TSTP Solution File: KLE010+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE010+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 2.11s 2.37s
% Output : Refutation 2.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE010+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n004.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 15:59:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.45/1.00 ============================== Prover9 ===============================
% 0.45/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.00 Process 19648 was started by sandbox2 on n004.cluster.edu,
% 0.45/1.00 Thu Jun 16 15:59:09 2022
% 0.45/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19494_n004.cluster.edu".
% 0.45/1.00 ============================== end of head ===========================
% 0.45/1.00
% 0.45/1.00 ============================== INPUT =================================
% 0.45/1.00
% 0.45/1.00 % Reading from file /tmp/Prover9_19494_n004.cluster.edu
% 0.45/1.00
% 0.45/1.00 set(prolog_style_variables).
% 0.45/1.00 set(auto2).
% 0.45/1.00 % set(auto2) -> set(auto).
% 0.45/1.00 % set(auto) -> set(auto_inference).
% 0.45/1.00 % set(auto) -> set(auto_setup).
% 0.45/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.00 % set(auto) -> set(auto_limits).
% 0.45/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.00 % set(auto) -> set(auto_denials).
% 0.45/1.00 % set(auto) -> set(auto_process).
% 0.45/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.00 % set(auto2) -> assign(stats, some).
% 0.45/1.00 % set(auto2) -> clear(echo_input).
% 0.45/1.00 % set(auto2) -> set(quiet).
% 0.45/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.00 % set(auto2) -> clear(print_given).
% 0.45/1.00 assign(lrs_ticks,-1).
% 0.45/1.00 assign(sos_limit,10000).
% 0.45/1.00 assign(order,kbo).
% 0.45/1.00 set(lex_order_vars).
% 0.45/1.00 clear(print_given).
% 0.45/1.00
% 0.45/1.00 % formulas(sos). % not echoed (19 formulas)
% 0.45/1.00
% 0.45/1.00 ============================== end of input ==========================
% 0.45/1.00
% 0.45/1.00 % From the command line: assign(max_seconds, 300).
% 0.45/1.00
% 0.45/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.00
% 0.45/1.00 % Formulas that are not ordinary clauses:
% 0.45/1.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 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].
% 0.45/1.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 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].
% 0.45/1.00 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 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].
% 0.45/1.00 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].
% 0.45/1.00 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 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].
% 2.11/2.37 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 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].
% 2.11/2.37 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].
% 2.11/2.37 19 -(all X0 all X1 (test(X1) & test(X0) -> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.11/2.37
% 2.11/2.37 ============================== end of process non-clausal formulas ===
% 2.11/2.37
% 2.11/2.37 ============================== PROCESS INITIAL CLAUSES ===============
% 2.11/2.37
% 2.11/2.37 ============================== PREDICATE ELIMINATION =================
% 2.11/2.37 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.11/2.37 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.11/2.37 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.11/2.37 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 2.11/2.37 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.11/2.37 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 2.11/2.37 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 2.11/2.37 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 2.11/2.37 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.11/2.37 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 2.11/2.37 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 2.11/2.37 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 2.11/2.37 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 2.11/2.37 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.11/2.37 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 2.11/2.37 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 2.11/2.37 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 2.11/2.37 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 2.11/2.37 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.11/2.37 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.11/2.37
% 2.11/2.37 ============================== end predicate elimination =============
% 2.11/2.37
% 2.11/2.37 Auto_denials: (non-Horn, no changes).
% 2.11/2.37
% 2.11/2.37 Term ordering decisions:
% 2.11/2.37 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 2.11/2.37
% 2.11/2.37 ============================== end of process initial clauses ========
% 2.11/2.37
% 2.11/2.37 ============================== CLAUSES FOR SEARCH ====================
% 2.11/2.37
% 2.11/2.37 ============================== end of clauses for search =============
% 2.11/2.37
% 2.11/2.37 ============================== SEARCH ================================
% 2.11/2.37
% 2.11/2.37 % Starting search at 0.01 seconds.
% 2.11/2.37
% 2.11/2.37 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 102 (0.00 of 0.95 sec).
% 2.11/2.37
% 2.11/2.37 ============================== PROOF =================================
% 2.11/2.37 % SZS status Theorem
% 2.11/2.37 % SZS output start Refutation
% 2.11/2.37
% 2.11/2.37 % Proof 1 at 1.35 (+ 0.03) seconds.
% 2.11/2.37 % Length of proof is 175.
% 2.11/2.37 % Level of proof is 22.
% 2.11/2.37 % Maximum clause weight is 26.000.
% 2.11/2.37 % Given clauses 595.
% 2.11/2.37
% 2.11/2.37 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 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].
% 2.11/2.37 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 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].
% 2.11/2.37 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 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].
% 2.11/2.37 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].
% 2.11/2.37 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 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].
% 2.11/2.37 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.11/2.37 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].
% 2.11/2.37 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].
% 2.11/2.37 19 -(all X0 all X1 (test(X1) & test(X0) -> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.11/2.37 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.11/2.37 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.11/2.37 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.11/2.37 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.11/2.37 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 2.11/2.37 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.11/2.37 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.11/2.37 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 2.11/2.37 30 test(c2) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.11/2.37 31 test(c1) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.11/2.37 32 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.11/2.37 33 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 2.11/2.37 34 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 2.11/2.37 35 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 2.11/2.37 36 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.11/2.37 37 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 2.11/2.37 38 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.11/2.37 39 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.11/2.37 40 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 2.11/2.37 41 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(40),rewrite([39(2)]),flip(a)].
% 2.11/2.37 42 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 2.11/2.37 43 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.11/2.37 44 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(43),flip(a)].
% 2.11/2.37 45 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.11/2.37 46 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(45),flip(a)].
% 2.11/2.37 47 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)].
% 2.11/2.37 48 addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1)))) != one. [copy(47),rewrite([46(8),39(10),39(15),41(15,R),39(14),39(21),41(21,R),39(20),41(20,R),39(19)])].
% 2.11/2.37 49 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)].
% 2.11/2.37 50 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(49),flip(c)].
% 2.11/2.37 51 -test(A) | -test(B) | c(multiplication(A,B)) = addition(c(A),c(B)) # label(test_deMorgan2) # label(axiom). [clausify(18)].
% 2.11/2.37 52 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(A,B)). [copy(51),flip(c)].
% 2.11/2.37 53 multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 2.11/2.37 54 multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 2.11/2.37 55 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 2.11/2.37 56 -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 2.11/2.37 57 -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 2.11/2.37 58 -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 2.11/2.37 59 -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 2.11/2.37 60 -test(A) | c(A) != B | addition(A,B) = one. [copy(59),rewrite([39(4)])].
% 2.11/2.37 61 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 2.11/2.37 62 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 2.11/2.37 63 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 2.11/2.37 64 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(50,a,b),rewrite([33(5)])].
% 2.11/2.37 68 addition(A,addition(A,B)) = addition(A,B). [para(41(a,1),33(a,1)),rewrite([39(1),39(2),41(2,R),33(1),39(3)])].
% 2.11/2.37 69 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(32(a,1),44(a,2,2)),rewrite([36(3),39(3)])].
% 2.11/2.37 70 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(34(a,1),44(a,1,1)),rewrite([39(4)]),flip(a)].
% 2.11/2.37 72 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(42(a,1),46(a,1,1)),rewrite([39(6)])].
% 2.11/2.37 74 addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2))))) != one. [para(41(a,1),48(a,1,2)),rewrite([44(19)])].
% 2.11/2.37 75 addition(multiplication(c(c1),c(c2)),addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c2,c(c2)),c1))) != one. [para(41(a,1),48(a,1)),rewrite([46(20),39(19),41(19,R),39(18)])].
% 2.11/2.37 76 -test(A) | multiplication(c(B),c(A)) = c(addition(A,B)) | c(B) = zero. [resolve(50,a,38,a),rewrite([39(5)])].
% 2.11/2.37 77 -test(A) | multiplication(c(c1),c(A)) = c(addition(A,c1)). [resolve(50,a,31,a),rewrite([39(7)])].
% 2.11/2.37 78 -test(A) | multiplication(c(c2),c(A)) = c(addition(A,c2)). [resolve(50,a,30,a),rewrite([39(7)])].
% 2.11/2.37 80 -test(A) | multiplication(c(A),c(c1)) = c(addition(A,c1)). [resolve(50,b,31,a)].
% 2.11/2.37 82 -test(A) | addition(c(A),c(B)) = c(multiplication(B,A)) | c(B) = zero. [resolve(52,a,38,a),rewrite([39(4)])].
% 2.11/2.37 84 -test(A) | addition(c(A),c(c2)) = c(multiplication(c2,A)). [resolve(52,a,30,a),rewrite([39(5)])].
% 2.11/2.37 87 -test(A) | addition(c(A),c(c2)) = c(multiplication(A,c2)). [resolve(52,b,30,a)].
% 2.11/2.37 89 multiplication(c1,f1(c1)) = zero. [resolve(53,b,31,a)].
% 2.11/2.37 90 multiplication(c2,f1(c2)) = zero. [resolve(53,b,30,a)].
% 2.11/2.37 95 addition(c1,f1(c1)) = one. [resolve(55,b,31,a)].
% 2.11/2.37 96 addition(c2,f1(c2)) = one. [resolve(55,b,30,a)].
% 2.11/2.37 98 c(c1) != A | test(A). [resolve(56,a,31,a)].
% 2.11/2.37 99 c(c2) != A | test(A). [resolve(56,a,30,a)].
% 2.11/2.37 101 c(c1) != A | multiplication(A,c1) = zero. [resolve(57,a,31,a)].
% 2.11/2.37 102 c(c2) != A | multiplication(A,c2) = zero. [resolve(57,a,30,a)].
% 2.11/2.37 104 c(c1) != A | multiplication(c1,A) = zero. [resolve(58,a,31,a)].
% 2.11/2.37 105 c(c2) != A | multiplication(c2,A) = zero. [resolve(58,a,30,a)].
% 2.11/2.37 107 c(c1) != A | addition(A,c1) = one. [resolve(60,a,31,a),rewrite([39(5)])].
% 2.11/2.37 108 c(c2) != A | addition(A,c2) = one. [resolve(60,a,30,a),rewrite([39(5)])].
% 2.11/2.37 112 test(one). [resolve(62,c,32,a),rewrite([36(3),34(6)]),xx(a),xx(b)].
% 2.11/2.37 113 one != A | test(A). [para(32(a,1),62(c,1)),rewrite([36(2),37(5)]),flip(c),xx(a),xx(b)].
% 2.11/2.37 125 multiplication(c(c1),c(c1)) = c(c1). [resolve(64,a,31,a)].
% 2.11/2.37 126 multiplication(c(c2),c(c2)) = c(c2). [resolve(64,a,30,a)].
% 2.11/2.37 137 addition(one,f1(one)) = one. [resolve(112,a,55,b)].
% 2.11/2.37 138 f1(one) = zero. [resolve(112,a,54,b),rewrite([34(4)])].
% 2.11/2.37 142 addition(zero,one) = one. [back_rewrite(137),rewrite([138(3),39(3)])].
% 2.11/2.37 143 -test(zero) | c(zero) = one. [para(138(a,1),61(a,1)),rewrite([138(4)]),unit_del(c,112)].
% 2.11/2.37 144 test(zero). [resolve(142,a,62,c),rewrite([34(3),36(6)]),xx(a),xx(b)].
% 2.11/2.37 145 c(zero) = one. [back_unit_del(143),unit_del(a,144)].
% 2.11/2.37 148 -test(A) | addition(one,c(A)) = one. [resolve(144,a,52,b),rewrite([145(4),39(4),36(6),145(6)])].
% 2.11/2.37 167 multiplication(c2,addition(A,f1(c2))) = multiplication(c2,A). [para(90(a,1),44(a,1,1)),rewrite([69(4),39(6)]),flip(a)].
% 2.11/2.37 169 addition(zero,c2) = c2. [para(90(a,1),70(a,2,2)),rewrite([39(5),167(6),34(3),39(4)]),flip(a)].
% 2.11/2.37 194 addition(one,c2) = one. [para(96(a,1),68(a,1,2)),rewrite([39(3),96(7)])].
% 2.11/2.37 200 multiplication(addition(c1,multiplication(A,B)),f1(c1)) = multiplication(A,multiplication(B,f1(c1))). [para(89(a,1),72(a,1,2)),rewrite([39(6),69(6)]),flip(a)].
% 2.11/2.37 216 addition(A,multiplication(c2,A)) = A. [para(194(a,1),46(a,2,1)),rewrite([35(2),35(5)])].
% 2.11/2.37 217 test(c(c1)). [resolve(98,a,35,a(flip)),rewrite([35(4)])].
% 2.11/2.37 221 multiplication(A,c(c1)) != zero | multiplication(c(c1),A) != zero | addition(A,c(c1)) != one | c(c(c1)) = A. [resolve(217,a,63,d)].
% 2.11/2.37 225 c(c(c1)) != A | test(A). [resolve(217,a,56,a)].
% 2.11/2.37 258 test(c(c2)). [resolve(99,a,35,a(flip)),rewrite([35(4)])].
% 2.11/2.37 259 test(addition(zero,c(c2))). [resolve(99,a,32,a(flip)),rewrite([39(4)])].
% 2.11/2.37 261 multiplication(c(c(c2)),c(c(c2))) = c(c(c2)). [resolve(258,a,64,a)].
% 2.11/2.37 262 multiplication(A,c(c2)) != zero | multiplication(c(c2),A) != zero | addition(A,c(c2)) != one | c(c(c2)) = A. [resolve(258,a,63,d)].
% 2.11/2.37 266 c(c(c2)) != A | test(A). [resolve(258,a,56,a)].
% 2.11/2.37 297 multiplication(c(A),c(c1)) = c(addition(A,c1)) | c(A) = zero. [resolve(76,a,31,a),rewrite([39(6)])].
% 2.11/2.37 345 multiplication(c(c1),c(c2)) = c(addition(c1,c2)). [resolve(77,a,30,a),rewrite([39(8)])].
% 2.11/2.37 346 addition(c(addition(c1,c2)),addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c2,c(c2)),c1))) != one. [back_rewrite(75),rewrite([345(5)])].
% 2.11/2.37 353 multiplication(c(c2),c(c1)) = c(addition(c1,c2)). [resolve(78,a,31,a)].
% 2.11/2.37 362 multiplication(c(addition(zero,c(c2))),c(c1)) = c(addition(zero,addition(c1,c(c2)))). [resolve(80,a,259,a),rewrite([39(14),41(14,R),39(13)])].
% 2.11/2.37 363 multiplication(c(c(c2)),c(c1)) = c(addition(c1,c(c2))). [resolve(80,a,258,a),rewrite([39(10)])].
% 2.11/2.37 366 test(c(c(c1))). [resolve(225,a,216,a(flip)),rewrite([216(9)])].
% 2.11/2.37 371 multiplication(c(c1),c(c(c(c1)))) = c(addition(c1,c(c(c1)))). [resolve(366,a,77,a),rewrite([39(12)])].
% 2.11/2.37 407 test(c(c(c2))). [resolve(266,a,216,a(flip)),rewrite([216(9)])].
% 2.11/2.37 418 multiplication(c(c2),c(c(c(c2)))) = c(addition(c2,c(c(c2)))). [resolve(407,a,78,a),rewrite([39(12)])].
% 2.11/2.37 456 multiplication(c(c1),multiplication(c(c1),A)) = multiplication(c(c1),A). [para(125(a,1),42(a,1,1)),flip(a)].
% 2.11/2.37 473 addition(c(A),c(B)) = c(multiplication(B,A)) | c(B) = zero | c(A) = zero. [resolve(82,a,38,a)].
% 2.11/2.37 479 addition(zero,c(c2)) = c(c2). [para(126(a,1),69(a,1,2)),rewrite([126(9)])].
% 2.11/2.37 483 c(addition(zero,addition(c1,c(c2)))) = c(addition(c1,c(c2))). [back_rewrite(362),rewrite([479(4),363(6)]),flip(a)].
% 2.11/2.37 485 addition(one,c(c(c(c2)))) = one. [resolve(148,a,407,a)].
% 2.11/2.37 487 addition(one,c(c(c(c1)))) = one. [resolve(148,a,366,a)].
% 2.11/2.37 490 addition(one,c(c1)) = one. [resolve(148,a,31,a)].
% 2.11/2.37 491 addition(one,c(c2)) = one. [resolve(148,a,30,a)].
% 2.11/2.37 493 addition(A,multiplication(c(c1),A)) = A. [para(490(a,1),46(a,2,1)),rewrite([35(2),35(6)])].
% 2.11/2.37 503 addition(A,multiplication(c(c2),A)) = A. [para(491(a,1),46(a,2,1)),rewrite([35(2),35(6)])].
% 2.11/2.37 707 addition(A,multiplication(A,c(c(c(c2))))) = A. [para(485(a,1),44(a,2,2)),rewrite([34(2),34(8)])].
% 2.11/2.37 709 addition(A,multiplication(A,c(c(c(c1))))) = A. [para(487(a,1),44(a,2,2)),rewrite([34(2),34(8)])].
% 2.11/2.37 806 multiplication(c(c1),c1) = zero. [resolve(101,a,493,a(flip)),rewrite([125(7),33(5)])].
% 2.11/2.37 812 multiplication(c(c1),addition(A,c1)) = multiplication(c(c1),A). [para(806(a,1),44(a,1,1)),rewrite([69(5),39(7)]),flip(a)].
% 2.11/2.37 855 multiplication(c(c2),c2) = zero. [resolve(102,a,503,a(flip)),rewrite([126(7),33(5)])].
% 2.11/2.37 888 multiplication(c1,c(c1)) = zero. [resolve(104,a,493,a(flip)),rewrite([125(8),33(6)])].
% 2.11/2.37 898 multiplication(c2,c(c2)) = zero. [resolve(105,a,503,a(flip)),rewrite([126(8),33(6)])].
% 2.11/2.37 916 addition(c1,c(c1)) = one. [resolve(107,a,493,a(flip)),rewrite([125(7),33(5),39(4)])].
% 2.11/2.37 920 addition(c2,addition(c(addition(c1,c2)),multiplication(addition(c2,c(c2)),c1))) != one. [back_rewrite(346),rewrite([916(8),35(7),41(13,R),39(12)])].
% 2.11/2.37 922 addition(c2,c(c2)) = one. [resolve(108,a,503,a(flip)),rewrite([126(7),33(5),39(4)])].
% 2.11/2.37 924 addition(c1,addition(c2,c(addition(c1,c2)))) != one. [back_rewrite(920),rewrite([922(9),35(8),39(7),41(8,R),39(7)])].
% 2.11/2.37 928 addition(one,multiplication(c1,c2)) != one. [back_rewrite(74),rewrite([922(7),35(6),922(10),34(8),916(7),39(5)])].
% 2.11/2.37 970 addition(addition(c1,c2),c(addition(c1,c2))) != one. [para(41(a,1),924(a,1)),rewrite([39(8)])].
% 2.11/2.37 971 -test(addition(c1,c2)). [ur(60,b,xx,c,970,a)].
% 2.11/2.37 972 c(addition(c1,c2)) = zero. [resolve(971,a,38,a)].
% 2.11/2.37 978 addition(c1,c2) != one. [ur(113,b,971,a),flip(a)].
% 2.11/2.37 986 multiplication(c(c2),c(c1)) = zero. [back_rewrite(353),rewrite([972(9)])].
% 2.11/2.37 990 multiplication(addition(A,c(c2)),c(c1)) = multiplication(A,c(c1)). [para(986(a,1),46(a,1,1)),rewrite([69(5),39(6)]),flip(a)].
% 2.11/2.37 1505 multiplication(c2,c2) = c2. [para(96(a,1),167(a,1,2)),rewrite([34(3)]),flip(a)].
% 2.11/2.37 1512 multiplication(c2,multiplication(c2,A)) = multiplication(c2,A). [para(1505(a,1),42(a,1,1)),flip(a)].
% 2.11/2.37 1851 test(addition(c(c2),c(addition(c2,c(c(c2)))))). [resolve(707,a,99,a(flip)),rewrite([418(9)])].
% 2.11/2.37 1867 test(addition(c(c1),c(addition(c1,c(c(c1)))))). [resolve(709,a,98,a(flip)),rewrite([371(9)])].
% 2.11/2.37 2767 c(addition(c(c2),c(addition(c2,c(c(c2)))))) != addition(c1,c2). [ur(56,a,1851,a,c,971,a)].
% 2.11/2.37 2857 addition(c(c2),c(addition(c(c1),c(addition(c1,c(c(c1))))))) = c(multiplication(addition(c(c1),c(addition(c1,c(c(c1))))),c2)). [resolve(1867,a,87,a),rewrite([39(13)])].
% 2.11/2.37 2860 c(multiplication(addition(c(c1),c(addition(c1,c(c(c1))))),c2)) = c(multiplication(c2,addition(c(c1),c(addition(c1,c(c(c1))))))). [resolve(1867,a,84,a),rewrite([39(13),2857(13)])].
% 2.11/2.37 2884 addition(c(c2),c(addition(c(c1),c(addition(c1,c(c(c1))))))) = c(multiplication(c2,addition(c(c1),c(addition(c1,c(c(c1))))))). [back_rewrite(2857),rewrite([2860(25)])].
% 2.11/2.37 3182 multiplication(c(c(c2)),multiplication(c(c(c2)),A)) = multiplication(c(c(c2)),A). [para(261(a,1),42(a,1,1)),flip(a)].
% 2.11/2.37 4448 multiplication(c(c1),f1(c1)) = f1(c1). [para(125(a,1),200(a,1,1,2)),rewrite([916(4),35(4),456(10)]),flip(a)].
% 2.11/2.37 4458 multiplication(addition(c1,c2),f1(c1)) = multiplication(c2,f1(c1)). [para(1505(a,1),200(a,1,1,2)),rewrite([1512(12)])].
% 2.11/2.37 4467 multiplication(addition(c1,c(c(c2))),f1(c1)) = multiplication(c(c(c2)),f1(c1)). [para(261(a,1),200(a,1,1,2)),rewrite([3182(18)])].
% 2.11/2.37 5970 c(c(c1)) = c1. [resolve(221,c,916,a),rewrite([888(4),806(7)]),xx(a),xx(b)].
% 2.11/2.37 5980 c(multiplication(c2,c(c1))) = addition(c1,c(c2)). [back_rewrite(2884),rewrite([5970(8),33(7),33(7),5970(5),39(4),5970(11),33(10),33(10)]),flip(a)].
% 2.11/2.37 7270 f1(c1) = c(c1). [para(4448(a,1),812(a,2)),rewrite([39(6),95(6),34(4)]),flip(a)].
% 2.11/2.37 7525 multiplication(addition(c1,c(c(c2))),c(c1)) = c(addition(c1,c(c2))). [back_rewrite(4467),rewrite([7270(7),7270(13),363(14)])].
% 2.11/2.37 7531 multiplication(addition(c1,c2),c(c1)) = multiplication(c2,c(c1)). [back_rewrite(4458),rewrite([7270(5),7270(9)])].
% 2.11/2.37 7619 c(c(c2)) = c2. [resolve(262,c,922,a),rewrite([898(4),855(7)]),xx(a),xx(b)].
% 2.11/2.37 7626 c(addition(c1,c(c2))) = multiplication(c2,c(c1)). [back_rewrite(7525),rewrite([7619(4),7531(6)]),flip(a)].
% 2.11/2.37 7633 addition(c1,c2) != c2. [back_rewrite(2767),rewrite([7619(6),33(5),33(5),7619(3)]),flip(a)].
% 2.11/2.37 7647 c(addition(zero,addition(c1,c(c2)))) = multiplication(c2,c(c1)). [back_rewrite(483),rewrite([7626(12)])].
% 2.11/2.37 7915 c(addition(c1,multiplication(c2,c(c1)))) = zero | addition(c1,c(c2)) = zero. [para(5980(a,1),297(a,1,1)),rewrite([990(7),888(4),39(7),5980(14)]),flip(a)].
% 2.11/2.37 8856 c2 = zero | c1 = zero. [para(986(a,1),473(a,2,1)),rewrite([5970(3),7619(4),145(5),7619(8),5970(11)]),unit_del(a,978)].
% 2.11/2.37 8967 c1 = zero. [para(8856(a,1),928(a,1,2,2)),rewrite([36(7),39(6),142(6)]),xx(b)].
% 2.11/2.37 9002 c(c2) = zero. [back_rewrite(7915),rewrite([8967(1),8967(3),145(4),34(4),169(3),8967(5),479(8)]),merge(b)].
% 2.11/2.37 9004 c2 = one. [back_rewrite(7647),rewrite([8967(2),9002(4),33(4),33(3),145(2),8967(3),145(4),34(4)]),flip(a)].
% 2.11/2.37 9005 $F. [back_rewrite(7633),rewrite([8967(1),9004(2),142(3),9004(2)]),xx(a)].
% 2.11/2.37
% 2.11/2.37 % SZS output end Refutation
% 2.11/2.37 ============================== end of proof ==========================
% 2.11/2.37
% 2.11/2.37 ============================== STATISTICS ============================
% 2.11/2.37
% 2.11/2.37 Given=595. Generated=43757. Kept=8968. proofs=1.
% 2.11/2.37 Usable=320. Sos=4659. Demods=1393. Limbo=38, Disabled=3988. Hints=0.
% 2.11/2.37 Megabytes=9.95.
% 2.11/2.37 User_CPU=1.35, System_CPU=0.03, Wall_clock=2.
% 2.11/2.37
% 2.11/2.37 ============================== end of statistics =====================
% 2.11/2.37
% 2.11/2.37 ============================== end of search =========================
% 2.11/2.37
% 2.11/2.37 THEOREM PROVED
% 2.11/2.37 % SZS status Theorem
% 2.11/2.37
% 2.11/2.37 Exiting with 1 proof.
% 2.11/2.37
% 2.11/2.37 Process 19648 exit (max_proofs) Thu Jun 16 15:59:11 2022
% 2.11/2.37 Prover9 interrupted
%------------------------------------------------------------------------------