TSTP Solution File: KLE015+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE015+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 02:21:44 EDT 2022
% Result : Theorem 2.07s 2.36s
% Output : Refutation 2.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE015+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n003.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 : Thu Jun 16 15:02:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/0.98 ============================== Prover9 ===============================
% 0.43/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.98 Process 24495 was started by sandbox on n003.cluster.edu,
% 0.43/0.98 Thu Jun 16 15:02:27 2022
% 0.43/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24342_n003.cluster.edu".
% 0.43/0.98 ============================== end of head ===========================
% 0.43/0.98
% 0.43/0.98 ============================== INPUT =================================
% 0.43/0.98
% 0.43/0.98 % Reading from file /tmp/Prover9_24342_n003.cluster.edu
% 0.43/0.98
% 0.43/0.98 set(prolog_style_variables).
% 0.43/0.98 set(auto2).
% 0.43/0.98 % set(auto2) -> set(auto).
% 0.43/0.98 % set(auto) -> set(auto_inference).
% 0.43/0.98 % set(auto) -> set(auto_setup).
% 0.43/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.98 % set(auto) -> set(auto_limits).
% 0.43/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.98 % set(auto) -> set(auto_denials).
% 0.43/0.98 % set(auto) -> set(auto_process).
% 0.43/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.98 % set(auto2) -> assign(stats, some).
% 0.43/0.98 % set(auto2) -> clear(echo_input).
% 0.43/0.98 % set(auto2) -> set(quiet).
% 0.43/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.98 % set(auto2) -> clear(print_given).
% 0.43/0.98 assign(lrs_ticks,-1).
% 0.43/0.98 assign(sos_limit,10000).
% 0.43/0.98 assign(order,kbo).
% 0.43/0.98 set(lex_order_vars).
% 0.43/0.98 clear(print_given).
% 0.43/0.98
% 0.43/0.98 % formulas(sos). % not echoed (17 formulas)
% 0.43/0.98
% 0.43/0.98 ============================== end of input ==========================
% 0.43/0.98
% 0.43/0.98 % From the command line: assign(max_seconds, 300).
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.98
% 0.43/0.98 % Formulas that are not ordinary clauses:
% 0.43/0.98 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 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].
% 0.43/0.98 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 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].
% 0.43/0.98 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 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].
% 0.43/0.98 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].
% 0.43/0.98 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 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].
% 2.07/2.36 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 17 -(all X0 all X1 (test(X1) & test(X0) -> multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.07/2.36
% 2.07/2.36 ============================== end of process non-clausal formulas ===
% 2.07/2.36
% 2.07/2.36 ============================== PROCESS INITIAL CLAUSES ===============
% 2.07/2.36
% 2.07/2.36 ============================== PREDICATE ELIMINATION =================
% 2.07/2.36 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.07/2.36 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.07/2.36 20 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.07/2.36 21 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.07/2.36 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.07/2.36 Derived: complement(f1(c2),c2). [resolve(18,a,19,a)].
% 2.07/2.36 Derived: complement(f1(c1),c1). [resolve(18,a,20,a)].
% 2.07/2.36 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,21,a)].
% 2.07/2.36 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 2.07/2.36 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.07/2.36 Derived: c(c2) != A | complement(c2,A). [resolve(23,a,19,a)].
% 2.07/2.36 Derived: c(c1) != A | complement(c1,A). [resolve(23,a,20,a)].
% 2.07/2.36 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(23,a,21,a)].
% 2.07/2.36 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(23,a,22,a)].
% 2.07/2.36 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.07/2.36 Derived: c(c2) = A | -complement(c2,A). [resolve(24,a,19,a)].
% 2.07/2.36 Derived: c(c1) = A | -complement(c1,A). [resolve(24,a,20,a)].
% 2.07/2.36 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(24,a,21,a)].
% 2.07/2.36 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 2.07/2.36 25 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.07/2.36 26 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.07/2.36
% 2.07/2.36 ============================== end predicate elimination =============
% 2.07/2.36
% 2.07/2.36 Auto_denials: (non-Horn, no changes).
% 2.07/2.36
% 2.07/2.36 Term ordering decisions:
% 2.07/2.36 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 2.07/2.36
% 2.07/2.36 ============================== end of process initial clauses ========
% 2.07/2.36
% 2.07/2.36 ============================== CLAUSES FOR SEARCH ====================
% 2.07/2.36
% 2.07/2.36 ============================== end of clauses for search =============
% 2.07/2.36
% 2.07/2.36 ============================== SEARCH ================================
% 2.07/2.36
% 2.07/2.36 % Starting search at 0.01 seconds.
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=82.000, iters=3367
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=74.000, iters=3466
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=68.000, iters=3436
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=67.000, iters=3381
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=64.000, iters=3361
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=60.000, iters=3424
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=58.000, iters=3366
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=54.000, iters=3485
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=53.000, iters=3420
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=52.000, iters=3417
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=48.000, iters=3350
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=46.000, iters=3339
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=44.000, iters=3340
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=42.000, iters=3343
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=40.000, iters=3346
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=39.000, iters=3362
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=37.000, iters=3342
% 2.07/2.36
% 2.07/2.36 Low Water (keep): wt=36.000, iters=3393
% 2.07/2.36
% 2.07/2.36 ============================== PROOF =================================
% 2.07/2.36 % SZS status Theorem
% 2.07/2.36 % SZS output start Refutation
% 2.07/2.36
% 2.07/2.36 % Proof 1 at 1.36 (+ 0.03) seconds.
% 2.07/2.36 % Length of proof is 72.
% 2.07/2.36 % Level of proof is 10.
% 2.07/2.36 % Maximum clause weight is 18.000.
% 2.07/2.36 % Given clauses 427.
% 2.07/2.36
% 2.07/2.36 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 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].
% 2.07/2.36 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 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].
% 2.07/2.36 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 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].
% 2.07/2.36 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].
% 2.07/2.36 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 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].
% 2.07/2.36 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.07/2.36 17 -(all X0 all X1 (test(X1) & test(X0) -> multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) = zero)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.07/2.36 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.07/2.36 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.07/2.36 20 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.07/2.36 21 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.07/2.36 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.07/2.36 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.07/2.36 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.07/2.36 27 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.07/2.36 28 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 2.07/2.36 29 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 2.07/2.36 30 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 2.07/2.36 31 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.07/2.36 32 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 2.07/2.36 33 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.07/2.36 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 2.07/2.36 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([33(2)]),flip(a)].
% 2.07/2.36 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 2.07/2.36 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.07/2.36 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 2.07/2.36 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.07/2.36 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 2.07/2.36 41 multiplication(multiplication(addition(c1,c2),c(c1)),c(c2)) != zero # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.07/2.36 42 multiplication(addition(c1,c2),multiplication(c(c1),c(c2))) != zero. [copy(41),rewrite([36(9)])].
% 2.07/2.36 44 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.07/2.36 45 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 2.07/2.36 46 -complement(A,B) | addition(A,B) = one. [copy(45),rewrite([33(2)])].
% 2.07/2.36 47 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 2.07/2.36 48 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(A,B) != one. [copy(47),rewrite([33(8)])].
% 2.07/2.36 52 complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 2.07/2.36 53 c(c2) != A | complement(c2,A). [resolve(23,a,19,a)].
% 2.07/2.36 54 c(c1) != A | complement(c1,A). [resolve(23,a,20,a)].
% 2.07/2.36 59 c(A) = B | -complement(A,B) | c(A) = zero. [resolve(24,a,21,a)].
% 2.07/2.36 60 c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 2.07/2.36 62 c(A) = zero | -complement(A,zero). [factor(59,a,c)].
% 2.07/2.36 64 addition(A,addition(A,B)) = addition(A,B). [para(35(a,1),28(a,1)),rewrite([33(1),33(2),35(2,R),28(1),33(3)])].
% 2.07/2.36 65 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(27(a,1),38(a,2,2)),rewrite([31(3),33(3)])].
% 2.07/2.36 68 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(36(a,1),40(a,1,1)),rewrite([33(6)])].
% 2.07/2.36 73 complement(one,zero). [resolve(48,d,27,a),rewrite([29(6),31(9)]),xx(b),xx(c)].
% 2.07/2.36 87 complement(c2,c(c2)). [resolve(53,a,30,a(flip)),rewrite([30(5)])].
% 2.07/2.36 89 complement(c1,c(c1)). [resolve(54,a,30,a(flip)),rewrite([30(5)])].
% 2.07/2.36 101 c(one) = zero. [resolve(73,a,62,b)].
% 2.07/2.36 105 addition(zero,one) = one. [resolve(73,a,46,a),rewrite([33(3)])].
% 2.07/2.36 110 multiplication(c2,c(c2)) = zero. [resolve(87,a,44,a)].
% 2.07/2.36 114 complement(f1(c(c1)),c(c1)). [resolve(89,a,52,b)].
% 2.07/2.36 116 multiplication(c1,c(c1)) = zero. [resolve(89,a,44,a)].
% 2.07/2.36 121 complement(zero,one). [resolve(105,a,48,d),rewrite([31(6),29(9)]),xx(b),xx(c)].
% 2.07/2.36 122 zero = A | -complement(one,A). [resolve(121,a,60,c),rewrite([101(2)])].
% 2.07/2.36 236 multiplication(addition(c2,multiplication(A,B)),c(c2)) = multiplication(A,multiplication(B,c(c2))). [para(110(a,1),68(a,1,2)),rewrite([33(6),65(6)]),flip(a)].
% 2.07/2.36 252 addition(c(c1),f1(c(c1))) = one. [resolve(114,a,46,a),rewrite([33(6)])].
% 2.07/2.36 255 multiplication(c1,multiplication(c(c1),A)) = zero. [para(116(a,1),36(a,1,1)),rewrite([32(2)]),flip(a)].
% 2.07/2.36 284 -complement(one,multiplication(addition(c1,c2),multiplication(c(c1),c(c2)))). [ur(122,a,42,a(flip))].
% 2.07/2.36 388 addition(one,c(c1)) = one. [para(252(a,1),64(a,1,2)),rewrite([33(4),252(10)])].
% 2.07/2.36 396 addition(A,multiplication(A,c(c1))) = A. [para(388(a,1),38(a,2,2)),rewrite([29(2),29(6)])].
% 2.07/2.36 8024 multiplication(c2,multiplication(c(c1),c(c2))) = zero. [para(396(a,1),236(a,1,1)),rewrite([110(4)]),flip(a)].
% 2.07/2.36 8071 multiplication(addition(A,c2),multiplication(c(c1),c(c2))) = multiplication(A,multiplication(c(c1),c(c2))). [para(8024(a,1),40(a,1,1)),rewrite([65(8),33(8)]),flip(a)].
% 2.07/2.36 8094 $F. [back_rewrite(284),rewrite([8071(10),255(8)]),unit_del(a,73)].
% 2.07/2.36
% 2.07/2.36 % SZS output end Refutation
% 2.07/2.36 ============================== end of proof ==========================
% 2.07/2.36
% 2.07/2.36 ============================== STATISTICS ============================
% 2.07/2.36
% 2.07/2.36 Given=427. Generated=37227. Kept=8061. proofs=1.
% 2.07/2.36 Usable=393. Sos=7231. Demods=1732. Limbo=23, Disabled=451. Hints=0.
% 2.07/2.36 Megabytes=10.36.
% 2.07/2.36 User_CPU=1.36, System_CPU=0.03, Wall_clock=1.
% 2.07/2.36
% 2.07/2.36 ============================== end of statistics =====================
% 2.07/2.36
% 2.07/2.36 ============================== end of search =========================
% 2.07/2.36
% 2.07/2.36 THEOREM PROVED
% 2.07/2.36 % SZS status Theorem
% 2.07/2.36
% 2.07/2.36 Exiting with 1 proof.
% 2.07/2.36
% 2.07/2.36 Process 24495 exit (max_proofs) Thu Jun 16 15:02:28 2022
% 2.07/2.36 Prover9 interrupted
%------------------------------------------------------------------------------