TSTP Solution File: RNG004-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG004-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 : Mon Jul 18 20:39:08 EDT 2022
% Result : Unsatisfiable 49.35s 49.67s
% Output : Refutation 49.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG004-10 : TPTP v8.1.0. Released v7.5.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.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 : Mon May 30 05:40:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 40.40/40.70 ============================== Prover9 ===============================
% 40.40/40.70 Prover9 (32) version 2009-11A, November 2009.
% 40.40/40.70 Process 31872 was started by sandbox2 on n021.cluster.edu,
% 40.40/40.70 Mon May 30 05:40:44 2022
% 40.40/40.70 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31719_n021.cluster.edu".
% 40.40/40.70 ============================== end of head ===========================
% 40.40/40.70
% 40.40/40.70 ============================== INPUT =================================
% 40.40/40.70
% 40.40/40.70 % Reading from file /tmp/Prover9_31719_n021.cluster.edu
% 40.40/40.70
% 40.40/40.70 set(prolog_style_variables).
% 40.40/40.70 set(auto2).
% 40.40/40.70 % set(auto2) -> set(auto).
% 40.40/40.70 % set(auto) -> set(auto_inference).
% 40.40/40.70 % set(auto) -> set(auto_setup).
% 40.40/40.70 % set(auto_setup) -> set(predicate_elim).
% 40.40/40.70 % set(auto_setup) -> assign(eq_defs, unfold).
% 40.40/40.70 % set(auto) -> set(auto_limits).
% 40.40/40.70 % set(auto_limits) -> assign(max_weight, "100.000").
% 40.40/40.70 % set(auto_limits) -> assign(sos_limit, 20000).
% 40.40/40.70 % set(auto) -> set(auto_denials).
% 40.40/40.70 % set(auto) -> set(auto_process).
% 40.40/40.70 % set(auto2) -> assign(new_constants, 1).
% 40.40/40.70 % set(auto2) -> assign(fold_denial_max, 3).
% 40.40/40.70 % set(auto2) -> assign(max_weight, "200.000").
% 40.40/40.70 % set(auto2) -> assign(max_hours, 1).
% 40.40/40.70 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 40.40/40.70 % set(auto2) -> assign(max_seconds, 0).
% 40.40/40.70 % set(auto2) -> assign(max_minutes, 5).
% 40.40/40.70 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 40.40/40.70 % set(auto2) -> set(sort_initial_sos).
% 40.40/40.70 % set(auto2) -> assign(sos_limit, -1).
% 40.40/40.70 % set(auto2) -> assign(lrs_ticks, 3000).
% 40.40/40.70 % set(auto2) -> assign(max_megs, 400).
% 40.40/40.70 % set(auto2) -> assign(stats, some).
% 40.40/40.70 % set(auto2) -> clear(echo_input).
% 40.40/40.70 % set(auto2) -> set(quiet).
% 40.40/40.70 % set(auto2) -> clear(print_initial_clauses).
% 40.40/40.70 % set(auto2) -> clear(print_given).
% 40.40/40.70 assign(lrs_ticks,-1).
% 40.40/40.70 assign(sos_limit,10000).
% 40.40/40.70 assign(order,kbo).
% 40.40/40.70 set(lex_order_vars).
% 40.40/40.70 clear(print_given).
% 40.40/40.70
% 40.40/40.70 % formulas(sos). % not echoed (22 formulas)
% 40.40/40.70
% 40.40/40.70 ============================== end of input ==========================
% 40.40/40.70
% 40.40/40.70 % From the command line: assign(max_seconds, 300).
% 40.40/40.70
% 40.40/40.70 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 40.40/40.70
% 40.40/40.70 % Formulas that are not ordinary clauses:
% 40.40/40.70
% 40.40/40.70 ============================== end of process non-clausal formulas ===
% 40.40/40.70
% 40.40/40.70 ============================== PROCESS INITIAL CLAUSES ===============
% 40.40/40.70
% 40.40/40.70 ============================== PREDICATE ELIMINATION =================
% 40.40/40.70
% 40.40/40.70 ============================== end predicate elimination =============
% 40.40/40.70
% 40.40/40.70 Auto_denials:
% 40.40/40.70 % copying label prove_c_equals_d to answer in negative clause
% 40.40/40.70
% 40.40/40.70 Term ordering decisions:
% 40.40/40.70
% 40.40/40.70 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (14).
% 40.40/40.70 Function symbol KB weights: true=1. additive_identity=1. a=1. b=1. c=1. d=1. add=1. multiply=1. product=1. sum=1. ifeq=1. ifeq2=1. additive_inverse=0.
% 40.40/40.70
% 40.40/40.70 ============================== end of process initial clauses ========
% 40.40/40.70
% 40.40/40.70 ============================== CLAUSES FOR SEARCH ====================
% 40.40/40.70
% 40.40/40.70 ============================== end of clauses for search =============
% 40.40/40.70
% 40.40/40.70 ============================== SEARCH ================================
% 40.40/40.70
% 40.40/40.70 % Starting search at 0.01 seconds.
% 40.40/40.70
% 40.40/40.70 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 0.76 sec).
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=42.000, iters=3344
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=35.000, iters=3351
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=34.000, iters=3382
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=32.000, iters=3391
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=31.000, iters=3531
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=30.000, iters=3344
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=29.000, iters=3374
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=28.000, iters=3451
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=27.000, iters=3338
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=26.000, iters=3367
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=25.000, iters=3342
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=24.000, iters=3335
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=23.000, iters=3333
% 40.40/40.70
% 40.40/40.70 Low Water (displace): id=8960, wt=42.000
% 40.40/40.70
% 40.40/40.70 Low Water (displace): id=8998, wt=41.000
% 40.40/40.70
% 40.40/40.70 Low Water (displace): id=17670, wt=22.000
% 40.40/40.70
% 40.40/40.70 Low Water (displace): id=17797, wt=21.000
% 40.40/40.70
% 40.40/40.70 Low Water (displace): id=17809, wt=20.000
% 40.40/40.70
% 40.40/40.70 Low Water (displace): id=18705, wt=17.000
% 40.40/40.70
% 40.40/40.70 Low Water (displace): id=18711, wt=13.000
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=22.000, iters=3337
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=21.000, iters=3338
% 40.40/40.70
% 40.40/40.70 Low Water (keep): wt=20.000, iters=3337
% 49.35/49.67
% 49.35/49.67 Low Water (displace): id=36228, wt=12.000
% 49.35/49.67
% 49.35/49.67 Low Water (keep): wt=19.000, iters=3333
% 49.35/49.67
% 49.35/49.67 ============================== PROOF =================================
% 49.35/49.67 % SZS status Unsatisfiable
% 49.35/49.67 % SZS output start Refutation
% 49.35/49.67
% 49.35/49.67 % Proof 1 at 48.06 (+ 0.61) seconds: prove_c_equals_d.
% 49.35/49.67 % Length of proof is 88.
% 49.35/49.67 % Level of proof is 19.
% 49.35/49.67 % Maximum clause weight is 34.000.
% 49.35/49.67 % Given clauses 4952.
% 49.35/49.67
% 49.35/49.67 1 sum(additive_identity,A,A) = true # label(additive_identity1) # label(axiom). [assumption].
% 49.35/49.67 2 sum(A,additive_identity,A) = true # label(additive_identity2) # label(axiom). [assumption].
% 49.35/49.67 3 product(a,b,c) = true # label(a_times_b) # label(hypothesis). [assumption].
% 49.35/49.67 4 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 49.35/49.67 5 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 49.35/49.67 6 sum(additive_inverse(A),A,additive_identity) = true # label(left_inverse) # label(axiom). [assumption].
% 49.35/49.67 8 product(A,B,multiply(A,B)) = true # label(closure_of_multiplication) # label(axiom). [assumption].
% 49.35/49.67 9 sum(A,B,add(A,B)) = true # label(closure_of_addition) # label(axiom). [assumption].
% 49.35/49.67 10 product(additive_inverse(a),additive_inverse(b),d) = true # label(a_inverse_times_b_inverse) # label(hypothesis). [assumption].
% 49.35/49.67 11 ifeq(sum(A,B,C),true,sum(B,A,C),true) = true # label(commutativity_of_addition) # label(axiom). [assumption].
% 49.35/49.67 12 ifeq2(sum(A,B,C),true,ifeq2(sum(A,B,D),true,D,C),C) = C # label(addition_is_well_defined) # label(axiom). [assumption].
% 49.35/49.67 13 ifeq2(product(A,B,C),true,ifeq2(product(A,B,D),true,D,C),C) = C # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 49.35/49.67 14 ifeq(sum(A,B,C),true,ifeq(sum(D,B,E),true,ifeq(sum(F,D,A),true,sum(F,E,C),true),true),true) = true # label(associativity_of_addition1) # label(axiom). [assumption].
% 49.35/49.67 15 ifeq(sum(A,B,C),true,ifeq(sum(D,C,E),true,ifeq(sum(D,A,F),true,sum(F,B,E),true),true),true) = true # label(associativity_of_addition2) # label(axiom). [assumption].
% 49.35/49.67 18 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].
% 49.35/49.67 20 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].
% 49.35/49.67 22 c != d # label(prove_c_equals_d) # label(negated_conjecture) # answer(prove_c_equals_d). [assumption].
% 49.35/49.67 23 d != c # answer(prove_c_equals_d). [copy(22),flip(a)].
% 49.35/49.67 24 sum(A,B,add(B,A)) = true. [para(9(a,1),11(a,1,1)),rewrite([5(6)])].
% 49.35/49.67 25 ifeq2(sum(additive_identity,A,B),true,B,A) = A. [para(1(a,1),12(a,1,1)),rewrite([4(7)])].
% 49.35/49.67 27 ifeq2(sum(A,additive_identity,B),true,B,A) = A. [para(2(a,1),12(a,1,1)),rewrite([4(7)])].
% 49.35/49.67 29 ifeq2(sum(additive_inverse(A),A,B),true,B,additive_identity) = additive_identity. [para(6(a,1),12(a,1,1)),rewrite([4(9)])].
% 49.35/49.67 33 ifeq2(sum(A,B,C),true,C,add(A,B)) = add(A,B). [para(9(a,1),12(a,1,1)),rewrite([4(8)])].
% 49.35/49.67 34 ifeq2(sum(A,B,C),true,add(A,B),C) = C. [para(9(a,1),12(a,1,3,1)),rewrite([4(6)])].
% 49.35/49.67 38 ifeq2(product(A,B,C),true,multiply(A,B),C) = C. [para(8(a,1),13(a,1,3,1)),rewrite([4(6)])].
% 49.35/49.67 41 ifeq(sum(A,B,C),true,ifeq(sum(D,A,additive_identity),true,sum(D,C,B),true),true) = true. [para(1(a,1),14(a,1,1)),rewrite([5(14)])].
% 49.35/49.67 59 ifeq(sum(add(A,B),C,D),true,ifeq(sum(B,C,E),true,sum(A,E,D),true),true) = true. [para(9(a,1),14(a,1,3,3,1)),rewrite([5(10)])].
% 49.35/49.67 107 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),18(a,1,3,3,3,1)),rewrite([5(12)])].
% 49.35/49.67 114 ifeq(product(A,additive_identity,B),true,ifeq(product(A,C,D),true,ifeq(product(A,additive_inverse(C),E),true,sum(E,D,B),true),true),true) = true. [para(6(a,1),18(a,1,3,3,3,1)),rewrite([5(13)])].
% 49.35/49.67 146 ifeq(product(A,B,C),true,ifeq(product(A,B,D),true,ifeq(product(additive_identity,B,E),true,sum(E,D,C),true),true),true) = true. [para(1(a,1),20(a,1,3,3,3,1)),rewrite([5(12)])].
% 49.35/49.67 151 ifeq(product(A,b,B),true,ifeq(product(C,b,D),true,ifeq(sum(C,a,A),true,sum(D,c,B),true),true),true) = true. [para(3(a,1),20(a,1,3,1)),rewrite([5(19)])].
% 49.35/49.67 205 add(A,additive_identity) = A. [para(24(a,1),25(a,1,1)),rewrite([4(5)])].
% 49.35/49.67 208 add(A,additive_inverse(A)) = additive_identity. [para(24(a,1),29(a,1,1)),rewrite([4(6)])].
% 49.35/49.67 209 add(A,B) = add(B,A). [para(24(a,1),34(a,1,1)),rewrite([4(5)])].
% 49.35/49.67 210 multiply(additive_inverse(a),additive_inverse(b)) = d. [para(10(a,1),38(a,1,1)),rewrite([4(9)])].
% 49.35/49.67 216 ifeq(sum(A,additive_inverse(B),additive_identity),true,sum(A,additive_identity,B),true) = true. [para(6(a,1),41(a,1,1)),rewrite([5(12)])].
% 49.35/49.67 217 ifeq(sum(A,B,C),true,sum(additive_inverse(A),C,B),true) = true. [para(6(a,1),41(a,1,3,1)),rewrite([5(8)])].
% 49.35/49.67 248 sum(additive_inverse(additive_inverse(A)),additive_identity,A) = true. [para(6(a,1),216(a,1,1)),rewrite([5(8)])].
% 49.35/49.67 272 additive_inverse(additive_inverse(A)) = A. [para(248(a,1),27(a,1,1)),rewrite([4(5)]),flip(a)].
% 49.35/49.67 285 sum(additive_inverse(A),add(A,B),B) = true. [para(9(a,1),217(a,1,1)),rewrite([5(7)])].
% 49.35/49.67 307 ifeq(sum(A,B,add(C,D)),true,ifeq(sum(additive_inverse(C),A,E),true,sum(E,B,D),true),true) = true. [para(285(a,1),15(a,1,3,1)),rewrite([5(13)])].
% 49.35/49.67 318 add(additive_inverse(A),add(A,B)) = B. [para(285(a,1),34(a,1,1)),rewrite([4(6)])].
% 49.35/49.67 319 add(additive_inverse(A),add(B,A)) = B. [para(285(a,1),33(a,1,1)),rewrite([209(4),4(6),209(2)]),flip(a)].
% 49.35/49.67 324 sum(A,add(B,additive_inverse(A)),B) = true. [para(272(a,1),285(a,1,1)),rewrite([209(2)])].
% 49.35/49.67 329 add(A,add(B,additive_inverse(A))) = B. [para(272(a,1),318(a,1,1)),rewrite([209(2)])].
% 49.35/49.67 330 add(A,additive_inverse(add(B,A))) = additive_inverse(B). [para(318(a,1),319(a,1,2)),rewrite([209(3)])].
% 49.35/49.67 334 sum(additive_inverse(A),B,add(B,additive_inverse(A))) = true. [para(329(a,1),285(a,1,2))].
% 49.35/49.67 400 add(additive_identity,additive_inverse(A)) = additive_inverse(A). [para(205(a,1),330(a,1,2,1))].
% 49.35/49.67 404 additive_inverse(add(A,B)) = add(additive_inverse(A),additive_inverse(B)). [para(330(a,1),318(a,1,2)),rewrite([209(4)]),flip(a)].
% 49.35/49.67 405 add(A,add(additive_inverse(A),additive_inverse(B))) = additive_inverse(B). [para(330(a,1),330(a,1,2,1)),rewrite([404(2),272(5),209(4)])].
% 49.35/49.67 459 ifeq2(sum(additive_inverse(A),B,C),true,add(B,additive_inverse(A)),C) = C. [para(334(a,1),12(a,1,3,1)),rewrite([4(8)])].
% 49.35/49.67 480 add(add(A,B),add(C,add(additive_inverse(A),additive_inverse(B)))) = C. [para(404(a,1),329(a,1,2,2))].
% 49.35/49.67 482 sum(add(A,B),add(C,add(additive_inverse(A),additive_inverse(B))),C) = true. [para(404(a,1),324(a,1,2,2))].
% 49.35/49.67 776 add(A,add(additive_inverse(A),add(B,C))) = add(B,C). [para(480(a,1),319(a,1,2)),rewrite([404(5),404(5),272(3),272(3),209(4)])].
% 49.35/49.67 927 ifeq(sum(A,B,C),true,sum(D,C,add(B,add(A,D))),true) = true. [para(9(a,1),59(a,1,1)),rewrite([209(5),209(6),5(11)])].
% 49.35/49.67 1219 sum(add(A,add(B,C)),add(D,add(additive_inverse(A),add(additive_inverse(B),additive_inverse(C)))),D) = true. [para(404(a,1),482(a,1,2,2,2))].
% 49.35/49.67 2648 ifeq(product(A,B,C),true,ifeq(product(A,additive_identity,D),true,sum(D,C,multiply(A,B)),true),true) = true. [para(8(a,1),107(a,1,1)),rewrite([5(15)])].
% 49.35/49.67 3051 ifeq(product(A,B,C),true,ifeq(product(A,additive_inverse(B),D),true,sum(D,C,multiply(A,additive_identity)),true),true) = true. [para(8(a,1),114(a,1,1)),rewrite([5(16)])].
% 49.35/49.67 5131 ifeq(product(a,b,A),true,ifeq(product(additive_identity,b,B),true,sum(B,A,c),true),true) = true. [para(3(a,1),146(a,1,1)),rewrite([5(18)])].
% 49.35/49.67 5835 ifeq(product(additive_identity,b,A),true,ifeq(product(additive_inverse(a),b,B),true,sum(B,c,A),true),true) = true. [para(6(a,1),151(a,1,3,3,1)),rewrite([5(15)])].
% 49.35/49.67 7601 sum(A,add(B,C),add(C,add(A,B))) = true. [para(9(a,1),927(a,1,1)),rewrite([209(4),5(8)])].
% 49.35/49.67 7671 add(A,add(B,C)) = add(C,add(A,B)). [para(7601(a,1),34(a,1,1)),rewrite([4(7)])].
% 49.35/49.67 7705 add(add(A,B),additive_inverse(C)) = add(A,add(B,additive_inverse(C))). [para(7601(a,1),459(a,1,1)),rewrite([209(7),7671(8,R),209(7),4(9),209(5),7671(6,R),209(5)])].
% 49.35/49.67 8527 add(A,add(B,add(C,additive_inverse(A)))) = add(B,C). [back_rewrite(776),rewrite([7671(3),209(2),7671(3,R),209(2)])].
% 49.35/49.67 9125 add(A,add(B,add(additive_inverse(A),additive_inverse(C)))) = add(B,additive_inverse(C)). [para(405(a,1),7671(a,2,2)),rewrite([209(4)])].
% 49.35/49.67 9362 add(additive_identity,add(additive_inverse(A),additive_inverse(B))) = add(additive_inverse(A),additive_inverse(B)). [para(400(a,1),7705(a,1,1)),flip(a)].
% 49.35/49.67 9626 add(additive_identity,add(additive_inverse(A),add(additive_inverse(B),additive_inverse(C)))) = add(additive_inverse(A),add(additive_inverse(B),additive_inverse(C))). [para(404(a,1),9362(a,1,2,1)),rewrite([7705(6),404(9),7705(12)])].
% 49.35/49.67 12863 ifeq(sum(add(A,B),C,add(A,D)),true,sum(B,C,D),true) = true. [para(285(a,1),307(a,1,3,1)),rewrite([5(9)])].
% 49.35/49.67 17003 sum(add(A,B),add(add(C,D),add(additive_inverse(A),add(additive_inverse(B),additive_inverse(C)))),D) = true. [para(1219(a,1),12863(a,1,1)),rewrite([7671(9),209(8),7671(9,R),209(8),5(13)])].
% 49.35/49.67 18375 add(add(A,B),add(add(C,D),add(additive_inverse(A),add(additive_inverse(B),additive_inverse(C))))) = D. [para(17003(a,1),34(a,1,1)),rewrite([4(12)])].
% 49.35/49.67 28406 ifeq(product(additive_inverse(a),additive_identity,A),true,sum(A,d,d),true) = true. [para(10(a,1),2648(a,1,1)),rewrite([210(13),5(14)])].
% 49.35/49.67 28420 sum(multiply(additive_inverse(a),additive_identity),d,d) = true. [para(8(a,1),28406(a,1,1)),rewrite([5(11)])].
% 49.35/49.67 28424 add(d,multiply(additive_inverse(a),additive_identity)) = d. [para(28420(a,1),34(a,1,1)),rewrite([209(8),4(10)])].
% 49.35/49.67 29294 multiply(additive_inverse(a),additive_identity) = additive_identity. [para(28424(a,1),18375(a,1,2,1)),rewrite([8527(9),7671(5),209(4),7671(4),209(3),208(3),205(3),209(2),208(2)]),flip(a)].
% 49.35/49.67 29352 add(additive_identity,d) = d. [back_rewrite(28424),rewrite([29294(5),209(3)])].
% 49.35/49.67 35995 ifeq(product(additive_inverse(a),b,A),true,sum(A,d,additive_identity),true) = true. [para(10(a,1),3051(a,1,1)),rewrite([272(7),29294(12),5(14)])].
% 49.35/49.67 36006 sum(multiply(additive_inverse(a),b),d,additive_identity) = true. [para(8(a,1),35995(a,1,1)),rewrite([5(11)])].
% 49.35/49.67 36010 add(d,multiply(additive_inverse(a),b)) = additive_identity. [para(36006(a,1),34(a,1,1)),rewrite([209(8),4(10)])].
% 49.35/49.67 36657 multiply(additive_inverse(a),b) = additive_inverse(d). [para(36010(a,1),18375(a,1,2,1)),rewrite([9626(9),7671(8,R),7671(7),209(6),9125(7),7671(5,R),209(4),405(5)]),flip(a)].
% 49.35/49.67 40442 ifeq(product(additive_identity,b,A),true,sum(A,c,c),true) = true. [para(3(a,1),5131(a,1,1)),rewrite([5(13)])].
% 49.35/49.67 40444 sum(multiply(additive_identity,b),c,c) = true. [para(8(a,1),40442(a,1,1)),rewrite([5(10)])].
% 49.35/49.67 40448 add(c,multiply(additive_identity,b)) = c. [para(40444(a,1),34(a,1,1)),rewrite([209(7),4(9)])].
% 49.35/49.67 41089 multiply(additive_identity,b) = additive_identity. [para(40448(a,1),18375(a,1,2,1)),rewrite([8527(9),7671(5),209(4),7671(4),209(3),208(3),205(3),209(2),208(2)]),flip(a)].
% 49.35/49.67 41462 ifeq(product(additive_inverse(a),b,A),true,sum(A,c,additive_identity),true) = true. [para(8(a,1),5835(a,1,1)),rewrite([41089(11),5(14)])].
% 49.35/49.67 43477 sum(additive_inverse(d),c,additive_identity) = true. [para(8(a,1),41462(a,1,1)),rewrite([36657(6),5(9)])].
% 49.35/49.67 43481 add(c,additive_inverse(d)) = additive_identity. [para(43477(a,1),34(a,1,1)),rewrite([209(6),4(8)])].
% 49.35/49.67 43667 d = c. [para(43481(a,1),329(a,1,2)),rewrite([209(3),29352(3)])].
% 49.35/49.67 43668 $F # answer(prove_c_equals_d). [resolve(43667,a,23,a)].
% 49.35/49.67
% 49.35/49.67 % SZS output end Refutation
% 49.35/49.67 ============================== end of proof ==========================
% 49.35/49.67
% 49.35/49.67 ============================== STATISTICS ============================
% 49.35/49.67
% 49.35/49.67 Given=4952. Generated=1302874. Kept=43666. proofs=1.
% 49.35/49.67 Usable=4698. Sos=9999. Demods=14666. Limbo=2, Disabled=28988. Hints=0.
% 49.35/49.67 Megabytes=34.07.
% 49.35/49.67 User_CPU=48.06, System_CPU=0.61, Wall_clock=49.
% 49.35/49.67
% 49.35/49.67 ============================== end of statistics =====================
% 49.35/49.67
% 49.35/49.67 ============================== end of search =========================
% 49.35/49.67
% 49.35/49.67 THEOREM PROVED
% 49.35/49.67 % SZS status Unsatisfiable
% 49.35/49.67
% 49.35/49.67 Exiting with 1 proof.
% 49.35/49.67
% 49.35/49.67 Process 31872 exit (max_proofs) Mon May 30 05:41:33 2022
% 49.35/49.67 Prover9 interrupted
%------------------------------------------------------------------------------