TSTP Solution File: RNG006-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG006-10 : TPTP v8.1.0. Released v7.3.0.
% 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 : Mon Jul 18 20:39:09 EDT 2022
% Result : Unsatisfiable 181.89s 182.14s
% Output : Refutation 181.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG006-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n026.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 : Mon May 30 08:43:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.52/2.85 ============================== Prover9 ===============================
% 2.52/2.85 Prover9 (32) version 2009-11A, November 2009.
% 2.52/2.85 Process 3053 was started by sandbox2 on n026.cluster.edu,
% 2.52/2.85 Mon May 30 08:43:56 2022
% 2.52/2.85 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2900_n026.cluster.edu".
% 2.52/2.85 ============================== end of head ===========================
% 2.52/2.85
% 2.52/2.85 ============================== INPUT =================================
% 2.52/2.85
% 2.52/2.85 % Reading from file /tmp/Prover9_2900_n026.cluster.edu
% 2.52/2.85
% 2.52/2.85 set(prolog_style_variables).
% 2.52/2.85 set(auto2).
% 2.52/2.85 % set(auto2) -> set(auto).
% 2.52/2.85 % set(auto) -> set(auto_inference).
% 2.52/2.85 % set(auto) -> set(auto_setup).
% 2.52/2.85 % set(auto_setup) -> set(predicate_elim).
% 2.52/2.85 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.52/2.85 % set(auto) -> set(auto_limits).
% 2.52/2.85 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.52/2.85 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.52/2.85 % set(auto) -> set(auto_denials).
% 2.52/2.85 % set(auto) -> set(auto_process).
% 2.52/2.85 % set(auto2) -> assign(new_constants, 1).
% 2.52/2.85 % set(auto2) -> assign(fold_denial_max, 3).
% 2.52/2.85 % set(auto2) -> assign(max_weight, "200.000").
% 2.52/2.85 % set(auto2) -> assign(max_hours, 1).
% 2.52/2.85 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.52/2.85 % set(auto2) -> assign(max_seconds, 0).
% 2.52/2.85 % set(auto2) -> assign(max_minutes, 5).
% 2.52/2.85 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.52/2.85 % set(auto2) -> set(sort_initial_sos).
% 2.52/2.85 % set(auto2) -> assign(sos_limit, -1).
% 2.52/2.85 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.52/2.85 % set(auto2) -> assign(max_megs, 400).
% 2.52/2.85 % set(auto2) -> assign(stats, some).
% 2.52/2.85 % set(auto2) -> clear(echo_input).
% 2.52/2.85 % set(auto2) -> set(quiet).
% 2.52/2.85 % set(auto2) -> clear(print_initial_clauses).
% 2.52/2.85 % set(auto2) -> clear(print_given).
% 2.52/2.85 assign(lrs_ticks,-1).
% 2.52/2.85 assign(sos_limit,10000).
% 2.52/2.85 assign(order,kbo).
% 2.52/2.85 set(lex_order_vars).
% 2.52/2.85 clear(print_given).
% 2.52/2.85
% 2.52/2.85 % formulas(sos). % not echoed (24 formulas)
% 2.52/2.85
% 2.52/2.85 ============================== end of input ==========================
% 2.52/2.85
% 2.52/2.85 % From the command line: assign(max_seconds, 300).
% 2.52/2.85
% 2.52/2.85 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.52/2.85
% 2.52/2.85 % Formulas that are not ordinary clauses:
% 2.52/2.85
% 2.52/2.85 ============================== end of process non-clausal formulas ===
% 2.52/2.85
% 2.52/2.85 ============================== PROCESS INITIAL CLAUSES ===============
% 2.52/2.85
% 2.52/2.85 ============================== PREDICATE ELIMINATION =================
% 2.52/2.85
% 2.52/2.85 ============================== end predicate elimination =============
% 2.52/2.85
% 2.52/2.85 Auto_denials:
% 2.52/2.85 % copying label prove_a_times_bS_Ic_is_aPb_S__IaPc to answer in negative clause
% 2.52/2.85
% 2.52/2.85 Term ordering decisions:
% 2.52/2.85
% 2.52/2.85 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (17).
% 2.52/2.85 Function symbol KB weights: true=1. additive_identity=1. a=1. aPb=1. aPc=1. b=1. c=1. aPb_S_IaPc=1. bS_Ic=1. add=1. multiply=1. sum=1. product=1. ifeq=1. ifeq2=1. additive_inverse=0.
% 2.52/2.85
% 2.52/2.85 ============================== end of process initial clauses ========
% 2.52/2.85
% 2.52/2.85 ============================== CLAUSES FOR SEARCH ====================
% 2.52/2.85
% 2.52/2.85 ============================== end of clauses for search =============
% 2.52/2.85
% 2.52/2.85 ============================== SEARCH ================================
% 2.52/2.85
% 2.52/2.85 % Starting search at 0.01 seconds.
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=38.000, iters=3337
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=37.000, iters=3352
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=33.000, iters=3350
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=32.000, iters=3355
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=31.000, iters=3341
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=28.000, iters=3382
% 2.52/2.85
% 2.52/2.85 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.12 sec).
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=27.000, iters=3345
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=26.000, iters=3368
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=25.000, iters=3385
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=24.000, iters=3341
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=23.000, iters=3336
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=22.000, iters=3357
% 2.52/2.85
% 2.52/2.85 Low Water (displace): id=7547, wt=38.000
% 2.52/2.85
% 2.52/2.85 Low Water (displace): id=6891, wt=37.000
% 2.52/2.85
% 2.52/2.85 Low Water (displace): id=7447, wt=36.000
% 2.52/2.85
% 2.52/2.85 Low Water (displace): id=12670, wt=19.000
% 2.52/2.85
% 2.52/2.85 Low Water (displace): id=12733, wt=17.000
% 2.52/2.85
% 2.52/2.85 Low Water (displace): id=12851, wt=16.000
% 2.52/2.85
% 2.52/2.85 Low Water (displace): id=13099, wt=15.000
% 2.52/2.85
% 2.52/2.85 Low Water (displace): id=13116, wt=14.000
% 2.52/2.85
% 2.52/2.85 Low Water (keep): wt=21.000, iters=3333
% 181.89/182.14
% 181.89/182.14 Low Water (displace): id=14019, wt=13.000
% 181.89/182.14
% 181.89/182.14 Low Water (keep): wt=20.000, iters=3363
% 181.89/182.14
% 181.89/182.14 Low Water (keep): wt=19.000, iters=3335
% 181.89/182.14
% 181.89/182.14 Low Water (keep): wt=18.000, iters=3351
% 181.89/182.14
% 181.89/182.14 Low Water (keep): wt=17.000, iters=3350
% 181.89/182.14
% 181.89/182.14 Low Water (displace): id=31367, wt=12.000
% 181.89/182.14
% 181.89/182.14 Low Water (displace): id=31378, wt=10.000
% 181.89/182.14
% 181.89/182.14 Low Water (keep): wt=16.000, iters=3333
% 181.89/182.14
% 181.89/182.14 Low Water (keep): wt=15.000, iters=3333
% 181.89/182.14
% 181.89/182.14 ============================== PROOF =================================
% 181.89/182.14 % SZS status Unsatisfiable
% 181.89/182.14 % SZS output start Refutation
% 181.89/182.14
% 181.89/182.14 % Proof 1 at 179.50 (+ 1.60) seconds: prove_a_times_bS_Ic_is_aPb_S__IaPc.
% 181.89/182.14 % Length of proof is 100.
% 181.89/182.14 % Level of proof is 19.
% 181.89/182.14 % Maximum clause weight is 70.000.
% 181.89/182.14 % Given clauses 17661.
% 181.89/182.14
% 181.89/182.14 1 sum(additive_identity,A,A) = true # label(additive_identity1) # label(axiom). [assumption].
% 181.89/182.14 2 sum(A,additive_identity,A) = true # label(additive_identity2) # label(axiom). [assumption].
% 181.89/182.14 3 product(a,b,aPb) = true # label(a_times_b) # label(hypothesis). [assumption].
% 181.89/182.14 4 true = product(a,b,aPb). [copy(3),flip(a)].
% 181.89/182.14 5 product(a,c,aPc) = true # label(a_times_c) # label(hypothesis). [assumption].
% 181.89/182.14 6 product(a,c,aPc) = product(a,b,aPb). [copy(5),rewrite([4(5)])].
% 181.89/182.14 7 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 181.89/182.14 8 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom). [assumption].
% 181.89/182.14 9 sum(additive_inverse(A),A,additive_identity) = true # label(left_inverse) # label(axiom). [assumption].
% 181.89/182.14 10 product(a,b,aPb) = sum(additive_inverse(A),A,additive_identity). [copy(9),rewrite([4(4)]),flip(a)].
% 181.89/182.14 13 sum(b,additive_inverse(c),bS_Ic) = true # label(b_plus_inverse_c) # label(hypothesis). [assumption].
% 181.89/182.14 14 product(a,b,aPb) = sum(b,additive_inverse(c),bS_Ic). [copy(13),rewrite([4(6)]),flip(a)].
% 181.89/182.14 15 sum(aPb,additive_inverse(aPc),aPb_S_IaPc) = true # label(aPb_plus_IaPc) # label(hypothesis). [assumption].
% 181.89/182.14 16 sum(b,additive_inverse(c),bS_Ic) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [copy(15),rewrite([4(6),14(9)]),flip(a)].
% 181.89/182.14 17 product(A,B,multiply(A,B)) = true # label(closure_of_multiplication) # label(axiom). [assumption].
% 181.89/182.14 18 product(A,B,multiply(A,B)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [copy(17),rewrite([4(3),14(6),16(7)])].
% 181.89/182.14 19 sum(A,B,add(A,B)) = true # label(closure_of_addition) # label(axiom). [assumption].
% 181.89/182.14 20 sum(A,B,add(A,B)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [copy(19),rewrite([4(3),14(6),16(7)])].
% 181.89/182.14 21 ifeq(sum(A,B,C),true,sum(B,A,C),true) = true # label(commutativity_of_addition) # label(axiom). [assumption].
% 181.89/182.14 22 ifeq(sum(A,B,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),sum(B,A,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [copy(21),rewrite([4(2),14(5),16(6),4(8),14(11),16(12),4(14),14(17),16(18)])].
% 181.89/182.14 23 ifeq2(sum(A,B,C),true,ifeq2(sum(A,B,D),true,D,C),C) = C # label(addition_is_well_defined) # label(axiom). [assumption].
% 181.89/182.14 24 ifeq2(sum(A,B,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq2(sum(A,B,D),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),D,C),C) = C. [copy(23),rewrite([4(2),14(5),16(6),4(8),14(11),16(12)])].
% 181.89/182.14 25 ifeq2(product(A,B,C),true,ifeq2(product(A,B,D),true,D,C),C) = C # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 181.89/182.14 26 ifeq2(product(A,B,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq2(product(A,B,D),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),D,C),C) = C. [copy(25),rewrite([4(2),14(5),16(6),4(8),14(11),16(12)])].
% 181.89/182.14 29 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].
% 181.89/182.14 30 ifeq(sum(A,B,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(D,C,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(D,A,F),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),sum(F,B,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [copy(29),rewrite([4(2),14(5),16(6),4(8),14(11),16(12),4(14),14(17),16(18),4(20),14(23),16(24),4(26),14(29),16(30),4(32),14(35),16(36),4(38),14(41),16(42)])].
% 181.89/182.14 37 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].
% 181.89/182.14 38 ifeq(product(A,B,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(product(A,D,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(E,C,F),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(D,B,V6),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),product(A,V6,F),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [copy(37),rewrite([4(2),14(5),16(6),4(8),14(11),16(12),4(14),14(17),16(18),4(20),14(23),16(24),4(26),14(29),16(30),4(32),14(35),16(36),4(38),14(41),16(42),4(44),14(47),16(48),4(50),14(53),16(54)])].
% 181.89/182.14 41 ifeq(product(A,B,C),true,ifeq(product(D,B,E),true,ifeq(sum(E,C,F),true,ifeq(sum(D,A,V6),true,product(V6,B,F),true),true),true),true) = true # label(distributivity4) # label(axiom). [assumption].
% 181.89/182.14 42 ifeq(product(A,B,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(product(D,B,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(E,C,F),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(D,A,V6),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),product(V6,B,F),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [copy(41),rewrite([4(2),14(5),16(6),4(8),14(11),16(12),4(14),14(17),16(18),4(20),14(23),16(24),4(26),14(29),16(30),4(32),14(35),16(36),4(38),14(41),16(42),4(44),14(47),16(48),4(50),14(53),16(54)])].
% 181.89/182.14 43 product(a,bS_Ic,aPb_S_IaPc) != true # label(prove_a_times_bS_Ic_is_aPb_S__IaPc) # label(negated_conjecture) # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc). [assumption].
% 181.89/182.14 44 product(a,bS_Ic,aPb_S_IaPc) != sum(aPb,additive_inverse(aPc),aPb_S_IaPc) # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc). [copy(43),rewrite([4(5),14(8),16(9)])].
% 181.89/182.14 45 sum(aPb,additive_inverse(aPc),aPb_S_IaPc) = sum(A,additive_identity,A). [back_rewrite(2),rewrite([4(3),14(6),16(7)]),flip(a)].
% 181.89/182.14 46 sum(aPb,additive_inverse(aPc),aPb_S_IaPc) = sum(additive_identity,A,A). [back_rewrite(1),rewrite([4(3),14(6),16(7)]),flip(a)].
% 181.89/182.14 48 sum(additive_inverse(A),A,additive_identity) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [back_rewrite(10),rewrite([14(4),16(5)]),flip(a)].
% 181.89/182.14 49 product(a,c,aPc) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [back_rewrite(6),rewrite([14(8),16(9)])].
% 181.89/182.14 51 product(a,b,aPb) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [back_rewrite(14),rewrite([16(9)])].
% 181.89/182.14 52 sum(additive_inverse(aPc),aPb,aPb_S_IaPc) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [para(22(a,1),8(a,1)),flip(a)].
% 181.89/182.14 54 sum(A,B,add(B,A)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [para(20(a,1),22(a,1,1)),rewrite([8(18)])].
% 181.89/182.14 60 ifeq2(sum(A,B,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),add(A,B),C) = C. [para(20(a,1),24(a,1,3,1)),rewrite([7(18)])].
% 181.89/182.14 62 ifeq2(product(A,B,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),multiply(A,B),C) = C. [para(18(a,1),26(a,1,3,1)),rewrite([7(18)])].
% 181.89/182.14 109 ifeq(product(A,B,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(multiply(A,D),C,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(D,B,F),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),product(A,F,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [para(18(a,1),38(a,1,3,1)),rewrite([8(48)])].
% 181.89/182.14 126 ifeq(product(A,B,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(C,multiply(D,B),E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(A,D,F),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),product(F,B,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [para(18(a,1),42(a,1,1)),rewrite([8(54)])].
% 181.89/182.14 136 ifeq2(sum(A,B,C),sum(D,additive_identity,D),ifeq2(sum(A,B,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),E,C),C) = C. [para(45(a,1),24(a,1,2))].
% 181.89/182.14 141 ifeq2(product(A,B,C),sum(D,additive_identity,D),ifeq2(product(A,B,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),E,C),C) = C. [para(45(a,1),26(a,1,2))].
% 181.89/182.14 156 ifeq(sum(A,B,C),sum(D,additive_identity,D),ifeq(sum(E,C,F),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(E,A,V6),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),sum(V6,B,F),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [para(45(a,1),30(a,1,2))].
% 181.89/182.14 166 ifeq(sum(A,B,additive_identity),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(C,A,D),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),sum(D,B,C),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [para(45(a,2),30(a,1,3,1)),rewrite([8(36)])].
% 181.89/182.14 228 ifeq(product(additive_identity,A,B),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(product(C,A,D),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(D,B,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),product(C,A,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [para(45(a,2),42(a,1,3,3,3,1)),rewrite([8(36)])].
% 181.89/182.14 229 product(a,bS_Ic,aPb_S_IaPc) != sum(A,additive_identity,A) # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc). [para(45(a,1),44(a,2))].
% 181.89/182.14 230 sum(A,additive_identity,A) = sum(B,additive_identity,B). [para(45(a,1),45(a,1))].
% 181.89/182.14 231 sum(A,additive_identity,A) = c_0. [new_symbol(230)].
% 181.89/182.14 232 product(a,bS_Ic,aPb_S_IaPc) != c_0 # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc). [back_rewrite(229),rewrite([231(6)])].
% 181.89/182.14 293 ifeq(sum(A,B,C),c_0,ifeq(sum(D,C,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),ifeq(sum(D,A,F),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),sum(F,B,E),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),sum(aPb,additive_inverse(aPc),aPb_S_IaPc)) = sum(aPb,additive_inverse(aPc),aPb_S_IaPc). [back_rewrite(156),rewrite([231(3)])].
% 181.89/182.14 304 ifeq2(product(A,B,C),c_0,ifeq2(product(A,B,D),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),D,C),C) = C. [back_rewrite(141),rewrite([231(3)])].
% 181.89/182.14 307 ifeq2(sum(A,B,C),c_0,ifeq2(sum(A,B,D),sum(aPb,additive_inverse(aPc),aPb_S_IaPc),D,C),C) = C. [back_rewrite(136),rewrite([231(3)])].
% 181.89/182.14 312 sum(aPb,additive_inverse(aPc),aPb_S_IaPc) = c_0. [back_rewrite(45),rewrite([231(7)])].
% 181.89/182.14 314 ifeq2(sum(A,B,C),c_0,ifeq2(sum(A,B,D),c_0,D,C),C) = C. [back_rewrite(307),rewrite([312(8)])].
% 181.89/182.14 316 ifeq2(product(A,B,C),c_0,ifeq2(product(A,B,D),c_0,D,C),C) = C. [back_rewrite(304),rewrite([312(8)])].
% 181.89/182.14 321 ifeq(sum(A,B,C),c_0,ifeq(sum(D,C,E),c_0,ifeq(sum(D,A,F),c_0,sum(F,B,E),c_0),c_0),c_0) = c_0. [back_rewrite(293),rewrite([312(8),312(10),312(12),312(14),312(16),312(18)])].
% 181.89/182.14 339 ifeq(product(additive_identity,A,B),c_0,ifeq(product(C,A,D),c_0,ifeq(sum(D,B,E),c_0,product(C,A,E),c_0),c_0),c_0) = c_0. [back_rewrite(228),rewrite([312(7),312(9),312(11),312(13),312(15),312(17),312(19)])].
% 181.89/182.14 349 ifeq(sum(A,B,additive_identity),c_0,ifeq(sum(C,A,D),c_0,sum(D,B,C),c_0),c_0) = c_0. [back_rewrite(166),rewrite([312(7),312(9),312(11),312(13),312(15)])].
% 181.89/182.14 362 ifeq(product(A,B,C),c_0,ifeq(sum(C,multiply(D,B),E),c_0,ifeq(sum(A,D,F),c_0,product(F,B,E),c_0),c_0),c_0) = c_0. [back_rewrite(126),rewrite([312(6),312(9),312(11),312(13),312(15),312(17),312(19)])].
% 181.89/182.14 376 ifeq(product(A,B,C),c_0,ifeq(sum(multiply(A,D),C,E),c_0,ifeq(sum(D,B,F),c_0,product(A,F,E),c_0),c_0),c_0) = c_0. [back_rewrite(109),rewrite([312(6),312(9),312(11),312(13),312(15),312(17),312(19)])].
% 181.89/182.14 416 ifeq2(product(A,B,C),c_0,multiply(A,B),C) = C. [back_rewrite(62),rewrite([312(6)])].
% 181.89/182.14 418 ifeq2(sum(A,B,C),c_0,add(A,B),C) = C. [back_rewrite(60),rewrite([312(6)])].
% 181.89/182.14 423 sum(A,B,add(B,A)) = c_0. [back_rewrite(54),rewrite([312(7)])].
% 181.89/182.14 425 sum(additive_inverse(aPc),aPb,aPb_S_IaPc) = c_0. [back_rewrite(52),rewrite([312(10)])].
% 181.89/182.14 426 product(a,b,aPb) = c_0. [back_rewrite(51),rewrite([312(9)])].
% 181.89/182.14 428 product(a,c,aPc) = c_0. [back_rewrite(49),rewrite([312(9)])].
% 181.89/182.14 429 sum(additive_inverse(A),A,additive_identity) = c_0. [back_rewrite(48),rewrite([312(8)])].
% 181.89/182.14 431 sum(additive_identity,A,A) = c_0. [back_rewrite(46),rewrite([312(5)]),flip(a)].
% 181.89/182.14 432 sum(A,B,add(A,B)) = c_0. [back_rewrite(20),rewrite([312(7)])].
% 181.89/182.14 433 product(A,B,multiply(A,B)) = c_0. [back_rewrite(18),rewrite([312(7)])].
% 181.89/182.14 434 sum(b,additive_inverse(c),bS_Ic) = c_0. [back_rewrite(16),rewrite([312(10)])].
% 181.89/182.14 435 ifeq2(sum(additive_identity,A,B),c_0,B,A) = A. [para(431(a,1),314(a,1,1)),rewrite([7(7)])].
% 181.89/182.14 452 ifeq2(product(a,b,A),c_0,A,aPb) = aPb. [para(426(a,1),316(a,1,1)),rewrite([7(10)])].
% 181.89/182.14 533 ifeq(sum(A,B,aPb),c_0,ifeq(sum(additive_inverse(aPc),A,C),c_0,sum(C,B,aPb_S_IaPc),c_0),c_0) = c_0. [para(425(a,1),321(a,1,3,1)),rewrite([8(15)])].
% 181.89/182.14 537 ifeq(sum(A,B,C),c_0,ifeq(sum(additive_inverse(C),A,D),c_0,sum(D,B,additive_identity),c_0),c_0) = c_0. [para(429(a,1),321(a,1,3,1)),rewrite([8(13)])].
% 181.89/182.14 557 add(A,B) = add(B,A). [para(423(a,1),418(a,1,1)),rewrite([7(5)])].
% 181.89/182.14 1147 ifeq(product(additive_identity,A,B),c_0,ifeq(product(C,A,D),c_0,product(C,A,add(B,D)),c_0),c_0) = c_0. [para(432(a,1),339(a,1,3,3,1)),rewrite([557(8),8(11)])].
% 181.89/182.14 1956 ifeq(sum(A,additive_inverse(B),C),c_0,sum(C,B,A),c_0) = c_0. [para(429(a,1),349(a,1,1)),rewrite([8(10)])].
% 181.89/182.14 2767 ifeq(product(additive_identity,A,B),c_0,ifeq(sum(B,multiply(C,A),D),c_0,product(C,A,D),c_0),c_0) = c_0. [para(431(a,1),362(a,1,3,3,1)),rewrite([8(11)])].
% 181.89/182.14 3543 ifeq(sum(multiply(a,A),aPc,B),c_0,ifeq(sum(A,c,C),c_0,product(a,C,B),c_0),c_0) = c_0. [para(428(a,1),376(a,1,1)),rewrite([8(18)])].
% 181.89/182.14 3687 sum(bS_Ic,c,b) = c_0. [para(434(a,1),1956(a,1,1)),rewrite([8(8)])].
% 181.89/182.14 13852 ifeq(sum(aPc,A,aPb),c_0,sum(additive_identity,A,aPb_S_IaPc),c_0) = c_0. [para(429(a,1),533(a,1,3,1)),rewrite([8(11)])].
% 181.89/182.14 14376 ifeq(sum(A,B,A),c_0,sum(additive_identity,B,additive_identity),c_0) = c_0. [para(429(a,1),537(a,1,3,1)),rewrite([8(9)])].
% 181.89/182.14 19952 ifeq(product(additive_identity,A,B),c_0,product(C,A,add(B,multiply(C,A))),c_0) = c_0. [para(433(a,1),1147(a,1,3,1)),rewrite([8(10)])].
% 181.89/182.14 27925 ifeq(sum(multiply(a,bS_Ic),aPc,A),c_0,product(a,b,A),c_0) = c_0. [para(3687(a,1),3543(a,1,3,1)),rewrite([8(13)])].
% 181.89/182.14 50589 product(A,B,add(multiply(additive_identity,B),multiply(A,B))) = c_0. [para(433(a,1),19952(a,1,1)),rewrite([8(9)])].
% 181.89/182.14 50596 add(multiply(additive_identity,A),multiply(B,A)) = multiply(B,A). [para(50589(a,1),416(a,1,1)),rewrite([7(8)]),flip(a)].
% 181.89/182.14 50607 sum(multiply(additive_identity,A),multiply(B,A),multiply(B,A)) = c_0. [para(50596(a,1),432(a,1,3))].
% 181.89/182.14 50725 sum(additive_identity,multiply(additive_identity,A),additive_identity) = c_0. [para(50607(a,1),14376(a,1,1)),rewrite([8(9)])].
% 181.89/182.14 50730 multiply(additive_identity,A) = additive_identity. [para(50725(a,1),435(a,1,1)),rewrite([7(6)]),flip(a)].
% 181.89/182.14 51089 product(additive_identity,A,additive_identity) = c_0. [para(50730(a,1),433(a,1,3))].
% 181.89/182.14 66881 product(a,b,add(aPc,multiply(a,bS_Ic))) = c_0. [para(432(a,1),27925(a,1,1)),rewrite([557(9),8(12)])].
% 181.89/182.14 66890 add(aPc,multiply(a,bS_Ic)) = aPb. [para(66881(a,1),452(a,1,1)),rewrite([7(9)])].
% 181.89/182.14 66891 sum(aPc,multiply(a,bS_Ic),aPb) = c_0. [para(66890(a,1),432(a,1,3))].
% 181.89/182.14 67062 sum(additive_identity,multiply(a,bS_Ic),aPb_S_IaPc) = c_0. [para(66891(a,1),13852(a,1,1)),rewrite([8(10)])].
% 181.89/182.14 67147 product(a,bS_Ic,aPb_S_IaPc) = c_0. [para(67062(a,1),2767(a,1,3,1)),rewrite([51089(4),8(10),8(8)])].
% 181.89/182.14 67148 $F # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc). [resolve(67147,a,232,a)].
% 181.89/182.14
% 181.89/182.14 % SZS output end Refutation
% 181.89/182.14 ============================== end of proof ==========================
% 181.89/182.14
% 181.89/182.14 ============================== STATISTICS ============================
% 181.89/182.14
% 181.89/182.14 Given=17661. Generated=2750020. Kept=67127. proofs=1.
% 181.89/182.14 Usable=5476. Sos=9998. Demods=15445. Limbo=3, Disabled=51673. Hints=0.
% 181.89/182.14 Megabytes=47.45.
% 181.89/182.14 User_CPU=179.50, System_CPU=1.60, Wall_clock=181.
% 181.89/182.14
% 181.89/182.14 ============================== end of statistics =====================
% 181.89/182.14
% 181.89/182.14 ============================== end of search =========================
% 181.89/182.14
% 181.89/182.14 THEOREM PROVED
% 181.89/182.14 % SZS status Unsatisfiable
% 181.89/182.14
% 181.89/182.14 Exiting with 1 proof.
% 181.89/182.14
% 181.89/182.14 Process 3053 exit (max_proofs) Mon May 30 08:46:57 2022
% 181.89/182.14 Prover9 interrupted
%------------------------------------------------------------------------------