TSTP Solution File: BOO015-10 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO015-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 14.81s 15.13s
% Output : Refutation 14.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO015-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.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 16:28:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 14.81/15.13 ============================== Prover9 ===============================
% 14.81/15.13 Prover9 (32) version 2009-11A, November 2009.
% 14.81/15.13 Process 15385 was started by sandbox2 on n026.cluster.edu,
% 14.81/15.13 Wed Jun 1 16:28:27 2022
% 14.81/15.13 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_15232_n026.cluster.edu".
% 14.81/15.13 ============================== end of head ===========================
% 14.81/15.13
% 14.81/15.13 ============================== INPUT =================================
% 14.81/15.13
% 14.81/15.13 % Reading from file /tmp/Prover9_15232_n026.cluster.edu
% 14.81/15.13
% 14.81/15.13 set(prolog_style_variables).
% 14.81/15.13 set(auto2).
% 14.81/15.13 % set(auto2) -> set(auto).
% 14.81/15.13 % set(auto) -> set(auto_inference).
% 14.81/15.13 % set(auto) -> set(auto_setup).
% 14.81/15.13 % set(auto_setup) -> set(predicate_elim).
% 14.81/15.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 14.81/15.13 % set(auto) -> set(auto_limits).
% 14.81/15.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 14.81/15.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 14.81/15.13 % set(auto) -> set(auto_denials).
% 14.81/15.13 % set(auto) -> set(auto_process).
% 14.81/15.13 % set(auto2) -> assign(new_constants, 1).
% 14.81/15.13 % set(auto2) -> assign(fold_denial_max, 3).
% 14.81/15.13 % set(auto2) -> assign(max_weight, "200.000").
% 14.81/15.13 % set(auto2) -> assign(max_hours, 1).
% 14.81/15.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 14.81/15.13 % set(auto2) -> assign(max_seconds, 0).
% 14.81/15.13 % set(auto2) -> assign(max_minutes, 5).
% 14.81/15.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 14.81/15.13 % set(auto2) -> set(sort_initial_sos).
% 14.81/15.13 % set(auto2) -> assign(sos_limit, -1).
% 14.81/15.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 14.81/15.13 % set(auto2) -> assign(max_megs, 400).
% 14.81/15.13 % set(auto2) -> assign(stats, some).
% 14.81/15.13 % set(auto2) -> clear(echo_input).
% 14.81/15.13 % set(auto2) -> set(quiet).
% 14.81/15.13 % set(auto2) -> clear(print_initial_clauses).
% 14.81/15.13 % set(auto2) -> clear(print_given).
% 14.81/15.13 assign(lrs_ticks,-1).
% 14.81/15.13 assign(sos_limit,10000).
% 14.81/15.13 assign(order,kbo).
% 14.81/15.13 set(lex_order_vars).
% 14.81/15.13 clear(print_given).
% 14.81/15.13
% 14.81/15.13 % formulas(sos). % not echoed (27 formulas)
% 14.81/15.13
% 14.81/15.13 ============================== end of input ==========================
% 14.81/15.13
% 14.81/15.13 % From the command line: assign(max_seconds, 300).
% 14.81/15.13
% 14.81/15.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 14.81/15.13
% 14.81/15.13 % Formulas that are not ordinary clauses:
% 14.81/15.13
% 14.81/15.13 ============================== end of process non-clausal formulas ===
% 14.81/15.13
% 14.81/15.13 ============================== PROCESS INITIAL CLAUSES ===============
% 14.81/15.13
% 14.81/15.13 ============================== PREDICATE ELIMINATION =================
% 14.81/15.13
% 14.81/15.13 ============================== end predicate elimination =============
% 14.81/15.13
% 14.81/15.13 Auto_denials:
% 14.81/15.13 % copying label prove_equation to answer in negative clause
% 14.81/15.13
% 14.81/15.13 Term ordering decisions:
% 14.81/15.13
% 14.81/15.13 % Assigning unary symbol inverse kb_weight 0 and highest precedence (15).
% 14.81/15.13 Function symbol KB weights: true=1. additive_identity=1. multiplicative_identity=1. x=1. y=1. x_inverse_plus_y_inverse=1. x_times_y=1. add=1. multiply=1. product=1. sum=1. ifeq=1. ifeq2=1. inverse=0.
% 14.81/15.13
% 14.81/15.13 ============================== end of process initial clauses ========
% 14.81/15.13
% 14.81/15.13 ============================== CLAUSES FOR SEARCH ====================
% 14.81/15.13
% 14.81/15.13 ============================== end of clauses for search =============
% 14.81/15.13
% 14.81/15.13 ============================== SEARCH ================================
% 14.81/15.13
% 14.81/15.13 % Starting search at 0.01 seconds.
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=35.000, iters=3361
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=34.000, iters=3354
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=31.000, iters=3361
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=30.000, iters=3347
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=29.000, iters=3422
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=28.000, iters=3340
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=27.000, iters=3366
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=26.000, iters=3335
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=24.000, iters=3355
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=23.000, iters=3337
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=22.000, iters=3353
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=21.000, iters=3341
% 14.81/15.13
% 14.81/15.13 Low Water (displace): id=12503, wt=31.000
% 14.81/15.13
% 14.81/15.13 Low Water (displace): id=13249, wt=30.000
% 14.81/15.13
% 14.81/15.13 Low Water (displace): id=13253, wt=29.000
% 14.81/15.13
% 14.81/15.13 Low Water (displace): id=13634, wt=28.000
% 14.81/15.13
% 14.81/15.13 Low Water (displace): id=14610, wt=27.000
% 14.81/15.13
% 14.81/15.13 Low Water (displace): id=25419, wt=20.000
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=20.000, iters=3349
% 14.81/15.13
% 14.81/15.13 Low Water (displace): id=25728, wt=19.000
% 14.81/15.13
% 14.81/15.13 Low Water (displace): id=25735, wt=18.000
% 14.81/15.13
% 14.81/15.13 Low Water (displace): id=25743, wt=15.000
% 14.81/15.13
% 14.81/15.13 Low Water (keep): wt=19.000, iters=3338
% 14.81/15.13
% 14.81/15.13 ============================== PROOF =================================
% 14.81/15.13 % SZS status Unsatisfiable
% 14.81/15.13 % SZS output start Refutation
% 14.81/15.13
% 14.81/15.13 % Proof 1 at 13.93 (+ 0.18) seconds: prove_equation.
% 14.81/15.13 % Length of proof is 125.
% 14.81/15.13 % Level of proof is 28.
% 14.81/15.13 % Maximum clause weight is 34.000.
% 14.81/15.13 % Given clauses 4597.
% 14.81/15.13
% 14.81/15.13 1 sum(additive_identity,A,A) = true # label(additive_identity1) # label(axiom). [assumption].
% 14.81/15.13 2 sum(A,additive_identity,A) = true # label(additive_identity2) # label(axiom). [assumption].
% 14.81/15.13 3 product(multiplicative_identity,A,A) = true # label(multiplicative_identity1) # label(axiom). [assumption].
% 14.81/15.13 4 product(A,multiplicative_identity,A) = true # label(multiplicative_identity2) # label(axiom). [assumption].
% 14.81/15.13 5 product(x,y,x_times_y) = true # label(x_times_y) # label(negated_conjecture). [assumption].
% 14.81/15.13 6 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 14.81/15.13 7 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 14.81/15.13 8 sum(inverse(A),A,multiplicative_identity) = true # label(additive_inverse1) # label(axiom). [assumption].
% 14.81/15.13 9 sum(A,inverse(A),multiplicative_identity) = true # label(additive_inverse2) # label(axiom). [assumption].
% 14.81/15.13 10 product(inverse(A),A,additive_identity) = true # label(multiplicative_inverse1) # label(axiom). [assumption].
% 14.81/15.13 11 product(A,inverse(A),additive_identity) = true # label(multiplicative_inverse2) # label(axiom). [assumption].
% 14.81/15.13 12 sum(A,B,add(A,B)) = true # label(closure_of_addition) # label(axiom). [assumption].
% 14.81/15.13 13 product(A,B,multiply(A,B)) = true # label(closure_of_multiplication) # label(axiom). [assumption].
% 14.81/15.13 14 sum(inverse(x),inverse(y),x_inverse_plus_y_inverse) = true # label(x_inverse_plus_y_inverse) # label(negated_conjecture). [assumption].
% 14.81/15.13 15 ifeq(sum(A,B,C),true,sum(B,A,C),true) = true # label(commutativity_of_addition) # label(axiom). [assumption].
% 14.81/15.13 16 ifeq(product(A,B,C),true,product(B,A,C),true) = true # label(commutativity_of_multiplication) # label(axiom). [assumption].
% 14.81/15.13 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].
% 14.81/15.13 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].
% 14.81/15.13 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].
% 14.81/15.13 20 ifeq(product(A,B,C),true,ifeq(product(A,D,E),true,ifeq(sum(E,C,F),true,ifeq(sum(D,B,V6),true,product(A,V6,F),true),true),true),true) = true # label(distributivity2) # label(axiom). [assumption].
% 14.81/15.13 21 ifeq(product(A,B,C),true,ifeq(product(D,B,E),true,ifeq(product(F,B,V6),true,ifeq(sum(F,D,A),true,sum(V6,E,C),true),true),true),true) = true # label(distributivity3) # label(axiom). [assumption].
% 14.81/15.13 23 ifeq(product(A,B,C),true,ifeq(sum(D,C,E),true,ifeq(sum(D,B,F),true,ifeq(sum(D,A,V6),true,product(V6,F,E),true),true),true),true) = true # label(distributivity5) # label(axiom). [assumption].
% 14.81/15.13 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].
% 14.81/15.13 27 inverse(x_times_y) != x_inverse_plus_y_inverse # label(prove_equation) # label(negated_conjecture) # answer(prove_equation). [assumption].
% 14.81/15.13 28 sum(A,B,add(B,A)) = true. [para(12(a,1),15(a,1,1)),rewrite([7(6)])].
% 14.81/15.13 29 sum(inverse(y),inverse(x),x_inverse_plus_y_inverse) = true. [para(14(a,1),15(a,1,1)),rewrite([7(10)])].
% 14.81/15.13 30 product(y,x,x_times_y) = true. [para(5(a,1),16(a,1,1)),rewrite([7(8)])].
% 14.81/15.13 31 product(A,B,multiply(B,A)) = true. [para(13(a,1),16(a,1,1)),rewrite([7(6)])].
% 14.81/15.13 32 ifeq2(sum(additive_identity,A,B),true,B,A) = A. [para(1(a,1),17(a,1,1)),rewrite([6(7)])].
% 14.81/15.13 34 ifeq2(sum(A,additive_identity,B),true,B,A) = A. [para(2(a,1),17(a,1,1)),rewrite([6(7)])].
% 14.81/15.13 40 ifeq2(sum(A,B,C),true,C,add(A,B)) = add(A,B). [para(12(a,1),17(a,1,1)),rewrite([6(8)])].
% 14.81/15.13 46 ifeq2(product(A,multiplicative_identity,B),true,B,A) = A. [para(4(a,1),18(a,1,1)),rewrite([6(7)])].
% 14.81/15.13 55 ifeq2(product(A,B,C),true,multiply(A,B),C) = C. [para(13(a,1),18(a,1,3,1)),rewrite([6(6)])].
% 14.81/15.13 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)])].
% 14.81/15.13 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)])].
% 14.81/15.13 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)])].
% 14.81/15.13 66 ifeq(product(x,A,B),true,ifeq(product(x,C,D),true,ifeq(sum(C,A,y),true,sum(D,B,x_times_y),true),true),true) = true. [para(5(a,1),19(a,1,1)),rewrite([7(21)])].
% 14.81/15.13 73 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)])].
% 14.81/15.13 82 ifeq(product(A,B,C),true,ifeq(product(A,D,E),true,ifeq(sum(D,F,B),true,sum(E,multiply(A,F),C),true),true),true) = true. [para(13(a,1),19(a,1,3,1)),rewrite([7(16)])].
% 14.81/15.13 90 ifeq(product(A,additive_identity,B),true,ifeq(product(A,C,D),true,ifeq(sum(D,B,E),true,product(A,C,E),true),true),true) = true. [para(2(a,1),20(a,1,3,3,3,1)),rewrite([7(12)])].
% 14.81/15.13 121 ifeq(product(A,B,C),true,ifeq(product(D,B,E),true,ifeq(sum(D,A,multiplicative_identity),true,sum(E,C,B),true),true),true) = true. [para(3(a,1),21(a,1,1)),rewrite([7(18)])].
% 14.81/15.13 181 ifeq(product(A,B,additive_identity),true,ifeq(sum(C,B,D),true,ifeq(sum(C,A,E),true,product(E,D,C),true),true),true) = true. [para(2(a,1),23(a,1,3,1)),rewrite([7(16)])].
% 14.81/15.13 239 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)])].
% 14.81/15.13 399 add(A,B) = add(B,A). [para(28(a,1),40(a,1,1)),rewrite([6(5)])].
% 14.81/15.13 402 multiply(A,B) = multiply(B,A). [para(31(a,1),55(a,1,1)),rewrite([6(5)])].
% 14.81/15.13 423 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)])].
% 14.81/15.13 513 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)])].
% 14.81/15.13 596 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)])].
% 14.81/15.13 598 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)])].
% 14.81/15.13 722 ifeq(product(x,A,B),true,ifeq(sum(y,A,y),true,sum(x_times_y,B,x_times_y),true),true) = true. [para(5(a,1),66(a,1,3,1)),rewrite([7(16)])].
% 14.81/15.13 815 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),73(a,1,1)),rewrite([7(16)])].
% 14.81/15.13 1057 ifeq(product(A,x_inverse_plus_y_inverse,B),true,ifeq(product(A,inverse(x),C),true,sum(C,multiply(A,inverse(y)),B),true),true) = true. [para(14(a,1),82(a,1,3,3,1)),rewrite([7(15)])].
% 14.81/15.13 1212 ifeq(product(A,additive_identity,B),true,ifeq(sum(multiply(A,C),B,D),true,product(A,C,D),true),true) = true. [para(13(a,1),90(a,1,3,1)),rewrite([7(13)])].
% 14.81/15.13 1954 ifeq(product(A,B,C),true,ifeq(sum(multiplicative_identity,A,multiplicative_identity),true,sum(B,C,B),true),true) = true. [para(3(a,1),121(a,1,3,1)),rewrite([7(13)])].
% 14.81/15.13 3414 ifeq(product(A,B,additive_identity),true,ifeq(sum(inverse(B),A,C),true,product(C,multiplicative_identity,inverse(B)),true),true) = true. [para(8(a,1),181(a,1,3,1)),rewrite([7(15)])].
% 14.81/15.13 5146 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)])].
% 14.81/15.13 6456 ifeq(product(multiplicative_identity,A,B),true,sum(B,C,add(A,C)),true) = true. [para(12(a,1),513(a,1,3,1)),rewrite([7(9)])].
% 14.81/15.13 6943 sum(multiplicative_identity,A,add(A,multiplicative_identity)) = true. [para(4(a,1),6456(a,1,1)),rewrite([399(5),7(8)])].
% 14.81/15.13 11920 ifeq(product(A,additive_identity,B),true,sum(B,additive_identity,additive_identity),true) = true. [para(11(a,1),423(a,1,1)),rewrite([7(12)])].
% 14.81/15.13 11955 sum(multiply(A,additive_identity),additive_identity,additive_identity) = true. [para(13(a,1),11920(a,1,1)),rewrite([7(9)])].
% 14.81/15.13 11959 multiply(A,additive_identity) = additive_identity. [para(11955(a,1),34(a,1,1)),rewrite([6(6)]),flip(a)].
% 14.81/15.13 12025 product(A,additive_identity,additive_identity) = true. [para(11959(a,1),13(a,1,3))].
% 14.81/15.13 12030 ifeq(sum(A,B,C),true,product(C,B,B),true) = true. [back_rewrite(5146),rewrite([12025(3),7(9)])].
% 14.81/15.13 12238 product(add(A,B),B,B) = true. [para(12(a,1),12030(a,1,1)),rewrite([7(6)])].
% 14.81/15.13 12239 product(x_inverse_plus_y_inverse,inverse(y),inverse(y)) = true. [para(14(a,1),12030(a,1,1)),rewrite([7(10)])].
% 14.81/15.13 12240 product(x_inverse_plus_y_inverse,inverse(x),inverse(x)) = true. [para(29(a,1),12030(a,1,1)),rewrite([7(10)])].
% 14.81/15.13 12515 add(A,multiplicative_identity) = multiplicative_identity. [para(12238(a,1),46(a,1,1)),rewrite([6(6)]),flip(a)].
% 14.81/15.13 12517 multiply(A,add(B,A)) = A. [para(12238(a,1),55(a,1,1)),rewrite([402(4),6(5)])].
% 14.81/15.13 12772 sum(multiplicative_identity,A,multiplicative_identity) = true. [back_rewrite(6943),rewrite([12515(3)])].
% 14.81/15.13 12781 ifeq(product(A,B,C),true,sum(B,C,B),true) = true. [back_rewrite(1954),rewrite([12772(5),7(7)])].
% 14.81/15.13 13057 product(inverse(y),x_inverse_plus_y_inverse,inverse(y)) = true. [para(12239(a,1),16(a,1,1)),rewrite([7(10)])].
% 14.81/15.13 13244 product(inverse(x),x_inverse_plus_y_inverse,inverse(x)) = true. [para(12240(a,1),16(a,1,1)),rewrite([7(10)])].
% 14.81/15.13 14487 sum(y,x_times_y,y) = true. [para(5(a,1),12781(a,1,1)),rewrite([7(8)])].
% 14.81/15.13 14489 sum(x,x_times_y,x) = true. [para(30(a,1),12781(a,1,1)),rewrite([7(8)])].
% 14.81/15.13 14491 sum(x_inverse_plus_y_inverse,inverse(y),x_inverse_plus_y_inverse) = true. [para(13057(a,1),12781(a,1,1)),rewrite([7(9)])].
% 14.81/15.13 14492 sum(x_inverse_plus_y_inverse,inverse(x),x_inverse_plus_y_inverse) = true. [para(13244(a,1),12781(a,1,1)),rewrite([7(9)])].
% 14.81/15.13 14592 sum(x_times_y,y,y) = true. [para(14487(a,1),15(a,1,1)),rewrite([7(8)])].
% 14.81/15.13 14783 sum(x_times_y,x,x) = true. [para(14489(a,1),15(a,1,1)),rewrite([7(8)])].
% 14.81/15.13 15716 sum(inverse(y),x_inverse_plus_y_inverse,x_inverse_plus_y_inverse) = true. [para(14491(a,1),15(a,1,1)),rewrite([7(9)])].
% 14.81/15.13 15838 sum(inverse(x),x_inverse_plus_y_inverse,x_inverse_plus_y_inverse) = true. [para(14492(a,1),15(a,1,1)),rewrite([7(9)])].
% 14.81/15.13 16273 ifeq(product(A,inverse(inverse(A)),B),true,sum(B,additive_identity,A),true) = true. [para(11(a,1),596(a,1,1)),rewrite([7(12)])].
% 14.81/15.13 17447 ifeq(sum(y,A,y),true,sum(x_times_y,multiply(A,x),x_times_y),true) = true. [para(13(a,1),722(a,1,1)),rewrite([402(9),7(15)])].
% 14.81/15.13 18117 ifeq(product(inverse(y),x_times_y,A),true,sum(A,additive_identity,additive_identity),true) = true. [para(14592(a,1),815(a,1,3,1)),rewrite([7(12)])].
% 14.81/15.13 18118 ifeq(product(inverse(x),x_times_y,A),true,sum(A,additive_identity,additive_identity),true) = true. [para(14783(a,1),815(a,1,3,1)),rewrite([7(12)])].
% 14.81/15.13 18119 ifeq(product(inverse(x_inverse_plus_y_inverse),inverse(y),A),true,sum(A,additive_identity,additive_identity),true) = true. [para(15716(a,1),815(a,1,3,1)),rewrite([7(13)])].
% 14.81/15.13 18120 ifeq(product(inverse(x_inverse_plus_y_inverse),inverse(x),A),true,sum(A,additive_identity,additive_identity),true) = true. [para(15838(a,1),815(a,1,3,1)),rewrite([7(13)])].
% 14.81/15.13 18502 sum(multiply(x_times_y,inverse(y)),additive_identity,additive_identity) = true. [para(13(a,1),18117(a,1,1)),rewrite([402(6),7(11)])].
% 14.81/15.13 18506 multiply(x_times_y,inverse(y)) = additive_identity. [para(18502(a,1),34(a,1,1)),rewrite([6(8)]),flip(a)].
% 14.81/15.13 18860 sum(multiply(x_times_y,inverse(x)),additive_identity,additive_identity) = true. [para(13(a,1),18118(a,1,1)),rewrite([402(6),7(11)])].
% 14.81/15.13 18864 multiply(x_times_y,inverse(x)) = additive_identity. [para(18860(a,1),34(a,1,1)),rewrite([6(8)]),flip(a)].
% 14.81/15.13 18875 product(x_times_y,inverse(x),additive_identity) = true. [para(18864(a,1),13(a,1,3))].
% 14.81/15.13 19713 sum(multiply(A,inverse(inverse(A))),additive_identity,A) = true. [para(13(a,1),16273(a,1,1)),rewrite([7(9)])].
% 14.81/15.13 19765 multiply(A,inverse(inverse(A))) = A. [para(19713(a,1),34(a,1,1)),rewrite([6(6)]),flip(a)].
% 14.81/15.13 19772 product(A,inverse(inverse(A)),A) = true. [para(19765(a,1),13(a,1,3))].
% 14.81/15.13 19792 product(inverse(inverse(A)),A,A) = true. [para(19772(a,1),16(a,1,1)),rewrite([7(7)])].
% 14.81/15.13 19978 sum(A,additive_identity,inverse(inverse(A))) = true. [para(19792(a,1),598(a,1,1)),rewrite([9(5),7(10),7(8)])].
% 14.81/15.13 20032 inverse(inverse(A)) = A. [para(19978(a,1),34(a,1,1)),rewrite([6(5)])].
% 14.81/15.13 20118 ifeq(product(x_times_y,x_inverse_plus_y_inverse,A),true,sum(additive_identity,additive_identity,A),true) = true. [para(18875(a,1),1057(a,1,3,1)),rewrite([18506(11),7(11)])].
% 14.81/15.13 20119 sum(additive_identity,additive_identity,multiply(x_inverse_plus_y_inverse,x_times_y)) = true. [para(13(a,1),20118(a,1,1)),rewrite([402(7),7(10)])].
% 14.81/15.13 20122 multiply(x_inverse_plus_y_inverse,x_times_y) = additive_identity. [para(20119(a,1),32(a,1,1)),rewrite([6(7)])].
% 14.81/15.13 20123 product(x_inverse_plus_y_inverse,x_times_y,additive_identity) = true. [para(20122(a,1),13(a,1,3))].
% 14.81/15.13 20156 product(x_times_y,x_inverse_plus_y_inverse,additive_identity) = true. [para(20123(a,1),16(a,1,1)),rewrite([7(8)])].
% 14.81/15.13 20469 ifeq(product(x_times_y,inverse(x_inverse_plus_y_inverse),A),true,sum(A,additive_identity,x_times_y),true) = true. [para(20156(a,1),596(a,1,1)),rewrite([7(14)])].
% 14.81/15.13 20975 sum(multiply(x_times_y,inverse(x_inverse_plus_y_inverse)),additive_identity,x_times_y) = true. [para(13(a,1),20469(a,1,1)),rewrite([7(11)])].
% 14.81/15.13 20979 multiply(x_times_y,inverse(x_inverse_plus_y_inverse)) = x_times_y. [para(20975(a,1),34(a,1,1)),rewrite([6(8)]),flip(a)].
% 14.81/15.13 25188 sum(multiply(inverse(y),inverse(x_inverse_plus_y_inverse)),additive_identity,additive_identity) = true. [para(13(a,1),18119(a,1,1)),rewrite([402(7),7(12)])].
% 14.81/15.13 25193 product(inverse(y),inverse(x_inverse_plus_y_inverse),additive_identity) = true. [para(25188(a,1),1212(a,1,3,1)),rewrite([12025(5),7(12),7(10)])].
% 14.81/15.13 25215 product(inverse(x_inverse_plus_y_inverse),inverse(y),additive_identity) = true. [para(25193(a,1),16(a,1,1)),rewrite([7(10)])].
% 14.81/15.13 25305 sum(multiply(inverse(x),inverse(x_inverse_plus_y_inverse)),additive_identity,additive_identity) = true. [para(13(a,1),18120(a,1,1)),rewrite([402(7),7(12)])].
% 14.81/15.13 25310 product(inverse(x),inverse(x_inverse_plus_y_inverse),additive_identity) = true. [para(25305(a,1),1212(a,1,3,1)),rewrite([12025(5),7(12),7(10)])].
% 14.81/15.13 25337 product(inverse(x_inverse_plus_y_inverse),inverse(x),additive_identity) = true. [para(25310(a,1),16(a,1,1)),rewrite([7(10)])].
% 14.81/15.13 31198 ifeq(sum(y,inverse(x_inverse_plus_y_inverse),A),true,product(A,multiplicative_identity,y),true) = true. [para(25215(a,1),3414(a,1,1)),rewrite([20032(5),20032(11),7(14)])].
% 14.81/15.13 31199 ifeq(sum(x,inverse(x_inverse_plus_y_inverse),A),true,product(A,multiplicative_identity,x),true) = true. [para(25337(a,1),3414(a,1,1)),rewrite([20032(5),20032(11),7(14)])].
% 14.81/15.13 31207 product(add(y,inverse(x_inverse_plus_y_inverse)),multiplicative_identity,y) = true. [para(12(a,1),31198(a,1,1)),rewrite([7(11)])].
% 14.81/15.13 31226 add(y,inverse(x_inverse_plus_y_inverse)) = y. [para(31207(a,1),46(a,1,1)),rewrite([6(8)]),flip(a)].
% 14.81/15.13 31241 sum(y,inverse(x_inverse_plus_y_inverse),y) = true. [para(31226(a,1),12(a,1,3))].
% 14.81/15.13 31284 sum(x_times_y,multiply(x,inverse(x_inverse_plus_y_inverse)),x_times_y) = true. [para(31241(a,1),17447(a,1,1)),rewrite([402(7),7(11)])].
% 14.81/15.13 31464 add(x_times_y,multiply(x,inverse(x_inverse_plus_y_inverse))) = x_times_y. [para(31284(a,1),40(a,1,1)),rewrite([6(10)]),flip(a)].
% 14.81/15.13 31525 multiply(x_times_y,multiply(x,inverse(x_inverse_plus_y_inverse))) = multiply(x,inverse(x_inverse_plus_y_inverse)). [para(31464(a,1),12517(a,1,2)),rewrite([402(6)])].
% 14.81/15.13 31842 product(add(x,inverse(x_inverse_plus_y_inverse)),multiplicative_identity,x) = true. [para(12(a,1),31199(a,1,1)),rewrite([7(11)])].
% 14.81/15.13 31846 add(x,inverse(x_inverse_plus_y_inverse)) = x. [para(31842(a,1),46(a,1,1)),rewrite([6(8)]),flip(a)].
% 14.81/15.13 31873 multiply(x,inverse(x_inverse_plus_y_inverse)) = inverse(x_inverse_plus_y_inverse). [para(31846(a,1),12517(a,1,2)),rewrite([402(4)])].
% 14.81/15.13 31908 inverse(x_inverse_plus_y_inverse) = x_times_y. [back_rewrite(31525),rewrite([31873(5),20979(4),31873(5)]),flip(a)].
% 14.81/15.13 32349 inverse(x_times_y) = x_inverse_plus_y_inverse. [para(31908(a,1),20032(a,1,1))].
% 14.81/15.13 32350 $F # answer(prove_equation). [resolve(32349,a,27,a)].
% 14.81/15.13
% 14.81/15.13 % SZS output end Refutation
% 14.81/15.13 ============================== end of proof ==========================
% 14.81/15.13
% 14.81/15.13 ============================== STATISTICS ============================
% 14.81/15.13
% 14.81/15.13 Given=4597. Generated=329464. Kept=32349. proofs=1.
% 14.81/15.13 Usable=2881. Sos=9035. Demods=11928. Limbo=13, Disabled=20446. Hints=0.
% 14.81/15.13 Megabytes=27.15.
% 14.81/15.13 User_CPU=13.93, System_CPU=0.18, Wall_clock=14.
% 14.81/15.13
% 14.81/15.13 ============================== end of statistics =====================
% 14.81/15.13
% 14.81/15.13 ============================== end of search =========================
% 14.81/15.13
% 14.81/15.13 THEOREM PROVED
% 14.81/15.13 % SZS status Unsatisfiable
% 14.81/15.13
% 14.81/15.13 Exiting with 1 proof.
% 14.81/15.13
% 14.81/15.13 Process 15385 exit (max_proofs) Wed Jun 1 16:28:41 2022
% 14.81/15.13 Prover9 interrupted
%------------------------------------------------------------------------------