TSTP Solution File: GRP002-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP002-10 : TPTP v8.1.0. Released v7.3.0.
% 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 : Sat Jul 16 11:16:37 EDT 2022
% Result : Unsatisfiable 4.00s 4.33s
% Output : Refutation 4.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP002-10 : TPTP v8.1.0. Released v7.3.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.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 17:37:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.00/4.33 ============================== Prover9 ===============================
% 4.00/4.33 Prover9 (32) version 2009-11A, November 2009.
% 4.00/4.33 Process 31896 was started by sandbox on n020.cluster.edu,
% 4.00/4.33 Mon Jun 13 17:37:50 2022
% 4.00/4.33 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31743_n020.cluster.edu".
% 4.00/4.33 ============================== end of head ===========================
% 4.00/4.33
% 4.00/4.33 ============================== INPUT =================================
% 4.00/4.33
% 4.00/4.33 % Reading from file /tmp/Prover9_31743_n020.cluster.edu
% 4.00/4.33
% 4.00/4.33 set(prolog_style_variables).
% 4.00/4.33 set(auto2).
% 4.00/4.33 % set(auto2) -> set(auto).
% 4.00/4.33 % set(auto) -> set(auto_inference).
% 4.00/4.33 % set(auto) -> set(auto_setup).
% 4.00/4.33 % set(auto_setup) -> set(predicate_elim).
% 4.00/4.33 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.00/4.33 % set(auto) -> set(auto_limits).
% 4.00/4.33 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.00/4.33 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.00/4.33 % set(auto) -> set(auto_denials).
% 4.00/4.33 % set(auto) -> set(auto_process).
% 4.00/4.33 % set(auto2) -> assign(new_constants, 1).
% 4.00/4.33 % set(auto2) -> assign(fold_denial_max, 3).
% 4.00/4.33 % set(auto2) -> assign(max_weight, "200.000").
% 4.00/4.33 % set(auto2) -> assign(max_hours, 1).
% 4.00/4.33 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.00/4.33 % set(auto2) -> assign(max_seconds, 0).
% 4.00/4.33 % set(auto2) -> assign(max_minutes, 5).
% 4.00/4.33 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.00/4.33 % set(auto2) -> set(sort_initial_sos).
% 4.00/4.33 % set(auto2) -> assign(sos_limit, -1).
% 4.00/4.33 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.00/4.33 % set(auto2) -> assign(max_megs, 400).
% 4.00/4.33 % set(auto2) -> assign(stats, some).
% 4.00/4.33 % set(auto2) -> clear(echo_input).
% 4.00/4.33 % set(auto2) -> set(quiet).
% 4.00/4.33 % set(auto2) -> clear(print_initial_clauses).
% 4.00/4.33 % set(auto2) -> clear(print_given).
% 4.00/4.33 assign(lrs_ticks,-1).
% 4.00/4.33 assign(sos_limit,10000).
% 4.00/4.33 assign(order,kbo).
% 4.00/4.33 set(lex_order_vars).
% 4.00/4.33 clear(print_given).
% 4.00/4.33
% 4.00/4.33 % formulas(sos). % not echoed (18 formulas)
% 4.00/4.33
% 4.00/4.33 ============================== end of input ==========================
% 4.00/4.33
% 4.00/4.33 % From the command line: assign(max_seconds, 300).
% 4.00/4.33
% 4.00/4.33 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.00/4.33
% 4.00/4.33 % Formulas that are not ordinary clauses:
% 4.00/4.33
% 4.00/4.33 ============================== end of process non-clausal formulas ===
% 4.00/4.33
% 4.00/4.33 ============================== PROCESS INITIAL CLAUSES ===============
% 4.00/4.33
% 4.00/4.33 ============================== PREDICATE ELIMINATION =================
% 4.00/4.33
% 4.00/4.33 ============================== end predicate elimination =============
% 4.00/4.33
% 4.00/4.33 Auto_denials:
% 4.00/4.33 % copying label prove_k_times_inverse_b_is_e to answer in negative clause
% 4.00/4.33
% 4.00/4.33 Term ordering decisions:
% 4.00/4.33
% 4.00/4.33 % Assigning unary symbol inverse kb_weight 0 and highest precedence (15).
% 4.00/4.33 Function symbol KB weights: true=1. identity=1. b=1. h=1. a=1. c=1. d=1. j=1. k=1. multiply=1. product=1. ifeq=1. ifeq2=1. inverse=0.
% 4.00/4.33
% 4.00/4.33 ============================== end of process initial clauses ========
% 4.00/4.33
% 4.00/4.33 ============================== CLAUSES FOR SEARCH ====================
% 4.00/4.33
% 4.00/4.33 ============================== end of clauses for search =============
% 4.00/4.33
% 4.00/4.33 ============================== SEARCH ================================
% 4.00/4.33
% 4.00/4.33 % Starting search at 0.01 seconds.
% 4.00/4.33
% 4.00/4.33 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 0.50 sec).
% 4.00/4.33
% 4.00/4.33 Low Water (keep): wt=26.000, iters=3363
% 4.00/4.33
% 4.00/4.33 Low Water (keep): wt=25.000, iters=3538
% 4.00/4.33
% 4.00/4.33 Low Water (keep): wt=21.000, iters=3340
% 4.00/4.33
% 4.00/4.33 Low Water (keep): wt=20.000, iters=3336
% 4.00/4.33
% 4.00/4.33 Low Water (keep): wt=19.000, iters=3362
% 4.00/4.33
% 4.00/4.33 Low Water (keep): wt=18.000, iters=3373
% 4.00/4.33
% 4.00/4.33 Low Water (keep): wt=17.000, iters=3344
% 4.00/4.33
% 4.00/4.33 ============================== PROOF =================================
% 4.00/4.33 % SZS status Unsatisfiable
% 4.00/4.33 % SZS output start Refutation
% 4.00/4.33
% 4.00/4.33 % Proof 1 at 3.20 (+ 0.07) seconds: prove_k_times_inverse_b_is_e.
% 4.00/4.33 % Length of proof is 157.
% 4.00/4.33 % Level of proof is 28.
% 4.00/4.33 % Maximum clause weight is 48.000.
% 4.00/4.33 % Given clauses 1995.
% 4.00/4.33
% 4.00/4.33 1 product(identity,A,A) = true # label(left_identity) # label(axiom). [assumption].
% 4.00/4.33 2 product(A,identity,A) = true # label(right_identity) # label(axiom). [assumption].
% 4.00/4.33 3 product(a,b,c) = true # label(a_times_b_is_c) # label(negated_conjecture). [assumption].
% 4.00/4.33 4 true = product(a,b,c). [copy(3),flip(a)].
% 4.00/4.33 5 product(h,b,j) = true # label(h_times_b_is_j) # label(negated_conjecture). [assumption].
% 4.00/4.33 6 product(a,b,c) = product(h,b,j). [copy(5),rewrite([4(5)]),flip(a)].
% 4.00/4.33 7 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 4.00/4.33 8 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 4.00/4.33 9 product(inverse(A),A,identity) = true # label(left_inverse) # label(axiom). [assumption].
% 4.00/4.33 10 product(inverse(A),A,identity) = product(h,b,j). [copy(9),rewrite([4(4),6(7)])].
% 4.00/4.33 11 product(A,inverse(A),identity) = true # label(right_inverse) # label(axiom). [assumption].
% 4.00/4.33 12 product(h,b,j) = product(A,inverse(A),identity). [copy(11),rewrite([4(4),6(7)]),flip(a)].
% 4.00/4.33 13 product(c,inverse(a),d) = true # label(c_times_inverse_a_is_d) # label(negated_conjecture). [assumption].
% 4.00/4.33 14 product(c,inverse(a),d) = product(h,b,j). [copy(13),rewrite([4(6),6(9)])].
% 4.00/4.33 15 product(d,inverse(b),h) = true # label(d_times_inverse_b_is_h) # label(negated_conjecture). [assumption].
% 4.00/4.33 16 product(d,inverse(b),h) = product(h,b,j). [copy(15),rewrite([4(6),6(9)])].
% 4.00/4.33 17 product(j,inverse(h),k) = true # label(j_times_inverse_h_is_k) # label(negated_conjecture). [assumption].
% 4.00/4.33 18 product(j,inverse(h),k) = product(h,b,j). [copy(17),rewrite([4(6),6(9)])].
% 4.00/4.33 19 product(A,B,multiply(A,B)) = true # label(total_function1) # label(axiom). [assumption].
% 4.00/4.33 20 product(A,B,multiply(A,B)) = product(h,b,j). [copy(19),rewrite([4(3),6(6)])].
% 4.00/4.33 21 ifeq(product(A,A,B),true,product(A,B,identity),true) = true # label(x_cubed_is_identity_1) # label(hypothesis). [assumption].
% 4.00/4.33 22 ifeq(product(A,A,B),product(h,b,j),product(A,B,identity),product(h,b,j)) = product(h,b,j). [copy(21),rewrite([4(2),6(5),4(8),6(11),4(13),6(16)])].
% 4.00/4.33 23 ifeq(product(A,A,B),true,product(B,A,identity),true) = true # label(x_cubed_is_identity_2) # label(hypothesis). [assumption].
% 4.00/4.33 24 ifeq(product(A,A,B),product(h,b,j),product(B,A,identity),product(h,b,j)) = product(h,b,j). [copy(23),rewrite([4(2),6(5),4(8),6(11),4(13),6(16)])].
% 4.00/4.33 25 ifeq2(product(A,B,C),true,ifeq2(product(A,B,D),true,D,C),C) = C # label(total_function2) # label(axiom). [assumption].
% 4.00/4.33 26 ifeq2(product(A,B,C),product(h,b,j),ifeq2(product(A,B,D),product(h,b,j),D,C),C) = C. [copy(25),rewrite([4(2),6(5),4(7),6(10)])].
% 4.00/4.33 27 ifeq(product(A,B,C),true,ifeq(product(D,B,E),true,ifeq(product(F,D,A),true,product(F,E,C),true),true),true) = true # label(associativity1) # label(axiom). [assumption].
% 4.00/4.33 28 ifeq(product(A,B,C),product(h,b,j),ifeq(product(D,B,E),product(h,b,j),ifeq(product(F,D,A),product(h,b,j),product(F,E,C),product(h,b,j)),product(h,b,j)),product(h,b,j)) = product(h,b,j). [copy(27),rewrite([4(2),6(5),4(7),6(10),4(12),6(15),4(17),6(20),4(22),6(25),4(27),6(30),4(32),6(35)])].
% 4.00/4.33 29 ifeq(product(A,B,C),true,ifeq(product(D,C,E),true,ifeq(product(D,A,F),true,product(F,B,E),true),true),true) = true # label(associativity2) # label(axiom). [assumption].
% 4.00/4.33 30 ifeq(product(A,B,C),product(h,b,j),ifeq(product(D,C,E),product(h,b,j),ifeq(product(D,A,F),product(h,b,j),product(F,B,E),product(h,b,j)),product(h,b,j)),product(h,b,j)) = product(h,b,j). [copy(29),rewrite([4(2),6(5),4(7),6(10),4(12),6(15),4(17),6(20),4(22),6(25),4(27),6(30),4(32),6(35)])].
% 4.00/4.33 31 product(k,inverse(b),identity) != true # label(prove_k_times_inverse_b_is_e) # label(negated_conjecture) # answer(prove_k_times_inverse_b_is_e). [assumption].
% 4.00/4.33 32 product(k,inverse(b),identity) != product(h,b,j) # answer(prove_k_times_inverse_b_is_e). [copy(31),rewrite([4(6),6(9)])].
% 4.00/4.33 33 product(h,b,j) = product(A,identity,A). [back_rewrite(2),rewrite([4(3),6(6)]),flip(a)].
% 4.00/4.33 34 product(h,b,j) = product(identity,A,A). [back_rewrite(1),rewrite([4(3),6(6)]),flip(a)].
% 4.00/4.33 36 product(inverse(A),A,identity) = product(inverse(B),B,identity). [para(10(a,2),10(a,2))].
% 4.00/4.33 37 product(inverse(A),A,identity) = c_0. [new_symbol(36)].
% 4.00/4.33 38 product(h,b,j) = c_0. [back_rewrite(10),rewrite([37(3)]),flip(a)].
% 4.00/4.33 40 product(identity,A,A) = c_0. [back_rewrite(34),rewrite([38(4)]),flip(a)].
% 4.00/4.33 41 product(A,identity,A) = c_0. [back_rewrite(33),rewrite([38(4)]),flip(a)].
% 4.00/4.33 42 product(k,inverse(b),identity) != c_0 # answer(prove_k_times_inverse_b_is_e). [back_rewrite(32),rewrite([38(9)])].
% 4.00/4.33 43 ifeq(product(A,B,C),c_0,ifeq(product(D,C,E),c_0,ifeq(product(D,A,F),c_0,product(F,B,E),c_0),c_0),c_0) = c_0. [back_rewrite(30),rewrite([38(5),38(7),38(9),38(11),38(13),38(15),38(17)])].
% 4.00/4.33 44 ifeq(product(A,B,C),c_0,ifeq(product(D,B,E),c_0,ifeq(product(F,D,A),c_0,product(F,E,C),c_0),c_0),c_0) = c_0. [back_rewrite(28),rewrite([38(5),38(7),38(9),38(11),38(13),38(15),38(17)])].
% 4.00/4.33 45 ifeq2(product(A,B,C),c_0,ifeq2(product(A,B,D),c_0,D,C),C) = C. [back_rewrite(26),rewrite([38(5),38(7)])].
% 4.00/4.33 46 ifeq(product(A,A,B),c_0,product(B,A,identity),c_0) = c_0. [back_rewrite(24),rewrite([38(5),38(8),38(10)])].
% 4.00/4.33 47 ifeq(product(A,A,B),c_0,product(A,B,identity),c_0) = c_0. [back_rewrite(22),rewrite([38(5),38(8),38(10)])].
% 4.00/4.33 48 product(A,B,multiply(A,B)) = c_0. [back_rewrite(20),rewrite([38(6)])].
% 4.00/4.33 49 product(j,inverse(h),k) = c_0. [back_rewrite(18),rewrite([38(9)])].
% 4.00/4.33 50 product(d,inverse(b),h) = c_0. [back_rewrite(16),rewrite([38(9)])].
% 4.00/4.33 51 product(c,inverse(a),d) = c_0. [back_rewrite(14),rewrite([38(9)])].
% 4.00/4.33 52 product(A,inverse(A),identity) = c_0. [back_rewrite(12),rewrite([38(4)]),flip(a)].
% 4.00/4.33 53 product(a,b,c) = c_0. [back_rewrite(6),rewrite([38(8)])].
% 4.00/4.33 54 ifeq(product(A,identity,B),c_0,ifeq(product(A,inverse(C),D),c_0,product(D,C,B),c_0),c_0) = c_0. [para(37(a,1),43(a,1,1)),rewrite([8(15)])].
% 4.00/4.33 55 ifeq(product(A,B,C),c_0,ifeq(product(inverse(C),A,D),c_0,product(D,B,identity),c_0),c_0) = c_0. [para(37(a,1),43(a,1,3,1)),rewrite([8(13)])].
% 4.00/4.33 58 ifeq(product(A,j,B),c_0,ifeq(product(A,h,C),c_0,product(C,b,B),c_0),c_0) = c_0. [para(38(a,1),43(a,1,1)),rewrite([8(16)])].
% 4.00/4.33 60 ifeq(product(b,A,B),c_0,ifeq(product(h,B,C),c_0,product(j,A,C),c_0),c_0) = c_0. [para(38(a,1),43(a,1,3,3,1)),rewrite([8(12)])].
% 4.00/4.33 67 ifeq(product(A,B,identity),c_0,ifeq(product(C,A,D),c_0,product(D,B,C),c_0),c_0) = c_0. [para(41(a,1),43(a,1,3,1)),rewrite([8(12)])].
% 4.00/4.33 70 ifeq(product(A,c,B),c_0,ifeq(product(A,a,C),c_0,product(C,b,B),c_0),c_0) = c_0. [para(53(a,1),43(a,1,1)),rewrite([8(16)])].
% 4.00/4.33 82 ifeq(product(A,d,B),c_0,ifeq(product(A,c,C),c_0,product(C,inverse(a),B),c_0),c_0) = c_0. [para(51(a,1),43(a,1,1)),rewrite([8(17)])].
% 4.00/4.33 84 ifeq(product(inverse(a),A,B),c_0,ifeq(product(c,B,C),c_0,product(d,A,C),c_0),c_0) = c_0. [para(51(a,1),43(a,1,3,3,1)),rewrite([8(13)])].
% 4.00/4.33 94 ifeq(product(A,B,C),c_0,ifeq(product(D,A,identity),c_0,product(D,C,B),c_0),c_0) = c_0. [para(40(a,1),44(a,1,1)),rewrite([8(14)])].
% 4.00/4.33 126 ifeq(product(A,multiply(B,C),D),c_0,ifeq(product(A,B,E),c_0,product(E,C,D),c_0),c_0) = c_0. [para(48(a,1),43(a,1,1)),rewrite([8(14)])].
% 4.00/4.33 132 ifeq(product(multiply(A,B),C,D),c_0,ifeq(product(B,C,E),c_0,product(A,E,D),c_0),c_0) = c_0. [para(48(a,1),44(a,1,3,3,1)),rewrite([8(10)])].
% 4.00/4.33 138 product(multiply(A,A),A,identity) = c_0. [para(48(a,1),46(a,1,1)),rewrite([8(7)])].
% 4.00/4.33 149 ifeq2(product(h,b,A),c_0,A,j) = j. [para(38(a,1),45(a,1,1)),rewrite([7(10)])].
% 4.00/4.33 151 ifeq2(product(identity,A,B),c_0,B,A) = A. [para(40(a,1),45(a,1,1)),rewrite([7(7)])].
% 4.00/4.33 166 ifeq2(product(A,B,C),c_0,multiply(A,B),C) = C. [para(48(a,1),45(a,1,3,1)),rewrite([7(6)])].
% 4.00/4.33 171 multiply(identity,A) = A. [para(48(a,1),151(a,1,1)),rewrite([7(5)])].
% 4.00/4.33 173 product(A,multiply(A,A),identity) = c_0. [para(48(a,1),47(a,1,1)),rewrite([8(7)])].
% 4.00/4.33 191 ifeq(product(A,inverse(B),C),c_0,product(C,B,A),c_0) = c_0. [para(41(a,1),54(a,1,1)),rewrite([8(10)])].
% 4.00/4.33 194 ifeq(product(j,identity,A),c_0,product(k,h,A),c_0) = c_0. [para(49(a,1),54(a,1,3,1)),rewrite([8(11)])].
% 4.00/4.33 196 ifeq(product(d,identity,A),c_0,product(h,b,A),c_0) = c_0. [para(50(a,1),54(a,1,3,1)),rewrite([8(11)])].
% 4.00/4.33 225 ifeq(product(inverse(multiply(A,B)),A,C),c_0,product(C,B,identity),c_0) = c_0. [para(48(a,1),55(a,1,1)),rewrite([8(12)])].
% 4.00/4.33 226 ifeq(product(A,B,C),c_0,product(multiply(inverse(C),A),B,identity),c_0) = c_0. [para(48(a,1),55(a,1,3,1)),rewrite([8(10)])].
% 4.00/4.33 275 ifeq(product(A,j,B),c_0,product(multiply(A,h),b,B),c_0) = c_0. [para(48(a,1),58(a,1,3,1)),rewrite([8(11)])].
% 4.00/4.33 294 ifeq(product(b,A,identity),c_0,product(j,A,h),c_0) = c_0. [para(41(a,1),60(a,1,3,1)),rewrite([8(11)])].
% 4.00/4.33 301 ifeq(product(b,A,B),c_0,product(j,A,multiply(h,B)),c_0) = c_0. [para(48(a,1),60(a,1,3,1)),rewrite([8(11)])].
% 4.00/4.33 307 multiply(multiply(A,A),A) = identity. [para(138(a,1),166(a,1,1)),rewrite([7(6)])].
% 4.00/4.33 341 product(k,h,j) = c_0. [para(41(a,1),194(a,1,1)),rewrite([8(8)])].
% 4.00/4.33 384 product(h,b,d) = c_0. [para(41(a,1),196(a,1,1)),rewrite([8(8)])].
% 4.00/4.33 418 j = d. [para(384(a,1),149(a,1,1)),rewrite([7(5)]),flip(a)].
% 4.00/4.33 459 product(k,h,d) = c_0. [back_rewrite(341),rewrite([418(3)])].
% 4.00/4.33 474 ifeq(product(b,A,B),c_0,product(d,A,multiply(h,B)),c_0) = c_0. [back_rewrite(301),rewrite([418(4)])].
% 4.00/4.33 480 ifeq(product(b,A,identity),c_0,product(d,A,h),c_0) = c_0. [back_rewrite(294),rewrite([418(5)])].
% 4.00/4.33 493 ifeq(product(A,d,B),c_0,product(multiply(A,h),b,B),c_0) = c_0. [back_rewrite(275),rewrite([418(1)])].
% 4.00/4.33 568 ifeq(product(A,B,identity),c_0,product(multiply(C,A),B,C),c_0) = c_0. [para(48(a,1),67(a,1,3,1)),rewrite([8(9)])].
% 4.00/4.33 574 ifeq(product(h,A,identity),c_0,product(d,A,k),c_0) = c_0. [para(459(a,1),67(a,1,3,1)),rewrite([8(11)])].
% 4.00/4.33 658 ifeq(product(A,a,B),c_0,product(B,b,multiply(A,c)),c_0) = c_0. [para(48(a,1),70(a,1,1)),rewrite([8(13)])].
% 4.00/4.33 792 product(d,multiply(b,b),h) = c_0. [para(173(a,1),480(a,1,1)),rewrite([8(10)])].
% 4.00/4.33 842 ifeq(product(A,c,B),c_0,product(B,inverse(a),multiply(A,d)),c_0) = c_0. [para(48(a,1),82(a,1,1)),rewrite([8(14)])].
% 4.00/4.33 866 ifeq(product(inverse(a),A,B),c_0,product(d,A,multiply(c,B)),c_0) = c_0. [para(48(a,1),84(a,1,3,1)),rewrite([8(12)])].
% 4.00/4.33 1045 product(d,multiply(h,h),k) = c_0. [para(173(a,1),574(a,1,1)),rewrite([8(10)])].
% 4.00/4.33 1086 ifeq(product(A,a,identity),c_0,product(A,c,b),c_0) = c_0. [para(53(a,1),94(a,1,1)),rewrite([8(13)])].
% 4.00/4.33 1262 product(multiply(a,a),c,b) = c_0. [para(138(a,1),1086(a,1,1)),rewrite([8(10)])].
% 4.00/4.33 1701 ifeq(product(A,multiply(B,C),D),c_0,product(multiply(A,B),C,D),c_0) = c_0. [para(48(a,1),126(a,1,3,1)),rewrite([8(9)])].
% 4.00/4.33 1709 ifeq(product(d,b,A),c_0,product(A,b,h),c_0) = c_0. [para(792(a,1),126(a,1,1)),rewrite([8(13)])].
% 4.00/4.33 1714 ifeq(product(d,h,A),c_0,product(A,h,k),c_0) = c_0. [para(1045(a,1),126(a,1,1)),rewrite([8(13)])].
% 4.00/4.33 1906 ifeq(product(a,c,A),c_0,product(a,A,b),c_0) = c_0. [para(1262(a,1),132(a,1,1)),rewrite([8(13)])].
% 4.00/4.33 1917 product(multiply(d,b),b,h) = c_0. [para(48(a,1),1709(a,1,1)),rewrite([8(10)])].
% 4.00/4.33 1928 multiply(multiply(d,b),b) = h. [para(1917(a,1),166(a,1,1)),rewrite([7(9)])].
% 4.00/4.33 2034 product(multiply(d,h),h,k) = c_0. [para(48(a,1),1714(a,1,1)),rewrite([8(10)])].
% 4.00/4.33 2064 multiply(multiply(d,h),h) = k. [para(2034(a,1),166(a,1,1)),rewrite([7(9)])].
% 4.00/4.33 2200 product(a,multiply(a,c),b) = c_0. [para(48(a,1),1906(a,1,1)),rewrite([8(10)])].
% 4.00/4.33 2211 multiply(a,multiply(a,c)) = b. [para(2200(a,1),166(a,1,1)),rewrite([7(9)])].
% 4.00/4.33 2558 product(identity,A,inverse(inverse(A))) = c_0. [para(37(a,1),191(a,1,1)),rewrite([8(8)])].
% 4.00/4.33 2559 product(multiply(A,inverse(B)),B,A) = c_0. [para(48(a,1),191(a,1,1)),rewrite([8(7)])].
% 4.00/4.33 2569 inverse(inverse(A)) = A. [para(2558(a,1),151(a,1,1)),rewrite([7(5)])].
% 4.00/4.33 2580 multiply(multiply(A,inverse(B)),B) = A. [para(2559(a,1),166(a,1,1)),rewrite([7(6)])].
% 4.00/4.33 2663 multiply(inverse(A),inverse(A)) = A. [para(307(a,1),2580(a,1,1)),rewrite([171(2)]),flip(a)].
% 4.00/4.33 2664 multiply(multiply(A,B),inverse(B)) = A. [para(2569(a,1),2580(a,1,1,2))].
% 4.00/4.33 2674 multiply(A,A) = inverse(A). [para(2569(a,1),2663(a,1,1)),rewrite([2569(2)])].
% 4.00/4.33 2675 product(A,A,inverse(A)) = c_0. [para(2663(a,1),2559(a,1,1))].
% 4.00/4.33 2761 multiply(d,b) = multiply(h,inverse(b)). [para(1928(a,1),2664(a,1,1)),flip(a)].
% 4.00/4.33 2763 multiply(k,inverse(h)) = multiply(d,h). [para(2064(a,1),2664(a,1,1))].
% 4.00/4.33 2765 multiply(b,inverse(multiply(a,c))) = a. [para(2211(a,1),2664(a,1,1))].
% 4.00/4.33 3357 product(multiply(inverse(multiply(A,B)),A),B,identity) = c_0. [para(48(a,1),225(a,1,1)),rewrite([8(9)])].
% 4.00/4.33 3393 product(multiply(inverse(b),a),multiply(a,c),identity) = c_0. [para(2200(a,1),226(a,1,1)),rewrite([8(13)])].
% 4.00/4.33 4441 multiply(multiply(inverse(multiply(A,B)),A),B) = identity. [para(3357(a,1),166(a,1,1)),rewrite([7(8)])].
% 4.00/4.33 4500 multiply(inverse(multiply(A,B)),A) = inverse(B). [para(4441(a,1),2664(a,1,1)),rewrite([171(3)]),flip(a)].
% 4.00/4.33 4532 inverse(multiply(a,c)) = multiply(inverse(b),a). [para(2211(a,1),4500(a,1,1,1)),flip(a)].
% 4.00/4.33 4538 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(4500(a,1),2664(a,1,1)),flip(a)].
% 4.00/4.33 4539 multiply(inverse(A),multiply(A,B)) = B. [para(2664(a,1),4500(a,1,1,1)),rewrite([2569(5)])].
% 4.00/4.33 4542 multiply(multiply(inverse(h),inverse(d)),k) = h. [para(2763(a,1),4500(a,1,1,1)),rewrite([4538(4),2569(10)])].
% 4.00/4.33 4544 multiply(inverse(a),b) = multiply(a,c). [para(2765(a,1),4500(a,1,1,1)),rewrite([4538(8),4538(10),2569(7),2569(8)])].
% 4.00/4.33 4657 multiply(inverse(c),inverse(a)) = multiply(inverse(b),a). [back_rewrite(4532),rewrite([4538(4)])].
% 4.00/4.33 4884 product(inverse(A),multiply(A,B),B) = c_0. [para(4539(a,1),48(a,1,3))].
% 4.00/4.33 5005 multiply(inverse(h),inverse(d)) = multiply(h,inverse(k)). [para(4542(a,1),2664(a,1,1)),flip(a)].
% 4.00/4.33 6982 product(d,A,multiply(h,multiply(b,A))) = c_0. [para(48(a,1),474(a,1,1)),rewrite([8(10)])].
% 4.00/4.33 6998 multiply(h,multiply(b,A)) = multiply(d,A). [para(6982(a,1),166(a,1,1)),rewrite([7(9)]),flip(a)].
% 4.00/4.33 7012 multiply(inverse(h),multiply(d,A)) = multiply(b,A). [para(6998(a,1),4539(a,1,2))].
% 4.00/4.33 7172 multiply(h,inverse(k)) = multiply(b,d). [para(2674(a,1),7012(a,1,2)),rewrite([5005(5)])].
% 4.00/4.33 7282 multiply(inverse(d),inverse(b)) = multiply(d,h). [para(7172(a,1),4538(a,1,1)),rewrite([4538(4),2569(8),2763(9)])].
% 4.00/4.33 7557 product(multiply(A,h),b,multiply(A,d)) = c_0. [para(48(a,1),493(a,1,1)),rewrite([8(10)])].
% 4.00/4.33 7885 multiply(multiply(A,h),b) = multiply(A,d). [para(7557(a,1),166(a,1,1)),rewrite([7(9)])].
% 4.00/4.33 9232 product(multiply(A,multiply(inverse(b),a)),multiply(a,c),A) = c_0. [para(3393(a,1),568(a,1,1)),rewrite([8(13)])].
% 4.00/4.33 10050 product(multiply(A,a),b,multiply(A,c)) = c_0. [para(48(a,1),658(a,1,1)),rewrite([8(10)])].
% 4.00/4.33 10058 multiply(multiply(A,a),b) = multiply(A,c). [para(10050(a,1),166(a,1,1)),rewrite([7(9)])].
% 4.00/4.33 10104 multiply(multiply(A,inverse(a)),c) = multiply(A,b). [para(2580(a,1),10058(a,1,1)),flip(a)].
% 4.00/4.33 10105 multiply(multiply(A,c),inverse(b)) = multiply(A,a). [para(10058(a,1),2664(a,1,1))].
% 4.00/4.33 10182 multiply(multiply(A,b),inverse(c)) = multiply(A,inverse(a)). [para(10104(a,1),2664(a,1,1))].
% 4.00/4.33 10197 multiply(multiply(A,inverse(c)),a) = multiply(A,inverse(b)). [para(2580(a,1),10105(a,1,1)),flip(a)].
% 4.00/4.33 10861 multiply(multiply(A,d),inverse(c)) = multiply(multiply(A,h),inverse(a)). [para(7885(a,1),10182(a,1,1))].
% 4.00/4.33 11140 product(inverse(c),inverse(a),multiply(c,d)) = c_0. [para(2675(a,1),842(a,1,1)),rewrite([8(12)])].
% 4.00/4.33 11150 multiply(inverse(b),a) = multiply(c,d). [para(11140(a,1),166(a,1,1)),rewrite([4657(7),7(10)])].
% 4.00/4.33 11186 product(multiply(A,multiply(c,d)),multiply(a,c),A) = c_0. [back_rewrite(9232),rewrite([11150(4)])].
% 4.00/4.33 11283 multiply(inverse(c),inverse(a)) = multiply(c,d). [back_rewrite(4657),rewrite([11150(9)])].
% 4.00/4.33 11299 multiply(inverse(d),inverse(c)) = multiply(a,c). [para(11150(a,1),4538(a,1,1)),rewrite([4538(4),2569(10),4544(9)])].
% 4.00/4.33 11418 multiply(multiply(a,c),a) = multiply(d,h). [para(11299(a,1),10197(a,1,1)),rewrite([7282(10)])].
% 4.00/4.33 11648 product(d,multiply(a,A),multiply(c,A)) = c_0. [para(4884(a,1),866(a,1,1)),rewrite([8(10)])].
% 4.00/4.33 11833 multiply(d,multiply(a,A)) = multiply(c,A). [para(11648(a,1),166(a,1,1)),rewrite([7(9)])].
% 4.00/4.33 11860 multiply(c,multiply(a,c)) = multiply(h,inverse(b)). [para(2211(a,1),11833(a,1,2)),rewrite([2761(3)]),flip(a)].
% 4.00/4.33 12000 multiply(multiply(c,h),inverse(a)) = multiply(b,inverse(h)). [para(11860(a,1),4538(a,1,1)),rewrite([4538(5),2569(3),4538(8),11283(9),10861(10)]),flip(a)].
% 4.00/4.33 12743 product(multiply(a,c),multiply(a,c),multiply(c,d)) = c_0. [para(2674(a,1),11186(a,1,1)),rewrite([4538(4),11299(5)])].
% 4.00/4.33 14680 product(multiply(d,h),c,multiply(c,d)) = c_0. [para(12743(a,1),1701(a,1,1)),rewrite([11418(7),8(12)])].
% 4.00/4.33 14939 multiply(multiply(d,h),c) = multiply(c,d). [para(14680(a,1),166(a,1,1)),rewrite([7(11)])].
% 4.00/4.33 14968 multiply(d,h) = multiply(b,inverse(h)). [para(14939(a,1),2664(a,1,1)),rewrite([10861(6),12000(6)]),flip(a)].
% 4.00/4.33 15127 k = b. [back_rewrite(2064),rewrite([14968(3),2580(6)]),flip(a)].
% 4.00/4.33 16527 $F # answer(prove_k_times_inverse_b_is_e). [back_rewrite(42),rewrite([15127(1),52(5)]),xx(a)].
% 4.00/4.33
% 4.00/4.33 % SZS output end Refutation
% 4.00/4.33 ============================== end of proof ==========================
% 4.00/4.33
% 4.00/4.33 ============================== STATISTICS ============================
% 4.00/4.33
% 4.00/4.33 Given=1995. Generated=112935. Kept=16512. proofs=1.
% 4.00/4.33 Usable=1312. Sos=6690. Demods=9402. Limbo=1400, Disabled=7128. Hints=0.
% 4.00/4.33 Megabytes=13.40.
% 4.00/4.33 User_CPU=3.20, System_CPU=0.07, Wall_clock=4.
% 4.00/4.33
% 4.00/4.33 ============================== end of statistics =====================
% 4.00/4.33
% 4.00/4.33 ============================== end of search =========================
% 4.00/4.33
% 4.00/4.33 THEOREM PROVED
% 4.00/4.33 % SZS status Unsatisfiable
% 4.00/4.33
% 4.00/4.33 Exiting with 1 proof.
% 4.00/4.33
% 4.00/4.33 Process 31896 exit (max_proofs) Mon Jun 13 17:37:54 2022
% 4.00/4.33 Prover9 interrupted
%------------------------------------------------------------------------------