TSTP Solution File: GRP711+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP711+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 : Sat Jul 16 11:20:45 EDT 2022
% Result : Theorem 0.73s 1.07s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP711+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 09:14:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.07 ============================== Prover9 ===============================
% 0.73/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.07 Process 30657 was started by sandbox2 on n012.cluster.edu,
% 0.73/1.07 Mon Jun 13 09:14:26 2022
% 0.73/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30504_n012.cluster.edu".
% 0.73/1.07 ============================== end of head ===========================
% 0.73/1.07
% 0.73/1.07 ============================== INPUT =================================
% 0.73/1.07
% 0.73/1.07 % Reading from file /tmp/Prover9_30504_n012.cluster.edu
% 0.73/1.07
% 0.73/1.07 set(prolog_style_variables).
% 0.73/1.07 set(auto2).
% 0.73/1.07 % set(auto2) -> set(auto).
% 0.73/1.07 % set(auto) -> set(auto_inference).
% 0.73/1.07 % set(auto) -> set(auto_setup).
% 0.73/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.07 % set(auto) -> set(auto_limits).
% 0.73/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.07 % set(auto) -> set(auto_denials).
% 0.73/1.07 % set(auto) -> set(auto_process).
% 0.73/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.07 % set(auto2) -> assign(stats, some).
% 0.73/1.07 % set(auto2) -> clear(echo_input).
% 0.73/1.07 % set(auto2) -> set(quiet).
% 0.73/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.07 % set(auto2) -> clear(print_given).
% 0.73/1.07 assign(lrs_ticks,-1).
% 0.73/1.07 assign(sos_limit,10000).
% 0.73/1.07 assign(order,kbo).
% 0.73/1.07 set(lex_order_vars).
% 0.73/1.07 clear(print_given).
% 0.73/1.07
% 0.73/1.07 % formulas(sos). % not echoed (6 formulas)
% 0.73/1.07
% 0.73/1.07 ============================== end of input ==========================
% 0.73/1.07
% 0.73/1.07 % From the command line: assign(max_seconds, 300).
% 0.73/1.07
% 0.73/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.07
% 0.73/1.07 % Formulas that are not ordinary clauses:
% 0.73/1.07 1 (all A mult(A,unit) = A) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.07 2 (all A mult(unit,A) = A) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.07 3 (all C all B all A mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C)) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.07 4 (all A mult(A,i(A)) = unit) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.07 5 (all A mult(i(A),A) = unit) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.07 6 -(all X6 all X7 all X8 ((mult(X6,X7) = mult(X6,X8) -> X7 = X8) & (mult(X7,X6) = mult(X8,X6) -> X7 = X8))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.07
% 0.73/1.07 ============================== end of process non-clausal formulas ===
% 0.73/1.07
% 0.73/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.07
% 0.73/1.07 ============================== PREDICATE ELIMINATION =================
% 0.73/1.07
% 0.73/1.07 ============================== end predicate elimination =============
% 0.73/1.07
% 0.73/1.07 Auto_denials: (non-Horn, no changes).
% 0.73/1.07
% 0.73/1.07 Term ordering decisions:
% 0.73/1.07
% 0.73/1.07 % Assigning unary symbol i kb_weight 0 and highest precedence (7).
% 0.73/1.07 Function symbol KB weights: unit=1. c1=1. c2=1. c3=1. mult=1. i=0.
% 0.73/1.07
% 0.73/1.07 ============================== end of process initial clauses ========
% 0.73/1.07
% 0.73/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.07
% 0.73/1.07 ============================== end of clauses for search =============
% 0.73/1.07
% 0.73/1.07 ============================== SEARCH ================================
% 0.73/1.07
% 0.73/1.07 % Starting search at 0.01 seconds.
% 0.73/1.07
% 0.73/1.07 ============================== PROOF =================================
% 0.73/1.07 % SZS status Theorem
% 0.73/1.07 % SZS output start Refutation
% 0.73/1.07
% 0.73/1.07 % Proof 1 at 0.08 (+ 0.00) seconds.
% 0.73/1.07 % Length of proof is 47.
% 0.73/1.07 % Level of proof is 22.
% 0.73/1.07 % Maximum clause weight is 22.000.
% 0.73/1.07 % Given clauses 50.
% 0.73/1.07
% 0.73/1.07 1 (all A mult(A,unit) = A) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.07 2 (all A mult(unit,A) = A) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.07 3 (all C all B all A mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C)) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.07 4 (all A mult(A,i(A)) = unit) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.07 5 (all A mult(i(A),A) = unit) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.07 6 -(all X6 all X7 all X8 ((mult(X6,X7) = mult(X6,X8) -> X7 = X8) & (mult(X7,X6) = mult(X8,X6) -> X7 = X8))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.07 7 mult(A,unit) = A # label(f01) # label(axiom). [clausify(1)].
% 0.73/1.07 8 mult(unit,A) = A # label(f02) # label(axiom). [clausify(2)].
% 0.73/1.07 9 mult(A,i(A)) = unit # label(f04) # label(axiom). [clausify(4)].
% 0.73/1.07 10 mult(i(A),A) = unit # label(f05) # label(axiom). [clausify(5)].
% 0.73/1.07 11 mult(c1,c3) = mult(c1,c2) | mult(c3,c1) = mult(c2,c1) # label(goals) # label(negated_conjecture). [clausify(6)].
% 0.73/1.07 12 mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))) # label(f03) # label(axiom). [clausify(3)].
% 0.73/1.07 13 c3 != c2 # label(goals) # label(negated_conjecture). [clausify(6)].
% 0.73/1.07 15 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(12(a,1),7(a,1)),rewrite([7(2)]),flip(a)].
% 0.73/1.07 16 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(8(a,1),12(a,1,1,1)),rewrite([8(6)])].
% 0.73/1.07 17 mult(A,mult(B,mult(B,i(mult(A,mult(B,B)))))) = unit. [para(12(a,1),9(a,1)),rewrite([15(2)])].
% 0.73/1.07 20 mult(i(A),mult(A,mult(A,B))) = mult(A,B). [para(10(a,1),12(a,1,1,1)),rewrite([8(2)]),flip(a)].
% 0.73/1.07 30 mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))). [back_rewrite(12),rewrite([15(2)])].
% 0.73/1.07 36 mult(A,mult(i(A),i(A))) = i(A). [para(9(a,1),15(a,1,1)),rewrite([8(3)]),flip(a)].
% 0.73/1.07 37 mult(i(A),mult(A,A)) = A. [para(10(a,1),15(a,1,1)),rewrite([8(2)]),flip(a)].
% 0.73/1.07 41 mult(A,mult(A,i(mult(A,A)))) = unit. [para(16(a,1),9(a,1))].
% 0.73/1.07 45 mult(A,mult(A,mult(i(mult(A,A)),i(mult(A,A))))) = i(mult(A,A)). [para(16(a,1),36(a,1))].
% 0.73/1.07 53 i(i(A)) = A. [para(37(a,1),20(a,1,2,2)),rewrite([10(4),7(4),37(5)])].
% 0.73/1.07 56 mult(A,i(mult(A,A))) = i(A). [para(41(a,1),20(a,1,2)),rewrite([7(3)]),flip(a)].
% 0.73/1.07 58 mult(A,mult(i(mult(A,A)),i(mult(A,A)))) = mult(i(A),i(mult(A,A))). [para(56(a,1),15(a,1,1)),flip(a)].
% 0.73/1.07 60 mult(A,mult(i(A),i(mult(A,A)))) = i(mult(A,A)). [back_rewrite(45),rewrite([58(6)])].
% 0.73/1.07 73 i(mult(A,A)) = mult(i(A),i(A)). [para(60(a,1),20(a,1,2,2)),rewrite([56(4),60(8)]),flip(a)].
% 0.73/1.07 101 mult(i(A),mult(A,B)) = B. [para(10(a,1),30(a,1,1)),rewrite([8(2),73(2),16(6),20(5)]),flip(a)].
% 0.73/1.07 120 mult(c1,c3) = mult(c1,c2) | mult(i(c3),mult(c2,c1)) = c1. [para(11(b,1),101(a,1,2))].
% 0.73/1.07 122 mult(i(mult(A,B)),mult(A,mult(B,B))) = B. [para(15(a,1),101(a,1,2))].
% 0.73/1.07 123 mult(A,mult(A,i(mult(B,mult(A,A))))) = i(B). [para(17(a,1),101(a,1,2)),rewrite([7(3)]),flip(a)].
% 0.73/1.07 124 mult(A,mult(i(A),B)) = B. [para(53(a,1),101(a,1,1))].
% 0.73/1.07 172 mult(A,i(mult(B,mult(A,A)))) = mult(i(A),i(B)). [para(123(a,1),101(a,1,2)),flip(a)].
% 0.73/1.07 176 mult(A,i(mult(B,mult(A,mult(A,mult(A,A)))))) = mult(i(A),i(mult(B,mult(A,A)))). [para(15(a,1),172(a,1,2,1)),rewrite([16(3)])].
% 0.73/1.07 177 i(mult(A,mult(B,B))) = mult(i(B),mult(i(B),i(A))). [para(172(a,1),16(a,1)),rewrite([73(2),16(5),16(8),176(11),124(11)]),flip(a)].
% 0.73/1.07 266 i(mult(i(A),mult(i(A),i(B)))) = mult(B,mult(A,A)). [para(177(a,1),53(a,1,1))].
% 0.73/1.07 318 i(mult(A,mult(A,i(B)))) = mult(B,mult(i(A),i(A))). [para(53(a,1),266(a,1,1,1)),rewrite([53(2)])].
% 0.73/1.07 324 i(mult(A,mult(A,B))) = mult(i(B),mult(i(A),i(A))). [para(53(a,1),318(a,1,1,2,2))].
% 0.73/1.07 338 mult(i(mult(A,B)),mult(A,A)) = i(mult(i(A),B)). [para(101(a,1),324(a,1,1,2)),rewrite([53(7),53(7)]),flip(a)].
% 0.73/1.07 356 mult(i(mult(i(mult(A,B)),A)),i(mult(i(A),B))) = A. [para(338(a,1),122(a,1,2))].
% 0.73/1.07 532 mult(i(mult(i(A),i(B))),i(A)) = B. [para(101(a,1),356(a,1,2,1)),rewrite([324(3),30(6),10(4),7(4)])].
% 0.73/1.07 539 mult(c1,c3) = mult(c1,c2) | mult(i(mult(i(mult(c3,mult(c2,c1))),c3)),i(c1)) = c3. [para(120(b,1),356(a,1,2,1))].
% 0.73/1.07 614 i(mult(A,i(B))) = mult(B,i(A)). [para(532(a,1),15(a,1,1)),rewrite([338(10),53(4)]),flip(a)].
% 0.73/1.07 621 mult(i(mult(A,B)),A) = i(B). [para(532(a,1),101(a,1,2)),rewrite([614(4),53(2)])].
% 0.73/1.07 639 mult(mult(A,B),i(B)) = A. [back_rewrite(532),rewrite([614(4),53(2)])].
% 0.73/1.07 647 mult(c1,c3) = mult(c1,c2). [back_rewrite(539),rewrite([621(15),53(12),639(13)]),flip(b),unit_del(b,13)].
% 0.73/1.07 651 $F. [para(647(a,1),101(a,1,2)),rewrite([101(6)]),flip(a),unit_del(a,13)].
% 0.73/1.07
% 0.73/1.07 % SZS output end Refutation
% 0.73/1.07 ============================== end of proof ==========================
% 0.73/1.07
% 0.73/1.07 ============================== STATISTICS ============================
% 0.73/1.07
% 0.73/1.07 Given=50. Generated=2258. Kept=644. proofs=1.
% 0.73/1.07 Usable=27. Sos=233. Demods=260. Limbo=1, Disabled=390. Hints=0.
% 0.73/1.07 Megabytes=1.04.
% 0.73/1.07 User_CPU=0.08, System_CPU=0.00, Wall_clock=0.
% 0.73/1.07
% 0.73/1.07 ============================== end of statistics =====================
% 0.73/1.07
% 0.73/1.07 ============================== end of search =========================
% 0.73/1.07
% 0.73/1.07 THEOREM PROVED
% 0.73/1.07 % SZS status Theorem
% 0.73/1.07
% 0.73/1.07 Exiting with 1 proof.
% 0.73/1.07
% 0.73/1.07 Process 30657 exit (max_proofs) Mon Jun 13 09:14:26 2022
% 0.73/1.07 Prover9 interrupted
%------------------------------------------------------------------------------