TSTP Solution File: KLE027+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE027+4 : 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 02:21:50 EDT 2022
% Result : Theorem 0.98s 1.24s
% Output : Refutation 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE027+4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n003.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 : Thu Jun 16 09:37:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/0.98 ============================== Prover9 ===============================
% 0.44/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.44/0.98 Process 1821 was started by sandbox2 on n003.cluster.edu,
% 0.44/0.98 Thu Jun 16 09:37:42 2022
% 0.44/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1653_n003.cluster.edu".
% 0.44/0.98 ============================== end of head ===========================
% 0.44/0.98
% 0.44/0.98 ============================== INPUT =================================
% 0.44/0.98
% 0.44/0.98 % Reading from file /tmp/Prover9_1653_n003.cluster.edu
% 0.44/0.98
% 0.44/0.98 set(prolog_style_variables).
% 0.44/0.98 set(auto2).
% 0.44/0.98 % set(auto2) -> set(auto).
% 0.44/0.98 % set(auto) -> set(auto_inference).
% 0.44/0.98 % set(auto) -> set(auto_setup).
% 0.44/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.44/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/0.98 % set(auto) -> set(auto_limits).
% 0.44/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/0.98 % set(auto) -> set(auto_denials).
% 0.44/0.98 % set(auto) -> set(auto_process).
% 0.44/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.44/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.44/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.44/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.44/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.44/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.44/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.44/0.98 % set(auto2) -> assign(stats, some).
% 0.44/0.98 % set(auto2) -> clear(echo_input).
% 0.44/0.98 % set(auto2) -> set(quiet).
% 0.44/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.44/0.98 % set(auto2) -> clear(print_given).
% 0.44/0.98 assign(lrs_ticks,-1).
% 0.44/0.98 assign(sos_limit,10000).
% 0.44/0.98 assign(order,kbo).
% 0.44/0.98 set(lex_order_vars).
% 0.44/0.98 clear(print_given).
% 0.44/0.98
% 0.44/0.98 % formulas(sos). % not echoed (19 formulas)
% 0.44/0.98
% 0.44/0.98 ============================== end of input ==========================
% 0.44/0.98
% 0.44/0.98 % From the command line: assign(max_seconds, 300).
% 0.44/0.98
% 0.44/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/0.98
% 0.44/0.98 % Formulas that are not ordinary clauses:
% 0.44/0.98 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.98 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].
% 0.44/0.98 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.98 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.98 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].
% 0.44/0.98 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.98 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.98 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].
% 0.44/0.98 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].
% 0.44/0.98 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.98 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.98 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.98 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.98 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].
% 0.98/1.24 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 17 (all X0 all X1 (test(X0) & test(X1) -> c(addition(X0,X1)) = multiplication(c(X0),c(X1)))) # label(test_deMorgan1) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 18 (all X0 all X1 (test(X0) & test(X1) -> c(multiplication(X0,X1)) = addition(c(X0),c(X1)))) # label(test_deMorgan2) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 19 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X4) -> leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) & leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.98/1.24
% 0.98/1.24 ============================== end of process non-clausal formulas ===
% 0.98/1.24
% 0.98/1.24 ============================== PROCESS INITIAL CLAUSES ===============
% 0.98/1.24
% 0.98/1.24 ============================== PREDICATE ELIMINATION =================
% 0.98/1.24 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.98/1.24 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.98/1.24 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.98/1.24 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 0.98/1.24 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.98/1.24 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.98/1.24 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.98/1.24 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.98/1.24 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.98/1.24 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 0.98/1.24 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 0.98/1.24 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 0.98/1.24 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 0.98/1.24 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.98/1.24 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.98/1.24 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.98/1.24 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.98/1.24 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 0.98/1.24
% 0.98/1.24 ============================== end predicate elimination =============
% 0.98/1.24
% 0.98/1.24 Auto_denials: (non-Horn, no changes).
% 0.98/1.24
% 0.98/1.24 Term ordering decisions:
% 0.98/1.24 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. c4=1. c5=1. multiplication=1. addition=1. c=1. f1=1.
% 0.98/1.24
% 0.98/1.24 ============================== end of process initial clauses ========
% 0.98/1.24
% 0.98/1.24 ============================== CLAUSES FOR SEARCH ====================
% 0.98/1.24
% 0.98/1.24 ============================== end of clauses for search =============
% 0.98/1.24
% 0.98/1.24 ============================== SEARCH ================================
% 0.98/1.24
% 0.98/1.24 % Starting search at 0.01 seconds.
% 0.98/1.24
% 0.98/1.24 ============================== PROOF =================================
% 0.98/1.24 % SZS status Theorem
% 0.98/1.24 % SZS output start Refutation
% 0.98/1.24
% 0.98/1.24 % Proof 1 at 0.27 (+ 0.01) seconds.
% 0.98/1.24 % Length of proof is 76.
% 0.98/1.24 % Level of proof is 14.
% 0.98/1.24 % Maximum clause weight is 48.000.
% 0.98/1.24 % Given clauses 291.
% 0.98/1.24
% 0.98/1.24 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 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].
% 0.98/1.24 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 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].
% 0.98/1.24 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].
% 0.98/1.24 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 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].
% 0.98/1.24 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 17 (all X0 all X1 (test(X0) & test(X1) -> c(addition(X0,X1)) = multiplication(c(X0),c(X1)))) # label(test_deMorgan1) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 18 (all X0 all X1 (test(X0) & test(X1) -> c(multiplication(X0,X1)) = addition(c(X0),c(X1)))) # label(test_deMorgan2) # label(axiom) # label(non_clause). [assumption].
% 0.98/1.24 19 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X4) -> leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) & leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.98/1.24 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.98/1.24 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.98/1.24 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.98/1.24 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.98/1.24 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.98/1.24 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.98/1.24 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.98/1.25 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.98/1.25 28 test(c4) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.98/1.25 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.98/1.25 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.98/1.25 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.98/1.25 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.98/1.25 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.98/1.25 35 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 0.98/1.25 37 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.98/1.25 40 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.98/1.25 41 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.98/1.25 42 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(41),flip(a)].
% 0.98/1.25 43 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.98/1.25 44 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(43),flip(a)].
% 0.98/1.25 45 -leq(addition(multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2))),multiplication(c(c4),c3)),addition(multiplication(c4,c1),multiplication(c(c4),c3))) | -leq(addition(multiplication(c4,c1),multiplication(c(c4),c3)),addition(multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2))),multiplication(c(c4),c3))) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.98/1.25 46 -leq(addition(multiplication(c(c4),c3),multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2)))),addition(multiplication(c4,c1),multiplication(c(c4),c3))) | -leq(addition(multiplication(c4,c1),multiplication(c(c4),c3)),addition(multiplication(c(c4),c3),multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2))))). [copy(45),rewrite([37(15),37(47)])].
% 0.98/1.25 48 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.98/1.25 49 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)].
% 0.98/1.25 50 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(49),flip(c)].
% 0.98/1.25 51 -test(A) | -test(B) | c(multiplication(A,B)) = addition(c(A),c(B)) # label(test_deMorgan2) # label(axiom). [clausify(18)].
% 0.98/1.25 52 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(A,B)). [copy(51),flip(c)].
% 0.98/1.25 53 multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 0.98/1.25 54 multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.98/1.25 55 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.98/1.25 58 -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 0.98/1.25 61 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.98/1.25 62 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.98/1.25 64 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(50,a,b),rewrite([31(5)])].
% 0.98/1.25 69 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),42(a,2,2)),rewrite([34(3),37(3)])].
% 0.98/1.25 74 leq(A,A). [resolve(48,b,31,a)].
% 0.98/1.25 86 -test(A) | addition(c(A),c(c4)) = c(multiplication(c4,A)). [resolve(52,a,28,a),rewrite([37(5)])].
% 0.98/1.25 92 multiplication(c4,f1(c4)) = zero. [resolve(53,b,28,a)].
% 0.98/1.25 98 addition(c4,f1(c4)) = one. [resolve(55,b,28,a)].
% 0.98/1.25 107 c(c4) != A | multiplication(c4,A) = zero. [resolve(58,a,28,a)].
% 0.98/1.25 114 test(one). [resolve(62,c,30,a),rewrite([34(3),32(6)]),xx(a),xx(b)].
% 0.98/1.25 128 multiplication(c(c4),c(c4)) = c(c4). [resolve(64,a,28,a)].
% 0.98/1.25 140 addition(one,f1(one)) = one. [resolve(114,a,55,b)].
% 0.98/1.25 141 f1(one) = zero. [resolve(114,a,54,b),rewrite([32(4)])].
% 0.98/1.25 145 addition(zero,one) = one. [back_rewrite(140),rewrite([141(3),37(3)])].
% 0.98/1.25 146 -test(zero) | c(zero) = one. [para(141(a,1),61(a,1)),rewrite([141(4)]),unit_del(c,114)].
% 0.98/1.25 151 test(zero). [resolve(145,a,62,c),rewrite([32(3),34(6)]),xx(a),xx(b)].
% 0.98/1.25 153 c(zero) = one. [back_unit_del(146),unit_del(a,151)].
% 0.98/1.25 194 multiplication(c4,addition(A,f1(c4))) = multiplication(c4,A). [para(92(a,1),42(a,1,1)),rewrite([69(4),37(6)]),flip(a)].
% 0.98/1.25 558 addition(one,c(c4)) = one. [resolve(86,a,151,a),rewrite([153(2),34(7),153(6)])].
% 0.98/1.25 563 addition(A,multiplication(c(c4),A)) = A. [para(558(a,1),44(a,2,1)),rewrite([33(2),33(6)])].
% 0.98/1.25 997 multiplication(c4,c(c4)) = zero. [resolve(107,a,563,a(flip)),rewrite([128(8),31(6)])].
% 0.98/1.25 999 multiplication(c4,multiplication(c(c4),A)) = zero. [para(997(a,1),40(a,1,1)),rewrite([35(2)]),flip(a)].
% 0.98/1.25 1008 multiplication(c4,addition(A,multiplication(c(c4),B))) = multiplication(c4,A). [para(999(a,1),42(a,1,1)),rewrite([69(4),37(7)]),flip(a)].
% 0.98/1.25 1012 -leq(addition(multiplication(c(c4),c3),multiplication(c4,multiplication(c4,c1))),addition(multiplication(c4,c1),multiplication(c(c4),c3))) | -leq(addition(multiplication(c4,c1),multiplication(c(c4),c3)),addition(multiplication(c(c4),c3),multiplication(c4,multiplication(c4,c1)))). [back_rewrite(46),rewrite([1008(14),1008(41)])].
% 0.98/1.25 2359 multiplication(c4,c4) = c4. [para(98(a,1),194(a,1,2)),rewrite([32(3)]),flip(a)].
% 0.98/1.25 2377 multiplication(c4,multiplication(c4,A)) = multiplication(c4,A). [para(2359(a,1),40(a,1,1)),flip(a)].
% 0.98/1.25 2384 $F. [back_rewrite(1012),rewrite([2377(9),37(8),2377(34),37(33)]),merge(b),unit_del(a,74)].
% 0.98/1.25
% 0.98/1.25 % SZS output end Refutation
% 0.98/1.25 ============================== end of proof ==========================
% 0.98/1.25
% 0.98/1.25 ============================== STATISTICS ============================
% 0.98/1.25
% 0.98/1.25 Given=291. Generated=8158. Kept=2349. proofs=1.
% 0.98/1.25 Usable=268. Sos=1735. Demods=582. Limbo=7, Disabled=376. Hints=0.
% 0.98/1.25 Megabytes=2.50.
% 0.98/1.25 User_CPU=0.27, System_CPU=0.01, Wall_clock=0.
% 0.98/1.25
% 0.98/1.25 ============================== end of statistics =====================
% 0.98/1.25
% 0.98/1.25 ============================== end of search =========================
% 0.98/1.25
% 0.98/1.25 THEOREM PROVED
% 0.98/1.25 % SZS status Theorem
% 0.98/1.25
% 0.98/1.25 Exiting with 1 proof.
% 0.98/1.25
% 0.98/1.25 Process 1821 exit (max_proofs) Thu Jun 16 09:37:42 2022
% 0.98/1.25 Prover9 interrupted
%------------------------------------------------------------------------------