TSTP Solution File: GRP660-10 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP660-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 11:20:22 EDT 2022
% Result : Unsatisfiable 2.12s 2.43s
% Output : Refutation 2.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP660-10 : TPTP v8.1.0. Released v8.1.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n026.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 : Tue Jun 14 05:52:06 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.12/2.43 ============================== Prover9 ===============================
% 2.12/2.43 Prover9 (32) version 2009-11A, November 2009.
% 2.12/2.43 Process 26509 was started by sandbox on n026.cluster.edu,
% 2.12/2.43 Tue Jun 14 05:52:07 2022
% 2.12/2.43 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26271_n026.cluster.edu".
% 2.12/2.43 ============================== end of head ===========================
% 2.12/2.43
% 2.12/2.43 ============================== INPUT =================================
% 2.12/2.43
% 2.12/2.43 % Reading from file /tmp/Prover9_26271_n026.cluster.edu
% 2.12/2.43
% 2.12/2.43 set(prolog_style_variables).
% 2.12/2.43 set(auto2).
% 2.12/2.43 % set(auto2) -> set(auto).
% 2.12/2.43 % set(auto) -> set(auto_inference).
% 2.12/2.43 % set(auto) -> set(auto_setup).
% 2.12/2.43 % set(auto_setup) -> set(predicate_elim).
% 2.12/2.43 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.12/2.43 % set(auto) -> set(auto_limits).
% 2.12/2.43 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.12/2.43 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.12/2.43 % set(auto) -> set(auto_denials).
% 2.12/2.43 % set(auto) -> set(auto_process).
% 2.12/2.43 % set(auto2) -> assign(new_constants, 1).
% 2.12/2.43 % set(auto2) -> assign(fold_denial_max, 3).
% 2.12/2.43 % set(auto2) -> assign(max_weight, "200.000").
% 2.12/2.43 % set(auto2) -> assign(max_hours, 1).
% 2.12/2.43 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.12/2.43 % set(auto2) -> assign(max_seconds, 0).
% 2.12/2.43 % set(auto2) -> assign(max_minutes, 5).
% 2.12/2.43 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.12/2.43 % set(auto2) -> set(sort_initial_sos).
% 2.12/2.43 % set(auto2) -> assign(sos_limit, -1).
% 2.12/2.43 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.12/2.43 % set(auto2) -> assign(max_megs, 400).
% 2.12/2.43 % set(auto2) -> assign(stats, some).
% 2.12/2.43 % set(auto2) -> clear(echo_input).
% 2.12/2.43 % set(auto2) -> set(quiet).
% 2.12/2.43 % set(auto2) -> clear(print_initial_clauses).
% 2.12/2.43 % set(auto2) -> clear(print_given).
% 2.12/2.43 assign(lrs_ticks,-1).
% 2.12/2.43 assign(sos_limit,10000).
% 2.12/2.43 assign(order,kbo).
% 2.12/2.43 set(lex_order_vars).
% 2.12/2.43 clear(print_given).
% 2.12/2.43
% 2.12/2.43 % formulas(sos). % not echoed (6 formulas)
% 2.12/2.43
% 2.12/2.43 ============================== end of input ==========================
% 2.12/2.43
% 2.12/2.43 % From the command line: assign(max_seconds, 300).
% 2.12/2.43
% 2.12/2.43 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.12/2.43
% 2.12/2.43 % Formulas that are not ordinary clauses:
% 2.12/2.43
% 2.12/2.43 ============================== end of process non-clausal formulas ===
% 2.12/2.43
% 2.12/2.43 ============================== PROCESS INITIAL CLAUSES ===============
% 2.12/2.43
% 2.12/2.43 ============================== PREDICATE ELIMINATION =================
% 2.12/2.43
% 2.12/2.43 ============================== end predicate elimination =============
% 2.12/2.43
% 2.12/2.43 Auto_denials:
% 2.12/2.43 % copying label goal to answer in negative clause
% 2.12/2.43
% 2.12/2.43 Term ordering decisions:
% 2.12/2.43 Function symbol KB weights: mult=1. ld=1. rd=1. tuple=1. x1=1. x1_2=1.
% 2.12/2.43
% 2.12/2.43 ============================== end of process initial clauses ========
% 2.12/2.43
% 2.12/2.43 ============================== CLAUSES FOR SEARCH ====================
% 2.12/2.43
% 2.12/2.43 ============================== end of clauses for search =============
% 2.12/2.43
% 2.12/2.43 ============================== SEARCH ================================
% 2.12/2.43
% 2.12/2.43 % Starting search at 0.01 seconds.
% 2.12/2.43
% 2.12/2.43 ============================== PROOF =================================
% 2.12/2.43 % SZS status Unsatisfiable
% 2.12/2.43 % SZS output start Refutation
% 2.12/2.43
% 2.12/2.43 % Proof 1 at 1.43 (+ 0.03) seconds: goal.
% 2.12/2.43 % Length of proof is 173.
% 2.12/2.43 % Level of proof is 28.
% 2.12/2.43 % Maximum clause weight is 43.000.
% 2.12/2.43 % Given clauses 141.
% 2.12/2.43
% 2.12/2.43 1 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [assumption].
% 2.12/2.43 2 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [assumption].
% 2.12/2.43 3 mult(rd(A,B),B) = A # label(f03) # label(axiom). [assumption].
% 2.12/2.43 4 rd(mult(A,B),B) = A # label(f04) # label(axiom). [assumption].
% 2.12/2.43 5 mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))) # label(f05) # label(axiom). [assumption].
% 2.12/2.43 6 tuple(mult(A,x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # label(goal) # label(negated_conjecture) # answer(goal). [assumption].
% 2.12/2.43 7 ld(rd(A,B),A) = B. [para(3(a,1),2(a,1,2))].
% 2.12/2.43 8 rd(A,ld(B,A)) = B. [para(1(a,1),4(a,1,1))].
% 2.12/2.43 9 mult(A,mult(ld(A,B),mult(C,A))) = mult(mult(B,C),A). [para(1(a,1),5(a,1,1,1)),flip(a)].
% 2.12/2.43 10 mult(A,mult(B,mult(ld(mult(A,B),C),A))) = mult(C,A). [para(1(a,1),5(a,1,1)),flip(a)].
% 2.12/2.43 11 ld(mult(mult(A,B),C),mult(A,mult(B,mult(C,A)))) = A. [para(5(a,1),2(a,1,2))].
% 2.12/2.43 12 mult(rd(A,B),mult(B,mult(C,rd(A,B)))) = mult(mult(A,C),rd(A,B)). [para(3(a,1),5(a,1,1,1)),flip(a)].
% 2.12/2.43 13 rd(mult(A,mult(B,mult(C,A))),A) = mult(mult(A,B),C). [para(5(a,1),4(a,1,1))].
% 2.12/2.43 16 mult(ld(A,B),mult(ld(ld(A,B),C),B)) = mult(mult(C,A),ld(A,B)). [para(1(a,1),9(a,1,2,2))].
% 2.12/2.43 17 ld(A,mult(mult(B,C),A)) = mult(ld(A,B),mult(C,A)). [para(9(a,1),2(a,1,2))].
% 2.12/2.43 18 mult(mult(A,rd(B,C)),C) = mult(C,mult(ld(C,A),B)). [para(3(a,1),9(a,1,2,2)),flip(a)].
% 2.12/2.43 24 mult(A,mult(ld(mult(B,A),C),B)) = ld(B,mult(C,B)). [para(10(a,1),2(a,1,2)),flip(a)].
% 2.12/2.43 34 ld(mult(mult(mult(A,B),B),ld(B,C)),mult(mult(A,B),mult(mult(C,A),B))) = mult(A,B). [para(9(a,1),11(a,1,2,2))].
% 2.12/2.43 35 rd(mult(mult(A,B),rd(A,C)),mult(C,mult(B,rd(A,C)))) = rd(A,C). [para(12(a,1),4(a,1,1))].
% 2.12/2.43 43 rd(mult(A,mult(B,C)),A) = mult(mult(A,B),rd(C,A)). [para(3(a,1),13(a,1,1,2,2))].
% 2.12/2.43 44 mult(mult(A,rd(B,mult(C,A))),C) = rd(mult(A,B),A). [para(3(a,1),13(a,1,1,2)),flip(a)].
% 2.12/2.43 47 mult(ld(A,B),mult(ld(B,C),A)) = ld(A,mult(C,A)). [para(1(a,1),17(a,1,2,1)),flip(a)].
% 2.12/2.43 50 mult(ld(A,rd(B,C)),mult(C,A)) = ld(A,mult(B,A)). [para(3(a,1),17(a,1,2,1)),flip(a)].
% 2.12/2.43 55 ld(mult(A,rd(B,C)),mult(C,mult(ld(C,A),B))) = C. [para(18(a,1),2(a,1,2))].
% 2.12/2.43 102 ld(A,ld(B,mult(C,B))) = mult(ld(mult(B,A),C),B). [para(24(a,1),2(a,1,2))].
% 2.12/2.43 103 ld(rd(A,B),mult(C,rd(A,B))) = mult(B,mult(ld(A,C),rd(A,B))). [para(3(a,1),24(a,1,2,1,1)),flip(a)].
% 2.12/2.43 146 mult(mult(A,B),rd(ld(B,C),A)) = rd(mult(A,C),A). [para(1(a,1),43(a,1,1,2)),flip(a)].
% 2.12/2.43 147 mult(mult(A,rd(B,C)),rd(C,A)) = rd(mult(A,B),A). [para(3(a,1),43(a,1,1,2)),flip(a)].
% 2.12/2.43 163 rd(mult(ld(A,B),C),ld(A,B)) = mult(mult(ld(A,B),rd(C,B)),A). [para(1(a,1),44(a,1,1,2,2)),flip(a)].
% 2.12/2.43 165 rd(rd(mult(A,B),A),C) = mult(A,rd(B,mult(C,A))). [para(44(a,1),4(a,1,1))].
% 2.12/2.43 266 ld(ld(A,B),mult(C,ld(A,B))) = mult(ld(ld(A,B),rd(C,A)),B). [para(1(a,1),50(a,1,2)),flip(a)].
% 2.12/2.43 267 mult(ld(A,rd(B,rd(C,A))),C) = ld(A,mult(B,A)). [para(3(a,1),50(a,1,2))].
% 2.12/2.43 325 mult(ld(mult(A,B),A),A) = ld(B,A). [para(2(a,1),102(a,1,2)),flip(a)].
% 2.12/2.43 326 mult(ld(mult(A,B),rd(C,A)),A) = ld(B,ld(A,C)). [para(3(a,1),102(a,1,2,2)),flip(a)].
% 2.12/2.43 349 ld(ld(A,B),A) = mult(ld(B,A),A). [para(1(a,1),325(a,1,1,1)),flip(a)].
% 2.12/2.43 350 ld(ld(mult(A,B),A),ld(B,A)) = A. [para(325(a,1),2(a,1,2))].
% 2.12/2.43 351 mult(ld(A,rd(A,B)),rd(A,B)) = ld(B,rd(A,B)). [para(3(a,1),325(a,1,1,1))].
% 2.12/2.43 352 rd(ld(A,B),B) = ld(mult(B,A),B). [para(325(a,1),4(a,1,1))].
% 2.12/2.43 388 rd(A,mult(ld(B,A),A)) = ld(A,B). [para(349(a,1),8(a,1,2))].
% 2.12/2.43 397 ld(mult(ld(A,B),B),ld(B,A)) = mult(ld(B,ld(B,A)),ld(B,A)). [para(349(a,1),349(a,1,1))].
% 2.12/2.43 469 ld(mult(mult(A,B),A),mult(A,B)) = rd(B,mult(A,B)). [para(2(a,1),352(a,1,1)),flip(a)].
% 2.12/2.43 470 ld(mult(A,rd(A,B)),A) = rd(B,A). [para(7(a,1),352(a,1,1)),flip(a)].
% 2.12/2.43 479 rd(A,mult(B,A)) = ld(A,rd(A,B)). [para(7(a,1),388(a,1,2,1))].
% 2.12/2.43 481 ld(mult(mult(A,B),A),mult(A,B)) = ld(B,rd(B,A)). [back_rewrite(469),rewrite([479(6)])].
% 2.12/2.43 484 rd(A,rd(B,A)) = mult(A,rd(A,B)). [para(470(a,1),8(a,1,2))].
% 2.12/2.43 498 ld(ld(A,B),rd(ld(A,B),A)) = ld(mult(B,A),B). [para(1(a,1),479(a,1,2)),rewrite([352(2)]),flip(a)].
% 2.12/2.43 503 rd(A,mult(A,mult(ld(A,B),C))) = ld(A,rd(A,mult(B,rd(C,A)))). [para(18(a,1),479(a,1,2))].
% 2.12/2.43 566 rd(mult(A,B),ld(B,rd(B,A))) = mult(mult(A,B),A). [para(4(a,1),484(a,2,2)),rewrite([479(3)])].
% 2.12/2.43 574 mult(A,rd(ld(ld(B,A),C),B)) = rd(mult(B,C),B). [para(1(a,1),146(a,1,1))].
% 2.12/2.43 575 ld(mult(A,B),rd(mult(A,C),A)) = rd(ld(B,C),A). [para(146(a,1),2(a,1,2))].
% 2.12/2.43 576 rd(mult(rd(A,B),C),rd(A,B)) = mult(A,rd(ld(B,C),rd(A,B))). [para(3(a,1),146(a,1,1)),flip(a)].
% 2.12/2.43 705 mult(A,rd(ld(A,B),mult(C,A))) = rd(rd(B,A),C). [para(1(a,1),165(a,1,1,1)),flip(a)].
% 2.12/2.43 735 rd(ld(A,mult(B,A)),C) = ld(A,rd(B,rd(C,A))). [para(267(a,1),4(a,1,1))].
% 2.12/2.43 777 ld(ld(A,B),ld(A,C)) = mult(ld(B,rd(C,A)),A). [para(1(a,1),326(a,1,1,1)),flip(a)].
% 2.12/2.43 780 rd(ld(A,ld(B,C)),B) = ld(mult(B,A),rd(C,B)). [para(326(a,1),4(a,1,1))].
% 2.12/2.43 1022 rd(rd(ld(A,B),A),ld(mult(B,A),B)) = ld(A,B). [para(498(a,1),8(a,1,2))].
% 2.12/2.43 1036 ld(ld(A,A),ld(mult(A,A),A)) = ld(mult(A,A),A). [para(352(a,1),498(a,1,2))].
% 2.12/2.43 1060 mult(ld(A,rd(B,A)),ld(B,rd(B,A))) = rd(ld(A,rd(B,A)),A). [para(351(a,1),566(a,1,1)),rewrite([8(7),7(4),351(7)]),flip(a)].
% 2.12/2.43 1106 rd(ld(ld(A,B),C),A) = ld(B,rd(mult(A,C),A)). [para(574(a,1),2(a,1,2)),flip(a)].
% 2.12/2.43 1203 rd(ld(A,B),mult(C,A)) = ld(A,rd(rd(B,A),C)). [para(705(a,1),2(a,1,2)),flip(a)].
% 2.12/2.43 1204 rd(rd(A,B),rd(C,B)) = mult(B,rd(ld(B,A),C)). [para(3(a,1),705(a,1,2,2)),flip(a)].
% 2.12/2.43 1273 ld(mult(mult(A,B),B),mult(A,B)) = ld(B,rd(A,A)). [para(735(a,1),352(a,1)),rewrite([4(2)]),flip(a)].
% 2.12/2.43 1383 mult(ld(A,rd(mult(B,C),B)),B) = ld(ld(B,A),C). [para(2(a,1),777(a,1,2)),flip(a)].
% 2.12/2.43 1471 ld(mult(A,rd(ld(A,B),C)),rd(B,A)) = rd(C,A). [para(7(a,1),780(a,1,1)),flip(a)].
% 2.12/2.43 1507 rd(ld(mult(A,A),A),ld(mult(A,A),A)) = ld(A,A). [para(352(a,1),1022(a,1,1))].
% 2.12/2.43 1596 mult(ld(mult(A,A),A),mult(ld(ld(mult(A,A),A),B),ld(A,A))) = mult(ld(ld(A,A),rd(B,A)),A). [para(1036(a,1),47(a,1,1)),rewrite([266(12)])].
% 2.12/2.43 1599 mult(ld(mult(A,A),A),ld(mult(A,A),A)) = ld(A,ld(mult(A,A),A)). [para(1036(a,1),349(a,2,1)),rewrite([350(4)]),flip(a)].
% 2.12/2.43 1643 ld(A,rd(mult(A,ld(mult(A,A),A)),A)) = ld(mult(A,mult(A,A)),A). [para(1036(a,1),1106(a,1,1)),rewrite([352(3)]),flip(a)].
% 2.12/2.43 1830 ld(rd(A,A),rd(A,A)) = rd(A,A). [para(147(a,1),1273(a,1,1)),rewrite([4(2),2(3)]),flip(a)].
% 2.12/2.43 1849 mult(rd(A,A),rd(A,A)) = rd(A,A). [para(1830(a,1),1(a,1,2))].
% 2.12/2.43 1850 mult(A,ld(mult(A,A),A)) = rd(A,A). [para(1830(a,1),8(a,1,2)),rewrite([1204(3),352(2)])].
% 2.12/2.43 1851 mult(rd(A,A),mult(rd(A,A),mult(B,rd(A,A)))) = mult(mult(rd(A,A),B),rd(A,A)). [para(1830(a,1),9(a,1,2,1))].
% 2.12/2.43 1853 mult(rd(A,A),mult(ld(rd(A,A),B),rd(A,A))) = mult(A,mult(ld(A,B),rd(A,A))). [para(1830(a,1),47(a,1,1)),rewrite([103(10)])].
% 2.12/2.43 1855 ld(mult(rd(A,A),rd(B,rd(A,A))),mult(rd(A,A),mult(rd(A,A),B))) = rd(A,A). [para(1830(a,1),55(a,1,2,2,1))].
% 2.12/2.43 1856 mult(mult(A,rd(B,B)),rd(B,B)) = mult(B,mult(ld(B,A),rd(B,B))). [para(1830(a,1),16(a,1,1)),rewrite([1830(4),1853(6),1830(9)]),flip(a)].
% 2.12/2.43 1864 mult(ld(rd(A,A),rd(B,rd(A,A))),rd(A,A)) = ld(rd(A,A),ld(rd(A,A),B)). [para(1830(a,1),777(a,1,1)),flip(a)].
% 2.12/2.43 1869 ld(mult(A,mult(A,A)),A) = ld(A,rd(rd(A,A),A)). [back_rewrite(1643),rewrite([1850(3)]),flip(a)].
% 2.12/2.43 1873 mult(A,mult(ld(A,rd(A,A)),A)) = A. [para(1849(a,1),18(a,1,1)),rewrite([3(2)]),flip(a)].
% 2.12/2.43 1876 mult(rd(A,A),mult(rd(A,A),B)) = mult(A,rd(ld(A,B),rd(A,A))). [para(1849(a,1),44(a,1,1,2,2)),rewrite([18(6),1830(4),576(8)])].
% 2.12/2.43 1878 ld(rd(A,A),ld(rd(A,A),B)) = mult(A,mult(ld(A,B),rd(A,A))). [para(1849(a,1),50(a,1,2)),rewrite([1864(6),103(8)])].
% 2.12/2.43 1887 rd(mult(A,rd(ld(A,B),rd(A,A))),rd(A,A)) = mult(rd(A,A),rd(B,rd(A,A))). [para(1849(a,1),165(a,2,2,2)),rewrite([576(4)])].
% 2.12/2.43 1898 ld(rd(A,A),rd(rd(B,rd(A,A)),rd(A,A))) = rd(ld(rd(A,A),B),rd(A,A)). [para(1849(a,1),1203(a,1,2)),flip(a)].
% 2.12/2.43 1902 ld(mult(rd(A,A),rd(B,rd(A,A))),mult(A,rd(ld(A,B),rd(A,A)))) = rd(A,A). [back_rewrite(1855),rewrite([1876(8)])].
% 2.12/2.43 1903 mult(A,rd(ld(A,mult(B,rd(A,A))),rd(A,A))) = mult(mult(rd(A,A),B),rd(A,A)). [back_rewrite(1851),rewrite([1876(6)])].
% 2.12/2.43 1904 mult(ld(rd(A,A),rd(B,rd(A,A))),rd(A,A)) = mult(A,mult(ld(A,B),rd(A,A))). [back_rewrite(1864),rewrite([1878(10)])].
% 2.12/2.43 1907 ld(mult(A,A),A) = ld(A,rd(A,A)). [para(1850(a,1),2(a,1,2)),flip(a)].
% 2.12/2.43 1923 rd(ld(A,rd(A,A)),A) = ld(A,ld(A,rd(A,A))). [back_rewrite(1599),rewrite([1907(2),1907(4),1060(5),1907(5)])].
% 2.12/2.43 1926 mult(ld(A,rd(A,A)),mult(ld(ld(A,rd(A,A)),B),ld(A,A))) = mult(ld(ld(A,A),rd(B,A)),A). [back_rewrite(1596),rewrite([1907(2),1907(4)])].
% 2.12/2.43 1928 rd(ld(A,rd(A,A)),ld(A,rd(A,A))) = ld(A,A). [back_rewrite(1507),rewrite([1907(2),1907(4)])].
% 2.12/2.43 2023 mult(ld(A,rd(A,A)),A) = ld(A,A). [para(1873(a,1),2(a,1,2)),flip(a)].
% 2.12/2.43 2036 ld(ld(A,A),rd(A,A)) = ld(A,A). [para(1873(a,1),1273(a,1,1,1)),rewrite([2023(3),1(2),2023(3),1(2),2023(4)]),flip(a)].
% 2.12/2.43 2048 mult(ld(rd(rd(A,A),A),rd(rd(A,A),A)),A) = A. [para(1907(a,1),350(a,1,2)),rewrite([1869(3),777(6)])].
% 2.12/2.43 2050 ld(A,rd(rd(A,A),A)) = ld(A,ld(A,rd(A,A))). [para(1907(a,1),352(a,1,1)),rewrite([1923(3),1869(6)]),flip(a)].
% 2.12/2.43 2057 mult(ld(A,ld(A,rd(A,A))),A) = ld(A,rd(A,A)). [para(1907(a,1),498(a,2)),rewrite([352(3),1907(3),777(4),2050(3)])].
% 2.12/2.43 2091 mult(ld(A,A),ld(A,A)) = ld(A,A). [para(2023(a,1),47(a,1,2)),rewrite([3(5)])].
% 2.12/2.43 2102 mult(ld(ld(A,A),rd(B,ld(A,rd(A,A)))),ld(A,rd(A,A))) = ld(A,ld(ld(A,rd(A,A)),B)). [para(2023(a,1),326(a,1,1,1))].
% 2.12/2.43 2121 mult(ld(A,ld(A,A)),ld(A,A)) = ld(A,ld(A,A)). [para(2023(a,1),1273(a,1,1,1)),rewrite([2023(5),397(4),1928(9)])].
% 2.12/2.43 2179 mult(A,rd(B,mult(mult(A,mult(rd(B,A),rd(A,A))),A))) = rd(A,A). [para(147(a,1),35(a,1,1)),rewrite([165(7)])].
% 2.12/2.43 2214 rd(A,A) = ld(A,A). [para(2036(a,1),1(a,1,2)),rewrite([2091(3)]),flip(a)].
% 2.12/2.43 2215 mult(ld(A,ld(A,A)),A) = ld(A,A). [para(2036(a,1),8(a,1,2)),rewrite([2214(1),2214(3),777(3),2214(1)])].
% 2.12/2.43 2218 mult(ld(A,A),mult(ld(ld(A,A),B),ld(A,A))) = mult(ld(ld(A,A),rd(B,A)),A). [para(2036(a,1),47(a,1,1)),rewrite([2214(2),266(10)])].
% 2.12/2.43 2221 mult(ld(ld(A,A),rd(B,A)),A) = mult(mult(B,ld(A,A)),ld(A,A)). [para(2036(a,1),16(a,1,1)),rewrite([2214(3),777(4),2214(2),2215(4),2214(4),2218(6),2214(8),777(9),2214(7),2215(9)])].
% 2.12/2.43 2233 mult(ld(ld(A,A),rd(B,ld(A,A))),ld(A,A)) = ld(ld(A,A),ld(ld(A,A),B)). [para(2036(a,1),777(a,1,1)),rewrite([2214(5)]),flip(a)].
% 2.12/2.43 2235 ld(ld(A,A),mult(A,mult(ld(A,ld(A,A)),B))) = rd(ld(ld(A,A),B),ld(A,A)). [para(2036(a,1),1106(a,1,1,1)),rewrite([2214(5),163(9),18(9)]),flip(a)].
% 2.12/2.43 2238 ld(mult(mult(mult(A,ld(B,B)),ld(B,B)),ld(B,B)),mult(mult(A,ld(B,B)),mult(mult(ld(B,B),A),ld(B,B)))) = mult(A,ld(B,B)). [para(2036(a,1),34(a,1,1,2)),rewrite([2214(9)])].
% 2.12/2.43 2252 mult(A,rd(B,mult(mult(A,mult(rd(B,A),ld(A,A))),A))) = ld(A,A). [back_rewrite(2179),rewrite([2214(2),2214(8)])].
% 2.12/2.43 2295 mult(ld(ld(A,A),rd(B,ld(A,ld(A,A)))),ld(A,ld(A,A))) = ld(A,ld(ld(A,ld(A,A)),B)). [back_rewrite(2102),rewrite([2214(2),2214(6),2214(9)])].
% 2.12/2.43 2331 mult(ld(A,ld(A,ld(A,A))),A) = ld(A,ld(A,A)). [back_rewrite(2057),rewrite([2214(1),2214(5)])].
% 2.12/2.43 2338 mult(ld(A,A),A) = A. [back_rewrite(2048),rewrite([2214(1),352(2),1907(2),2214(1),2214(3),352(4),1907(4),2214(3),777(5),352(3),1907(3),2214(2),777(4),352(2),1907(2),2214(1),2331(4),2215(3)])].
% 2.12/2.43 2356 mult(mult(A,ld(B,B)),ld(B,B)) = mult(mult(A,B),ld(B,ld(B,B))). [back_rewrite(1926),rewrite([2214(1),2214(3),16(8),2221(8)]),flip(a)].
% 2.12/2.43 2372 ld(mult(A,A),A) = ld(A,ld(A,A)). [back_rewrite(1907),rewrite([2214(3)])].
% 2.12/2.43 2373 ld(ld(A,A),ld(ld(A,A),B)) = mult(A,mult(ld(A,B),ld(A,A))). [back_rewrite(1904),rewrite([2214(1),2214(2),2214(5),2233(6),2214(6)])].
% 2.12/2.43 2374 mult(A,rd(ld(A,mult(B,ld(A,A))),ld(A,A))) = mult(mult(ld(A,A),B),ld(A,A)). [back_rewrite(1903),rewrite([2214(1),2214(4),2214(7),2214(9)])].
% 2.12/2.43 2375 ld(mult(ld(A,A),rd(B,ld(A,A))),mult(A,rd(ld(A,B),ld(A,A)))) = ld(A,A). [back_rewrite(1902),rewrite([2214(1),2214(2),2214(6),2214(10)])].
% 2.12/2.43 2378 ld(ld(A,A),rd(rd(B,ld(A,A)),ld(A,A))) = rd(ld(ld(A,A),B),ld(A,A)). [back_rewrite(1898),rewrite([2214(1),2214(2),2214(4),2214(7),2214(9)])].
% 2.12/2.43 2384 rd(mult(A,rd(ld(A,B),ld(A,A))),ld(A,A)) = mult(ld(A,A),rd(B,ld(A,A))). [back_rewrite(1887),rewrite([2214(2),2214(5),2214(7),2214(8)])].
% 2.12/2.43 2399 mult(mult(A,B),ld(B,ld(B,B))) = mult(B,mult(ld(B,A),ld(B,B))). [back_rewrite(1856),rewrite([2214(1),2214(3),2356(4),2214(6)])].
% 2.12/2.43 2459 mult(ld(A,A),mult(ld(ld(A,A),B),ld(A,A))) = mult(A,mult(ld(A,B),ld(A,A))). [back_rewrite(2218),rewrite([2221(10),2356(10),2399(10)])].
% 2.12/2.43 2462 ld(mult(mult(A,mult(ld(A,B),ld(A,A))),ld(A,A)),mult(mult(B,ld(A,A)),mult(mult(ld(A,A),B),ld(A,A)))) = mult(B,ld(A,A)). [back_rewrite(2238),rewrite([2356(4),2399(4)])].
% 2.12/2.43 2463 mult(ld(ld(A,A),rd(B,A)),A) = mult(A,mult(ld(A,B),ld(A,A))). [back_rewrite(2221),rewrite([2356(8),2399(8)])].
% 2.12/2.43 2468 mult(ld(ld(A,A),rd(B,ld(A,A))),ld(A,A)) = mult(A,mult(ld(A,B),ld(A,A))). [back_rewrite(2233),rewrite([2373(10)])].
% 2.12/2.43 2469 mult(mult(A,ld(B,B)),ld(B,B)) = mult(B,mult(ld(B,A),ld(B,B))). [back_rewrite(2356),rewrite([2399(8)])].
% 2.12/2.43 2471 mult(mult(A,ld(B,B)),B) = mult(B,mult(ld(B,A),B)). [para(2214(a,1),18(a,1,1,2))].
% 2.12/2.43 2477 mult(mult(A,ld(B,B)),rd(B,A)) = rd(mult(A,B),A). [para(2214(a,1),147(a,1,1,2))].
% 2.12/2.43 2481 mult(ld(A,rd(B,ld(A,A))),A) = ld(A,mult(B,A)). [para(2214(a,1),267(a,1,1,2,2))].
% 2.12/2.43 2490 ld(rd(A,B),rd(A,B)) = mult(B,ld(mult(A,B),A)). [para(2214(a,1),1204(a,1)),rewrite([352(5)])].
% 2.12/2.43 2516 mult(ld(A,A),rd(A,mult(B,ld(A,A)))) = rd(A,B). [para(2338(a,1),165(a,1,1,1)),rewrite([8(2)]),flip(a)].
% 2.12/2.43 2523 rd(ld(A,B),ld(A,A)) = mult(ld(A,ld(A,A)),B). [para(2338(a,1),575(a,1,1)),rewrite([163(4),18(4),2(5)]),flip(a)].
% 2.12/2.43 2538 rd(mult(A,mult(ld(A,ld(A,A)),B)),ld(A,A)) = mult(ld(A,A),rd(B,ld(A,A))). [back_rewrite(2384),rewrite([2523(3)])].
% 2.12/2.43 2541 ld(mult(ld(A,A),rd(B,ld(A,A))),mult(A,mult(ld(A,ld(A,A)),B))) = ld(A,A). [back_rewrite(2375),rewrite([2523(7)])].
% 2.12/2.43 2542 mult(A,mult(ld(A,ld(A,A)),mult(B,ld(A,A)))) = mult(mult(ld(A,A),B),ld(A,A)). [back_rewrite(2374),rewrite([2523(5)])].
% 2.12/2.43 2620 rd(mult(A,mult(ld(A,B),ld(A,A))),ld(A,A)) = ld(ld(A,A),rd(B,ld(A,A))). [para(2091(a,1),780(a,2,1)),rewrite([2373(4)])].
% 2.12/2.43 3302 mult(ld(A,ld(A,A)),mult(A,B)) = mult(A,mult(ld(A,ld(A,A)),B)). [para(2121(a,1),44(a,1,1,2,2)),rewrite([18(8),777(6),2214(4),777(5),2214(3),2215(5),2338(4),163(8),18(8)])].
% 2.12/2.43 3304 ld(A,ld(ld(A,ld(A,A)),B)) = mult(A,mult(ld(A,B),ld(A,A))). [para(2121(a,1),50(a,1,2)),rewrite([2295(8),266(8),2463(8)])].
% 2.12/2.43 4758 ld(ld(rd(mult(A,B),A),mult(A,ld(B,B))),ld(rd(B,A),mult(A,ld(B,B)))) = mult(A,ld(B,B)). [para(2477(a,1),350(a,1,1,1))].
% 2.12/2.43 4816 mult(mult(A,mult(ld(A,B),ld(A,A))),rd(A,mult(B,ld(A,A)))) = rd(mult(A,mult(ld(A,B),A)),mult(B,ld(A,A))). [para(2471(a,1),2477(a,1,1)),rewrite([2459(6),777(7),2214(5),2215(7),777(11),2214(9),2215(11),2471(11),777(14),2214(12),2215(14)])].
% 2.12/2.43 5179 mult(mult(ld(ld(A,A),rd(B,ld(A,A))),rd(A,rd(B,ld(A,A)))),ld(A,A)) = mult(mult(A,mult(ld(A,B),ld(A,A))),rd(A,ld(ld(A,A),rd(B,ld(A,A))))). [para(2481(a,1),2477(a,1,1)),rewrite([266(4),2463(4),777(8),2214(6),2215(8),777(14),2214(12),2215(14),777(19),2214(17),2215(19),163(20)]),flip(a)].
% 2.12/2.43 5617 ld(ld(A,rd(mult(A,B),A)),B) = mult(mult(A,ld(B,rd(B,A))),A). [para(2490(a,1),1383(a,1,1)),rewrite([481(4)]),flip(a)].
% 2.12/2.43 5618 mult(ld(rd(A,B),mult(A,rd(ld(B,C),rd(A,B)))),rd(A,B)) = ld(mult(B,ld(mult(A,B),A)),C). [para(2490(a,1),1383(a,2,1)),rewrite([576(5)])].
% 2.12/2.43 5686 rd(A,mult(B,ld(A,A))) = ld(ld(A,A),rd(A,B)). [para(2516(a,1),2(a,1,2)),flip(a)].
% 2.12/2.43 5687 rd(A,rd(B,ld(A,A))) = mult(ld(A,A),rd(A,B)). [para(3(a,1),2516(a,1,2,2)),flip(a)].
% 2.12/2.43 5714 mult(ld(A,A),ld(A,rd(A,mult(B,ld(A,ld(A,A)))))) = ld(ld(A,A),rd(A,B)). [para(2471(a,1),2516(a,1,2,2)),rewrite([2459(7),503(6),352(3),2372(3),777(10),2214(8),2215(10),5686(10)])].
% 2.12/2.43 5720 rd(A,ld(ld(A,A),rd(B,ld(A,A)))) = ld(ld(A,A),rd(A,B)). [para(2481(a,1),2516(a,1,2,2)),rewrite([266(5),2463(5),503(6),352(3),2372(3),5714(7),777(7),2214(5),2215(7)]),flip(a)].
% 2.12/2.43 5721 mult(mult(A,mult(ld(A,B),ld(A,A))),ld(ld(A,A),rd(A,B))) = rd(mult(A,mult(ld(A,B),A)),mult(B,ld(A,A))). [back_rewrite(4816),rewrite([5686(7)])].
% 2.12/2.43 5726 mult(mult(ld(ld(A,A),rd(B,ld(A,A))),mult(ld(A,A),rd(A,B))),ld(A,A)) = rd(mult(A,mult(ld(A,B),A)),mult(B,ld(A,A))). [back_rewrite(5179),rewrite([5687(7),5720(19),5721(18)])].
% 2.12/2.43 5825 ld(ld(A,A),rd(B,ld(A,A))) = B. [para(1(a,1),2523(a,2)),rewrite([3304(4),2620(6)])].
% 2.12/2.43 5826 mult(A,mult(ld(A,ld(A,A)),B)) = rd(B,ld(A,A)). [para(2(a,1),2523(a,1,1)),rewrite([3302(6)]),flip(a)].
% 2.12/2.43 5887 ld(rd(A,ld(B,B)),rd(A,B)) = ld(B,ld(B,B)). [para(2523(a,1),1471(a,1,1,2)),rewrite([5826(4),352(6),2372(6)])].
% 2.12/2.43 5906 rd(mult(A,mult(ld(A,B),A)),mult(B,ld(A,A))) = mult(mult(B,mult(ld(A,A),rd(A,B))),ld(A,A)). [back_rewrite(5726),rewrite([5825(4)]),flip(a)].
% 2.12/2.43 5907 ld(ld(A,A),rd(A,B)) = rd(A,B). [back_rewrite(5720),rewrite([5825(4)]),flip(a)].
% 2.12/2.43 5909 mult(A,mult(ld(A,B),ld(A,A))) = mult(B,ld(A,A)). [back_rewrite(2468),rewrite([5825(4)]),flip(a)].
% 2.12/2.43 5910 rd(ld(ld(A,A),B),ld(A,A)) = rd(B,ld(A,A)). [back_rewrite(2378),rewrite([5825(6)]),flip(a)].
% 2.12/2.43 5943 mult(mult(ld(A,A),B),ld(A,A)) = B. [back_rewrite(2542),rewrite([5826(6),4(4)]),flip(a)].
% 2.12/2.43 5944 ld(mult(ld(A,A),rd(B,ld(A,A))),rd(B,ld(A,A))) = ld(A,A). [back_rewrite(2541),rewrite([5826(8)])].
% 2.12/2.43 5945 rd(rd(A,ld(B,B)),ld(B,B)) = mult(ld(B,B),rd(A,ld(B,B))). [back_rewrite(2538),rewrite([5826(4)])].
% 2.12/2.43 5950 rd(A,ld(B,B)) = A. [back_rewrite(2235),rewrite([5826(5),5825(4),5910(4)]),flip(a)].
% 2.12/2.43 6026 ld(A,mult(B,A)) = mult(ld(A,B),A). [back_rewrite(2481),rewrite([5950(2)]),flip(a)].
% 2.12/2.43 6035 mult(mult(A,mult(ld(B,B),rd(B,A))),ld(B,B)) = rd(mult(A,B),A). [back_rewrite(5721),rewrite([5909(4),5907(5),2477(4),5906(8)]),flip(a)].
% 2.12/2.43 6082 mult(mult(A,ld(B,B)),ld(B,B)) = mult(A,ld(B,B)). [back_rewrite(2469),rewrite([5909(8)])].
% 2.12/2.43 6084 mult(A,ld(B,B)) = A. [back_rewrite(2462),rewrite([5909(4),6082(4),5943(8),2(6)]),flip(a)].
% 2.12/2.43 6115 mult(ld(A,A),B) = B. [back_rewrite(5945),rewrite([5950(2),5950(2),5950(3)]),flip(a)].
% 2.12/2.43 6116 ld(A,A) = ld(B,B). [back_rewrite(5944),rewrite([5950(3),6115(2),5950(2)])].
% 2.12/2.43 6141 ld(A,rd(A,B)) = ld(B,ld(B,B)). [back_rewrite(5887),rewrite([5950(2)])].
% 2.12/2.43 6587 mult(ld(A,mult(B,C)),A) = mult(ld(A,B),mult(C,A)). [back_rewrite(17),rewrite([6026(3)])].
% 2.12/2.43 6685 ld(ld(rd(mult(A,B),A),A),ld(rd(B,A),A)) = A. [back_rewrite(4758),rewrite([6084(4),6084(6),6084(8)])].
% 2.12/2.43 6702 rd(mult(A,B),A) = mult(A,rd(B,A)). [back_rewrite(6035),rewrite([6115(3),6084(4)]),flip(a)].
% 2.12/2.43 6907 mult(A,ld(B,rd(B,A))) = ld(A,A). [back_rewrite(2252),rewrite([6084(3),18(3),6115(2),479(2)])].
% 2.12/2.43 6976 ld(A,A) = c_0. [new_symbol(6116)].
% 2.12/2.43 7138 ld(mult(A,B),A) = ld(B,c_0). [back_rewrite(498),rewrite([6141(4),6976(1)]),flip(a)].
% 2.12/2.43 7374 ld(c_0,A) = A. [back_rewrite(5618),rewrite([6587(8),7(2),3(5),1(2),7138(2),1(3)]),flip(a)].
% 2.12/2.43 7408 mult(c_0,A) = A. [back_rewrite(5617),rewrite([6702(2),2(3),7(2),6907(3),6976(1)]),flip(a)].
% 2.12/2.43 7554 mult(A,c_0) = A. [back_rewrite(6685),rewrite([6702(2),7138(3),777(6),484(3),7374(4),147(4),6702(2),2214(1),6976(1)])].
% 2.12/2.43 10631 $F # answer(goal). [para(7408(a,1),6(a,1,1)),rewrite([7554(6)]),xx(a)].
% 2.12/2.43
% 2.12/2.43 % SZS output end Refutation
% 2.12/2.43 ============================== end of proof ==========================
% 2.12/2.43
% 2.12/2.43 ============================== STATISTICS ============================
% 2.12/2.43
% 2.12/2.43 Given=141. Generated=25404. Kept=10630. proofs=1.
% 2.12/2.43 Usable=39. Sos=2927. Demods=2944. Limbo=0, Disabled=7670. Hints=0.
% 2.12/2.43 Megabytes=16.43.
% 2.12/2.43 User_CPU=1.43, System_CPU=0.03, Wall_clock=1.
% 2.12/2.43
% 2.12/2.43 ============================== end of statistics =====================
% 2.12/2.43
% 2.12/2.43 ============================== end of search =========================
% 2.12/2.43
% 2.12/2.43 THEOREM PROVED
% 2.12/2.43 % SZS status Unsatisfiable
% 2.12/2.43
% 2.12/2.43 Exiting with 1 proof.
% 2.12/2.43
% 2.12/2.43 Process 26509 exit (max_proofs) Tue Jun 14 05:52:08 2022
% 2.12/2.43 Prover9 interrupted
%------------------------------------------------------------------------------