TSTP Solution File: BOO038-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO038-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 : Thu Jul 14 23:48:05 EDT 2022
% Result : Unsatisfiable 2.06s 2.37s
% Output : Refutation 2.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO038-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n029.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 : Wed Jun 1 20:18:01 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.06/2.37 ============================== Prover9 ===============================
% 2.06/2.37 Prover9 (32) version 2009-11A, November 2009.
% 2.06/2.37 Process 27920 was started by sandbox2 on n029.cluster.edu,
% 2.06/2.37 Wed Jun 1 20:18:01 2022
% 2.06/2.37 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27766_n029.cluster.edu".
% 2.06/2.37 ============================== end of head ===========================
% 2.06/2.37
% 2.06/2.37 ============================== INPUT =================================
% 2.06/2.37
% 2.06/2.37 % Reading from file /tmp/Prover9_27766_n029.cluster.edu
% 2.06/2.37
% 2.06/2.37 set(prolog_style_variables).
% 2.06/2.37 set(auto2).
% 2.06/2.37 % set(auto2) -> set(auto).
% 2.06/2.37 % set(auto) -> set(auto_inference).
% 2.06/2.37 % set(auto) -> set(auto_setup).
% 2.06/2.37 % set(auto_setup) -> set(predicate_elim).
% 2.06/2.37 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.06/2.37 % set(auto) -> set(auto_limits).
% 2.06/2.37 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.06/2.37 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.06/2.37 % set(auto) -> set(auto_denials).
% 2.06/2.37 % set(auto) -> set(auto_process).
% 2.06/2.37 % set(auto2) -> assign(new_constants, 1).
% 2.06/2.37 % set(auto2) -> assign(fold_denial_max, 3).
% 2.06/2.37 % set(auto2) -> assign(max_weight, "200.000").
% 2.06/2.37 % set(auto2) -> assign(max_hours, 1).
% 2.06/2.37 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.06/2.37 % set(auto2) -> assign(max_seconds, 0).
% 2.06/2.37 % set(auto2) -> assign(max_minutes, 5).
% 2.06/2.37 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.06/2.37 % set(auto2) -> set(sort_initial_sos).
% 2.06/2.37 % set(auto2) -> assign(sos_limit, -1).
% 2.06/2.37 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.06/2.37 % set(auto2) -> assign(max_megs, 400).
% 2.06/2.37 % set(auto2) -> assign(stats, some).
% 2.06/2.37 % set(auto2) -> clear(echo_input).
% 2.06/2.37 % set(auto2) -> set(quiet).
% 2.06/2.37 % set(auto2) -> clear(print_initial_clauses).
% 2.06/2.37 % set(auto2) -> clear(print_given).
% 2.06/2.37 assign(lrs_ticks,-1).
% 2.06/2.37 assign(sos_limit,10000).
% 2.06/2.37 assign(order,kbo).
% 2.06/2.37 set(lex_order_vars).
% 2.06/2.37 clear(print_given).
% 2.06/2.37
% 2.06/2.37 % formulas(sos). % not echoed (2 formulas)
% 2.06/2.37
% 2.06/2.37 ============================== end of input ==========================
% 2.06/2.37
% 2.06/2.37 % From the command line: assign(max_seconds, 300).
% 2.06/2.37
% 2.06/2.37 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.06/2.37
% 2.06/2.37 % Formulas that are not ordinary clauses:
% 2.06/2.37
% 2.06/2.37 ============================== end of process non-clausal formulas ===
% 2.06/2.37
% 2.06/2.37 ============================== PROCESS INITIAL CLAUSES ===============
% 2.06/2.37
% 2.06/2.37 ============================== PREDICATE ELIMINATION =================
% 2.06/2.37
% 2.06/2.37 ============================== end predicate elimination =============
% 2.06/2.37
% 2.06/2.37 Auto_denials:
% 2.06/2.37 % copying label huntinton to answer in negative clause
% 2.06/2.37
% 2.06/2.37 Term ordering decisions:
% 2.06/2.37
% 2.06/2.37 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 2.06/2.37 Function symbol KB weights: a=1. b=1. c=1. add=1. inverse=0.
% 2.06/2.37
% 2.06/2.37 ============================== end of process initial clauses ========
% 2.06/2.37
% 2.06/2.37 ============================== CLAUSES FOR SEARCH ====================
% 2.06/2.37
% 2.06/2.37 ============================== end of clauses for search =============
% 2.06/2.37
% 2.06/2.37 ============================== SEARCH ================================
% 2.06/2.37
% 2.06/2.37 % Starting search at 0.01 seconds.
% 2.06/2.37
% 2.06/2.37 ============================== PROOF =================================
% 2.06/2.37 % SZS status Unsatisfiable
% 2.06/2.37 % SZS output start Refutation
% 2.06/2.37
% 2.06/2.37 % Proof 1 at 1.35 (+ 0.03) seconds: huntinton.
% 2.06/2.37 % Length of proof is 175.
% 2.06/2.37 % Level of proof is 49.
% 2.06/2.37 % Maximum clause weight is 90.000.
% 2.06/2.37 % Given clauses 248.
% 2.06/2.37
% 2.06/2.37 1 inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,D)))))))) = C # label(dn1) # label(axiom). [assumption].
% 2.06/2.37 2 add(b,a) != add(a,b) | add(add(a,b),c) != add(a,add(b,c)) | add(inverse(add(inverse(a),b)),inverse(add(inverse(a),inverse(b)))) != a # label(huntinton) # label(negated_conjecture) # answer(huntinton). [assumption].
% 2.06/2.37 3 inverse(add(inverse(add(A,B)),inverse(add(inverse(add(inverse(add(C,D)),A)),inverse(add(inverse(B),inverse(add(B,E)))))))) = B. [para(1(a,1),1(a,1,1,1,1,1))].
% 2.06/2.37 4 inverse(add(A,inverse(add(inverse(add(B,C)),inverse(add(inverse(inverse(add(B,inverse(add(inverse(A),inverse(add(A,D))))))),inverse(add(inverse(add(B,inverse(add(inverse(A),inverse(add(A,D)))))),E)))))))) = inverse(add(B,inverse(add(inverse(A),inverse(add(A,D)))))). [para(1(a,1),1(a,1,1,1))].
% 2.06/2.37 16 inverse(add(inverse(add(A,inverse(A))),A)) = inverse(A). [para(1(a,1),3(a,1,1,2))].
% 2.06/2.37 20 inverse(add(inverse(A),inverse(add(A,inverse(add(inverse(A),inverse(add(A,B)))))))) = A. [para(16(a,1),1(a,1,1,1))].
% 2.06/2.37 25 inverse(add(inverse(add(A,B)),inverse(add(inverse(A),inverse(add(inverse(B),inverse(add(B,C)))))))) = B. [para(20(a,1),1(a,1,1,1,1,1))].
% 2.06/2.37 29 inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,C)))) = C. [para(20(a,1),1(a,1,1,2,1,2))].
% 2.06/2.37 50 inverse(add(A,inverse(add(inverse(add(B,C)),inverse(add(B,inverse(add(inverse(A),inverse(add(A,D)))))))))) = inverse(add(B,inverse(add(inverse(A),inverse(add(A,D)))))). [para(1(a,1),29(a,1,1,1))].
% 2.06/2.37 51 inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(A,B)),C)),D)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,E)))))))),C)) = inverse(add(A,inverse(add(inverse(C),inverse(add(C,E)))))). [para(1(a,1),29(a,1,1,2))].
% 2.06/2.37 56 inverse(add(inverse(add(A,B)),inverse(add(inverse(A),B)))) = B. [para(20(a,1),29(a,1,1,1,1,1))].
% 2.06/2.37 62 inverse(add(A,inverse(add(inverse(add(B,C)),inverse(add(B,A)))))) = inverse(add(B,A)). [para(29(a,1),29(a,1,1,1))].
% 2.06/2.37 63 inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(A,B)),C)),D)),inverse(add(A,C)))),C)) = inverse(add(A,C)). [para(29(a,1),29(a,1,1,2))].
% 2.06/2.37 66 inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(D,inverse(add(inverse(C),inverse(add(C,E)))))))))))) = C. [para(4(a,1),1(a,1,1,2,1,2,1,2))].
% 2.06/2.37 97 inverse(add(inverse(add(inverse(add(inverse(add(A,inverse(add(A,B)))),C)),A)),inverse(add(A,B)))) = A. [para(56(a,1),1(a,1,1,2))].
% 2.06/2.37 104 inverse(add(inverse(add(add(A,inverse(A)),A)),inverse(A))) = A. [para(16(a,1),56(a,1,1,2))].
% 2.06/2.37 114 inverse(add(inverse(add(A,B)),inverse(add(inverse(add(C,A)),B)))) = B. [para(56(a,1),29(a,1,1,1,1,1))].
% 2.06/2.37 115 inverse(add(A,inverse(add(B,inverse(add(inverse(B),A)))))) = inverse(add(inverse(B),A)). [para(56(a,1),29(a,1,1,1))].
% 2.06/2.37 141 inverse(add(A,inverse(add(add(A,inverse(A)),inverse(A))))) = inverse(A). [para(104(a,1),29(a,1,1,1))].
% 2.06/2.37 160 inverse(add(inverse(A),inverse(A))) = A. [para(141(a,1),20(a,1,1,2,1,2,1,2)),rewrite([115(9)])].
% 2.06/2.37 164 inverse(add(inverse(add(inverse(A),B)),inverse(add(A,B)))) = B. [para(141(a,1),29(a,1,1,1,1,1))].
% 2.06/2.37 181 add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,D))))))) = inverse(add(C,C)). [para(1(a,1),160(a,1,1,1)),rewrite([1(13)]),flip(a)].
% 2.06/2.37 184 add(inverse(add(A,inverse(A))),A) = A. [para(16(a,1),160(a,1,1,1)),rewrite([16(6),160(4)]),flip(a)].
% 2.06/2.37 191 inverse(add(inverse(add(inverse(add(inverse(A),B)),inverse(A))),A)) = inverse(A). [para(160(a,1),29(a,1,1,2))].
% 2.06/2.37 192 add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,C))) = inverse(add(C,C)). [para(29(a,1),160(a,1,1,1)),rewrite([29(8)]),flip(a)].
% 2.06/2.37 198 add(inverse(add(A,B)),inverse(add(inverse(A),B))) = inverse(add(B,B)). [para(56(a,1),160(a,1,1,1)),rewrite([56(7)]),flip(a)].
% 2.06/2.37 203 inverse(add(A,A)) = add(inverse(A),inverse(A)). [para(160(a,1),160(a,1,1,1)),rewrite([160(4)])].
% 2.06/2.37 208 add(inverse(inverse(A)),inverse(inverse(A))) = A. [back_rewrite(1),rewrite([181(12),203(2),203(4)])].
% 2.06/2.37 217 add(inverse(add(A,B)),inverse(add(inverse(A),B))) = add(inverse(B),inverse(B)). [back_rewrite(198),rewrite([203(8)])].
% 2.06/2.37 218 add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,C))) = add(inverse(C),inverse(C)). [back_rewrite(192),rewrite([203(9)])].
% 2.06/2.37 250 inverse(add(inverse(A),inverse(add(add(A,inverse(A)),A)))) = A. [para(184(a,1),164(a,1,1,1,1))].
% 2.06/2.37 252 add(inverse(add(inverse(A),B)),inverse(add(A,B))) = add(inverse(B),inverse(B)). [para(164(a,1),208(a,1,1,1)),rewrite([164(8)]),flip(a)].
% 2.06/2.37 321 add(inverse(A),inverse(add(add(A,inverse(A)),A))) = add(inverse(A),inverse(A)). [para(250(a,1),208(a,1,1,1)),rewrite([250(8)]),flip(a)].
% 2.06/2.37 377 inverse(add(inverse(add(inverse(A),A)),inverse(A))) = A. [para(184(a,1),114(a,1,1,2,1))].
% 2.06/2.37 378 add(inverse(add(A,B)),inverse(add(inverse(add(C,A)),B))) = add(inverse(B),inverse(B)). [para(114(a,1),208(a,1,1,1)),rewrite([114(9)]),flip(a)].
% 2.06/2.37 405 add(inverse(add(inverse(A),A)),inverse(A)) = add(inverse(A),inverse(A)). [para(377(a,1),208(a,1,1,1)),rewrite([377(7)]),flip(a)].
% 2.06/2.37 411 add(inverse(add(A,B)),inverse(add(inverse(A),inverse(add(inverse(B),inverse(add(B,C))))))) = add(inverse(B),inverse(B)). [para(25(a,1),208(a,1,1,1)),rewrite([25(13)]),flip(a)].
% 2.06/2.37 416 inverse(add(inverse(add(A,add(B,B))),inverse(add(inverse(A),inverse(add(add(inverse(B),inverse(B)),inverse(add(add(B,B),C)))))))) = add(B,B). [para(203(a,1),25(a,1,1,2,1,2,1,1))].
% 2.06/2.37 426 add(inverse(add(A,add(inverse(A),inverse(A)))),A) = add(A,A). [para(25(a,1),405(a,1,1,1,1)),rewrite([411(11),411(16),203(9),208(10),411(17),203(10),208(11),411(17),203(10),208(11)])].
% 2.06/2.37 441 add(inverse(add(inverse(add(inverse(A),B)),inverse(A))),A) = A. [para(191(a,1),208(a,1,1,1)),rewrite([191(10),208(5)]),flip(a)].
% 2.06/2.37 443 add(inverse(A),inverse(A)) = inverse(A). [para(405(a,1),191(a,1,1,1,1)),rewrite([203(4),208(5),203(2)])].
% 2.06/2.37 444 add(A,A) = A. [para(191(a,1),426(a,1,1,1,2,1)),rewrite([441(7),441(8),443(3),441(10),184(4),441(7),441(7)]),flip(a)].
% 2.06/2.37 447 inverse(inverse(A)) = A. [back_rewrite(416),rewrite([444(1),444(6),444(5),411(11),444(3),444(3)])].
% 2.06/2.37 451 add(inverse(add(A,B)),inverse(add(inverse(add(C,A)),B))) = inverse(B). [back_rewrite(378),rewrite([444(10)])].
% 2.06/2.37 460 add(inverse(A),inverse(add(add(A,inverse(A)),A))) = inverse(A). [back_rewrite(321),rewrite([444(9)])].
% 2.06/2.37 468 add(inverse(add(inverse(A),B)),inverse(add(A,B))) = inverse(B). [back_rewrite(252),rewrite([444(9)])].
% 2.06/2.37 474 add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,C))) = inverse(C). [back_rewrite(218),rewrite([444(10)])].
% 2.06/2.37 475 add(inverse(add(A,B)),inverse(add(inverse(A),B))) = inverse(B). [back_rewrite(217),rewrite([444(9)])].
% 2.06/2.37 586 add(A,inverse(add(inverse(add(B,C)),inverse(add(B,inverse(add(inverse(A),inverse(add(A,D))))))))) = add(B,inverse(add(inverse(A),inverse(add(A,D))))). [para(50(a,1),447(a,1,1)),rewrite([447(8)]),flip(a)].
% 2.06/2.37 637 inverse(add(inverse(add(inverse(add(add(A,B),C)),inverse(add(A,inverse(add(add(add(add(A,B),inverse(add(A,B))),add(A,B)),inverse(add(inverse(add(add(add(A,B),inverse(add(A,B))),add(A,B))),D)))))))),inverse(add(add(add(A,B),inverse(add(A,B))),add(A,B))))) = inverse(add(A,inverse(add(add(add(add(A,B),inverse(add(A,B))),add(A,B)),inverse(add(inverse(add(add(add(A,B),inverse(add(A,B))),add(A,B))),D)))))). [para(460(a,1),51(a,1,1,1,1,1,1,1,1)),rewrite([447(3),447(11),447(41)])].
% 2.06/2.37 664 add(A,inverse(add(add(B,A),inverse(add(inverse(B),A))))) = add(inverse(B),A). [para(475(a,1),468(a,1,1,1)),rewrite([447(2),447(11)])].
% 2.06/2.37 749 add(inverse(add(inverse(add(A,B)),C)),inverse(add(B,C))) = inverse(C). [para(468(a,1),451(a,1,2,1,1,1)),rewrite([447(6)])].
% 2.06/2.37 776 inverse(add(A,add(B,A))) = inverse(add(B,A)). [para(444(a,1),62(a,1,1,2,1)),rewrite([447(3)])].
% 2.06/2.37 777 add(A,inverse(add(inverse(add(B,C)),inverse(add(B,A))))) = add(B,A). [para(62(a,1),447(a,1,1)),rewrite([447(3)]),flip(a)].
% 2.06/2.37 787 add(inverse(add(A,inverse(B))),inverse(add(B,inverse(add(inverse(add(A,C)),inverse(add(A,inverse(B)))))))) = add(inverse(add(A,C)),inverse(add(A,inverse(B)))). [para(62(a,1),468(a,1,1)),rewrite([447(21)])].
% 2.06/2.37 810 inverse(add(inverse(add(inverse(add(A,B)),inverse(add(A,C)))),inverse(add(inverse(add(C,D)),inverse(add(A,C)))))) = inverse(add(A,C)). [para(62(a,1),62(a,1,1,2,1,2)),rewrite([777(21)])].
% 2.06/2.37 811 inverse(add(inverse(add(A,B)),inverse(add(A,inverse(add(inverse(add(A,B)),C)))))) = add(A,inverse(add(inverse(add(A,B)),C))). [para(62(a,1),62(a,1,1,2)),rewrite([444(13),447(7)]),flip(a)].
% 2.06/2.37 817 add(A,add(B,A)) = add(B,A). [para(776(a,1),447(a,1,1)),rewrite([447(3)]),flip(a)].
% 2.06/2.37 828 add(inverse(add(A,B)),inverse(B)) = inverse(B). [para(468(a,1),817(a,1,2)),rewrite([468(10)])].
% 2.06/2.37 829 add(inverse(add(A,inverse(B))),B) = B. [para(447(a,1),828(a,1,2)),rewrite([447(6)])].
% 2.06/2.37 863 inverse(add(add(A,B),B)) = inverse(add(A,B)). [para(828(a,1),63(a,1,1,1,1)),rewrite([447(3)])].
% 2.06/2.37 881 add(add(A,B),B) = add(A,B). [para(863(a,1),447(a,1,1)),rewrite([447(3)]),flip(a)].
% 2.06/2.37 885 add(inverse(A),inverse(add(B,A))) = inverse(A). [para(468(a,1),881(a,1,1)),rewrite([468(10)])].
% 2.06/2.37 886 add(A,inverse(add(B,inverse(A)))) = A. [para(447(a,1),885(a,1,1)),rewrite([447(6)])].
% 2.06/2.37 899 inverse(add(A,inverse(add(inverse(B),inverse(add(add(B,A),inverse(add(C,inverse(add(add(B,A),inverse(add(inverse(add(B,A)),D)))))))))))) = inverse(add(B,A)). [para(468(a,1),66(a,1,1,1,1)),rewrite([447(2),447(4),447(5)])].
% 2.06/2.37 932 add(A,inverse(add(inverse(B),inverse(add(B,A))))) = add(B,A). [para(468(a,1),474(a,1,1,1)),rewrite([447(2),447(9)])].
% 2.06/2.37 934 add(A,inverse(add(B,inverse(add(inverse(B),A))))) = add(inverse(B),A). [para(475(a,1),474(a,1,1,1)),rewrite([447(2),447(10)])].
% 2.06/2.37 937 add(A,inverse(add(B,inverse(add(inverse(add(C,B)),A))))) = add(inverse(add(C,B)),A). [para(451(a,1),474(a,1,1,1)),rewrite([447(2),447(12)])].
% 2.06/2.37 940 add(add(A,B),inverse(add(A,inverse(add(C,add(A,B)))))) = add(C,add(A,B)). [para(885(a,1),474(a,1,1,1)),rewrite([447(3),447(11)])].
% 2.06/2.37 969 add(inverse(add(A,B)),inverse(add(inverse(B),inverse(add(inverse(A),inverse(add(A,B))))))) = add(inverse(A),inverse(add(A,B))). [para(932(a,1),475(a,1,1,1)),rewrite([447(17)])].
% 2.06/2.37 970 add(inverse(add(A,inverse(add(inverse(B),inverse(add(B,inverse(A))))))),inverse(add(B,inverse(A)))) = add(inverse(B),inverse(add(B,inverse(A)))). [para(932(a,1),475(a,1,2,1)),rewrite([447(19)])].
% 2.06/2.37 971 add(inverse(add(A,B)),inverse(add(inverse(add(C,B)),inverse(add(inverse(A),inverse(add(A,B))))))) = add(inverse(A),inverse(add(A,B))). [para(932(a,1),451(a,1,1,1)),rewrite([447(18)])].
% 2.06/2.37 972 add(inverse(add(A,inverse(add(inverse(B),inverse(add(B,inverse(add(C,A)))))))),inverse(add(B,inverse(add(C,A))))) = add(inverse(B),inverse(add(B,inverse(add(C,A))))). [para(932(a,1),451(a,1,2,1)),rewrite([447(22)])].
% 2.06/2.37 973 add(inverse(add(A,inverse(add(B,C)))),inverse(add(B,inverse(add(inverse(A),inverse(add(A,inverse(add(B,C))))))))) = add(inverse(A),inverse(add(A,inverse(add(B,C))))). [para(932(a,1),474(a,1,1,1)),rewrite([447(22)])].
% 2.06/2.37 984 add(inverse(add(inverse(add(A,inverse(add(inverse(B),C)))),inverse(add(B,C)))),C) = add(B,C). [para(468(a,1),749(a,1,2,1)),rewrite([447(11),447(13)])].
% 2.06/2.37 985 add(inverse(add(inverse(add(A,inverse(add(B,C)))),inverse(add(inverse(B),C)))),C) = add(inverse(B),C). [para(475(a,1),749(a,1,2,1)),rewrite([447(11),447(14)])].
% 2.06/2.37 987 add(inverse(add(inverse(add(A,inverse(add(B,C)))),inverse(add(inverse(add(D,B)),C)))),C) = add(inverse(add(D,B)),C). [para(451(a,1),749(a,1,2,1)),rewrite([447(12),447(16)])].
% 2.06/2.37 988 add(inverse(add(inverse(add(A,add(B,C))),C)),inverse(add(B,C))) = inverse(C). [para(881(a,1),749(a,1,2,1))].
% 2.06/2.37 989 add(add(A,B),inverse(add(B,inverse(add(C,add(A,B)))))) = add(C,add(A,B)). [para(885(a,1),749(a,1,1,1)),rewrite([447(3),447(11)])].
% 2.06/2.37 1000 add(inverse(add(inverse(A),inverse(B))),inverse(add(B,inverse(add(A,inverse(add(inverse(A),inverse(B)))))))) = add(A,inverse(add(inverse(A),inverse(B)))). [para(934(a,1),468(a,1,1,1)),rewrite([447(20)])].
% 2.06/2.37 1002 add(inverse(add(inverse(A),B)),inverse(add(inverse(B),inverse(add(A,inverse(add(inverse(A),B))))))) = add(A,inverse(add(inverse(A),B))). [para(934(a,1),475(a,1,1,1)),rewrite([447(18)])].
% 2.06/2.37 1011 add(inverse(add(inverse(add(inverse(add(A,inverse(add(A,B)))),C)),A)),inverse(add(A,B))) = inverse(A). [para(97(a,1),447(a,1,1)),flip(a)].
% 2.06/2.37 1020 add(A,add(A,B)) = add(A,B). [para(97(a,1),828(a,1,1)),rewrite([447(3),447(5)])].
% 2.06/2.37 1021 inverse(add(A,inverse(add(inverse(A),B)))) = inverse(A). [para(828(a,1),97(a,1,1,1,1)),rewrite([447(2)])].
% 2.06/2.37 1022 inverse(add(inverse(A),inverse(add(A,B)))) = A. [para(829(a,1),97(a,1,1,1,1))].
% 2.06/2.37 1023 add(add(A,B),A) = add(A,B). [para(97(a,1),885(a,1,2)),rewrite([447(3),447(5)])].
% 2.06/2.37 1031 add(inverse(A),B) = add(B,inverse(A)). [para(97(a,1),932(a,1,2,1,1)),rewrite([1011(11),1021(5),1011(13)]),flip(a)].
% 2.06/2.37 1037 add(inverse(add(A,B)),inverse(add(B,inverse(add(A,C))))) = inverse(B). [para(97(a,1),749(a,1,1,1,1)),rewrite([1031(5)])].
% 2.06/2.37 1046 add(inverse(add(A,inverse(B))),inverse(add(inverse(B),inverse(A)))) = B. [back_rewrite(1002),rewrite([1031(2),1031(6),886(8),1031(6,R),1031(10),886(12)])].
% 2.06/2.37 1047 add(A,inverse(add(inverse(A),inverse(B)))) = A. [back_rewrite(1000),rewrite([1021(10),1031(8,R),1046(8)]),flip(a)].
% 2.06/2.37 1056 inverse(add(A,B)) = inverse(add(B,A)). [back_rewrite(899),rewrite([1031(6),886(8),886(7),1022(5)])].
% 2.06/2.37 1061 inverse(add(inverse(add(add(A,B),inverse(add(A,B)))),inverse(add(inverse(add(C,add(A,B))),inverse(add(A,inverse(add(add(A,B),inverse(add(A,B)))))))))) = inverse(add(A,inverse(add(add(A,B),inverse(add(A,B)))))). [back_rewrite(637),rewrite([1056(3),1023(9),1023(13),1031(13),886(15),1023(18),1031(18,R),1023(25),1023(29),1031(29),886(31)])].
% 2.06/2.37 1084 add(inverse(add(A,B)),inverse(add(A,inverse(add(B,C))))) = add(inverse(A),inverse(add(A,inverse(add(B,C))))). [back_rewrite(973),rewrite([1022(11),1056(6),1031(7,R)])].
% 2.06/2.37 1085 add(inverse(A),inverse(add(A,inverse(add(B,C))))) = inverse(A). [back_rewrite(972),rewrite([1056(3),1022(7),1056(4),1037(7),1056(4)]),flip(a)].
% 2.06/2.37 1086 add(inverse(A),inverse(add(A,B))) = inverse(A). [back_rewrite(971),rewrite([1056(4),1022(9),1031(5),1084(7),1085(6)]),flip(a)].
% 2.06/2.37 1087 add(inverse(add(A,B)),inverse(add(B,inverse(A)))) = inverse(B). [back_rewrite(970),rewrite([1086(5),447(2),1086(11)])].
% 2.06/2.37 1088 add(inverse(add(A,B)),inverse(add(A,inverse(B)))) = inverse(A). [back_rewrite(969),rewrite([1086(7),447(5),1031(4),1086(10)])].
% 2.06/2.37 1095 add(A,B) = add(B,A). [back_rewrite(932),rewrite([1056(3),885(4),447(2)])].
% 2.06/2.37 1105 add(A,inverse(add(inverse(add(B,C)),inverse(add(A,B))))) = add(A,B). [back_rewrite(586),rewrite([1086(6),447(4),1095(3),1086(11),447(9),1095(8)])].
% 2.06/2.37 1111 add(inverse(add(A,B)),inverse(add(B,inverse(add(C,add(A,B)))))) = inverse(B). [back_rewrite(988),rewrite([1095(4),1095(8)])].
% 2.06/2.37 1112 add(A,inverse(add(inverse(add(B,inverse(add(C,A)))),inverse(add(A,inverse(add(C,D))))))) = add(A,inverse(add(C,D))). [back_rewrite(987),rewrite([1095(5),1095(7),1095(11),1095(12),1095(14)])].
% 2.06/2.37 1113 add(A,inverse(add(inverse(add(A,inverse(B))),inverse(add(C,inverse(add(B,A))))))) = add(A,inverse(B)). [back_rewrite(985),rewrite([1095(6),1095(8),1095(10),1095(12)])].
% 2.06/2.37 1114 add(A,inverse(add(inverse(add(B,A)),inverse(add(C,inverse(add(A,inverse(B)))))))) = add(B,A). [back_rewrite(984),rewrite([1095(2),1095(8),1095(10)])].
% 2.06/2.37 1116 add(A,inverse(add(B,inverse(add(A,inverse(add(B,C))))))) = add(A,inverse(add(B,C))). [back_rewrite(937),rewrite([1095(1),1095(3),1095(8),1095(10)])].
% 2.06/2.37 1131 inverse(add(inverse(add(A,B)),inverse(add(A,inverse(add(C,inverse(add(A,B)))))))) = add(A,inverse(add(C,inverse(add(A,B))))). [back_rewrite(811),rewrite([1095(5),1095(13)])].
% 2.06/2.37 1144 add(A,inverse(add(add(A,B),inverse(add(A,inverse(B)))))) = add(A,inverse(B)). [back_rewrite(664),rewrite([1095(1),1095(3),1095(9)])].
% 2.06/2.37 1151 add(c,add(a,b)) != add(a,add(b,c)) # answer(huntinton). [back_rewrite(2),rewrite([1095(3),1095(12),1095(22),1087(30),447(21)]),xx(a),xx(c)].
% 2.06/2.37 1152 add(inverse(add(A,inverse(B))),inverse(add(inverse(A),inverse(B)))) = B. [back_rewrite(1046),rewrite([1095(6)])].
% 2.06/2.37 1154 add(inverse(add(A,B)),inverse(add(A,inverse(add(B,C))))) = inverse(A). [back_rewrite(1084),rewrite([1086(13)])].
% 2.06/2.37 1167 add(inverse(add(A,inverse(add(inverse(add(A,B)),inverse(add(A,inverse(A))))))),inverse(add(add(inverse(add(A,B)),inverse(add(A,inverse(A)))),inverse(add(inverse(add(A,B)),inverse(add(A,inverse(A)))))))) = add(inverse(add(A,B)),inverse(add(A,inverse(A)))). [para(787(a,1),787(a,1,2,1,2,1)),rewrite([787(38)])].
% 2.06/2.37 1173 add(A,add(B,A)) = add(B,A). [para(1087(a,1),1047(a,1,2,1)),rewrite([447(3),1095(2)])].
% 2.06/2.37 1196 add(inverse(A),inverse(add(add(B,inverse(A)),inverse(add(inverse(B),inverse(A)))))) = add(inverse(B),inverse(A)). [para(1152(a,1),1152(a,1,2,1)),rewrite([1095(10)])].
% 2.06/2.37 1205 inverse(add(inverse(add(inverse(add(A,B)),inverse(add(A,inverse(A))))),inverse(add(inverse(add(C,inverse(add(inverse(add(A,B)),inverse(add(A,inverse(A))))))),inverse(add(A,inverse(add(inverse(add(A,B)),inverse(add(A,inverse(A))))))))))) = inverse(add(A,inverse(add(inverse(add(A,B)),inverse(add(A,inverse(A))))))). [para(787(a,1),810(a,1,1,1,1)),rewrite([1095(15)])].
% 2.06/2.37 1226 add(A,inverse(add(inverse(add(A,B)),inverse(add(C,inverse(A)))))) = add(A,B). [para(1086(a,1),1037(a,1,1,1)),rewrite([447(2),1095(4),447(11)])].
% 2.06/2.37 1234 add(inverse(add(A,B)),inverse(add(B,inverse(add(C,A))))) = inverse(B). [para(1087(a,1),1037(a,1,2,1,2,1)),rewrite([1095(3),447(6),1095(5),1095(7)])].
% 2.06/2.37 1242 add(inverse(add(A,B)),inverse(add(C,inverse(add(inverse(add(A,B)),inverse(add(A,inverse(A)))))))) = inverse(add(A,B)). [back_rewrite(1205),rewrite([1226(24),1095(19),1131(22),1226(20)])].
% 2.06/2.38 1243 add(inverse(add(A,B)),inverse(add(A,inverse(A)))) = inverse(add(A,B)). [back_rewrite(1167),rewrite([1226(8),1242(18)]),flip(a)].
% 2.06/2.38 1245 add(inverse(add(A,B)),inverse(add(A,inverse(add(C,add(A,B)))))) = inverse(A). [para(1020(a,1),1154(a,1,1,1)),rewrite([1095(4)])].
% 2.06/2.38 1265 add(add(A,inverse(A)),add(A,B)) = add(A,inverse(A)). [para(1243(a,1),886(a,1,2,1)),rewrite([447(5)])].
% 2.06/2.38 1267 add(inverse(add(A,B)),inverse(add(B,inverse(B)))) = inverse(add(A,B)). [para(1095(a,1),1243(a,1,1,1)),rewrite([1095(7)])].
% 2.06/2.38 1269 add(A,inverse(add(add(A,B),inverse(add(A,B))))) = A. [para(1087(a,1),1243(a,1,1,1)),rewrite([447(2),1095(1),1095(3),447(5),1095(4),1095(7),1088(12),447(8)])].
% 2.06/2.38 1270 add(A,inverse(add(add(B,A),inverse(add(B,A))))) = A. [para(1087(a,1),1243(a,2,1)),rewrite([1087(6),447(2),447(5),1095(4),447(8)])].
% 2.06/2.38 1276 inverse(add(inverse(add(add(A,B),inverse(add(A,B)))),inverse(add(inverse(A),inverse(add(C,add(A,B))))))) = inverse(A). [back_rewrite(1061),rewrite([1269(14),1095(10),1269(19)])].
% 2.06/2.38 1286 add(inverse(A),add(A,B)) = add(A,inverse(A)). [para(1265(a,1),940(a,1,2,1,2,1)),rewrite([886(5),1095(3),1265(7)])].
% 2.06/2.38 1288 add(A,add(B,inverse(A))) = add(A,inverse(A)). [para(447(a,1),1286(a,1,1)),rewrite([1095(2),447(6),1095(5)])].
% 2.06/2.38 1290 add(add(A,B),inverse(add(A,B))) = add(inverse(B),add(A,B)). [para(1087(a,1),1286(a,1,2)),rewrite([447(3),1095(3),447(8),1095(7)]),flip(a)].
% 2.06/2.38 1298 inverse(add(inverse(add(inverse(A),add(B,A))),inverse(add(inverse(B),inverse(add(C,add(B,A))))))) = inverse(B). [back_rewrite(1276),rewrite([1290(4)])].
% 2.06/2.38 1299 add(A,inverse(add(inverse(B),add(A,B)))) = A. [back_rewrite(1270),rewrite([1095(1),1095(2),1290(4)])].
% 2.06/2.38 1301 add(A,inverse(A)) = add(B,inverse(B)). [para(1087(a,1),1288(a,1,2)),rewrite([1095(4),1286(4),1290(8),447(4),1288(5)])].
% 2.06/2.38 1313 add(A,inverse(A)) = c_0. [new_symbol(1301)].
% 2.06/2.38 1328 add(inverse(A),add(B,A)) = c_0. [back_rewrite(1290),rewrite([1313(4)]),flip(a)].
% 2.06/2.38 1331 add(inverse(A),add(A,B)) = c_0. [back_rewrite(1286),rewrite([1313(5)])].
% 2.06/2.38 1336 add(inverse(c_0),inverse(add(A,B))) = inverse(add(A,B)). [back_rewrite(1267),rewrite([1313(4),1095(5)])].
% 2.06/2.38 1341 add(A,inverse(c_0)) = A. [back_rewrite(1299),rewrite([1328(3)])].
% 2.06/2.38 1342 add(inverse(A),inverse(add(B,add(C,A)))) = inverse(A). [back_rewrite(1298),rewrite([1095(2),1331(3),1095(4),1336(9),447(7)])].
% 2.06/2.38 1375 inverse(add(add(A,B),inverse(add(C,inverse(B))))) = inverse(add(A,B)). [para(1328(a,1),1037(a,1,1,1)),rewrite([1095(5),1336(9)])].
% 2.06/2.38 1376 add(A,inverse(add(A,B))) = add(A,inverse(B)). [back_rewrite(1144),rewrite([1375(6)])].
% 2.06/2.38 1409 add(add(A,B),inverse(add(A,inverse(B)))) = add(A,B). [para(1376(a,1),886(a,1,2,1))].
% 2.06/2.38 1425 add(add(A,B),add(A,inverse(B))) = c_0. [para(1376(a,1),1328(a,1,2)),rewrite([447(3)])].
% 2.06/2.38 1426 add(add(A,B),add(B,inverse(A))) = c_0. [para(1095(a,1),1425(a,1,1))].
% 2.06/2.38 1430 add(inverse(c_0),add(A,B)) = add(A,B). [para(1425(a,1),1376(a,1,2,1)),rewrite([1095(4),1409(9)])].
% 2.06/2.38 1440 add(inverse(A),add(B,add(A,C))) = c_0. [para(940(a,1),1426(a,1,1)),rewrite([1095(10),1245(10),1095(4)])].
% 2.06/2.38 1442 add(inverse(A),add(B,add(C,A))) = c_0. [para(989(a,1),1426(a,1,1)),rewrite([1095(10),1111(10),1095(4)])].
% 2.06/2.38 1481 add(add(A,B),add(C,inverse(A))) = c_0. [para(1088(a,1),1440(a,1,2,2)),rewrite([447(3)])].
% 2.06/2.38 1486 add(add(inverse(A),inverse(B)),add(A,C)) = c_0. [para(1047(a,1),1442(a,1,2,2)),rewrite([447(5),1095(4)])].
% 2.06/2.38 1559 add(add(A,B),inverse(add(C,inverse(A)))) = add(A,B). [para(1481(a,1),1376(a,1,2,1)),rewrite([1095(4),1430(4)]),flip(a)].
% 2.06/2.38 1563 add(add(A,B),add(inverse(A),inverse(C))) = c_0. [para(1486(a,1),1095(a,1)),flip(a)].
% 2.06/2.38 1572 add(inverse(A),inverse(add(B,inverse(A)))) = add(inverse(A),inverse(B)). [back_rewrite(1196),rewrite([1095(6),1559(8),1095(8)])].
% 2.06/2.38 1643 add(add(A,B),add(inverse(B),inverse(C))) = c_0. [para(1095(a,1),1563(a,1,1))].
% 2.06/2.38 1677 add(add(inverse(A),inverse(B)),add(C,add(A,D))) = c_0. [para(1486(a,1),1105(a,1,2,1,2,1)),rewrite([1095(5),1095(9),1336(9),447(7),1486(11)])].
% 2.06/2.38 1697 add(add(A,inverse(B)),add(add(A,B),inverse(C))) = c_0. [para(1376(a,1),1643(a,1,1)),rewrite([447(5)])].
% 2.06/2.38 1699 add(add(A,B),add(C,add(inverse(B),inverse(D)))) = c_0. [para(1643(a,1),1105(a,1,2,1,2,1)),rewrite([1095(5),1095(9),1336(9),447(7),1643(11)])].
% 2.06/2.38 1730 add(inverse(A),add(add(B,add(A,C)),inverse(D))) = c_0. [para(1342(a,1),1643(a,1,1)),rewrite([1095(2),447(5)])].
% 2.06/2.38 2024 inverse(add(add(A,add(B,C)),inverse(add(D,add(inverse(B),inverse(E)))))) = inverse(add(A,add(B,C))). [para(1677(a,1),1037(a,1,1,1)),rewrite([1095(8),1336(12)])].
% 2.06/2.38 2027 add(add(A,add(B,C)),inverse(add(D,add(inverse(B),inverse(E))))) = add(A,add(B,C)). [para(1677(a,1),1112(a,1,2,1,1,1,2,1)),rewrite([1341(5),1095(9),2024(12),886(9),1095(8)]),flip(a)].
% 2.06/2.38 2031 add(A,inverse(add(B,inverse(add(A,B))))) = A. [para(1234(a,1),1116(a,1,2,1)),rewrite([447(2),444(1),1095(1),1095(3)]),flip(a)].
% 2.06/2.38 2047 add(A,add(B,inverse(add(A,B)))) = c_0. [para(2031(a,1),1376(a,1,2,1)),rewrite([1313(2),447(6)]),flip(a)].
% 2.06/2.38 2050 add(A,inverse(add(inverse(add(A,B)),add(B,C)))) = A. [para(1105(a,1),2031(a,1,2,1,2,1)),rewrite([1095(9),1572(9),447(5)])].
% 2.06/2.38 2063 add(A,add(inverse(add(A,B)),add(B,C))) = c_0. [para(1105(a,1),2047(a,1,2,2,1)),rewrite([1095(9),1572(9),447(5)])].
% 2.06/2.38 2161 add(A,add(add(B,C),inverse(add(A,B)))) = c_0. [para(1095(a,1),2063(a,1,2))].
% 2.06/2.38 2291 add(A,inverse(add(add(B,C),inverse(add(A,B))))) = A. [para(2161(a,1),1376(a,1,2,1)),rewrite([1341(3)]),flip(a)].
% 2.06/2.38 2674 inverse(add(inverse(add(A,inverse(B))),add(add(A,B),inverse(C)))) = inverse(add(add(A,B),inverse(C))). [para(1697(a,1),1087(a,1,1,1)),rewrite([1095(9),1336(11)])].
% 2.06/2.38 2681 add(inverse(add(A,inverse(B))),add(add(A,B),inverse(C))) = add(add(A,B),inverse(C)). [para(1697(a,1),1113(a,1,2,1,2,1,2,1)),rewrite([1095(10),2674(11),1341(10),1095(9),886(11),1095(10)]),flip(a)].
% 2.06/2.38 2714 add(add(A,B),inverse(add(C,add(inverse(B),inverse(D))))) = add(A,B). [para(1699(a,1),1376(a,1,2,1)),rewrite([1095(4),1430(4)]),flip(a)].
% 2.06/2.38 2877 inverse(add(add(add(A,add(B,C)),inverse(D)),inverse(add(E,inverse(B))))) = inverse(add(add(A,add(B,C)),inverse(D))). [para(1730(a,1),1037(a,1,1,1)),rewrite([1095(8),1336(12)])].
% 2.06/2.38 2879 add(add(add(A,add(B,C)),inverse(D)),inverse(add(E,inverse(B)))) = add(add(A,add(B,C)),inverse(D)). [para(1730(a,1),1112(a,1,2,1,1,1,2,1)),rewrite([1341(7),1095(11),2877(14),886(13),1095(10)]),flip(a)].
% 2.06/2.38 3347 add(add(A,B),add(A,C)) = add(C,add(A,B)). [para(2050(a,1),1113(a,1,2,1,2,1)),rewrite([1095(3),447(5),1095(7),1342(7),447(3),1095(2),1095(4),447(6)]),flip(a)].
% 2.06/2.38 3521 add(A,add(B,C)) = add(C,add(B,A)). [para(2291(a,1),1114(a,1,2,1,2,1)),rewrite([1095(2),3347(4),1095(6),1342(6),447(3),1095(2),1095(3),3347(5)])].
% 2.06/2.38 3526 add(add(A,B),inverse(add(A,C))) = add(add(A,B),inverse(C)). [para(2291(a,1),1116(a,1,2,1)),rewrite([1095(5)]),flip(a)].
% 2.06/2.38 3652 add(add(A,B),inverse(C)) = add(B,add(A,inverse(C))). [back_rewrite(2681),rewrite([3521(7),3526(6),447(4),1095(3),1173(3),3521(3)]),flip(a)].
% 2.06/2.38 3774 add(b,add(a,c)) != add(a,add(b,c)) # answer(huntinton). [back_rewrite(1151),rewrite([3521(5)])].
% 2.06/2.38 3884 add(add(A,B),add(C,inverse(D))) = add(B,add(A,add(C,inverse(D)))). [back_rewrite(2879),rewrite([3652(4),3652(8),3652(7),886(6),1095(3),3521(4),3652(8)]),flip(a)].
% 2.06/2.38 3904 add(A,add(B,inverse(add(C,add(inverse(A),inverse(D)))))) = add(B,A). [back_rewrite(2714),rewrite([3652(7)])].
% 2.06/2.38 3940 add(A,add(B,C)) = add(B,add(A,C)). [back_rewrite(2027),rewrite([3652(8),3884(8),3904(7),3521(2)])].
% 2.06/2.38 3941 $F # answer(huntinton). [resolve(3940,a,3774,a)].
% 2.06/2.38
% 2.06/2.38 % SZS output end Refutation
% 2.06/2.38 ============================== end of proof ==========================
% 2.06/2.38
% 2.06/2.38 ============================== STATISTICS ============================
% 2.06/2.38
% 2.06/2.38 Given=248. Generated=47199. Kept=3940. proofs=1.
% 2.06/2.38 Usable=86. Sos=1069. Demods=1439. Limbo=288, Disabled=2498. Hints=0.
% 2.06/2.38 Megabytes=5.14.
% 2.06/2.38 User_CPU=1.35, System_CPU=0.03, Wall_clock=2.
% 2.06/2.38
% 2.06/2.38 ============================== end of statistics =====================
% 2.06/2.38
% 2.06/2.38 ============================== end of search =========================
% 2.06/2.38
% 2.06/2.38 THEOREM PROVED
% 2.06/2.38 % SZS status Unsatisfiable
% 2.06/2.38
% 2.06/2.38 Exiting with 1 proof.
% 2.06/2.38
% 2.06/2.38 Process 27920 exit (max_proofs) Wed Jun 1 20:18:03 2022
% 2.06/2.38 Prover9 interrupted
%------------------------------------------------------------------------------