TSTP Solution File: KLE009+4 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE009+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 02:21:40 EDT 2022
% Result : Theorem 0.91s 1.17s
% Output : Refutation 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : KLE009+4 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 16:02:35 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.49/1.04 ============================== Prover9 ===============================
% 0.49/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.49/1.04 Process 32349 was started by sandbox2 on n014.cluster.edu,
% 0.49/1.04 Thu Jun 16 16:02:36 2022
% 0.49/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32196_n014.cluster.edu".
% 0.49/1.04 ============================== end of head ===========================
% 0.49/1.04
% 0.49/1.04 ============================== INPUT =================================
% 0.49/1.04
% 0.49/1.04 % Reading from file /tmp/Prover9_32196_n014.cluster.edu
% 0.49/1.04
% 0.49/1.04 set(prolog_style_variables).
% 0.49/1.04 set(auto2).
% 0.49/1.04 % set(auto2) -> set(auto).
% 0.49/1.04 % set(auto) -> set(auto_inference).
% 0.49/1.04 % set(auto) -> set(auto_setup).
% 0.49/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.49/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.49/1.04 % set(auto) -> set(auto_limits).
% 0.49/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.49/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.49/1.04 % set(auto) -> set(auto_denials).
% 0.49/1.04 % set(auto) -> set(auto_process).
% 0.49/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.49/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.49/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.49/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.49/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.49/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.49/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.49/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.49/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.49/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.49/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.49/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.49/1.04 % set(auto2) -> assign(stats, some).
% 0.49/1.04 % set(auto2) -> clear(echo_input).
% 0.49/1.04 % set(auto2) -> set(quiet).
% 0.49/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.49/1.04 % set(auto2) -> clear(print_given).
% 0.49/1.04 assign(lrs_ticks,-1).
% 0.49/1.04 assign(sos_limit,10000).
% 0.49/1.04 assign(order,kbo).
% 0.49/1.04 set(lex_order_vars).
% 0.49/1.04 clear(print_given).
% 0.49/1.04
% 0.49/1.04 % formulas(sos). % not echoed (19 formulas)
% 0.49/1.04
% 0.49/1.04 ============================== end of input ==========================
% 0.49/1.04
% 0.49/1.04 % From the command line: assign(max_seconds, 300).
% 0.49/1.04
% 0.49/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.49/1.04
% 0.49/1.04 % Formulas that are not ordinary clauses:
% 0.49/1.04 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.04 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].
% 0.49/1.04 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.04 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.04 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].
% 0.49/1.04 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.04 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.04 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].
% 0.49/1.04 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].
% 0.49/1.04 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.04 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.04 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.04 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.04 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].
% 0.91/1.17 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 19 -(all X0 all X1 (test(X1) & test(X0) -> leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.91/1.17
% 0.91/1.17 ============================== end of process non-clausal formulas ===
% 0.91/1.17
% 0.91/1.17 ============================== PROCESS INITIAL CLAUSES ===============
% 0.91/1.17
% 0.91/1.17 ============================== PREDICATE ELIMINATION =================
% 0.91/1.17 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.91/1.17 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.91/1.17 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.91/1.17 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 0.91/1.17 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.91/1.17 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.91/1.17 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.91/1.17 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.91/1.17 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.91/1.17 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 0.91/1.17 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 0.91/1.17 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 0.91/1.17 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 0.91/1.17 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.91/1.17 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.91/1.17 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.91/1.17 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.91/1.17 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 0.91/1.17
% 0.91/1.17 ============================== end predicate elimination =============
% 0.91/1.17
% 0.91/1.17 Auto_denials: (non-Horn, no changes).
% 0.91/1.17
% 0.91/1.17 Term ordering decisions:
% 0.91/1.17 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 0.91/1.17
% 0.91/1.17 ============================== end of process initial clauses ========
% 0.91/1.17
% 0.91/1.17 ============================== CLAUSES FOR SEARCH ====================
% 0.91/1.17
% 0.91/1.17 ============================== end of clauses for search =============
% 0.91/1.17
% 0.91/1.17 ============================== SEARCH ================================
% 0.91/1.17
% 0.91/1.17 % Starting search at 0.01 seconds.
% 0.91/1.17
% 0.91/1.17 ============================== PROOF =================================
% 0.91/1.17 % SZS status Theorem
% 0.91/1.17 % SZS output start Refutation
% 0.91/1.17
% 0.91/1.17 % Proof 1 at 0.14 (+ 0.01) seconds.
% 0.91/1.17 % Length of proof is 75.
% 0.91/1.17 % Level of proof is 12.
% 0.91/1.17 % Maximum clause weight is 38.000.
% 0.91/1.17 % Given clauses 189.
% 0.91/1.17
% 0.91/1.17 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 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].
% 0.91/1.17 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 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].
% 0.91/1.17 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 19 -(all X0 all X1 (test(X1) & test(X0) -> leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.91/1.17 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.91/1.17 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.91/1.17 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.91/1.17 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.91/1.17 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.91/1.17 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.91/1.17 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.91/1.17 28 test(c2) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.91/1.17 29 test(c1) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.91/1.17 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.91/1.17 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.91/1.17 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.91/1.17 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.91/1.17 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.91/1.17 37 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.91/1.17 38 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.91/1.17 39 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(38),rewrite([37(2)]),flip(a)].
% 0.91/1.17 41 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.91/1.17 42 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(41),flip(a)].
% 0.91/1.17 43 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.91/1.17 44 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(43),flip(a)].
% 0.91/1.17 45 -leq(one,addition(addition(addition(multiplication(c1,c2),multiplication(c1,c(c2))),multiplication(c(c1),c2)),multiplication(c(c1),c(c2)))) | -leq(addition(addition(addition(multiplication(c1,c2),multiplication(c1,c(c2))),multiplication(c(c1),c2)),multiplication(c(c1),c(c2))),one) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.91/1.17 46 -leq(one,addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(c1,addition(c2,c(c2)))))) | -leq(addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(c1,addition(c2,c(c2))))),one). [copy(45),rewrite([42(9),37(12),37(18),39(18,R),37(17),42(27),37(30),37(36),39(36,R),37(35)])].
% 0.91/1.17 48 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.91/1.17 49 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)].
% 0.91/1.17 50 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(49),flip(c)].
% 0.91/1.17 51 -test(A) | -test(B) | c(multiplication(A,B)) = addition(c(A),c(B)) # label(test_deMorgan2) # label(axiom). [clausify(18)].
% 0.91/1.17 52 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(A,B)). [copy(51),flip(c)].
% 0.91/1.17 54 multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.91/1.17 55 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.91/1.17 59 -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 0.91/1.17 60 -test(A) | c(A) != B | addition(A,B) = one. [copy(59),rewrite([37(4)])].
% 0.91/1.17 61 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.91/1.17 62 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.91/1.17 64 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(50,a,b),rewrite([31(5)])].
% 0.91/1.17 74 -leq(one,addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(c1,addition(c2,c(c2)))))) | -leq(multiplication(addition(c1,c(c1)),addition(c2,c(c2))),one). [para(39(a,1),46(b,1)),rewrite([42(35),44(33)])].
% 0.91/1.17 75 leq(A,A). [resolve(48,b,31,a)].
% 0.91/1.17 86 -test(A) | addition(c(A),c(c1)) = c(multiplication(c1,A)). [resolve(52,a,29,a),rewrite([37(5)])].
% 0.91/1.17 87 -test(A) | addition(c(A),c(c2)) = c(multiplication(c2,A)). [resolve(52,a,28,a),rewrite([37(5)])].
% 0.91/1.17 110 c(c1) != A | addition(A,c1) = one. [resolve(60,a,29,a),rewrite([37(5)])].
% 0.91/1.17 111 c(c2) != A | addition(A,c2) = one. [resolve(60,a,28,a),rewrite([37(5)])].
% 0.91/1.17 115 test(one). [resolve(62,c,30,a),rewrite([34(3),32(6)]),xx(a),xx(b)].
% 0.91/1.17 128 multiplication(c(c1),c(c1)) = c(c1). [resolve(64,a,29,a)].
% 0.91/1.17 129 multiplication(c(c2),c(c2)) = c(c2). [resolve(64,a,28,a)].
% 0.91/1.17 135 -leq(one,multiplication(addition(c1,c(c1)),addition(c2,c(c2)))) | -leq(multiplication(addition(c1,c(c1)),addition(c2,c(c2))),one). [para(39(a,1),74(a,2)),rewrite([42(17),44(15)])].
% 0.91/1.17 142 addition(one,f1(one)) = one. [resolve(115,a,55,b)].
% 0.91/1.17 143 f1(one) = zero. [resolve(115,a,54,b),rewrite([32(4)])].
% 0.91/1.17 147 addition(zero,one) = one. [back_rewrite(142),rewrite([143(3),37(3)])].
% 0.91/1.17 148 -test(zero) | c(zero) = one. [para(143(a,1),61(a,1)),rewrite([143(4)]),unit_del(c,115)].
% 0.91/1.17 153 test(zero). [resolve(147,a,62,c),rewrite([32(3),34(6)]),xx(a),xx(b)].
% 0.91/1.17 155 c(zero) = one. [back_unit_del(148),unit_del(a,153)].
% 0.91/1.17 540 addition(one,c(c1)) = one. [resolve(86,a,153,a),rewrite([155(2),34(7),155(6)])].
% 0.91/1.17 544 addition(A,multiplication(c(c1),A)) = A. [para(540(a,1),44(a,2,1)),rewrite([33(2),33(6)])].
% 0.91/1.17 562 addition(one,c(c2)) = one. [resolve(87,a,153,a),rewrite([155(2),34(7),155(6)])].
% 0.91/1.17 566 addition(A,multiplication(c(c2),A)) = A. [para(562(a,1),44(a,2,1)),rewrite([33(2),33(6)])].
% 0.91/1.17 1018 addition(c1,c(c1)) = one. [resolve(110,a,544,a(flip)),rewrite([128(7),31(5),37(4)])].
% 0.91/1.17 1025 -leq(one,addition(c2,c(c2))) | -leq(addition(c2,c(c2)),one). [back_rewrite(135),rewrite([1018(5),33(7),1018(10),33(12)])].
% 0.91/1.17 1048 addition(c2,c(c2)) = one. [resolve(111,a,566,a(flip)),rewrite([129(7),31(5),37(4)])].
% 0.91/1.17 1050 $F. [back_rewrite(1025),rewrite([1048(5),1048(7)]),merge(b),unit_del(a,75)].
% 0.91/1.17
% 0.91/1.17 % SZS output end Refutation
% 0.91/1.17 ============================== end of proof ==========================
% 0.91/1.17
% 0.91/1.17 ============================== STATISTICS ============================
% 0.91/1.17
% 0.91/1.17 Given=189. Generated=3117. Kept=1015. proofs=1.
% 0.91/1.17 Usable=171. Sos=663. Demods=368. Limbo=2, Disabled=216. Hints=0.
% 0.91/1.17 Megabytes=1.00.
% 0.91/1.17 User_CPU=0.14, System_CPU=0.01, Wall_clock=0.
% 0.91/1.17
% 0.91/1.17 ============================== end of statistics =====================
% 0.91/1.17
% 0.91/1.17 ============================== end of search =========================
% 0.91/1.17
% 0.91/1.17 THEOREM PROVED
% 0.91/1.17 % SZS status Theorem
% 0.91/1.17
% 0.91/1.17 Exiting with 1 proof.
% 0.91/1.17
% 0.91/1.17 Process 32349 exit (max_proofs) Thu Jun 16 16:02:36 2022
% 0.91/1.17 Prover9 interrupted
%------------------------------------------------------------------------------