TSTP Solution File: GRP715+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP715+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% 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 : 600s
% DateTime : Sat Jul 16 11:20:46 EDT 2022
% Result : Theorem 1.59s 1.90s
% Output : Refutation 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP715+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 11:02:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.67/0.97 ============================== Prover9 ===============================
% 0.67/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.97 Process 32359 was started by sandbox on n005.cluster.edu,
% 0.67/0.97 Mon Jun 13 11:02:24 2022
% 0.67/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32205_n005.cluster.edu".
% 0.67/0.97 ============================== end of head ===========================
% 0.67/0.97
% 0.67/0.97 ============================== INPUT =================================
% 0.67/0.97
% 0.67/0.97 % Reading from file /tmp/Prover9_32205_n005.cluster.edu
% 0.67/0.97
% 0.67/0.97 set(prolog_style_variables).
% 0.67/0.97 set(auto2).
% 0.67/0.97 % set(auto2) -> set(auto).
% 0.67/0.97 % set(auto) -> set(auto_inference).
% 0.67/0.97 % set(auto) -> set(auto_setup).
% 0.67/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.97 % set(auto) -> set(auto_limits).
% 0.67/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.97 % set(auto) -> set(auto_denials).
% 0.67/0.97 % set(auto) -> set(auto_process).
% 0.67/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.97 % set(auto2) -> assign(stats, some).
% 0.67/0.97 % set(auto2) -> clear(echo_input).
% 0.67/0.97 % set(auto2) -> set(quiet).
% 0.67/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.97 % set(auto2) -> clear(print_given).
% 0.67/0.97 assign(lrs_ticks,-1).
% 0.67/0.97 assign(sos_limit,10000).
% 0.67/0.97 assign(order,kbo).
% 0.67/0.97 set(lex_order_vars).
% 0.67/0.97 clear(print_given).
% 0.67/0.97
% 0.67/0.97 % formulas(sos). % not echoed (12 formulas)
% 0.67/0.97
% 0.67/0.97 ============================== end of input ==========================
% 0.67/0.97
% 0.67/0.97 % From the command line: assign(max_seconds, 300).
% 0.67/0.97
% 0.67/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.97
% 0.67/0.97 % Formulas that are not ordinary clauses:
% 0.67/0.97 1 (all C all B all A plus(plus(A,B),C) = plus(A,plus(B,C))) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 2 (all B all A plus(A,B) = plus(B,A)) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 3 (all A plus(A,op_0) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 4 (all A plus(A,minus(A)) = op_0) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 5 (all C all B all A mult(A,plus(B,C)) = plus(mult(A,B),mult(A,C))) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 6 (all C all B all A mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B))) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 7 (all B all A mult(A,mult(B,B)) = mult(mult(A,B),B)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 8 (all A mult(A,unit) = A) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 9 (all A mult(unit,A) = A) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 10 -(all X0 (mult(mult(X0,op_a),op_b) = X0 & mult(mult(X0,op_b),op_a) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.67/0.97
% 0.67/0.97 ============================== end of process non-clausal formulas ===
% 0.67/0.97
% 0.67/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.67/0.97
% 0.67/0.97 ============================== PREDICATE ELIMINATION =================
% 0.67/0.97
% 0.67/0.97 ============================== end predicate elimination =============
% 0.67/0.97
% 0.67/0.97 Auto_denials:
% 0.67/0.97 % copying label goals to answer in negative clause
% 0.67/0.97
% 0.67/0.97 Term ordering decisions:
% 0.67/0.97
% 0.67/0.97 % Assigning unary symbol minus kb_weight 0 and highest precedence (9).
% 0.67/0.97 Function symbol KB weights: unit=1. op_0=1. op_a=1. op_b=1. c1=1. mult=1. plus=1. minus=0.
% 0.67/0.97
% 0.67/0.97 ============================== end of process initial clauses ========
% 0.67/0.97
% 0.67/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.67/0.97
% 0.67/0.97 ============================== end of clauses for search =============
% 0.67/0.97
% 0.67/0.97 ============================== SEARCH ================================
% 1.59/1.90
% 1.59/1.90 % Starting search at 0.01 seconds.
% 1.59/1.90
% 1.59/1.90 Low Water (keep): wt=34.000, iters=4138
% 1.59/1.90
% 1.59/1.90 Low Water (keep): wt=33.000, iters=4100
% 1.59/1.90
% 1.59/1.90 Low Water (keep): wt=29.000, iters=3369
% 1.59/1.90
% 1.59/1.90 ============================== PROOF =================================
% 1.59/1.90 % SZS status Theorem
% 1.59/1.90 % SZS output start Refutation
% 1.59/1.90
% 1.59/1.90 % Proof 1 at 0.93 (+ 0.02) seconds: goals.
% 1.59/1.90 % Length of proof is 42.
% 1.59/1.90 % Level of proof is 11.
% 1.59/1.90 % Maximum clause weight is 19.000.
% 1.59/1.90 % Given clauses 272.
% 1.59/1.90
% 1.59/1.90 6 (all C all B all A mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B))) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.90 7 (all B all A mult(A,mult(B,B)) = mult(mult(A,B),B)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.90 8 (all A mult(A,unit) = A) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.90 9 (all A mult(unit,A) = A) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.90 10 -(all X0 (mult(mult(X0,op_a),op_b) = X0 & mult(mult(X0,op_b),op_a) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.59/1.90 12 mult(A,unit) = A # label(f08) # label(axiom). [clausify(8)].
% 1.59/1.90 13 mult(unit,A) = A # label(f09) # label(axiom). [clausify(9)].
% 1.59/1.90 14 mult(op_a,op_b) = unit # label(f10) # label(axiom). [assumption].
% 1.59/1.90 15 mult(op_b,op_a) = unit # label(f11) # label(axiom). [assumption].
% 1.59/1.90 20 mult(mult(A,B),B) = mult(A,mult(B,B)) # label(f07) # label(axiom). [clausify(7)].
% 1.59/1.90 23 mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) # label(f06) # label(axiom). [clausify(6)].
% 1.59/1.90 24 mult(mult(c1,op_a),op_b) != c1 | mult(mult(c1,op_b),op_a) != c1 # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)].
% 1.59/1.90 26 mult(op_a,mult(op_b,op_b)) = op_b. [para(14(a,1),20(a,1,1)),rewrite([13(3)]),flip(a)].
% 1.59/1.90 27 mult(op_b,mult(op_a,op_a)) = op_a. [para(15(a,1),20(a,1,1)),rewrite([13(3)]),flip(a)].
% 1.59/1.90 34 mult(op_a,mult(mult(op_b,A),op_b)) = mult(A,op_b). [para(14(a,1),23(a,1,1,1)),rewrite([13(2)]),flip(a)].
% 1.59/1.90 35 mult(op_b,mult(mult(op_a,A),op_a)) = mult(A,op_a). [para(15(a,1),23(a,1,1,1)),rewrite([13(2)]),flip(a)].
% 1.59/1.90 36 mult(mult(A,mult(mult(B,C),B)),B) = mult(mult(mult(A,B),C),mult(B,B)). [para(23(a,1),20(a,1,1))].
% 1.59/1.90 37 mult(mult(A,B),mult(B,B)) = mult(A,mult(B,mult(B,B))). [para(23(a,1),20(a,1)),rewrite([20(2)]),flip(a)].
% 1.59/1.90 43 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)). [para(23(a,1),23(a,1,1))].
% 1.59/1.90 52 mult(op_b,mult(mult(mult(op_a,op_a),A),mult(op_a,op_a))) = mult(mult(op_a,A),mult(op_a,op_a)). [para(27(a,1),23(a,1,1,1)),flip(a)].
% 1.59/1.90 115 mult(op_a,mult(op_b,mult(op_b,op_b))) = mult(op_b,op_b). [para(20(a,1),34(a,1,2))].
% 1.59/1.90 118 mult(mult(op_a,op_a),op_b) = op_a. [para(27(a,1),34(a,1,2,1)),rewrite([14(4),12(3)]),flip(a)].
% 1.59/1.90 122 mult(mult(op_a,op_a),mult(op_b,op_b)) = unit. [para(118(a,1),20(a,1,1)),rewrite([14(3)]),flip(a)].
% 1.59/1.90 124 mult(mult(op_a,op_a),mult(mult(op_b,A),op_b)) = mult(mult(op_a,A),op_b). [para(118(a,1),23(a,1,1,1)),flip(a)].
% 1.59/1.90 126 mult(mult(op_a,op_a),mult(op_b,mult(op_b,mult(op_b,op_b)))) = mult(op_b,op_b). [para(122(a,1),20(a,1,1)),rewrite([13(5),37(13)]),flip(a)].
% 1.59/1.90 147 mult(mult(op_b,op_b),op_a) = op_b. [para(26(a,1),35(a,1,2,1)),rewrite([15(4),12(3)]),flip(a)].
% 1.59/1.90 153 mult(mult(op_b,op_b),mult(op_a,op_a)) = unit. [para(147(a,1),20(a,1,1)),rewrite([15(3)]),flip(a)].
% 1.59/1.90 262 mult(mult(op_b,mult(op_b,op_b)),op_a) = mult(op_b,op_b). [para(115(a,1),35(a,1,2,1)),rewrite([147(6)]),flip(a)].
% 1.59/1.90 263 mult(mult(mult(A,op_a),mult(op_b,mult(op_b,op_b))),mult(op_a,op_a)) = mult(mult(A,op_b),op_a). [para(115(a,1),36(a,1,1,2,1)),rewrite([147(5)]),flip(a)].
% 1.59/1.90 283 mult(mult(op_a,op_a),mult(op_b,mult(op_b,op_b))) = op_b. [para(118(a,1),37(a,1,1)),rewrite([26(5)]),flip(a)].
% 1.59/1.90 321 mult(mult(op_b,mult(op_b,op_b)),mult(op_a,op_a)) = op_b. [para(262(a,1),20(a,1,1)),rewrite([147(5)]),flip(a)].
% 1.59/1.90 664 mult(mult(A,op_a),mult(op_b,mult(op_b,op_b))) = mult(A,mult(op_b,op_b)). [para(26(a,1),43(a,1,1,2,1)),rewrite([15(3),12(2),147(11)]),flip(a)].
% 1.59/1.90 714 mult(mult(A,mult(op_a,op_a)),mult(op_b,mult(op_b,mult(op_b,op_b)))) = mult(A,mult(op_b,op_b)). [para(283(a,1),43(a,1,1,2,1)),rewrite([27(5),664(8),321(17)]),flip(a)].
% 1.59/1.90 748 mult(mult(A,mult(op_b,op_b)),mult(op_a,op_a)) = mult(mult(A,op_b),op_a). [back_rewrite(263),rewrite([664(8)])].
% 1.59/1.90 1349 mult(op_b,mult(mult(mult(op_a,A),op_b),mult(op_a,op_a))) = mult(mult(A,op_b),mult(op_a,op_a)). [para(34(a,1),52(a,2,1)),rewrite([124(9)])].
% 1.59/1.90 6760 mult(mult(op_a,mult(mult(A,op_b),op_a)),op_a) = mult(mult(mult(op_a,A),op_b),mult(op_a,op_a)). [para(124(a,1),36(a,2,1)),rewrite([34(7)])].
% 1.59/1.90 6825 mult(mult(A,op_b),op_a) = A. [para(126(a,1),23(a,2,2,1)),rewrite([714(12),748(8),153(11),12(6)])].
% 1.59/1.90 6850 mult(mult(mult(op_a,A),op_b),mult(op_a,op_a)) = mult(mult(op_a,A),op_a). [back_rewrite(6760),rewrite([6825(5)]),flip(a)].
% 1.59/1.90 6881 mult(mult(c1,op_a),op_b) != c1 # answer(goals). [back_rewrite(24),rewrite([6825(12)]),xx(b)].
% 1.59/1.90 6897 mult(mult(A,op_b),mult(op_a,op_a)) = mult(A,op_a). [back_rewrite(1349),rewrite([6850(9),35(6)]),flip(a)].
% 1.59/1.90 7012 mult(mult(A,op_a),op_b) = A. [para(6897(a,1),23(a,1,1)),rewrite([27(9),14(7),12(6)])].
% 1.59/1.90 7013 $F # answer(goals). [resolve(7012,a,6881,a)].
% 1.59/1.90
% 1.59/1.90 % SZS output end Refutation
% 1.59/1.90 ============================== end of proof ==========================
% 1.59/1.90
% 1.59/1.90 ============================== STATISTICS ============================
% 1.59/1.90
% 1.59/1.90 Given=272. Generated=25439. Kept=7000. proofs=1.
% 1.59/1.90 Usable=224. Sos=5137. Demods=3838. Limbo=3, Disabled=1647. Hints=0.
% 1.59/1.90 Megabytes=10.62.
% 1.59/1.90 User_CPU=0.93, System_CPU=0.02, Wall_clock=1.
% 1.59/1.90
% 1.59/1.90 ============================== end of statistics =====================
% 1.59/1.90
% 1.59/1.90 ============================== end of search =========================
% 1.59/1.90
% 1.59/1.90 THEOREM PROVED
% 1.59/1.90 % SZS status Theorem
% 1.59/1.90
% 1.59/1.90 Exiting with 1 proof.
% 1.59/1.90
% 1.59/1.90 Process 32359 exit (max_proofs) Mon Jun 13 11:02:25 2022
% 1.59/1.90 Prover9 interrupted
%------------------------------------------------------------------------------