TSTP Solution File: KLE010+4 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE010+4 : 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 02:21:41 EDT 2022
% Result : Theorem 0.75s 1.16s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE010+4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % 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 11:51:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.01 ============================== Prover9 ===============================
% 0.72/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.01 Process 31843 was started by sandbox2 on n026.cluster.edu,
% 0.72/1.01 Thu Jun 16 11:51:09 2022
% 0.72/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31690_n026.cluster.edu".
% 0.72/1.01 ============================== end of head ===========================
% 0.72/1.01
% 0.72/1.01 ============================== INPUT =================================
% 0.72/1.01
% 0.72/1.01 % Reading from file /tmp/Prover9_31690_n026.cluster.edu
% 0.72/1.01
% 0.72/1.01 set(prolog_style_variables).
% 0.72/1.01 set(auto2).
% 0.72/1.01 % set(auto2) -> set(auto).
% 0.72/1.01 % set(auto) -> set(auto_inference).
% 0.72/1.01 % set(auto) -> set(auto_setup).
% 0.72/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.01 % set(auto) -> set(auto_limits).
% 0.72/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.01 % set(auto) -> set(auto_denials).
% 0.72/1.01 % set(auto) -> set(auto_process).
% 0.72/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.01 % set(auto2) -> assign(stats, some).
% 0.72/1.01 % set(auto2) -> clear(echo_input).
% 0.72/1.01 % set(auto2) -> set(quiet).
% 0.72/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.01 % set(auto2) -> clear(print_given).
% 0.72/1.01 assign(lrs_ticks,-1).
% 0.72/1.01 assign(sos_limit,10000).
% 0.72/1.01 assign(order,kbo).
% 0.72/1.01 set(lex_order_vars).
% 0.72/1.01 clear(print_given).
% 0.72/1.01
% 0.72/1.01 % formulas(sos). % not echoed (19 formulas)
% 0.72/1.01
% 0.72/1.01 ============================== end of input ==========================
% 0.72/1.01
% 0.72/1.01 % From the command line: assign(max_seconds, 300).
% 0.72/1.01
% 0.72/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.01
% 0.72/1.01 % Formulas that are not ordinary clauses:
% 0.72/1.01 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 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].
% 0.72/1.01 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 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].
% 0.72/1.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 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].
% 0.72/1.01 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].
% 0.72/1.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 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].
% 0.75/1.16 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 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].
% 0.75/1.16 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].
% 0.75/1.16 19 -(all X0 all X1 (test(X1) & test(X0) -> leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.16
% 0.75/1.16 ============================== end of process non-clausal formulas ===
% 0.75/1.16
% 0.75/1.16 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.16
% 0.75/1.16 ============================== PREDICATE ELIMINATION =================
% 0.75/1.16 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.75/1.16 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.75/1.16 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.16 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 0.75/1.16 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.16 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.75/1.16 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.16 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.75/1.16 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.75/1.16 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 0.75/1.16 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 0.75/1.16 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 0.75/1.16 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 0.75/1.16 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.75/1.16 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.75/1.16 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.16 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.75/1.16 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 0.75/1.16
% 0.75/1.16 ============================== end predicate elimination =============
% 0.75/1.16
% 0.75/1.16 Auto_denials: (non-Horn, no changes).
% 0.75/1.16
% 0.75/1.16 Term ordering decisions:
% 0.75/1.16 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 0.75/1.16
% 0.75/1.16 ============================== end of process initial clauses ========
% 0.75/1.16
% 0.75/1.16 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.16
% 0.75/1.16 ============================== end of clauses for search =============
% 0.75/1.16
% 0.75/1.16 ============================== SEARCH ================================
% 0.75/1.16
% 0.75/1.16 % Starting search at 0.02 seconds.
% 0.75/1.16
% 0.75/1.16 ============================== PROOF =================================
% 0.75/1.16 % SZS status Theorem
% 0.75/1.16 % SZS output start Refutation
% 0.75/1.16
% 0.75/1.16 % Proof 1 at 0.16 (+ 0.00) seconds.
% 0.75/1.16 % Length of proof is 100.
% 0.75/1.16 % Level of proof is 17.
% 0.75/1.16 % Maximum clause weight is 46.000.
% 0.75/1.16 % Given clauses 227.
% 0.75/1.16
% 0.75/1.16 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 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].
% 0.75/1.16 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 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].
% 0.75/1.16 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].
% 0.75/1.16 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 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].
% 0.75/1.16 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.16 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].
% 0.75/1.16 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].
% 0.75/1.16 19 -(all X0 all X1 (test(X1) & test(X0) -> leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.16 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.75/1.16 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.75/1.16 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.16 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.16 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.75/1.16 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.75/1.16 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.16 28 test(c2) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.75/1.16 29 test(c1) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.75/1.16 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.75/1.16 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.75/1.16 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.75/1.16 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.75/1.16 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.75/1.16 36 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 0.75/1.16 37 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.75/1.16 38 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.75/1.16 39 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(38),rewrite([37(2)]),flip(a)].
% 0.75/1.16 41 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.75/1.16 42 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(41),flip(a)].
% 0.75/1.16 43 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.75/1.16 44 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(43),flip(a)].
% 0.75/1.16 45 -leq(one,addition(addition(addition(addition(multiplication(c2,c1),multiplication(c(c2),c1)),multiplication(c1,c2)),multiplication(c(c1),c2)),multiplication(c(c1),c(c2)))) | -leq(addition(addition(addition(addition(multiplication(c2,c1),multiplication(c(c2),c1)),multiplication(c1,c2)),multiplication(c(c1),c2)),multiplication(c(c1),c(c2))),one) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.75/1.16 46 -leq(one,addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1))))) | -leq(addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1)))),one). [copy(45),rewrite([44(9),37(11),37(16),39(16,R),37(15),37(22),39(22,R),37(21),39(21,R),37(20),44(31),37(33),37(38),39(38,R),37(37),37(44),39(44,R),37(43),39(43,R),37(42)])].
% 0.75/1.16 48 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.75/1.16 49 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)].
% 0.75/1.16 50 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(49),flip(c)].
% 0.75/1.16 51 -test(A) | -test(B) | c(multiplication(A,B)) = addition(c(A),c(B)) # label(test_deMorgan2) # label(axiom). [clausify(18)].
% 0.75/1.16 52 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(A,B)). [copy(51),flip(c)].
% 0.75/1.16 54 multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.75/1.16 55 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.75/1.16 59 -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 0.75/1.16 60 -test(A) | c(A) != B | addition(A,B) = one. [copy(59),rewrite([37(4)])].
% 0.75/1.16 61 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.75/1.16 62 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.75/1.16 64 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(50,a,b),rewrite([31(5)])].
% 0.75/1.16 68 addition(A,addition(A,B)) = addition(A,B). [para(39(a,1),31(a,1)),rewrite([37(1),37(2),39(2,R),31(1),37(3)])].
% 0.75/1.16 69 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),42(a,2,2)),rewrite([34(3),37(3)])].
% 0.75/1.16 75 -leq(one,addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1))))) | -leq(addition(multiplication(c(c1),c(c2)),addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c2,c(c2)),c1))),one). [para(39(a,1),46(b,1)),rewrite([44(43),37(42),39(42,R),37(41)])].
% 0.75/1.16 81 -test(A) | multiplication(c(c1),c(A)) = c(addition(A,c1)). [resolve(50,a,29,a),rewrite([37(7)])].
% 0.75/1.16 87 -test(A) | addition(c(A),c(c1)) = c(multiplication(c1,A)). [resolve(52,a,29,a),rewrite([37(5)])].
% 0.75/1.16 88 -test(A) | addition(c(A),c(c2)) = c(multiplication(c2,A)). [resolve(52,a,28,a),rewrite([37(5)])].
% 0.75/1.16 99 addition(c1,f1(c1)) = one. [resolve(55,b,29,a)].
% 0.75/1.16 100 addition(c2,f1(c2)) = one. [resolve(55,b,28,a)].
% 0.75/1.16 111 c(c1) != A | addition(A,c1) = one. [resolve(60,a,29,a),rewrite([37(5)])].
% 0.75/1.16 112 c(c2) != A | addition(A,c2) = one. [resolve(60,a,28,a),rewrite([37(5)])].
% 0.75/1.16 113 c(f1(A)) = A | -test(A) | c(f1(A)) = zero. [resolve(61,a,36,a)].
% 0.75/1.16 114 c(f1(zero)) = zero | -test(zero). [factor(113,a,c)].
% 0.75/1.16 116 test(one). [resolve(62,c,30,a),rewrite([34(3),32(6)]),xx(a),xx(b)].
% 0.75/1.16 129 multiplication(c(c1),c(c1)) = c(c1). [resolve(64,a,29,a)].
% 0.75/1.16 130 multiplication(c(c2),c(c2)) = c(c2). [resolve(64,a,28,a)].
% 0.75/1.16 134 leq(A,addition(A,B)). [resolve(68,a,48,b)].
% 0.75/1.16 138 -leq(one,addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2)))))) | -leq(addition(multiplication(c(c1),c(c2)),addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c2,c(c2)),c1))),one). [para(39(a,1),75(a,2,2)),rewrite([42(20)])].
% 0.75/1.16 146 addition(one,f1(one)) = one. [resolve(116,a,55,b)].
% 0.75/1.16 147 f1(one) = zero. [resolve(116,a,54,b),rewrite([32(4)])].
% 0.75/1.16 151 addition(zero,one) = one. [back_rewrite(146),rewrite([147(3),37(3)])].
% 0.75/1.16 152 -test(zero) | c(zero) = one. [para(147(a,1),61(a,1)),rewrite([147(4)]),unit_del(c,116)].
% 0.75/1.16 157 test(zero). [resolve(151,a,62,c),rewrite([32(3),34(6)]),xx(a),xx(b)].
% 0.75/1.16 159 c(zero) = one. [back_unit_del(152),unit_del(a,157)].
% 0.75/1.16 160 c(f1(zero)) = zero. [back_unit_del(114),unit_del(b,157)].
% 0.75/1.16 161 addition(zero,f1(zero)) = one. [resolve(157,a,55,b)].
% 0.75/1.16 162 -test(A) | addition(one,c(A)) = one. [resolve(157,a,52,b),rewrite([159(4),37(4),34(6),159(6)])].
% 0.75/1.16 233 addition(one,c1) = one. [para(99(a,1),68(a,1,2)),rewrite([37(3),99(7)])].
% 0.75/1.16 250 addition(one,c2) = one. [para(100(a,1),68(a,1,2)),rewrite([37(3),100(7)])].
% 0.75/1.16 382 multiplication(A,f1(zero)) = A. [para(161(a,1),42(a,2,2)),rewrite([34(2),69(5),32(5)])].
% 0.75/1.16 392 multiplication(c(c1),c(c2)) = c(addition(c1,c2)). [resolve(81,a,28,a),rewrite([37(8)])].
% 0.75/1.16 394 -leq(one,addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2)))))) | -leq(addition(c(addition(c1,c2)),addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c2,c(c2)),c1))),one). [back_rewrite(138),rewrite([392(25)])].
% 0.75/1.16 399 f1(zero) = one. [para(382(a,1),33(a,1)),flip(a)].
% 0.75/1.16 400 c(one) = zero. [back_rewrite(160),rewrite([399(2)])].
% 0.75/1.16 548 addition(one,c(c1)) = one. [resolve(87,a,157,a),rewrite([159(2),34(7),159(6)])].
% 0.75/1.16 552 addition(A,multiplication(c(c1),A)) = A. [para(548(a,1),44(a,2,1)),rewrite([33(2),33(6)])].
% 0.75/1.16 570 addition(one,c(c2)) = one. [resolve(88,a,157,a),rewrite([159(2),34(7),159(6)])].
% 0.75/1.16 574 addition(A,multiplication(c(c2),A)) = A. [para(570(a,1),44(a,2,1)),rewrite([33(2),33(6)])].
% 0.75/1.16 1029 addition(c1,c(c1)) = one. [resolve(111,a,552,a(flip)),rewrite([129(7),31(5),37(4)])].
% 0.75/1.16 1038 -leq(one,addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2)))))) | -leq(addition(c2,addition(c(addition(c1,c2)),multiplication(addition(c2,c(c2)),c1))),one). [back_rewrite(394),rewrite([1029(28),33(27),39(33,R),37(32)])].
% 0.75/1.16 1063 addition(c2,c(c2)) = one. [resolve(112,a,574,a(flip)),rewrite([130(7),31(5),37(4)])].
% 0.75/1.16 1066 -leq(addition(c1,addition(c2,c(addition(c1,c2)))),one). [back_rewrite(1038),rewrite([1063(8),33(7),1063(11),32(9),1029(8),37(6),1063(16),33(15),37(14),39(15,R),37(14)]),unit_del(a,134)].
% 0.75/1.16 1113 addition(one,addition(c1,addition(c2,c(addition(c1,c2))))) != one. [ur(48,a,1066,a),rewrite([37(10)])].
% 0.75/1.16 1118 addition(one,addition(c2,c(addition(c1,c2)))) != one. [para(39(a,1),1113(a,1)),rewrite([233(9),37(8)])].
% 0.75/1.16 1160 addition(one,c(addition(c1,c2))) != one. [para(39(a,1),1118(a,1)),rewrite([250(7),37(6)])].
% 0.75/1.16 1161 -test(addition(c1,c2)). [ur(162,b,1160,a)].
% 0.75/1.16 1162 c(addition(c1,c2)) != zero. [ur(60,a,116,a,c,1160,a),rewrite([400(2)]),flip(a)].
% 0.75/1.16 1187 $F. [resolve(1161,a,36,a),unit_del(a,1162)].
% 0.75/1.16
% 0.75/1.16 % SZS output end Refutation
% 0.75/1.16 ============================== end of proof ==========================
% 0.75/1.16
% 0.75/1.16 ============================== STATISTICS ============================
% 0.75/1.16
% 0.75/1.16 Given=227. Generated=3913. Kept=1152. proofs=1.
% 0.75/1.16 Usable=196. Sos=712. Demods=369. Limbo=0, Disabled=281. Hints=0.
% 0.75/1.16 Megabytes=1.14.
% 0.75/1.16 User_CPU=0.16, System_CPU=0.00, Wall_clock=0.
% 0.75/1.16
% 0.75/1.16 ============================== end of statistics =====================
% 0.75/1.16
% 0.75/1.16 ============================== end of search =========================
% 0.75/1.16
% 0.75/1.16 THEOREM PROVED
% 0.75/1.16 % SZS status Theorem
% 0.75/1.16
% 0.75/1.16 Exiting with 1 proof.
% 0.75/1.16
% 0.75/1.16 Process 31843 exit (max_proofs) Thu Jun 16 11:51:09 2022
% 0.75/1.16 Prover9 interrupted
%------------------------------------------------------------------------------