1.00 % Reading from file /tmp/Prover9_31826_n012.cluster.edu
% 0.71/1.00
% 0.71/1.00 set(prolog_style_variables).
% 0.71/1.00 set(auto2).
% 0.71/1.00 % set(auto2) -> set(auto).
% 0.71/1.00 % set(auto) -> set(auto_inference).
% 0.71/1.00 % set(auto) -> set(auto_setup).
% 0.71/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.00 % set(auto) -> set(auto_limits).
% 0.71/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.00 % set(auto) -> set(auto_denials).
% 0.71/1.00 % set(auto) -> set(auto_process).
% 0.71/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.00 % set(auto2) -> assign(stats, some).
% 0.71/1.00 % set(auto2) -> clear(echo_input).
% 0.71/1.00 % set(auto2) -> set(quiet).
% 0.71/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.00 % set(auto2) -> clear(print_given).
% 0.71/1.00 assign(lrs_ticks,-1).
% 0.71/1.00 assign(sos_limit,10000).
% 0.71/1.00 assign(order,kbo).
% 0.71/1.00 set(lex_order_vars).
% 0.71/1.00 clear(print_given).
% 0.71/1.00
% 0.71/1.00 % formulas(sos). % not echoed (14 formulas)
% 0.71/1.00
% 0.71/1.00 ============================== end of input ==========================
% 0.71/1.00
% 0.71/1.00 % From the command line: assign(max_seconds, 300).
% 0.71/1.00
% 0.71/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.00
% 0.71/1.00 % Formulas that are not ordinary clauses:
% 0.71/1.00 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 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].
% 0.71/1.00 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].
% 0.71/1.00 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].
% 0.71/1.00 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].
% 0.71/1.00 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 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].
% 0.71/1.00 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 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].
% 0.71/1.00 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.00 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 14 -(all X0 all X1 all X2 composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.86/1.13
% 0.86/1.13 ============================== end of process non-clausal formulas ===
% 0.86/1.13
% 0.86/1.13 ============================== PROCESS INITIAL CLAUSES ===============
% 0.86/1.13
% 0.86/1.13 ============================== PREDICATE ELIMINATION =================
% 0.86/1.13
% 0.86/1.13 ============================== end predicate elimination =============
% 0.86/1.13
% 0.86/1.13 Auto_denials:
% 0.86/1.13 % copying label goals to answer in negative clause
% 0.86/1.13
% 0.86/1.13 Term ordering decisions:
% 0.86/1.13 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.
% 0.86/1.13
% 0.86/1.13 ============================== end of process initial clauses ========
% 0.86/1.13
% 0.86/1.13 ============================== CLAUSES FOR SEARCH ====================
% 0.86/1.13
% 0.86/1.13 ============================== end of clauses for search =============
% 0.86/1.13
% 0.86/1.13 ============================== SEARCH ================================
% 0.86/1.13
% 0.86/1.13 % Starting search at 0.01 seconds.
% 0.86/1.13
% 0.86/1.13 ============================== PROOF =================================
% 0.86/1.13 % SZS status Theorem
% 0.86/1.13 % SZS output start Refutation
% 0.86/1.13
% 0.86/1.13 % Proof 1 at 0.14 (+ 0.01) seconds: goals.
% 0.86/1.13 % Length of proof is 21.
% 0.86/1.13 % Level of proof is 6.
% 0.86/1.13 % Maximum clause weight is 17.000.
% 0.86/1.13 % Given clauses 125.
% 0.86/1.13
% 0.86/1.13 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 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].
% 0.86/1.13 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 14 -(all X0 all X1 all X2 composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.86/1.13 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 0.86/1.13 19 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 0.86/1.13 21 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 0.86/1.13 22 join(converse(A),converse(B)) = converse(join(A,B)). [copy(21),flip(a)].
% 0.86/1.13 23 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 0.86/1.13 24 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(23),flip(a)].
% 0.86/1.13 28 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 0.86/1.13 29 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(28),flip(a)].
% 0.86/1.13 34 composition(c1,join(c2,c3)) != join(composition(c1,c2),composition(c1,c3)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 0.86/1.13 35 join(composition(c1,c2),composition(c1,c3)) != composition(c1,join(c2,c3)) # answer(goals). [copy(34),flip(a)].
% 0.86/1.13 39 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),24(a,1,2)),flip(a)].
% 0.86/1.13 43 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(24(a,1),29(a,1,1)),rewrite([19(7)])].
% 0.86/1.13 74 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)). [para(39(a,1),22(a,1,1)),rewrite([19(7)]),flip(a)].
% 0.86/1.13 676 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(43(a,1),74(a,1,1)),rewrite([22(3),24(4),16(4),16(4),16(6)]),flip(a)].
% 0.86/1.13 677 $F # answer(goals). [resolve(676,a,35,a)].
% 0.86/1.13
% 0.86/1.13 % SZS output end Refutation
% 0.86/1.13 ============================== end of proof ==========================
% 0.86/1.13
% 0.86/1.13 ============================== STATISTICS ============================
% 0.86/1.13
% 0.86/1.13 Given=125. Generated=4263. Kept=655. proofs=1.
% 0.86/1.13 Usable=99. Sos=408. Demods=494. Limbo=5, Disabled=156. Hints=0.
% 0.86/1.13 Megabytes=0.84.
% 0.86/1.13 User_CPU=0.14, System_CPU=0.01, Wall_clock=0.
% 0.86/1.13
% 0.86/1.13 ============================== end of statistics =====================
% 0.86/1.13
% 0.86/1.13 ============================== end of search =========================
% 0.86/1.13
% 0.86/1.13 THEOREM PROVED
% 0.86/1.13 % SZS status Theorem
% 0.86/1.13
% 0.86/1.13 Exiting with 1 proof.
% 0.86/1.13
% 0.86/1.13 Process 31979 exit (max_proofs) Fri Jul 8 12:07:00 2022
% 0.86/1.13 Prover9 interrupted
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