TSTP Solution File: BOO028-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO028-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 23:48:04 EDT 2022
% Result : Unsatisfiable 1.09s 1.42s
% Output : Refutation 1.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : BOO028-1 : TPTP v8.1.0. Released v2.2.0.
% 0.02/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Wed Jun 1 20:30:00 EDT 2022
% 0.10/0.30 % CPUTime :
% 1.09/1.42 ============================== Prover9 ===============================
% 1.09/1.42 Prover9 (32) version 2009-11A, November 2009.
% 1.09/1.42 Process 30149 was started by sandbox2 on n032.cluster.edu,
% 1.09/1.42 Wed Jun 1 20:30:00 2022
% 1.09/1.42 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29996_n032.cluster.edu".
% 1.09/1.42 ============================== end of head ===========================
% 1.09/1.42
% 1.09/1.42 ============================== INPUT =================================
% 1.09/1.42
% 1.09/1.42 % Reading from file /tmp/Prover9_29996_n032.cluster.edu
% 1.09/1.42
% 1.09/1.42 set(prolog_style_variables).
% 1.09/1.42 set(auto2).
% 1.09/1.42 % set(auto2) -> set(auto).
% 1.09/1.42 % set(auto) -> set(auto_inference).
% 1.09/1.42 % set(auto) -> set(auto_setup).
% 1.09/1.42 % set(auto_setup) -> set(predicate_elim).
% 1.09/1.42 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.09/1.42 % set(auto) -> set(auto_limits).
% 1.09/1.42 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.09/1.42 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.09/1.42 % set(auto) -> set(auto_denials).
% 1.09/1.42 % set(auto) -> set(auto_process).
% 1.09/1.42 % set(auto2) -> assign(new_constants, 1).
% 1.09/1.42 % set(auto2) -> assign(fold_denial_max, 3).
% 1.09/1.42 % set(auto2) -> assign(max_weight, "200.000").
% 1.09/1.42 % set(auto2) -> assign(max_hours, 1).
% 1.09/1.42 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.09/1.42 % set(auto2) -> assign(max_seconds, 0).
% 1.09/1.42 % set(auto2) -> assign(max_minutes, 5).
% 1.09/1.42 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.09/1.42 % set(auto2) -> set(sort_initial_sos).
% 1.09/1.42 % set(auto2) -> assign(sos_limit, -1).
% 1.09/1.42 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.09/1.42 % set(auto2) -> assign(max_megs, 400).
% 1.09/1.42 % set(auto2) -> assign(stats, some).
% 1.09/1.42 % set(auto2) -> clear(echo_input).
% 1.09/1.42 % set(auto2) -> set(quiet).
% 1.09/1.42 % set(auto2) -> clear(print_initial_clauses).
% 1.09/1.42 % set(auto2) -> clear(print_given).
% 1.09/1.42 assign(lrs_ticks,-1).
% 1.09/1.42 assign(sos_limit,10000).
% 1.09/1.42 assign(order,kbo).
% 1.09/1.42 set(lex_order_vars).
% 1.09/1.42 clear(print_given).
% 1.09/1.42
% 1.09/1.42 % formulas(sos). % not echoed (11 formulas)
% 1.09/1.42
% 1.09/1.42 ============================== end of input ==========================
% 1.09/1.42
% 1.09/1.42 % From the command line: assign(max_seconds, 300).
% 1.09/1.42
% 1.09/1.42 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.09/1.42
% 1.09/1.42 % Formulas that are not ordinary clauses:
% 1.09/1.42
% 1.09/1.42 ============================== end of process non-clausal formulas ===
% 1.09/1.42
% 1.09/1.42 ============================== PROCESS INITIAL CLAUSES ===============
% 1.09/1.42
% 1.09/1.42 ============================== PREDICATE ELIMINATION =================
% 1.09/1.42
% 1.09/1.42 ============================== end predicate elimination =============
% 1.09/1.42
% 1.09/1.42 Auto_denials:
% 1.09/1.42 % copying label prove_multiply_add_property to answer in negative clause
% 1.09/1.42
% 1.09/1.42 Term ordering decisions:
% 1.09/1.42
% 1.09/1.42 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 1.09/1.42 Function symbol KB weights: a=1. b=1. c=1. add=1. multiply=1. inverse=0.
% 1.09/1.42
% 1.09/1.42 ============================== end of process initial clauses ========
% 1.09/1.42
% 1.09/1.42 ============================== CLAUSES FOR SEARCH ====================
% 1.09/1.42
% 1.09/1.42 ============================== end of clauses for search =============
% 1.09/1.42
% 1.09/1.42 ============================== SEARCH ================================
% 1.09/1.42
% 1.09/1.42 % Starting search at 0.01 seconds.
% 1.09/1.42
% 1.09/1.42 ============================== PROOF =================================
% 1.09/1.42 % SZS status Unsatisfiable
% 1.09/1.42 % SZS output start Refutation
% 1.09/1.42
% 1.09/1.42 % Proof 1 at 0.64 (+ 0.01) seconds: prove_multiply_add_property.
% 1.09/1.42 % Length of proof is 125.
% 1.09/1.42 % Level of proof is 29.
% 1.09/1.42 % Maximum clause weight is 26.000.
% 1.09/1.42 % Given clauses 196.
% 1.09/1.42
% 1.09/1.42 1 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 1.09/1.42 2 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 1.09/1.42 3 add(A,multiply(B,multiply(A,C))) = A # label(l1) # label(axiom). [assumption].
% 1.09/1.42 4 multiply(A,add(B,add(A,C))) = A # label(l2) # label(axiom). [assumption].
% 1.09/1.42 5 multiply(add(A,B),add(A,inverse(B))) = A # label(b1) # label(axiom). [assumption].
% 1.09/1.42 6 add(multiply(A,B),multiply(A,inverse(B))) = A # label(b2) # label(axiom). [assumption].
% 1.09/1.42 7 add(add(multiply(A,B),multiply(B,C)),B) = B # label(l3) # label(axiom). [assumption].
% 1.09/1.42 8 add(A,add(multiply(A,B),multiply(A,C))) = A. [copy(7),rewrite([1(4)]),rewrite([2(1)])].
% 1.09/1.42 9 multiply(multiply(add(A,B),add(B,C)),B) = B # label(l4) # label(axiom). [assumption].
% 1.09/1.42 10 multiply(A,multiply(add(A,B),add(A,C))) = A. [copy(9),rewrite([2(4)]),rewrite([1(1)])].
% 1.09/1.42 11 add(add(A,B),C) = add(A,add(B,C)) # label(associativity_of_add) # label(axiom). [assumption].
% 1.09/1.42 12 add(A,add(B,C)) = add(C,add(A,B)). [copy(11),rewrite([1(2)]),flip(a)].
% 1.09/1.42 13 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity_of_multiply) # label(axiom). [assumption].
% 1.09/1.42 14 multiply(A,multiply(B,C)) = multiply(C,multiply(A,B)). [copy(13),rewrite([2(2)]),flip(a)].
% 1.09/1.42 15 multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)) # label(prove_multiply_add_property) # label(negated_conjecture) # answer(prove_multiply_add_property). [assumption].
% 1.09/1.42 16 add(multiply(a,b),multiply(a,c)) != multiply(a,add(b,c)) # answer(prove_multiply_add_property). [copy(15),rewrite([2(8),2(11)]),flip(a)].
% 1.09/1.42 17 multiply(A,add(A,add(B,C))) = A. [back_rewrite(4),rewrite([12(2,R),1(1)])].
% 1.09/1.42 18 add(A,multiply(A,multiply(B,C))) = A. [back_rewrite(3),rewrite([14(2,R),2(1)])].
% 1.09/1.42 19 multiply(add(A,B),add(B,inverse(A))) = B. [para(1(a,1),5(a,1,1))].
% 1.09/1.42 20 add(multiply(A,B),multiply(B,inverse(A))) = B. [para(2(a,1),6(a,1,1))].
% 1.09/1.42 21 multiply(A,add(multiply(A,B),inverse(multiply(A,inverse(B))))) = multiply(A,B). [para(6(a,1),5(a,1,1))].
% 1.09/1.42 22 add(A,multiply(add(A,B),inverse(add(A,inverse(B))))) = add(A,B). [para(5(a,1),6(a,1,1))].
% 1.09/1.42 25 add(A,A) = A. [para(6(a,1),8(a,1,2))].
% 1.09/1.42 26 multiply(A,A) = A. [para(5(a,1),10(a,1,2))].
% 1.09/1.42 31 multiply(add(A,add(B,C)),add(B,inverse(add(A,C)))) = B. [para(12(a,1),5(a,1,1)),rewrite([1(3)])].
% 1.09/1.42 32 multiply(add(A,add(B,C)),add(C,inverse(add(A,B)))) = C. [para(12(a,2),5(a,1,1))].
% 1.09/1.42 34 add(multiply(A,multiply(B,C)),multiply(B,inverse(multiply(A,C)))) = B. [para(14(a,1),6(a,1,1)),rewrite([2(3)])].
% 1.09/1.42 35 add(multiply(A,multiply(B,C)),multiply(C,inverse(multiply(A,B)))) = C. [para(14(a,2),6(a,1,1))].
% 1.09/1.42 38 multiply(A,add(A,B)) = A. [para(6(a,1),17(a,1,2,2))].
% 1.09/1.42 40 add(A,multiply(A,B)) = A. [para(5(a,1),18(a,1,2,2))].
% 1.09/1.42 46 multiply(add(A,add(B,C)),add(add(A,B),inverse(C))) = add(A,B). [para(12(a,2),19(a,1,1))].
% 1.09/1.42 48 add(A,add(A,B)) = add(A,B). [para(25(a,1),12(a,1)),rewrite([1(3),12(4,R),1(3),12(3,R),25(2)]),flip(a)].
% 1.09/1.42 50 multiply(A,multiply(A,B)) = multiply(A,B). [para(26(a,1),14(a,1)),rewrite([2(3),14(4,R),2(3),14(3,R),26(2)]),flip(a)].
% 1.09/1.42 51 multiply(A,multiply(B,add(A,C))) = multiply(A,B). [para(38(a,1),14(a,2,2)),rewrite([2(2),2(4)])].
% 1.09/1.42 52 add(A,add(B,multiply(A,C))) = add(A,B). [para(40(a,1),12(a,2,2)),rewrite([1(2),1(4)])].
% 1.09/1.42 53 multiply(A,add(inverse(A),multiply(A,B))) = multiply(A,B). [para(40(a,1),19(a,1,1)),rewrite([1(3)])].
% 1.09/1.42 55 add(multiply(A,multiply(B,C)),multiply(multiply(A,C),inverse(B))) = multiply(A,C). [para(14(a,1),20(a,1,1)),rewrite([2(3),2(7)])].
% 1.09/1.42 60 add(A,multiply(B,A)) = A. [para(20(a,1),48(a,1,2)),rewrite([1(2),20(6)])].
% 1.09/1.42 63 multiply(A,add(B,A)) = A. [para(19(a,1),50(a,1,2)),rewrite([2(2),19(6)])].
% 1.09/1.42 70 add(multiply(A,B),multiply(inverse(A),add(multiply(A,B),inverse(multiply(A,inverse(B)))))) = add(multiply(A,B),inverse(multiply(A,inverse(B)))). [para(21(a,1),20(a,1,1)),rewrite([2(8)])].
% 1.09/1.42 77 add(multiply(A,B),multiply(B,multiply(inverse(A),add(A,C)))) = multiply(B,add(A,C)). [para(51(a,1),20(a,1,1)),rewrite([2(5),14(5,R),2(4)])].
% 1.09/1.42 84 add(multiply(A,B),add(multiply(B,inverse(A)),multiply(A,multiply(B,C)))) = B. [para(20(a,1),52(a,2)),rewrite([2(5),14(5),2(4),14(5,R),2(4)])].
% 1.09/1.42 85 multiply(add(A,B),add(A,multiply(B,C))) = add(A,multiply(B,C)). [para(52(a,1),63(a,1,2)),rewrite([1(3),2(4)])].
% 1.09/1.42 90 multiply(A,multiply(B,inverse(A))) = multiply(A,inverse(A)). [para(53(a,1),51(a,1,2)),rewrite([14(3),2(2),14(3,R),2(2),2(5)])].
% 1.09/1.42 91 add(multiply(A,inverse(A)),multiply(A,inverse(multiply(B,inverse(A))))) = A. [para(90(a,1),6(a,1,1))].
% 1.09/1.42 93 multiply(A,multiply(B,inverse(B))) = multiply(B,inverse(B)). [para(90(a,1),14(a,2)),rewrite([2(2)])].
% 1.09/1.42 94 add(multiply(A,inverse(A)),multiply(B,inverse(A))) = multiply(B,inverse(A)). [para(90(a,1),20(a,1,1)),rewrite([2(6),14(6,R),26(5)])].
% 1.09/1.42 98 multiply(add(A,B),add(inverse(A),multiply(add(A,B),inverse(add(A,inverse(B)))))) = multiply(add(A,B),inverse(add(A,inverse(B)))). [para(22(a,1),19(a,1,1)),rewrite([1(8)])].
% 1.09/1.42 104 add(multiply(A,inverse(A)),multiply(B,inverse(multiply(A,inverse(A))))) = B. [para(93(a,1),6(a,1,1))].
% 1.09/1.42 105 add(A,multiply(B,inverse(B))) = A. [para(93(a,1),40(a,1,2))].
% 1.09/1.42 107 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(93(a,1),53(a,1,2,2)),rewrite([105(4),93(5)])].
% 1.09/1.42 108 multiply(A,inverse(A)) = c_0. [new_symbol(107)].
% 1.09/1.42 110 add(A,c_0) = A. [back_rewrite(105),rewrite([108(2)])].
% 1.09/1.42 111 add(c_0,multiply(A,inverse(c_0))) = A. [back_rewrite(104),rewrite([108(2),108(3)])].
% 1.09/1.42 113 add(c_0,multiply(A,inverse(B))) = multiply(A,inverse(B)). [back_rewrite(94),rewrite([108(2)])].
% 1.09/1.42 114 multiply(A,c_0) = c_0. [back_rewrite(93),rewrite([108(2),108(4)])].
% 1.09/1.42 116 multiply(A,inverse(multiply(B,inverse(A)))) = A. [back_rewrite(91),rewrite([108(2),113(6)])].
% 1.09/1.42 118 multiply(A,inverse(c_0)) = A. [back_rewrite(111),rewrite([113(5)])].
% 1.09/1.42 120 multiply(A,inverse(inverse(A))) = A. [para(108(a,1),6(a,1,1)),rewrite([113(5)])].
% 1.09/1.42 122 multiply(add(A,B),add(multiply(B,C),inverse(add(A,multiply(B,inverse(C)))))) = multiply(B,C). [para(6(a,1),31(a,1,1,2))].
% 1.09/1.42 128 multiply(A,add(B,add(A,C))) = A. [para(31(a,1),50(a,1,2)),rewrite([2(3),31(9)])].
% 1.09/1.42 133 add(A,inverse(A)) = inverse(c_0). [para(118(a,1),20(a,1,1)),rewrite([2(4),118(4)])].
% 1.09/1.42 134 add(A,inverse(c_0)) = inverse(c_0). [para(118(a,1),60(a,1,2)),rewrite([1(3)])].
% 1.09/1.42 136 inverse(inverse(A)) = A. [para(120(a,1),20(a,1,1)),rewrite([2(4),108(4),110(2)]),flip(a)].
% 1.09/1.42 152 add(A,add(B,inverse(A))) = inverse(c_0). [para(133(a,1),12(a,2,2)),rewrite([1(2),134(6)])].
% 1.09/1.42 153 multiply(inverse(c_0),add(A,inverse(add(B,inverse(A))))) = A. [para(133(a,1),31(a,1,1,2)),rewrite([134(3)])].
% 1.09/1.42 154 multiply(inverse(c_0),add(A,B)) = add(A,B). [para(133(a,1),31(a,1,2)),rewrite([1(2),12(2,R),25(1),48(2),2(4)])].
% 1.09/1.42 155 add(inverse(A),inverse(add(B,A))) = inverse(A). [para(133(a,1),32(a,1,1,2)),rewrite([134(3),154(7)])].
% 1.09/1.42 156 add(A,inverse(add(B,inverse(A)))) = A. [back_rewrite(153),rewrite([154(7)])].
% 1.09/1.42 163 add(A,multiply(B,multiply(A,C))) = A. [para(34(a,1),48(a,1,2)),rewrite([1(3),34(9)])].
% 1.09/1.42 170 add(c_0,multiply(A,B)) = multiply(A,B). [para(108(a,1),34(a,1,2)),rewrite([2(2),14(2,R),26(1),50(2),1(3)])].
% 1.09/1.42 175 multiply(inverse(A),inverse(multiply(A,B))) = inverse(A). [para(136(a,1),116(a,1,2,1,2)),rewrite([2(2)])].
% 1.09/1.42 179 multiply(multiply(A,B),add(B,C)) = multiply(A,B). [para(20(a,1),128(a,1,2,2)),rewrite([1(2)])].
% 1.09/1.42 195 multiply(inverse(A),inverse(multiply(B,A))) = inverse(A). [para(108(a,1),35(a,1,1,2)),rewrite([114(2),170(6)])].
% 1.09/1.42 205 add(inverse(A),inverse(add(A,B))) = inverse(A). [para(152(a,1),32(a,1,1)),rewrite([154(7)])].
% 1.09/1.42 210 multiply(add(A,B),add(inverse(add(C,inverse(B))),inverse(add(A,B)))) = inverse(add(C,inverse(B))). [para(156(a,1),32(a,1,1,2))].
% 1.09/1.42 214 add(add(A,B),multiply(B,C)) = add(A,B). [para(19(a,1),163(a,1,2,2)),rewrite([2(2)])].
% 1.09/1.42 265 add(inverse(A),inverse(multiply(B,A))) = inverse(multiply(B,A)). [para(60(a,1),155(a,1,2,1)),rewrite([1(4)])].
% 1.09/1.42 356 multiply(inverse(A),add(B,inverse(multiply(A,C)))) = inverse(A). [para(175(a,1),179(a,1,1)),rewrite([1(4),175(9)])].
% 1.09/1.42 359 add(multiply(A,B),inverse(multiply(A,inverse(B)))) = add(inverse(A),multiply(A,B)). [back_rewrite(70),rewrite([356(8),1(3)]),flip(a)].
% 1.09/1.42 414 add(A,multiply(B,inverse(add(C,inverse(A))))) = A. [para(156(a,1),214(a,1,1)),rewrite([2(4),156(9)])].
% 1.09/1.42 416 add(inverse(A),multiply(B,inverse(add(A,C)))) = inverse(A). [para(155(a,1),214(a,1,1)),rewrite([1(2),2(4),1(7),205(9)])].
% 1.09/1.42 427 multiply(add(A,B),inverse(add(A,inverse(B)))) = multiply(inverse(A),add(A,B)). [back_rewrite(98),rewrite([416(8),2(3)]),flip(a)].
% 1.09/1.42 459 add(multiply(A,multiply(B,C)),multiply(A,multiply(C,multiply(inverse(B),add(B,D))))) = multiply(A,multiply(C,add(B,D))). [para(51(a,1),55(a,1,1,2)),rewrite([2(7),14(7,R),2(6),14(6,R),2(5)])].
% 1.09/1.42 461 add(multiply(A,inverse(B)),multiply(A,multiply(B,C))) = multiply(A,add(inverse(B),multiply(B,C))). [para(53(a,1),55(a,1,1,2)),rewrite([2(8),51(8),2(4),1(5)])].
% 1.09/1.42 528 multiply(A,inverse(add(A,B))) = c_0. [para(414(a,1),53(a,1,2)),rewrite([108(2),136(3),1(2)]),flip(a)].
% 1.09/1.42 542 multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = c_0. [para(55(a,1),528(a,1,2,1)),rewrite([2(5),14(5,R)])].
% 1.09/1.42 727 multiply(A,multiply(B,inverse(multiply(A,B)))) = c_0. [para(26(a,1),542(a,1,2,1))].
% 1.09/1.42 775 multiply(A,inverse(multiply(B,inverse(multiply(A,B))))) = A. [para(727(a,1),6(a,1,1)),rewrite([170(7)])].
% 1.09/1.42 776 multiply(A,inverse(multiply(A,B))) = multiply(A,inverse(B)). [para(727(a,1),20(a,1,1)),rewrite([2(2),2(6),14(6,R),2(5),195(5),170(4),2(3)]),flip(a)].
% 1.09/1.42 778 multiply(A,multiply(inverse(A),inverse(B))) = c_0. [para(175(a,1),727(a,1,2,2,1)),rewrite([136(5),2(4),776(4),14(4,R),2(3)])].
% 1.09/1.42 787 multiply(A,inverse(multiply(inverse(A),inverse(B)))) = A. [para(778(a,1),6(a,1,1)),rewrite([170(7)])].
% 1.09/1.42 794 add(A,multiply(B,inverse(A))) = inverse(multiply(inverse(A),inverse(B))). [para(787(a,1),20(a,1,1)),rewrite([2(6),776(6),136(3),2(2)])].
% 1.09/1.42 800 add(multiply(A,B),multiply(A,multiply(C,inverse(B)))) = multiply(A,inverse(multiply(inverse(B),inverse(C)))). [para(787(a,1),55(a,1,1,2)),rewrite([2(8),14(8,R),2(7),776(7),136(4),2(3)])].
% 1.09/1.42 818 inverse(multiply(A,multiply(inverse(multiply(B,A)),inverse(multiply(C,B))))) = inverse(multiply(A,inverse(multiply(B,A)))). [para(775(a,1),35(a,1,1,2)),rewrite([794(9),136(7),14(6,R)])].
% 1.09/1.42 852 multiply(A,multiply(B,inverse(multiply(A,C)))) = multiply(A,multiply(B,inverse(C))). [para(776(a,1),14(a,2,2)),rewrite([2(3),14(7,R),2(6)])].
% 1.09/1.42 865 add(inverse(A),multiply(A,B)) = inverse(multiply(A,inverse(B))). [para(776(a,1),265(a,1,2,1)),rewrite([136(3),359(5),776(6)])].
% 1.09/1.42 878 add(multiply(A,inverse(B)),multiply(A,multiply(B,C))) = multiply(A,inverse(multiply(B,inverse(C)))). [back_rewrite(461),rewrite([865(8)])].
% 1.09/1.42 915 add(multiply(A,multiply(B,C)),multiply(multiply(A,C),multiply(inverse(B),add(B,D)))) = multiply(multiply(A,C),add(B,D)). [para(14(a,1),77(a,1,1)),rewrite([2(3),2(9)])].
% 1.09/1.42 967 add(A,multiply(B,multiply(inverse(A),add(A,C)))) = multiply(inverse(multiply(inverse(A),inverse(B))),add(A,C)). [para(787(a,1),77(a,1,1)),rewrite([14(8,R),852(8),136(4),2(3),14(4,R),2(3)])].
% 1.09/1.42 1196 multiply(add(A,B),add(add(A,multiply(B,C)),inverse(multiply(B,inverse(multiply(C,inverse(D))))))) = add(A,multiply(B,C)). [para(84(a,1),46(a,1,1,2)),rewrite([2(2),14(7,R),2(6),878(8),2(11)])].
% 1.09/1.42 1266 multiply(add(A,B),add(A,multiply(C,add(A,B)))) = add(A,multiply(C,add(A,B))). [para(48(a,1),85(a,1,1)),rewrite([2(3),2(7)])].
% 1.09/1.42 1366 multiply(A,add(B,inverse(A))) = multiply(A,B). [para(60(a,1),122(a,1,2,2,1)),rewrite([1(2),2(3),136(5),1(4),40(4),2(3),2(4)])].
% 1.09/1.42 1432 multiply(add(A,B),inverse(add(C,inverse(B)))) = inverse(add(C,inverse(B))). [back_rewrite(210),rewrite([1366(8)])].
% 1.09/1.42 1433 multiply(inverse(A),add(A,B)) = inverse(add(A,inverse(B))). [back_rewrite(427),rewrite([1432(5)]),flip(a)].
% 1.09/1.42 1450 multiply(inverse(multiply(inverse(A),inverse(B))),add(A,C)) = add(A,multiply(B,inverse(add(A,inverse(C))))). [back_rewrite(967),rewrite([1433(3)]),flip(a)].
% 1.09/1.42 1462 add(multiply(A,multiply(B,C)),multiply(multiply(A,C),inverse(add(B,inverse(D))))) = multiply(multiply(A,C),add(B,D)). [back_rewrite(915),rewrite([1433(6)])].
% 1.09/1.42 1479 add(multiply(A,multiply(B,C)),multiply(A,multiply(C,inverse(add(B,inverse(D)))))) = multiply(A,multiply(C,add(B,D))). [back_rewrite(459),rewrite([1433(5)])].
% 1.09/1.42 1495 inverse(multiply(A,inverse(B))) = add(B,inverse(A)). [para(1366(a,1),20(a,1,1)),rewrite([2(5),63(5),1(3),865(3)])].
% 1.09/1.42 1497 inverse(add(A,inverse(B))) = multiply(B,inverse(A)). [para(136(a,1),1366(a,1,2,2)),rewrite([1(2),1433(3),2(5)])].
% 1.09/1.42 1518 multiply(add(A,B),add(A,C)) = add(A,multiply(B,multiply(C,inverse(A)))). [back_rewrite(1450),rewrite([1495(4),136(2),1(1),1497(6)])].
% 1.09/1.42 1541 multiply(add(A,B),add(add(A,multiply(B,C)),inverse(multiply(B,add(D,inverse(C)))))) = add(A,multiply(B,C)). [back_rewrite(1196),rewrite([1495(6)])].
% 1.09/1.42 1576 inverse(multiply(A,multiply(inverse(multiply(A,B)),inverse(multiply(B,C))))) = add(B,inverse(A)). [back_rewrite(818),rewrite([2(1),2(3),2(8),776(10),1495(10)])].
% 1.09/1.42 1584 add(multiply(A,B),multiply(A,multiply(C,inverse(B)))) = multiply(A,add(B,C)). [back_rewrite(800),rewrite([1495(9),136(7),1(6)])].
% 1.09/1.42 1611 add(multiply(A,multiply(B,C)),multiply(A,multiply(C,multiply(D,inverse(B))))) = multiply(A,multiply(C,add(B,D))). [back_rewrite(1479),rewrite([1497(5)])].
% 1.09/1.42 1625 multiply(multiply(A,B),add(C,D)) = multiply(A,multiply(B,add(C,D))). [back_rewrite(1462),rewrite([1497(6),14(6,R),14(5),2(4),14(5,R),2(4),14(6,R),2(5),14(5,R),2(4),1611(7)]),flip(a)].
% 1.09/1.42 1642 multiply(inverse(A),add(A,B)) = multiply(B,inverse(A)). [back_rewrite(1433),rewrite([1497(6)])].
% 1.09/1.42 1700 add(A,multiply(B,add(A,C))) = add(A,multiply(C,multiply(B,inverse(A)))). [back_rewrite(1266),rewrite([1518(5),2(4),14(4,R),2(3),1642(3),14(3,R),2(2),50(4)]),flip(a)].
% 1.09/1.42 1791 inverse(multiply(A,B)) = add(inverse(A),inverse(B)). [para(136(a,1),1495(a,1,1,2)),rewrite([1(5)])].
% 1.09/1.42 1809 multiply(A,multiply(add(B,inverse(A)),inverse(C))) = multiply(A,multiply(B,inverse(C))). [para(1495(a,1),1366(a,1,2,2)),rewrite([12(5,R),1(4),1625(6),1642(5),2(8),14(8,R),2(7)])].
% 1.09/1.42 1834 add(inverse(A),add(multiply(A,B),multiply(B,C))) = add(B,inverse(A)). [back_rewrite(1576),rewrite([1791(2),1791(5),1791(9),1791(9),1497(5),136(3),2(2),1497(6),136(4),2(3)])].
% 1.09/1.42 1840 add(A,multiply(B,multiply(C,inverse(A)))) = add(A,multiply(B,C)). [back_rewrite(1541),rewrite([1791(7),1497(7),12(8,R),12(7,R),12(8,R),1(7),1834(7),1518(5),1809(5)])].
% 1.09/1.42 1961 add(A,multiply(B,add(A,C))) = add(A,multiply(B,C)). [back_rewrite(1700),rewrite([14(6,R),2(5),1840(7)])].
% 1.09/1.42 2637 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [para(6(a,1),1961(a,1,2,2)),rewrite([2(2),14(7,R),2(6),1584(8)])].
% 1.09/1.42 2638 $F # answer(prove_multiply_add_property). [resolve(2637,a,16,a)].
% 1.09/1.42
% 1.09/1.42 % SZS output end Refutation
% 1.09/1.42 ============================== end of proof ==========================
% 1.09/1.42
% 1.09/1.42 ============================== STATISTICS ============================
% 1.09/1.42
% 1.09/1.42 Given=196. Generated=22631. Kept=2632. proofs=1.
% 1.09/1.42 Usable=90. Sos=643. Demods=729. Limbo=0, Disabled=1909. Hints=0.
% 1.09/1.42 Megabytes=2.18.
% 1.09/1.42 User_CPU=0.64, System_CPU=0.01, Wall_clock=1.
% 1.09/1.42
% 1.09/1.42 ============================== end of statistics =====================
% 1.09/1.42
% 1.09/1.42 ============================== end of search =========================
% 1.09/1.42
% 1.09/1.42 THEOREM PROVED
% 1.09/1.42 % SZS status Unsatisfiable
% 1.09/1.42
% 1.09/1.42 Exiting with 1 proof.
% 1.09/1.42
% 1.09/1.42 Process 30149 exit (max_proofs) Wed Jun 1 20:30:01 2022
% 1.09/1.42 Prover9 interrupted
%------------------------------------------------------------------------------