TSTP Solution File: BOO008-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO008-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 23:47:58 EDT 2022
% Result : Unsatisfiable 2.85s 3.20s
% Output : Refutation 2.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO008-4 : TPTP v8.1.0. Released v1.1.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n025.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 : Wed Jun 1 16:38:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.85/3.20 ============================== Prover9 ===============================
% 2.85/3.20 Prover9 (32) version 2009-11A, November 2009.
% 2.85/3.20 Process 11022 was started by sandbox on n025.cluster.edu,
% 2.85/3.20 Wed Jun 1 16:38:14 2022
% 2.85/3.20 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10869_n025.cluster.edu".
% 2.85/3.20 ============================== end of head ===========================
% 2.85/3.20
% 2.85/3.20 ============================== INPUT =================================
% 2.85/3.20
% 2.85/3.20 % Reading from file /tmp/Prover9_10869_n025.cluster.edu
% 2.85/3.20
% 2.85/3.20 set(prolog_style_variables).
% 2.85/3.20 set(auto2).
% 2.85/3.20 % set(auto2) -> set(auto).
% 2.85/3.20 % set(auto) -> set(auto_inference).
% 2.85/3.20 % set(auto) -> set(auto_setup).
% 2.85/3.20 % set(auto_setup) -> set(predicate_elim).
% 2.85/3.20 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.85/3.20 % set(auto) -> set(auto_limits).
% 2.85/3.20 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.85/3.20 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.85/3.20 % set(auto) -> set(auto_denials).
% 2.85/3.20 % set(auto) -> set(auto_process).
% 2.85/3.20 % set(auto2) -> assign(new_constants, 1).
% 2.85/3.20 % set(auto2) -> assign(fold_denial_max, 3).
% 2.85/3.20 % set(auto2) -> assign(max_weight, "200.000").
% 2.85/3.20 % set(auto2) -> assign(max_hours, 1).
% 2.85/3.20 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.85/3.20 % set(auto2) -> assign(max_seconds, 0).
% 2.85/3.20 % set(auto2) -> assign(max_minutes, 5).
% 2.85/3.20 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.85/3.20 % set(auto2) -> set(sort_initial_sos).
% 2.85/3.20 % set(auto2) -> assign(sos_limit, -1).
% 2.85/3.20 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.85/3.20 % set(auto2) -> assign(max_megs, 400).
% 2.85/3.20 % set(auto2) -> assign(stats, some).
% 2.85/3.20 % set(auto2) -> clear(echo_input).
% 2.85/3.20 % set(auto2) -> set(quiet).
% 2.85/3.20 % set(auto2) -> clear(print_initial_clauses).
% 2.85/3.20 % set(auto2) -> clear(print_given).
% 2.85/3.20 assign(lrs_ticks,-1).
% 2.85/3.20 assign(sos_limit,10000).
% 2.85/3.20 assign(order,kbo).
% 2.85/3.20 set(lex_order_vars).
% 2.85/3.20 clear(print_given).
% 2.85/3.20
% 2.85/3.20 % formulas(sos). % not echoed (9 formulas)
% 2.85/3.20
% 2.85/3.20 ============================== end of input ==========================
% 2.85/3.20
% 2.85/3.20 % From the command line: assign(max_seconds, 300).
% 2.85/3.20
% 2.85/3.20 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.85/3.20
% 2.85/3.20 % Formulas that are not ordinary clauses:
% 2.85/3.20
% 2.85/3.20 ============================== end of process non-clausal formulas ===
% 2.85/3.20
% 2.85/3.20 ============================== PROCESS INITIAL CLAUSES ===============
% 2.85/3.20
% 2.85/3.20 ============================== PREDICATE ELIMINATION =================
% 2.85/3.20
% 2.85/3.20 ============================== end predicate elimination =============
% 2.85/3.20
% 2.85/3.20 Auto_denials:
% 2.85/3.20 % copying label prove_associativity to answer in negative clause
% 2.85/3.20
% 2.85/3.20 Term ordering decisions:
% 2.85/3.20
% 2.85/3.20 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 2.85/3.20 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. a=1. b=1. c=1. add=1. multiply=1. inverse=0.
% 2.85/3.20
% 2.85/3.20 ============================== end of process initial clauses ========
% 2.85/3.20
% 2.85/3.20 ============================== CLAUSES FOR SEARCH ====================
% 2.85/3.20
% 2.85/3.20 ============================== end of clauses for search =============
% 2.85/3.20
% 2.85/3.20 ============================== SEARCH ================================
% 2.85/3.20
% 2.85/3.20 % Starting search at 0.01 seconds.
% 2.85/3.20
% 2.85/3.20 ============================== PROOF =================================
% 2.85/3.20 % SZS status Unsatisfiable
% 2.85/3.20 % SZS output start Refutation
% 2.85/3.20
% 2.85/3.20 % Proof 1 at 2.17 (+ 0.04) seconds: prove_associativity.
% 2.85/3.20 % Length of proof is 112.
% 2.85/3.20 % Level of proof is 30.
% 2.85/3.20 % Maximum clause weight is 27.000.
% 2.85/3.20 % Given clauses 265.
% 2.85/3.20
% 2.85/3.20 1 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 2.85/3.20 2 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 2.85/3.20 3 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 2.85/3.20 4 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 2.85/3.20 5 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 2.85/3.20 6 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 2.85/3.20 7 add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)) # label(distributivity1) # label(axiom). [assumption].
% 2.85/3.20 8 multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)). [copy(7),flip(a)].
% 2.85/3.20 9 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distributivity2) # label(axiom). [assumption].
% 2.85/3.20 10 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(9),flip(a)].
% 2.85/3.20 11 add(a,add(b,c)) != add(add(a,b),c) # label(prove_associativity) # label(negated_conjecture) # answer(prove_associativity). [assumption].
% 2.85/3.20 12 add(c,add(a,b)) != add(a,add(b,c)) # answer(prove_associativity). [copy(11),rewrite([5(10)]),flip(a)].
% 2.85/3.20 13 multiply(A,add(A,B)) = add(A,multiply(B,additive_identity)). [para(1(a,1),8(a,1,1)),rewrite([6(4)])].
% 2.85/3.20 14 multiply(multiplicative_identity,add(A,B)) = add(A,multiply(B,inverse(A))). [para(3(a,1),8(a,1,1)),rewrite([6(5)])].
% 2.85/3.20 15 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [para(5(a,1),8(a,1,1))].
% 2.85/3.20 16 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(A,B)). [para(2(a,1),10(a,1,1)),rewrite([5(4)]),flip(a)].
% 2.85/3.20 17 multiply(A,add(B,inverse(A))) = add(additive_identity,multiply(A,B)). [para(4(a,1),10(a,1,1)),rewrite([5(5)]),flip(a)].
% 2.85/3.20 18 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [para(6(a,1),10(a,1,1))].
% 2.85/3.20 19 multiply(multiply(A,add(B,C)),add(D,multiply(A,B))) = add(multiply(A,B),multiply(D,multiply(A,C))). [para(10(a,1),8(a,1,1)),rewrite([5(4),6(8)])].
% 2.85/3.20 20 multiply(add(A,multiply(B,C)),multiply(B,add(C,D))) = add(multiply(B,C),multiply(A,multiply(B,D))). [para(10(a,1),8(a,1,2)),rewrite([5(2)])].
% 2.85/3.20 22 add(add(A,multiply(B,C)),multiply(D,add(A,B))) = multiply(add(A,B),add(D,add(A,C))). [para(8(a,1),10(a,1,1)),rewrite([6(4),5(8)])].
% 2.85/3.20 23 add(multiply(A,add(B,C)),add(B,multiply(C,D))) = multiply(add(B,C),add(A,add(B,D))). [para(8(a,1),10(a,1,2)),rewrite([6(2)])].
% 2.85/3.20 25 multiply(A,A) = add(A,multiply(additive_identity,additive_identity)). [para(1(a,1),13(a,1,2))].
% 2.85/3.20 26 add(A,multiply(inverse(A),additive_identity)) = A. [para(3(a,1),13(a,1,2)),rewrite([2(2)]),flip(a)].
% 2.85/3.20 37 add(A,multiply(B,multiply(inverse(A),additive_identity))) = multiply(A,add(A,B)). [para(26(a,1),8(a,1,1)),rewrite([6(6)]),flip(a)].
% 2.85/3.20 40 add(multiplicative_identity,multiply(additive_identity,additive_identity)) = multiplicative_identity. [para(25(a,1),2(a,1))].
% 2.85/3.20 41 add(add(A,B),multiply(additive_identity,additive_identity)) = add(A,multiply(B,B)). [para(25(a,1),8(a,1))].
% 2.85/3.20 47 multiply(A,A) = add(A,add(additive_identity,multiply(additive_identity,additive_identity))). [para(25(a,1),13(a,2,2)),rewrite([1(2)])].
% 2.85/3.20 50 add(additive_identity,multiplicative_identity) = multiplicative_identity. [para(40(a,1),8(a,2)),rewrite([5(3),5(6),8(7),2(4)])].
% 2.85/3.20 54 multiply(multiplicative_identity,add(A,A)) = A. [para(4(a,1),14(a,2,2)),rewrite([1(5)])].
% 2.85/3.20 55 multiply(multiplicative_identity,add(A,B)) = add(B,multiply(A,inverse(B))). [para(14(a,2),5(a,2)),rewrite([5(3),5(5)]),flip(a)].
% 2.85/3.20 58 multiply(add(A,B),multiply(multiplicative_identity,add(A,C))) = add(A,multiply(B,multiply(C,inverse(A)))). [para(14(a,2),8(a,1,2))].
% 2.85/3.20 60 add(A,multiply(B,inverse(A))) = add(A,B). [para(14(a,1),10(a,2)),rewrite([6(2),2(2),6(2),2(2)]),flip(a)].
% 2.85/3.20 64 add(multiplicative_identity,multiply(A,additive_identity)) = add(A,multiplicative_identity). [para(14(a,1),13(a,1)),rewrite([60(5),5(2)]),flip(a)].
% 2.85/3.20 71 multiply(multiplicative_identity,add(A,B)) = add(A,B). [back_rewrite(55),rewrite([60(6),5(4)])].
% 2.85/3.20 72 add(A,multiply(B,multiply(C,inverse(A)))) = add(A,multiply(B,C)). [back_rewrite(58),rewrite([71(4),8(3)]),flip(a)].
% 2.85/3.20 75 add(A,A) = A. [back_rewrite(54),rewrite([71(3)])].
% 2.85/3.20 76 add(A,multiply(A,additive_identity)) = A. [para(50(a,1),10(a,2,2)),rewrite([2(4),5(3),2(5)])].
% 2.85/3.20 77 multiply(A,A) = A. [back_rewrite(47),rewrite([76(6),1(3)])].
% 2.85/3.20 78 add(additive_identity,add(A,B)) = add(A,B). [back_rewrite(41),rewrite([77(4),5(3),77(4)])].
% 2.85/3.20 79 multiply(A,add(A,B)) = add(A,multiply(A,B)). [para(75(a,1),8(a,1,1))].
% 2.85/3.20 81 add(A,multiply(B,multiply(inverse(A),additive_identity))) = add(A,multiply(A,B)). [back_rewrite(37),rewrite([79(7)])].
% 2.85/3.20 87 add(A,multiply(B,additive_identity)) = add(A,multiply(A,B)). [back_rewrite(13),rewrite([79(2)]),flip(a)].
% 2.85/3.20 89 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(1(a,1),15(a,1,1)),rewrite([5(2),1(2)]),flip(a)].
% 2.85/3.20 90 add(inverse(A),multiply(A,B)) = add(B,inverse(A)). [para(3(a,1),15(a,1,1)),rewrite([5(3),71(4)]),flip(a)].
% 2.85/3.20 95 multiply(A,add(B,A)) = add(A,multiply(B,A)). [para(26(a,1),15(a,1,2)),rewrite([6(2),81(7),6(3)])].
% 2.85/3.20 97 multiply(A,add(B,inverse(A))) = multiply(A,B). [back_rewrite(17),rewrite([89(6)])].
% 2.85/3.20 98 multiply(add(A,multiplicative_identity),add(B,multiplicative_identity)) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [para(64(a,1),8(a,1,1)),rewrite([5(4),6(9)])].
% 2.85/3.20 100 add(A,multiply(A,multiply(B,additive_identity))) = multiply(A,add(B,multiplicative_identity)). [para(64(a,1),10(a,2,2)),rewrite([2(2)])].
% 2.85/3.20 102 add(add(A,B),multiply(C,add(A,B))) = add(add(A,B),multiply(C,additive_identity)). [para(78(a,1),15(a,1,1)),rewrite([5(3),95(4),6(7)])].
% 2.85/3.20 104 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,A)). [para(16(a,1),6(a,2)),rewrite([6(3),6(4)])].
% 2.85/3.20 111 add(multiply(A,B),add(A,multiply(A,C))) = multiply(A,add(B,add(C,multiplicative_identity))). [para(16(a,1),10(a,1,2))].
% 2.85/3.20 118 multiply(add(A,B),add(C,multiplicative_identity)) = add(add(A,B),multiply(C,additive_identity)). [back_rewrite(102),rewrite([104(4,R)])].
% 2.85/3.20 119 add(add(A,multiplicative_identity),multiply(B,additive_identity)) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [back_rewrite(98),rewrite([118(5)])].
% 2.85/3.20 125 multiply(inverse(A),add(A,B)) = multiply(B,inverse(A)). [para(4(a,1),18(a,1,1)),rewrite([6(3),89(4)]),flip(a)].
% 2.85/3.20 128 add(add(A,multiply(B,C)),multiply(D,add(A,C))) = multiply(add(A,C),add(D,add(A,B))). [para(8(a,1),18(a,1,1)),rewrite([6(4),5(8)])].
% 2.85/3.20 132 add(multiply(A,B),add(B,multiply(B,C))) = multiply(B,add(A,add(C,multiplicative_identity))). [para(16(a,1),18(a,1,2))].
% 2.85/3.20 168 multiply(multiply(A,add(B,add(C,multiplicative_identity))),add(D,add(A,multiply(A,C)))) = add(multiply(A,add(C,multiplicative_identity)),multiply(D,multiply(A,B))). [para(16(a,1),19(a,1,2,2)),rewrite([5(3)])].
% 2.85/3.20 200 multiply(add(A,multiply(A,multiply(A,B))),multiply(A,add(B,multiply(A,B)))) = multiply(A,multiply(A,B)). [para(75(a,1),20(a,2)),rewrite([5(5)])].
% 2.85/3.20 285 multiply(add(A,multiply(B,additive_identity)),add(C,multiply(A,B))) = multiply(A,add(B,C)). [para(87(a,2),15(a,1,1)),rewrite([5(5),10(9)])].
% 2.85/3.20 288 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,additive_identity)). [para(87(a,2),16(a,2))].
% 2.85/3.20 297 multiply(add(A,multiply(B,additive_identity)),multiply(A,add(B,C))) = multiply(A,add(B,multiply(A,C))). [para(87(a,2),20(a,1,1)),rewrite([10(10)])].
% 2.85/3.20 300 multiply(add(A,multiply(B,additive_identity)),add(C,add(A,D))) = multiply(add(A,multiply(A,B)),add(C,add(A,D))). [para(87(a,1),22(a,2,1)),rewrite([6(3),128(9)])].
% 2.85/3.20 304 add(A,multiply(A,multiply(A,B))) = add(A,multiply(B,additive_identity)). [para(87(a,1),79(a,1,2)),rewrite([79(3),100(7),288(6)])].
% 2.85/3.20 314 multiply(multiply(A,add(B,add(C,multiplicative_identity))),add(D,add(A,multiply(A,C)))) = add(add(A,multiply(C,additive_identity)),multiply(D,multiply(A,B))). [back_rewrite(168),rewrite([288(11)])].
% 2.85/3.20 327 multiply(A,add(B,multiply(A,multiply(A,B)))) = multiply(A,multiply(A,B)). [back_rewrite(200),rewrite([304(3),297(7)])].
% 2.85/3.20 329 add(multiplicative_identity,inverse(A)) = multiplicative_identity. [para(2(a,1),90(a,1,2)),rewrite([5(2),3(2)]),flip(a)].
% 2.85/3.20 330 add(inverse(A),multiply(B,A)) = add(B,inverse(A)). [para(90(a,1),5(a,1)),rewrite([6(3),5(5)]),flip(a)].
% 2.85/3.20 347 add(additive_identity,inverse(A)) = inverse(A). [para(90(a,1),87(a,1)),rewrite([6(6),4(6),1(6)])].
% 2.85/3.20 349 add(multiplicative_identity,multiply(A,inverse(B))) = add(A,multiplicative_identity). [para(329(a,1),8(a,1,1)),rewrite([5(3),95(4),2(3),5(2),6(5)]),flip(a)].
% 2.85/3.20 352 add(add(A,multiplicative_identity),add(B,multiply(A,additive_identity))) = add(multiplicative_identity,multiply(B,multiply(A,additive_identity))). [para(329(a,1),22(a,2,2,2)),rewrite([349(4),5(4),288(5),5(8),288(11),119(11)])].
% 2.85/3.20 354 add(multiply(A,B),add(B,multiply(C,additive_identity))) = multiply(B,add(A,add(B,C))). [para(1(a,1),23(a,1,1,2)),rewrite([6(3),1(7)])].
% 2.85/3.20 377 add(multiply(A,add(B,multiply(C,additive_identity))),add(B,multiply(D,multiply(B,C)))) = multiply(add(B,multiply(B,C)),add(A,add(B,D))). [para(87(a,2),23(a,1,1,2)),rewrite([6(6)])].
% 2.85/3.20 386 multiply(A,additive_identity) = additive_identity. [para(347(a,1),97(a,1,2)),rewrite([4(2)]),flip(a)].
% 2.85/3.20 387 add(multiply(A,inverse(B)),multiply(C,inverse(B))) = multiply(inverse(B),add(A,C)). [para(347(a,1),22(a,1,2,2)),rewrite([6(3),89(4),347(8),5(8),1(8),5(7)])].
% 2.85/3.20 391 multiply(add(A,multiply(A,B)),add(C,add(A,D))) = add(multiply(C,A),add(A,multiply(D,multiply(A,B)))). [back_rewrite(377),rewrite([386(2),1(2)]),flip(a)].
% 2.85/3.20 395 multiply(A,add(B,add(A,C))) = add(A,multiply(B,A)). [back_rewrite(354),rewrite([386(3),1(3),5(2)]),flip(a)].
% 2.85/3.20 396 add(A,add(B,multiplicative_identity)) = multiplicative_identity. [back_rewrite(352),rewrite([386(4),1(4),5(3),386(6),386(6),5(6),50(6)])].
% 2.85/3.20 400 add(A,multiply(B,multiply(A,C))) = add(A,multiply(A,B)). [back_rewrite(314),rewrite([396(3),2(2),395(4),6(1),386(4),1(4)]),flip(a)].
% 2.85/3.20 408 add(A,multiply(A,B)) = A. [back_rewrite(300),rewrite([386(2),1(2),395(3),6(1),391(7),6(3),400(6),111(6),396(5),2(4)])].
% 2.85/3.20 413 multiply(A,add(B,multiply(A,C))) = multiply(A,add(C,B)). [back_rewrite(285),rewrite([386(2),1(2)])].
% 2.85/3.20 416 add(A,multiplicative_identity) = multiplicative_identity. [back_rewrite(64),rewrite([386(3),5(3),50(3)]),flip(a)].
% 2.85/3.20 419 add(A,multiply(B,A)) = A. [back_rewrite(132),rewrite([408(3),5(2),416(4),416(4),2(4)])].
% 2.85/3.20 425 add(A,multiply(B,multiply(A,C))) = A. [back_rewrite(400),rewrite([408(5)])].
% 2.85/3.20 431 multiply(A,add(A,B)) = A. [back_rewrite(79),rewrite([408(4)])].
% 2.85/3.20 434 multiply(A,multiply(A,B)) = multiply(A,B). [back_rewrite(327),rewrite([413(4),5(2),419(2)]),flip(a)].
% 2.85/3.20 443 multiply(A,add(B,add(A,C))) = A. [back_rewrite(395),rewrite([6(4),408(5)])].
% 2.85/3.20 456 add(A,multiply(B,multiply(C,multiply(D,inverse(A))))) = add(A,multiply(B,multiply(C,D))). [para(72(a,1),8(a,1,1)),rewrite([8(4),6(2),6(7)]),flip(a)].
% 2.85/3.20 460 add(A,multiply(inverse(A),multiply(B,C))) = add(A,multiply(B,C)). [para(72(a,1),60(a,2)),rewrite([6(5),456(6)])].
% 2.85/3.20 534 multiply(inverse(A),add(B,add(A,C))) = multiply(inverse(A),add(B,C)). [para(125(a,1),10(a,1,2)),rewrite([6(2),387(5)]),flip(a)].
% 2.85/3.20 544 multiply(inverse(A),multiply(A,B)) = additive_identity. [para(408(a,1),125(a,1,2)),rewrite([6(2),4(2),6(4)]),flip(a)].
% 2.85/3.20 557 multiply(inverse(inverse(A)),multiply(B,inverse(A))) = additive_identity. [para(125(a,1),544(a,1,2))].
% 2.85/3.20 583 multiply(inverse(A),multiply(B,multiply(A,C))) = additive_identity. [para(425(a,1),125(a,1,2)),rewrite([6(2),4(2),6(5)]),flip(a)].
% 2.85/3.20 757 add(A,multiply(B,inverse(inverse(A)))) = A. [para(557(a,1),72(a,1,2)),rewrite([1(2),6(3)]),flip(a)].
% 2.85/3.20 761 add(A,inverse(inverse(A))) = A. [para(77(a,1),757(a,1,2))].
% 2.85/3.20 801 inverse(inverse(A)) = A. [para(761(a,1),90(a,2)),rewrite([6(4),4(4),1(4)])].
% 2.85/3.20 835 multiply(A,multiply(B,multiply(C,inverse(A)))) = additive_identity. [para(125(a,1),583(a,1,2,2)),rewrite([801(2)])].
% 2.85/3.20 916 add(multiply(A,B),inverse(add(A,inverse(B)))) = add(B,inverse(add(A,inverse(B)))). [para(97(a,1),330(a,1,2)),rewrite([6(4),5(5)])].
% 2.85/3.20 920 add(A,inverse(multiply(A,B))) = multiplicative_identity. [para(434(a,1),330(a,1,2)),rewrite([5(4),3(4)]),flip(a)].
% 2.85/3.20 934 multiply(inverse(A),inverse(multiply(A,B))) = inverse(A). [para(920(a,1),125(a,1,2)),rewrite([2(3),6(5)]),flip(a)].
% 2.85/3.20 993 multiply(A,inverse(multiply(B,inverse(A)))) = A. [para(125(a,1),934(a,1,2,1)),rewrite([801(2),801(6)])].
% 2.85/3.20 1002 multiply(multiply(A,inverse(B)),multiply(B,C)) = additive_identity. [para(993(a,1),835(a,1,2,2)),rewrite([6(3)])].
% 2.85/3.20 1288 multiply(inverse(A),multiply(B,A)) = additive_identity. [para(934(a,1),1002(a,1,2)),rewrite([801(2),6(3)])].
% 2.85/3.20 1293 multiply(A,inverse(add(A,B))) = additive_identity. [para(431(a,1),1288(a,1,2)),rewrite([6(3)])].
% 2.85/3.20 1297 multiply(A,inverse(add(B,add(A,C)))) = additive_identity. [para(443(a,1),1288(a,1,2)),rewrite([6(4)])].
% 2.85/3.20 1310 add(inverse(A),inverse(add(A,B))) = inverse(A). [para(1293(a,1),90(a,1,2)),rewrite([1(3),5(5)]),flip(a)].
% 2.85/3.20 1564 add(inverse(A),inverse(add(B,add(A,C)))) = inverse(A). [para(1297(a,1),90(a,1,2)),rewrite([1(3),5(6)]),flip(a)].
% 2.85/3.20 1579 add(A,inverse(add(B,inverse(A)))) = A. [para(90(a,1),1310(a,1,2,1)),rewrite([801(2),801(6)])].
% 2.85/3.20 1590 add(multiply(A,B),inverse(add(A,inverse(B)))) = B. [back_rewrite(916),rewrite([1579(9)])].
% 2.85/3.20 5387 add(A,multiply(inverse(A),add(B,C))) = add(B,add(A,C)). [para(1564(a,1),1590(a,1,2,1)),rewrite([534(4),801(5),5(4)])].
% 2.85/3.20 6704 add(A,add(B,C)) = add(B,add(A,C)). [para(71(a,1),460(a,1,2,2)),rewrite([5387(4),71(5)])].
% 2.85/3.20 7996 $F # answer(prove_associativity). [back_rewrite(12),rewrite([6704(5),5(4)]),xx(a)].
% 2.85/3.20
% 2.85/3.20 % SZS output end Refutation
% 2.85/3.20 ============================== end of proof ==========================
% 2.85/3.20
% 2.85/3.20 ============================== STATISTICS ============================
% 2.85/3.20
% 2.85/3.20 Given=265. Generated=59246. Kept=7992. proofs=1.
% 2.85/3.20 Usable=171. Sos=2988. Demods=4221. Limbo=1292, Disabled=3550. Hints=0.
% 2.85/3.20 Megabytes=11.80.
% 2.85/3.20 User_CPU=2.17, System_CPU=0.04, Wall_clock=3.
% 2.85/3.20
% 2.85/3.20 ============================== end of statistics =====================
% 2.85/3.20
% 2.85/3.20 ============================== end of search =========================
% 2.85/3.20
% 2.85/3.20 THEOREM PROVED
% 2.85/3.20 % SZS status Unsatisfiable
% 2.85/3.20
% 2.85/3.20 Exiting with 1 proof.
% 2.85/3.20
% 2.85/3.20 Process 11022 exit (max_proofs) Wed Jun 1 16:38:17 2022
% 2.85/3.20 Prover9 interrupted
%------------------------------------------------------------------------------