TSTP Solution File: KLE008+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE008+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 02:21:39 EDT 2022
% Result : Theorem 2.72s 3.05s
% Output : Refutation 2.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE008+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 13:33:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.01 ============================== Prover9 ===============================
% 0.44/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.01 Process 18725 was started by sandbox on n026.cluster.edu,
% 0.44/1.01 Thu Jun 16 13:33:08 2022
% 0.44/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18571_n026.cluster.edu".
% 0.44/1.01 ============================== end of head ===========================
% 0.44/1.01
% 0.44/1.01 ============================== INPUT =================================
% 0.44/1.01
% 0.44/1.01 % Reading from file /tmp/Prover9_18571_n026.cluster.edu
% 0.44/1.01
% 0.44/1.01 set(prolog_style_variables).
% 0.44/1.01 set(auto2).
% 0.44/1.01 % set(auto2) -> set(auto).
% 0.44/1.01 % set(auto) -> set(auto_inference).
% 0.44/1.01 % set(auto) -> set(auto_setup).
% 0.44/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.01 % set(auto) -> set(auto_limits).
% 0.44/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.01 % set(auto) -> set(auto_denials).
% 0.44/1.01 % set(auto) -> set(auto_process).
% 0.44/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.01 % set(auto2) -> assign(stats, some).
% 0.44/1.01 % set(auto2) -> clear(echo_input).
% 0.44/1.01 % set(auto2) -> set(quiet).
% 0.44/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.01 % set(auto2) -> clear(print_given).
% 0.44/1.01 assign(lrs_ticks,-1).
% 0.44/1.01 assign(sos_limit,10000).
% 0.44/1.01 assign(order,kbo).
% 0.44/1.01 set(lex_order_vars).
% 0.44/1.01 clear(print_given).
% 0.44/1.01
% 0.44/1.01 % formulas(sos). % not echoed (17 formulas)
% 0.44/1.01
% 0.44/1.01 ============================== end of input ==========================
% 0.44/1.01
% 0.44/1.01 % From the command line: assign(max_seconds, 300).
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.01
% 0.44/1.01 % Formulas that are not ordinary clauses:
% 0.44/1.01 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 17 -(all X0 all X1 all X2 (test(X2) -> (leq(X0,multiplication(X2,X1)) <-> leq(X0,X1) & leq(multiplication(c(X2),X0),zero)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.72/3.05
% 2.72/3.05 ============================== end of process non-clausal formulas ===
% 2.72/3.05
% 2.72/3.05 ============================== PROCESS INITIAL CLAUSES ===============
% 2.72/3.05
% 2.72/3.05 ============================== PREDICATE ELIMINATION =================
% 2.72/3.05 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.72/3.05 19 test(c3) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.72/3.05 20 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.72/3.05 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.72/3.05 Derived: complement(f1(c3),c3). [resolve(18,a,19,a)].
% 2.72/3.05 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,20,a)].
% 2.72/3.05 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,21,a)].
% 2.72/3.05 22 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.72/3.05 Derived: c(c3) != A | complement(c3,A). [resolve(22,a,19,a)].
% 2.72/3.05 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(22,a,20,a)].
% 2.72/3.05 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(22,a,21,a)].
% 2.72/3.05 23 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.72/3.05 Derived: c(c3) = A | -complement(c3,A). [resolve(23,a,19,a)].
% 2.72/3.05 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(23,a,20,a)].
% 2.72/3.05 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(23,a,21,a)].
% 2.72/3.05
% 2.72/3.05 ============================== end predicate elimination =============
% 2.72/3.05
% 2.72/3.05 Auto_denials: (non-Horn, no changes).
% 2.72/3.05
% 2.72/3.05 Term ordering decisions:
% 2.72/3.05 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. c=1. f1=1.
% 2.72/3.05
% 2.72/3.05 ============================== end of process initial clauses ========
% 2.72/3.05
% 2.72/3.05 ============================== CLAUSES FOR SEARCH ====================
% 2.72/3.05
% 2.72/3.05 ============================== end of clauses for search =============
% 2.72/3.05
% 2.72/3.05 ============================== SEARCH ================================
% 2.72/3.05
% 2.72/3.05 % Starting search at 0.01 seconds.
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=74.000, iters=3505
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=56.000, iters=3339
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=52.000, iters=3355
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=51.000, iters=3336
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=48.000, iters=3383
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=42.000, iters=3340
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=41.000, iters=3367
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=40.000, iters=3333
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=38.000, iters=3378
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=36.000, iters=3339
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=35.000, iters=3395
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=25.000, iters=4420
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=22.000, iters=3362
% 2.72/3.05
% 2.72/3.05 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.26 sec).
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=5911, wt=107.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=5942, wt=88.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=5409, wt=85.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=5943, wt=82.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=6091, wt=81.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=5937, wt=80.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=4925, wt=79.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=5620, wt=74.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=5941, wt=72.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=5944, wt=68.000
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=21.000, iters=3347
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=5558, wt=67.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=5638, wt=66.000
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% 2.72/3.05 Low Water (displace): id=5940, wt=64.000
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% 2.72/3.05 Low Water (displace): id=11583, wt=20.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=11585, wt=18.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=11586, wt=16.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=11643, wt=15.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=11662, wt=14.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=12018, wt=13.000
% 2.72/3.05
% 2.72/3.05 Low Water (displace): id=12056, wt=12.000
% 2.72/3.05
% 2.72/3.05 Low Water (keep): wt=20.000, iters=3335
% 2.72/3.05
% 2.72/3.05 ============================== PROOF =================================
% 2.72/3.05 % SZS status Theorem
% 2.72/3.05 % SZS output start Refutation
% 2.72/3.05
% 2.72/3.05 % Proof 1 at 2.02 (+ 0.04) seconds.
% 2.72/3.05 % Length of proof is 67.
% 2.72/3.05 % Level of proof is 11.
% 2.72/3.05 % Maximum clause weight is 16.000.
% 2.72/3.05 % Given clauses 765.
% 2.72/3.05
% 2.72/3.05 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.72/3.05 17 -(all X0 all X1 all X2 (test(X2) -> (leq(X0,multiplication(X2,X1)) <-> leq(X0,X1) & leq(multiplication(c(X2),X0),zero)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.72/3.05 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.72/3.05 19 test(c3) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.72/3.05 22 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.72/3.05 24 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.72/3.05 25 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 2.72/3.05 27 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 2.72/3.05 28 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.72/3.05 29 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 2.72/3.05 30 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.72/3.05 31 leq(c1,multiplication(c3,c2)) | leq(c1,c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.72/3.05 32 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 2.72/3.05 33 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(32),rewrite([30(2)]),flip(a)].
% 2.72/3.05 34 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 2.72/3.05 35 leq(c1,multiplication(c3,c2)) | leq(multiplication(c(c3),c1),zero) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.72/3.05 36 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.72/3.05 37 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(36),flip(a)].
% 2.72/3.05 38 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.72/3.06 39 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(38),flip(a)].
% 2.72/3.06 40 -leq(c1,multiplication(c3,c2)) | -leq(c1,c2) | -leq(multiplication(c(c3),c1),zero) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.72/3.06 41 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.72/3.06 42 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.72/3.06 43 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.72/3.06 45 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 2.72/3.06 46 -complement(A,B) | addition(A,B) = one. [copy(45),rewrite([30(2)])].
% 2.72/3.06 49 complement(f1(c3),c3). [resolve(18,a,19,a)].
% 2.72/3.06 52 c(c3) != A | complement(c3,A). [resolve(22,a,19,a)].
% 2.72/3.06 61 addition(A,addition(A,B)) = addition(A,B). [para(33(a,1),25(a,1)),rewrite([30(1),30(2),33(2,R),25(1),30(3)])].
% 2.72/3.06 62 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(24(a,1),37(a,2,2)),rewrite([28(3),30(3)])].
% 2.72/3.06 67 multiplication(c(c3),c1) = zero | leq(c1,multiplication(c3,c2)). [resolve(41,a,35,b),rewrite([30(6),62(6)])].
% 2.72/3.06 68 addition(c1,multiplication(c3,c2)) = multiplication(c3,c2) | leq(c1,c2). [resolve(41,a,31,a)].
% 2.72/3.06 69 leq(A,A). [resolve(42,b,25,a)].
% 2.72/3.06 71 leq(multiplication(A,B),multiplication(A,C)) | multiplication(A,addition(B,C)) != multiplication(A,C). [para(37(a,1),42(b,1))].
% 2.72/3.06 79 addition(c3,f1(c3)) = one. [resolve(49,a,46,a),rewrite([30(4)])].
% 2.72/3.06 85 complement(c3,c(c3)). [resolve(52,a,27,a(flip)),rewrite([27(5)])].
% 2.72/3.06 104 addition(c3,c(c3)) = one. [resolve(85,a,46,a)].
% 2.72/3.06 106 multiplication(c(c3),c3) = zero. [resolve(85,a,43,a)].
% 2.72/3.06 172 addition(one,c3) = one. [para(79(a,1),61(a,1,2)),rewrite([30(3),79(7)])].
% 2.72/3.06 195 addition(A,multiplication(c3,A)) = A. [para(172(a,1),39(a,2,1)),rewrite([27(2),27(5)])].
% 2.72/3.06 201 multiplication(c(c3),c1) = zero | addition(c1,multiplication(c3,c2)) = multiplication(c3,c2). [resolve(67,b,41,a)].
% 2.72/3.06 214 addition(c1,multiplication(c3,c2)) = multiplication(c3,c2) | addition(c1,c2) = c2. [resolve(68,b,41,a)].
% 2.72/3.06 215 multiplication(c(c3),multiplication(c3,A)) = zero. [para(106(a,1),34(a,1,1)),rewrite([29(2)]),flip(a)].
% 2.72/3.06 280 addition(A,addition(B,multiplication(c3,A))) = addition(A,B). [para(195(a,1),33(a,2,2)),rewrite([30(3),30(5)])].
% 2.72/3.06 360 multiplication(c(c3),addition(A,multiplication(c3,B))) = multiplication(c(c3),A). [para(215(a,1),37(a,1,1)),rewrite([62(5),30(8)]),flip(a)].
% 2.72/3.06 7693 addition(c1,c2) = c2. [para(214(a,1),280(a,1,2)),rewrite([195(10),30(9)]),flip(b),merge(b)].
% 2.72/3.06 7697 leq(c1,c2). [resolve(7693,a,42,b)].
% 2.72/3.06 7699 leq(multiplication(A,c1),multiplication(A,c2)). [para(7693(a,1),71(b,1,2)),xx(b)].
% 2.72/3.06 7712 -leq(c1,multiplication(c3,c2)) | -leq(multiplication(c(c3),c1),zero). [back_unit_del(40),unit_del(b,7697)].
% 2.72/3.06 12134 multiplication(c(c3),c1) = zero. [para(201(b,1),360(a,1,2)),rewrite([215(12)]),flip(b),merge(b)].
% 2.72/3.06 12137 -leq(c1,multiplication(c3,c2)). [back_rewrite(7712),rewrite([12134(9)]),unit_del(b,69)].
% 2.72/3.06 12141 multiplication(addition(A,c(c3)),c1) = multiplication(A,c1). [para(12134(a,1),39(a,1,1)),rewrite([62(4),30(5)]),flip(a)].
% 2.72/3.06 12319 multiplication(c3,c1) = c1. [para(104(a,1),12141(a,1,1)),rewrite([27(3)]),flip(a)].
% 2.72/3.06 12378 $F. [para(12319(a,1),7699(a,1)),unit_del(a,12137)].
% 2.72/3.06
% 2.72/3.06 % SZS output end Refutation
% 2.72/3.06 ============================== end of proof ==========================
% 2.72/3.06
% 2.72/3.06 ============================== STATISTICS ============================
% 2.72/3.06
% 2.72/3.06 Given=765. Generated=65498. Kept=12349. proofs=1.
% 2.72/3.06 Usable=709. Sos=9999. Demods=929. Limbo=31, Disabled=1645. Hints=0.
% 2.72/3.06 Megabytes=12.94.
% 2.72/3.06 User_CPU=2.02, System_CPU=0.04, Wall_clock=3.
% 2.72/3.06
% 2.72/3.06 ============================== end of statistics =====================
% 2.72/3.06
% 2.72/3.06 ============================== end of search =========================
% 2.72/3.06
% 2.72/3.06 THEOREM PROVED
% 2.72/3.06 % SZS status Theorem
% 2.72/3.06
% 2.72/3.06 Exiting with 1 proof.
% 2.72/3.06
% 2.72/3.06 Process 18725 exit (max_proofs) Thu Jun 16 13:33:11 2022
% 2.72/3.06 Prover9 interrupted
%------------------------------------------------------------------------------