TSTP Solution File: BOO014-10 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO014-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 23:48:01 EDT 2022
% Result : Unsatisfiable 40.92s 41.28s
% Output : Refutation 40.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO014-10 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 1 20:57:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 12.05/12.40 ============================== Prover9 ===============================
% 12.05/12.40 Prover9 (32) version 2009-11A, November 2009.
% 12.05/12.40 Process 31052 was started by sandbox2 on n022.cluster.edu,
% 12.05/12.40 Wed Jun 1 20:57:52 2022
% 12.05/12.40 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30899_n022.cluster.edu".
% 12.05/12.40 ============================== end of head ===========================
% 12.05/12.40
% 12.05/12.40 ============================== INPUT =================================
% 12.05/12.40
% 12.05/12.40 % Reading from file /tmp/Prover9_30899_n022.cluster.edu
% 12.05/12.40
% 12.05/12.40 set(prolog_style_variables).
% 12.05/12.40 set(auto2).
% 12.05/12.40 % set(auto2) -> set(auto).
% 12.05/12.40 % set(auto) -> set(auto_inference).
% 12.05/12.40 % set(auto) -> set(auto_setup).
% 12.05/12.40 % set(auto_setup) -> set(predicate_elim).
% 12.05/12.40 % set(auto_setup) -> assign(eq_defs, unfold).
% 12.05/12.40 % set(auto) -> set(auto_limits).
% 12.05/12.40 % set(auto_limits) -> assign(max_weight, "100.000").
% 12.05/12.40 % set(auto_limits) -> assign(sos_limit, 20000).
% 12.05/12.40 % set(auto) -> set(auto_denials).
% 12.05/12.40 % set(auto) -> set(auto_process).
% 12.05/12.40 % set(auto2) -> assign(new_constants, 1).
% 12.05/12.40 % set(auto2) -> assign(fold_denial_max, 3).
% 12.05/12.40 % set(auto2) -> assign(max_weight, "200.000").
% 12.05/12.40 % set(auto2) -> assign(max_hours, 1).
% 12.05/12.40 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 12.05/12.40 % set(auto2) -> assign(max_seconds, 0).
% 12.05/12.40 % set(auto2) -> assign(max_minutes, 5).
% 12.05/12.40 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 12.05/12.40 % set(auto2) -> set(sort_initial_sos).
% 12.05/12.40 % set(auto2) -> assign(sos_limit, -1).
% 12.05/12.40 % set(auto2) -> assign(lrs_ticks, 3000).
% 12.05/12.40 % set(auto2) -> assign(max_megs, 400).
% 12.05/12.40 % set(auto2) -> assign(stats, some).
% 12.05/12.40 % set(auto2) -> clear(echo_input).
% 12.05/12.40 % set(auto2) -> set(quiet).
% 12.05/12.40 % set(auto2) -> clear(print_initial_clauses).
% 12.05/12.40 % set(auto2) -> clear(print_given).
% 12.05/12.40 assign(lrs_ticks,-1).
% 12.05/12.40 assign(sos_limit,10000).
% 12.05/12.40 assign(order,kbo).
% 12.05/12.40 set(lex_order_vars).
% 12.05/12.40 clear(print_given).
% 12.05/12.40
% 12.05/12.40 % formulas(sos). % not echoed (27 formulas)
% 12.05/12.40
% 12.05/12.40 ============================== end of input ==========================
% 12.05/12.40
% 12.05/12.40 % From the command line: assign(max_seconds, 300).
% 12.05/12.40
% 12.05/12.40 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 12.05/12.40
% 12.05/12.40 % Formulas that are not ordinary clauses:
% 12.05/12.40
% 12.05/12.40 ============================== end of process non-clausal formulas ===
% 12.05/12.40
% 12.05/12.40 ============================== PROCESS INITIAL CLAUSES ===============
% 12.05/12.40
% 12.05/12.40 ============================== PREDICATE ELIMINATION =================
% 12.05/12.40
% 12.05/12.40 ============================== end predicate elimination =============
% 12.05/12.40
% 12.05/12.40 Auto_denials:
% 12.05/12.40 % copying label prove_equation to answer in negative clause
% 12.05/12.40
% 12.05/12.40 Term ordering decisions:
% 12.05/12.40
% 12.05/12.40 % Assigning unary symbol inverse kb_weight 0 and highest precedence (15).
% 12.05/12.40 Function symbol KB weights: true=1. additive_identity=1. multiplicative_identity=1. x=1. y=1. x_inverse_times_y_inverse=1. x_plus_y=1. add=1. multiply=1. product=1. sum=1. ifeq=1. ifeq2=1. inverse=0.
% 12.05/12.40
% 12.05/12.40 ============================== end of process initial clauses ========
% 12.05/12.40
% 12.05/12.40 ============================== CLAUSES FOR SEARCH ====================
% 12.05/12.40
% 12.05/12.40 ============================== end of clauses for search =============
% 12.05/12.40
% 12.05/12.40 ============================== SEARCH ================================
% 12.05/12.40
% 12.05/12.40 % Starting search at 0.01 seconds.
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=39.000, iters=3354
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=37.000, iters=3336
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=33.000, iters=3354
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=32.000, iters=3435
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=31.000, iters=3336
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=30.000, iters=3367
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=29.000, iters=3389
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=28.000, iters=3365
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=27.000, iters=3335
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=26.000, iters=3348
% 12.05/12.40
% 12.05/12.40 Low Water (displace): id=5782, wt=43.000
% 12.05/12.40
% 12.05/12.40 Low Water (displace): id=6314, wt=41.000
% 12.05/12.40
% 12.05/12.40 Low Water (displace): id=6320, wt=39.000
% 12.05/12.40
% 12.05/12.40 Low Water (displace): id=6437, wt=37.000
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=25.000, iters=3366
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=24.000, iters=3347
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=23.000, iters=3389
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=22.000, iters=3337
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=21.000, iters=3338
% 12.05/12.40
% 12.05/12.40 Low Water (displace): id=25901, wt=18.000
% 12.05/12.40
% 12.05/12.40 Low Water (displace): id=25974, wt=16.000
% 12.05/12.40
% 12.05/12.40 Low Water (displace): id=26657, wt=15.000
% 12.05/12.40
% 12.05/12.40 Low Water (keep): wt=20.000, iters=3336
% 12.05/12.40
% 12.05/12.40 Low Water (displace): id=29707, wt=10.000
% 40.92/41.28
% 40.92/41.28 Low Water (keep): wt=19.000, iters=3382
% 40.92/41.28
% 40.92/41.28 Low Water (keep): wt=18.000, iters=3340
% 40.92/41.28
% 40.92/41.28 Low Water (keep): wt=17.000, iters=3337
% 40.92/41.28
% 40.92/41.28 Low Water (keep): wt=16.000, iters=3365
% 40.92/41.28
% 40.92/41.28 ============================== PROOF =================================
% 40.92/41.28 % SZS status Unsatisfiable
% 40.92/41.28 % SZS output start Refutation
% 40.92/41.28
% 40.92/41.28 % Proof 1 at 39.63 (+ 0.67) seconds: prove_equation.
% 40.92/41.28 % Length of proof is 128.
% 40.92/41.28 % Level of proof is 28.
% 40.92/41.28 % Maximum clause weight is 34.000.
% 40.92/41.28 % Given clauses 7860.
% 40.92/41.28
% 40.92/41.28 1 sum(additive_identity,A,A) = true # label(additive_identity1) # label(axiom). [assumption].
% 40.92/41.28 2 sum(A,additive_identity,A) = true # label(additive_identity2) # label(axiom). [assumption].
% 40.92/41.28 3 product(multiplicative_identity,A,A) = true # label(multiplicative_identity1) # label(axiom). [assumption].
% 40.92/41.28 4 product(A,multiplicative_identity,A) = true # label(multiplicative_identity2) # label(axiom). [assumption].
% 40.92/41.28 5 sum(x,y,x_plus_y) = true # label(x_plus_y) # label(negated_conjecture). [assumption].
% 40.92/41.28 6 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 40.92/41.28 7 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 40.92/41.28 8 sum(inverse(A),A,multiplicative_identity) = true # label(additive_inverse1) # label(axiom). [assumption].
% 40.92/41.28 9 sum(A,inverse(A),multiplicative_identity) = true # label(additive_inverse2) # label(axiom). [assumption].
% 40.92/41.28 10 product(inverse(A),A,additive_identity) = true # label(multiplicative_inverse1) # label(axiom). [assumption].
% 40.92/41.28 11 product(A,inverse(A),additive_identity) = true # label(multiplicative_inverse2) # label(axiom). [assumption].
% 40.92/41.28 12 sum(A,B,add(A,B)) = true # label(closure_of_addition) # label(axiom). [assumption].
% 40.92/41.28 13 product(A,B,multiply(A,B)) = true # label(closure_of_multiplication) # label(axiom). [assumption].
% 40.92/41.28 14 product(inverse(x),inverse(y),x_inverse_times_y_inverse) = true # label(x_inverse_times_y_inverse) # label(negated_conjecture). [assumption].
% 40.92/41.28 15 ifeq(sum(A,B,C),true,sum(B,A,C),true) = true # label(commutativity_of_addition) # label(axiom). [assumption].
% 40.92/41.28 16 ifeq(product(A,B,C),true,product(B,A,C),true) = true # label(commutativity_of_multiplication) # label(axiom). [assumption].
% 40.92/41.28 17 ifeq2(sum(A,B,C),true,ifeq2(sum(A,B,D),true,D,C),C) = C # label(addition_is_well_defined) # label(axiom). [assumption].
% 40.92/41.28 18 ifeq2(product(A,B,C),true,ifeq2(product(A,B,D),true,D,C),C) = C # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 40.92/41.28 19 ifeq(product(A,B,C),true,ifeq(product(A,D,E),true,ifeq(product(A,F,V6),true,ifeq(sum(F,D,B),true,sum(V6,E,C),true),true),true),true) = true # label(distributivity1) # label(axiom). [assumption].
% 40.92/41.28 25 ifeq(product(A,B,C),true,ifeq(sum(C,D,E),true,ifeq(sum(B,D,F),true,ifeq(sum(A,D,V6),true,product(V6,F,E),true),true),true),true) = true # label(distributivity7) # label(axiom). [assumption].
% 40.92/41.28 27 inverse(x_plus_y) != x_inverse_times_y_inverse # label(prove_equation) # label(negated_conjecture) # answer(prove_equation). [assumption].
% 40.92/41.28 28 sum(y,x,x_plus_y) = true. [para(5(a,1),15(a,1,1)),rewrite([7(8)])].
% 40.92/41.28 29 sum(A,B,add(B,A)) = true. [para(12(a,1),15(a,1,1)),rewrite([7(6)])].
% 40.92/41.28 30 product(A,B,multiply(B,A)) = true. [para(13(a,1),16(a,1,1)),rewrite([7(6)])].
% 40.92/41.28 31 product(inverse(y),inverse(x),x_inverse_times_y_inverse) = true. [para(14(a,1),16(a,1,1)),rewrite([7(10)])].
% 40.92/41.28 32 ifeq2(sum(additive_identity,A,B),true,B,A) = A. [para(1(a,1),17(a,1,1)),rewrite([6(7)])].
% 40.92/41.28 34 ifeq2(sum(A,additive_identity,B),true,B,A) = A. [para(2(a,1),17(a,1,1)),rewrite([6(7)])].
% 40.92/41.28 42 ifeq2(sum(A,B,C),true,C,add(A,B)) = add(A,B). [para(12(a,1),17(a,1,1)),rewrite([6(8)])].
% 40.92/41.28 43 ifeq2(sum(A,B,C),true,add(A,B),C) = C. [para(12(a,1),17(a,1,3,1)),rewrite([6(6)])].
% 40.92/41.28 46 ifeq2(product(A,multiplicative_identity,B),true,B,A) = A. [para(4(a,1),18(a,1,1)),rewrite([6(7)])].
% 40.92/41.28 53 ifeq2(product(A,B,C),true,multiply(A,B),C) = C. [para(13(a,1),18(a,1,3,1)),rewrite([6(6)])].
% 40.92/41.28 56 ifeq(product(A,B,C),true,ifeq(product(A,B,D),true,ifeq(product(A,additive_identity,E),true,sum(E,D,C),true),true),true) = true. [para(1(a,1),19(a,1,3,3,3,1)),rewrite([7(12)])].
% 40.92/41.28 60 ifeq(product(multiplicative_identity,A,B),true,ifeq(product(multiplicative_identity,C,D),true,ifeq(sum(C,A,E),true,sum(D,B,E),true),true),true) = true. [para(3(a,1),19(a,1,1)),rewrite([7(19)])].
% 40.92/41.28 63 ifeq(product(A,B,C),true,ifeq(product(A,D,E),true,ifeq(sum(D,B,multiplicative_identity),true,sum(E,C,A),true),true),true) = true. [para(4(a,1),19(a,1,1)),rewrite([7(18)])].
% 40.92/41.28 66 ifeq(product(A,x_plus_y,B),true,ifeq(product(A,y,C),true,ifeq(product(A,x,D),true,sum(D,C,B),true),true),true) = true. [para(5(a,1),19(a,1,3,3,3,1)),rewrite([7(14)])].
% 40.92/41.28 72 ifeq(product(inverse(A),B,C),true,ifeq(product(inverse(A),D,E),true,ifeq(sum(D,B,A),true,sum(E,C,additive_identity),true),true),true) = true. [para(10(a,1),19(a,1,1)),rewrite([7(20)])].
% 40.92/41.28 83 ifeq(product(inverse(x),A,B),true,ifeq(product(inverse(x),C,D),true,ifeq(sum(C,A,inverse(y)),true,sum(D,B,x_inverse_times_y_inverse),true),true),true) = true. [para(14(a,1),19(a,1,1)),rewrite([7(24)])].
% 40.92/41.28 239 ifeq(product(A,B,additive_identity),true,ifeq(sum(B,C,D),true,ifeq(sum(A,C,E),true,product(E,D,C),true),true),true) = true. [para(1(a,1),25(a,1,3,1)),rewrite([7(16)])].
% 40.92/41.28 398 add(A,B) = add(B,A). [para(29(a,1),42(a,1,1)),rewrite([6(5)])].
% 40.92/41.28 402 multiply(A,B) = multiply(B,A). [para(30(a,1),53(a,1,1)),rewrite([6(5)])].
% 40.92/41.28 415 ifeq(product(A,inverse(A),B),true,ifeq(product(A,additive_identity,C),true,sum(C,B,additive_identity),true),true) = true. [para(11(a,1),56(a,1,1)),rewrite([7(16)])].
% 40.92/41.28 418 ifeq(product(A,B,C),true,ifeq(product(A,additive_identity,D),true,sum(D,C,multiply(A,B)),true),true) = true. [para(13(a,1),56(a,1,1)),rewrite([7(15)])].
% 40.92/41.28 507 ifeq(product(multiplicative_identity,A,B),true,ifeq(sum(A,C,D),true,sum(B,C,D),true),true) = true. [para(3(a,1),60(a,1,1)),rewrite([7(14)])].
% 40.92/41.28 609 ifeq(product(A,B,C),true,ifeq(sum(B,multiplicative_identity,multiplicative_identity),true,sum(C,A,A),true),true) = true. [para(4(a,1),63(a,1,1)),rewrite([7(15)])].
% 40.92/41.28 610 ifeq(product(A,B,C),true,ifeq(sum(multiplicative_identity,B,multiplicative_identity),true,sum(A,C,A),true),true) = true. [para(4(a,1),63(a,1,3,1)),rewrite([7(13)])].
% 40.92/41.28 612 ifeq(product(A,B,C),true,ifeq(product(A,inverse(B),D),true,sum(D,C,A),true),true) = true. [para(8(a,1),63(a,1,3,3,1)),rewrite([7(10)])].
% 40.92/41.28 614 ifeq(product(inverse(A),B,C),true,ifeq(sum(B,A,multiplicative_identity),true,sum(C,additive_identity,inverse(A)),true),true) = true. [para(10(a,1),63(a,1,1)),rewrite([7(17)])].
% 40.92/41.28 720 ifeq(product(A,x_plus_y,B),true,ifeq(product(A,x,C),true,sum(C,multiply(A,y),B),true),true) = true. [para(13(a,1),66(a,1,3,1)),rewrite([7(15)])].
% 40.92/41.28 794 ifeq(product(inverse(A),B,C),true,ifeq(sum(B,A,A),true,sum(C,additive_identity,additive_identity),true),true) = true. [para(10(a,1),72(a,1,1)),rewrite([7(16)])].
% 40.92/41.28 795 ifeq(product(inverse(A),B,C),true,ifeq(sum(A,B,A),true,sum(additive_identity,C,additive_identity),true),true) = true. [para(10(a,1),72(a,1,3,1)),rewrite([7(14)])].
% 40.92/41.28 992 ifeq(product(inverse(x),A,B),true,ifeq(sum(A,inverse(y),inverse(y)),true,sum(B,x_inverse_times_y_inverse,x_inverse_times_y_inverse),true),true) = true. [para(14(a,1),83(a,1,1)),rewrite([7(21)])].
% 40.92/41.28 2043 ifeq(product(multiplicative_identity,A,B),true,sum(B,C,add(A,C)),true) = true. [para(12(a,1),507(a,1,3,1)),rewrite([7(9)])].
% 40.92/41.28 2800 sum(multiplicative_identity,A,add(A,multiplicative_identity)) = true. [para(4(a,1),2043(a,1,1)),rewrite([398(5),7(8)])].
% 40.92/41.28 9197 ifeq(product(A,additive_identity,additive_identity),true,ifeq(sum(A,B,C),true,product(C,B,B),true),true) = true. [para(1(a,1),239(a,1,3,1)),rewrite([7(13)])].
% 40.92/41.28 11534 ifeq(sum(A,multiplicative_identity,multiplicative_identity),true,sum(multiply(A,B),B,B),true) = true. [para(13(a,1),609(a,1,1)),rewrite([402(7),7(12)])].
% 40.92/41.28 11553 ifeq(sum(multiplicative_identity,A,multiplicative_identity),true,sum(B,multiply(A,B),B),true) = true. [para(13(a,1),610(a,1,1)),rewrite([402(7),7(12)])].
% 40.92/41.28 11554 ifeq(sum(multiplicative_identity,inverse(y),multiplicative_identity),true,sum(inverse(x),x_inverse_times_y_inverse,inverse(x)),true) = true. [para(14(a,1),610(a,1,1)),rewrite([7(18)])].
% 40.92/41.28 11555 ifeq(sum(multiplicative_identity,inverse(x),multiplicative_identity),true,sum(inverse(y),x_inverse_times_y_inverse,inverse(y)),true) = true. [para(31(a,1),610(a,1,1)),rewrite([7(18)])].
% 40.92/41.28 14267 ifeq(product(A,additive_identity,B),true,sum(B,additive_identity,additive_identity),true) = true. [para(11(a,1),415(a,1,1)),rewrite([7(12)])].
% 40.92/41.28 14284 sum(multiply(A,additive_identity),additive_identity,additive_identity) = true. [para(13(a,1),14267(a,1,1)),rewrite([7(9)])].
% 40.92/41.28 14298 multiply(A,additive_identity) = additive_identity. [para(14284(a,1),34(a,1,1)),rewrite([6(6)]),flip(a)].
% 40.92/41.28 14378 product(A,additive_identity,additive_identity) = true. [para(14298(a,1),13(a,1,3))].
% 40.92/41.28 14385 ifeq(sum(A,B,C),true,product(C,B,B),true) = true. [back_rewrite(9197),rewrite([14378(3),7(9)])].
% 40.92/41.28 14622 product(x_plus_y,y,y) = true. [para(5(a,1),14385(a,1,1)),rewrite([7(8)])].
% 40.92/41.28 14623 product(add(A,B),B,B) = true. [para(12(a,1),14385(a,1,1)),rewrite([7(6)])].
% 40.92/41.28 14624 product(x_plus_y,x,x) = true. [para(28(a,1),14385(a,1,1)),rewrite([7(8)])].
% 40.92/41.28 15053 ifeq(sum(y,multiplicative_identity,multiplicative_identity),true,sum(y,x_plus_y,x_plus_y),true) = true. [para(14622(a,1),609(a,1,1)),rewrite([7(15)])].
% 40.92/41.28 15231 ifeq(sum(x,multiplicative_identity,multiplicative_identity),true,sum(x,x_plus_y,x_plus_y),true) = true. [para(14624(a,1),609(a,1,1)),rewrite([7(15)])].
% 40.92/41.28 15609 add(A,multiplicative_identity) = multiplicative_identity. [para(14623(a,1),46(a,1,1)),rewrite([6(6)]),flip(a)].
% 40.92/41.28 15611 multiply(A,add(B,A)) = A. [para(14623(a,1),53(a,1,1)),rewrite([402(4),6(5)])].
% 40.92/41.28 15812 ifeq(product(add(A,B),additive_identity,C),true,sum(C,B,B),true) = true. [para(14623(a,1),418(a,1,1)),rewrite([402(8),15611(8),7(11)])].
% 40.92/41.28 16035 sum(multiplicative_identity,A,multiplicative_identity) = true. [back_rewrite(2800),rewrite([15609(3)])].
% 40.92/41.28 16043 sum(inverse(y),x_inverse_times_y_inverse,inverse(y)) = true. [back_rewrite(11555),rewrite([16035(5),7(10)])].
% 40.92/41.28 16044 sum(inverse(x),x_inverse_times_y_inverse,inverse(x)) = true. [back_rewrite(11554),rewrite([16035(5),7(10)])].
% 40.92/41.28 16045 sum(A,multiply(B,A),A) = true. [back_rewrite(11553),rewrite([16035(3),7(6)])].
% 40.92/41.28 16049 sum(A,multiplicative_identity,multiplicative_identity) = true. [para(15609(a,1),12(a,1,3))].
% 40.92/41.28 16073 sum(x,x_plus_y,x_plus_y) = true. [back_rewrite(15231),rewrite([16049(4),7(8)])].
% 40.92/41.28 16074 sum(y,x_plus_y,x_plus_y) = true. [back_rewrite(15053),rewrite([16049(4),7(8)])].
% 40.92/41.28 16077 sum(multiply(A,B),B,B) = true. [back_rewrite(11534),rewrite([16049(3),7(6)])].
% 40.92/41.28 17955 add(A,multiply(A,B)) = A. [para(16045(a,1),42(a,1,1)),rewrite([402(3),6(5),402(1)]),flip(a)].
% 40.92/41.28 18261 add(A,multiply(B,A)) = A. [para(16077(a,1),43(a,1,1)),rewrite([398(4),6(5)])].
% 40.92/41.28 18262 sum(multiply(A,B),A,A) = true. [para(402(a,1),16077(a,1,1))].
% 40.92/41.28 18664 ifeq(product(A,inverse(inverse(A)),B),true,sum(B,additive_identity,A),true) = true. [para(11(a,1),612(a,1,1)),rewrite([7(12)])].
% 40.92/41.28 18666 ifeq(product(A,inverse(B),C),true,sum(C,multiply(A,B),A),true) = true. [para(13(a,1),612(a,1,1)),rewrite([7(11)])].
% 40.92/41.28 19738 sum(multiply(additive_identity,add(A,B)),B,B) = true. [para(13(a,1),15812(a,1,1)),rewrite([402(5),7(8)])].
% 40.92/41.28 19744 add(A,multiply(additive_identity,add(B,A))) = A. [para(19738(a,1),43(a,1,1)),rewrite([398(6),6(7)])].
% 40.92/41.28 19770 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(17955(a,1),19744(a,1,2,2)),rewrite([402(3),14298(3),398(3)])].
% 40.92/41.28 19787 ifeq(product(inverse(x_plus_y),x,A),true,sum(A,additive_identity,additive_identity),true) = true. [para(16073(a,1),794(a,1,3,1)),rewrite([7(12)])].
% 40.92/41.28 19788 ifeq(product(inverse(x_plus_y),y,A),true,sum(A,additive_identity,additive_identity),true) = true. [para(16074(a,1),794(a,1,3,1)),rewrite([7(12)])].
% 40.92/41.28 19804 ifeq(product(inverse(inverse(y)),x_inverse_times_y_inverse,A),true,sum(additive_identity,A,additive_identity),true) = true. [para(16043(a,1),795(a,1,3,1)),rewrite([7(13)])].
% 40.92/41.28 19806 ifeq(product(inverse(inverse(x)),x_inverse_times_y_inverse,A),true,sum(additive_identity,A,additive_identity),true) = true. [para(16044(a,1),795(a,1,3,1)),rewrite([7(13)])].
% 40.92/41.28 19834 sum(multiply(x,inverse(x_plus_y)),additive_identity,additive_identity) = true. [para(13(a,1),19787(a,1,1)),rewrite([402(6),7(11)])].
% 40.92/41.28 19859 multiply(x,inverse(x_plus_y)) = additive_identity. [para(19834(a,1),34(a,1,1)),rewrite([6(8)]),flip(a)].
% 40.92/41.28 20237 sum(multiply(y,inverse(x_plus_y)),additive_identity,additive_identity) = true. [para(13(a,1),19788(a,1,1)),rewrite([402(6),7(11)])].
% 40.92/41.28 20241 multiply(y,inverse(x_plus_y)) = additive_identity. [para(20237(a,1),34(a,1,1)),rewrite([6(8)]),flip(a)].
% 40.92/41.28 20775 sum(multiply(A,inverse(inverse(A))),additive_identity,A) = true. [para(13(a,1),18664(a,1,1)),rewrite([7(9)])].
% 40.92/41.28 20779 multiply(A,inverse(inverse(A))) = A. [para(20775(a,1),34(a,1,1)),rewrite([6(6)]),flip(a)].
% 40.92/41.28 20790 product(A,inverse(inverse(A)),A) = true. [para(20779(a,1),13(a,1,3))].
% 40.92/41.28 20813 product(inverse(inverse(A)),A,A) = true. [para(20790(a,1),16(a,1,1)),rewrite([7(7)])].
% 40.92/41.28 20962 sum(A,additive_identity,inverse(inverse(A))) = true. [para(20813(a,1),614(a,1,1)),rewrite([9(5),7(10),7(8)])].
% 40.92/41.28 21003 inverse(inverse(A)) = A. [para(20962(a,1),34(a,1,1)),rewrite([6(5)])].
% 40.92/41.28 21018 ifeq(product(x,x_inverse_times_y_inverse,A),true,sum(additive_identity,A,additive_identity),true) = true. [back_rewrite(19806),rewrite([21003(3)])].
% 40.92/41.28 21019 ifeq(product(y,x_inverse_times_y_inverse,A),true,sum(additive_identity,A,additive_identity),true) = true. [back_rewrite(19804),rewrite([21003(3)])].
% 40.92/41.28 21026 sum(additive_identity,multiply(x,x_inverse_times_y_inverse),additive_identity) = true. [para(13(a,1),21018(a,1,1)),rewrite([7(10)])].
% 40.92/41.28 21030 multiply(x,x_inverse_times_y_inverse) = additive_identity. [para(21026(a,1),32(a,1,1)),rewrite([6(7)]),flip(a)].
% 40.92/41.28 21035 product(x,x_inverse_times_y_inverse,additive_identity) = true. [para(21030(a,1),13(a,1,3))].
% 40.92/41.28 21064 product(x_inverse_times_y_inverse,x,additive_identity) = true. [para(21035(a,1),16(a,1,1)),rewrite([7(8)])].
% 40.92/41.28 21387 ifeq(product(x_inverse_times_y_inverse,x_plus_y,A),true,sum(additive_identity,multiply(y,x_inverse_times_y_inverse),A),true) = true. [para(21064(a,1),720(a,1,3,1)),rewrite([402(10),7(13)])].
% 40.92/41.28 21402 sum(additive_identity,multiply(y,x_inverse_times_y_inverse),additive_identity) = true. [para(13(a,1),21019(a,1,1)),rewrite([7(10)])].
% 40.92/41.28 21406 multiply(y,x_inverse_times_y_inverse) = additive_identity. [para(21402(a,1),32(a,1,1)),rewrite([6(7)]),flip(a)].
% 40.92/41.28 21411 ifeq(product(x_inverse_times_y_inverse,x_plus_y,A),true,sum(additive_identity,additive_identity,A),true) = true. [back_rewrite(21387),rewrite([21406(8)])].
% 40.92/41.28 21821 sum(additive_identity,additive_identity,multiply(x_inverse_times_y_inverse,x_plus_y)) = true. [para(13(a,1),21411(a,1,1)),rewrite([7(10)])].
% 40.92/41.28 21824 multiply(x_inverse_times_y_inverse,x_plus_y) = additive_identity. [para(21821(a,1),32(a,1,1)),rewrite([6(7)])].
% 40.92/41.28 21827 product(x_inverse_times_y_inverse,x_plus_y,additive_identity) = true. [para(21824(a,1),13(a,1,3))].
% 40.92/41.28 21986 ifeq(product(x_inverse_times_y_inverse,inverse(x_plus_y),A),true,sum(A,additive_identity,x_inverse_times_y_inverse),true) = true. [para(21827(a,1),612(a,1,1)),rewrite([7(14)])].
% 40.92/41.28 23008 sum(multiply(x_inverse_times_y_inverse,inverse(x_plus_y)),additive_identity,x_inverse_times_y_inverse) = true. [para(13(a,1),21986(a,1,1)),rewrite([7(11)])].
% 40.92/41.28 23020 multiply(x_inverse_times_y_inverse,inverse(x_plus_y)) = x_inverse_times_y_inverse. [para(23008(a,1),34(a,1,1)),rewrite([6(8)]),flip(a)].
% 40.92/41.28 23035 add(x_inverse_times_y_inverse,inverse(x_plus_y)) = inverse(x_plus_y). [para(23020(a,1),18261(a,1,2)),rewrite([398(4)])].
% 40.92/41.28 45200 sum(multiply(A,inverse(B)),multiply(A,B),A) = true. [para(13(a,1),18666(a,1,1)),rewrite([7(8)])].
% 40.92/41.28 45212 add(multiply(A,B),multiply(A,inverse(B))) = A. [para(45200(a,1),42(a,1,1)),rewrite([398(6),6(7),398(4)]),flip(a)].
% 40.92/41.28 45309 add(multiply(A,B),multiply(B,inverse(A))) = B. [para(402(a,1),45212(a,1,1))].
% 40.92/41.28 45785 multiply(inverse(x),inverse(x_plus_y)) = inverse(x_plus_y). [para(19859(a,1),45309(a,1,1)),rewrite([402(6),19770(7)])].
% 40.92/41.28 45786 multiply(inverse(y),inverse(x_plus_y)) = inverse(x_plus_y). [para(20241(a,1),45309(a,1,1)),rewrite([402(6),19770(7)])].
% 40.92/41.28 45980 product(inverse(x),inverse(x_plus_y),inverse(x_plus_y)) = true. [para(45785(a,1),13(a,1,3))].
% 40.92/41.28 46022 sum(inverse(x_plus_y),inverse(y),inverse(y)) = true. [para(45786(a,1),18262(a,1,1))].
% 40.92/41.28 46072 sum(inverse(x_plus_y),x_inverse_times_y_inverse,x_inverse_times_y_inverse) = true. [para(45980(a,1),992(a,1,1)),rewrite([46022(9),7(11),7(9)])].
% 40.92/41.28 46091 inverse(x_plus_y) = x_inverse_times_y_inverse. [para(46072(a,1),42(a,1,1)),rewrite([398(7),23035(7),6(6),398(5),23035(5)]),flip(a)].
% 40.92/41.28 46092 $F # answer(prove_equation). [resolve(46091,a,27,a)].
% 40.92/41.28
% 40.92/41.28 % SZS output end Refutation
% 40.92/41.28 ============================== end of proof ==========================
% 40.92/41.28
% 40.92/41.28 ============================== STATISTICS ============================
% 40.92/41.28
% 40.92/41.28 Given=7860. Generated=1351100. Kept=46091. proofs=1.
% 40.92/41.28 Usable=5550. Sos=9999. Demods=15550. Limbo=2, Disabled=30566. Hints=0.
% 40.92/41.28 Megabytes=35.83.
% 40.92/41.28 User_CPU=39.63, System_CPU=0.67, Wall_clock=41.
% 40.92/41.28
% 40.92/41.28 ============================== end of statistics =====================
% 40.92/41.28
% 40.92/41.28 ============================== end of search =========================
% 40.92/41.28
% 40.92/41.28 THEOREM PROVED
% 40.92/41.28 % SZS status Unsatisfiable
% 40.92/41.28
% 40.92/41.28 Exiting with 1 proof.
% 40.92/41.28
% 40.92/41.28 Process 31052 exit (max_proofs) Wed Jun 1 20:58:33 2022
% 40.92/41.28 Prover9 interrupted
%------------------------------------------------------------------------------