TSTP Solution File: KLE011+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE011+3 : 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 02:21:42 EDT 2022
% Result : Theorem 2.26s 2.54s
% Output : Refutation 2.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : KLE011+3 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.37 % Computer : n003.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Thu Jun 16 10:40:26 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.53/1.09 ============================== Prover9 ===============================
% 0.53/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.53/1.09 Process 16771 was started by sandbox2 on n003.cluster.edu,
% 0.53/1.09 Thu Jun 16 10:40:27 2022
% 0.53/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16616_n003.cluster.edu".
% 0.53/1.09 ============================== end of head ===========================
% 0.53/1.09
% 0.53/1.09 ============================== INPUT =================================
% 0.53/1.09
% 0.53/1.09 % Reading from file /tmp/Prover9_16616_n003.cluster.edu
% 0.53/1.09
% 0.53/1.09 set(prolog_style_variables).
% 0.53/1.09 set(auto2).
% 0.53/1.09 % set(auto2) -> set(auto).
% 0.53/1.09 % set(auto) -> set(auto_inference).
% 0.53/1.09 % set(auto) -> set(auto_setup).
% 0.53/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.53/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.53/1.09 % set(auto) -> set(auto_limits).
% 0.53/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.53/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.53/1.09 % set(auto) -> set(auto_denials).
% 0.53/1.09 % set(auto) -> set(auto_process).
% 0.53/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.53/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.53/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.53/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.53/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.53/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.53/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.53/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.53/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.53/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.53/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.53/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.53/1.09 % set(auto2) -> assign(stats, some).
% 0.53/1.09 % set(auto2) -> clear(echo_input).
% 0.53/1.09 % set(auto2) -> set(quiet).
% 0.53/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.53/1.09 % set(auto2) -> clear(print_given).
% 0.53/1.09 assign(lrs_ticks,-1).
% 0.53/1.09 assign(sos_limit,10000).
% 0.53/1.09 assign(order,kbo).
% 0.53/1.09 set(lex_order_vars).
% 0.53/1.09 clear(print_given).
% 0.53/1.09
% 0.53/1.09 % formulas(sos). % not echoed (19 formulas)
% 0.53/1.09
% 0.53/1.09 ============================== end of input ==========================
% 0.53/1.09
% 0.53/1.09 % From the command line: assign(max_seconds, 300).
% 0.53/1.09
% 0.53/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.53/1.09
% 0.53/1.09 % Formulas that are not ordinary clauses:
% 0.53/1.09 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.09 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].
% 0.53/1.09 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.09 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.09 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].
% 0.53/1.09 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.09 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.09 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].
% 0.53/1.09 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].
% 0.53/1.09 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.09 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.09 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.09 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.09 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].
% 2.26/2.54 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 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].
% 2.26/2.54 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].
% 2.26/2.54 19 -(all X0 all X1 (test(X1) & test(X0) -> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.26/2.54
% 2.26/2.54 ============================== end of process non-clausal formulas ===
% 2.26/2.54
% 2.26/2.54 ============================== PROCESS INITIAL CLAUSES ===============
% 2.26/2.54
% 2.26/2.54 ============================== PREDICATE ELIMINATION =================
% 2.26/2.54 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.26/2.54 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.26/2.54 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.26/2.54 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 2.26/2.54 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.26/2.54 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 2.26/2.54 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 2.26/2.54 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 2.26/2.54 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.26/2.54 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 2.26/2.54 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 2.26/2.54 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 2.26/2.54 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 2.26/2.54 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.26/2.54 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 2.26/2.54 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 2.26/2.54 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 2.26/2.54 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 2.26/2.54 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.26/2.54 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.26/2.54
% 2.26/2.54 ============================== end predicate elimination =============
% 2.26/2.54
% 2.26/2.54 Auto_denials: (non-Horn, no changes).
% 2.26/2.54
% 2.26/2.54 Term ordering decisions:
% 2.26/2.54 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 2.26/2.54
% 2.26/2.54 ============================== end of process initial clauses ========
% 2.26/2.54
% 2.26/2.54 ============================== CLAUSES FOR SEARCH ====================
% 2.26/2.54
% 2.26/2.54 ============================== end of clauses for search =============
% 2.26/2.54
% 2.26/2.54 ============================== SEARCH ================================
% 2.26/2.54
% 2.26/2.54 % Starting search at 0.01 seconds.
% 2.26/2.54
% 2.26/2.54 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 104 (0.00 of 1.03 sec).
% 2.26/2.54
% 2.26/2.54 ============================== PROOF =================================
% 2.26/2.54 % SZS status Theorem
% 2.26/2.54 % SZS output start Refutation
% 2.26/2.54
% 2.26/2.54 % Proof 1 at 1.43 (+ 0.04) seconds.
% 2.26/2.54 % Length of proof is 174.
% 2.26/2.54 % Level of proof is 22.
% 2.26/2.54 % Maximum clause weight is 26.000.
% 2.26/2.54 % Given clauses 590.
% 2.26/2.54
% 2.26/2.54 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 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].
% 2.26/2.54 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 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].
% 2.26/2.54 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 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].
% 2.26/2.54 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].
% 2.26/2.54 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 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].
% 2.26/2.54 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.26/2.54 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].
% 2.26/2.54 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].
% 2.26/2.54 19 -(all X0 all X1 (test(X1) & test(X0) -> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.26/2.54 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.26/2.54 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.26/2.54 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.26/2.54 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.26/2.54 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 2.26/2.54 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.26/2.54 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.26/2.54 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 2.26/2.54 30 test(c2) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.26/2.54 31 test(c1) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.26/2.54 32 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.26/2.54 33 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 2.26/2.54 34 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 2.26/2.54 35 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 2.26/2.54 36 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.26/2.54 37 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 2.26/2.54 38 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.26/2.54 39 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.26/2.54 40 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 2.26/2.54 41 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(40),rewrite([39(2)]),flip(a)].
% 2.26/2.54 42 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 2.26/2.54 43 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.26/2.54 44 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(43),flip(a)].
% 2.26/2.54 45 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.26/2.54 46 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(45),flip(a)].
% 2.26/2.54 47 addition(addition(multiplication(addition(c2,c(c2)),c1),multiplication(addition(c1,c(c1)),c2)),multiplication(c(c1),c(c2))) != one # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.26/2.54 48 addition(multiplication(c(c1),c(c2)),addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c2,c(c2)),c1))) != one. [copy(47),rewrite([39(13),39(19)])].
% 2.26/2.54 49 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)].
% 2.26/2.54 50 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(49),flip(c)].
% 2.26/2.54 51 -test(A) | -test(B) | c(multiplication(A,B)) = addition(c(A),c(B)) # label(test_deMorgan2) # label(axiom). [clausify(18)].
% 2.26/2.54 52 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(A,B)). [copy(51),flip(c)].
% 2.26/2.54 53 multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 2.26/2.54 54 multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 2.26/2.54 55 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 2.26/2.54 56 -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 2.26/2.54 57 -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 2.26/2.54 58 -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 2.26/2.54 59 -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 2.26/2.54 60 -test(A) | c(A) != B | addition(A,B) = one. [copy(59),rewrite([39(4)])].
% 2.26/2.54 61 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 2.26/2.54 62 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 2.26/2.54 63 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 2.26/2.54 64 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(50,a,b),rewrite([33(5)])].
% 2.26/2.54 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)])].
% 2.26/2.54 69 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(32(a,1),44(a,2,2)),rewrite([36(3),39(3)])].
% 2.26/2.54 70 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(34(a,1),44(a,1,1)),rewrite([39(4)]),flip(a)].
% 2.26/2.54 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)])].
% 2.26/2.54 74 -test(A) | multiplication(c(B),c(A)) = c(addition(A,B)) | c(B) = zero. [resolve(50,a,38,a),rewrite([39(5)])].
% 2.26/2.54 75 -test(A) | multiplication(c(c1),c(A)) = c(addition(A,c1)). [resolve(50,a,31,a),rewrite([39(7)])].
% 2.26/2.54 76 -test(A) | multiplication(c(c2),c(A)) = c(addition(A,c2)). [resolve(50,a,30,a),rewrite([39(7)])].
% 2.26/2.54 78 -test(A) | multiplication(c(A),c(c1)) = c(addition(A,c1)). [resolve(50,b,31,a)].
% 2.26/2.54 80 -test(A) | addition(c(A),c(B)) = c(multiplication(B,A)) | c(B) = zero. [resolve(52,a,38,a),rewrite([39(4)])].
% 2.26/2.54 82 -test(A) | addition(c(A),c(c2)) = c(multiplication(c2,A)). [resolve(52,a,30,a),rewrite([39(5)])].
% 2.26/2.54 85 -test(A) | addition(c(A),c(c2)) = c(multiplication(A,c2)). [resolve(52,b,30,a)].
% 2.26/2.54 87 multiplication(c1,f1(c1)) = zero. [resolve(53,b,31,a)].
% 2.26/2.54 88 multiplication(c2,f1(c2)) = zero. [resolve(53,b,30,a)].
% 2.26/2.54 93 addition(c1,f1(c1)) = one. [resolve(55,b,31,a)].
% 2.26/2.54 94 addition(c2,f1(c2)) = one. [resolve(55,b,30,a)].
% 2.26/2.54 96 c(c1) != A | test(A). [resolve(56,a,31,a)].
% 2.26/2.54 97 c(c2) != A | test(A). [resolve(56,a,30,a)].
% 2.26/2.54 99 c(c1) != A | multiplication(A,c1) = zero. [resolve(57,a,31,a)].
% 2.26/2.54 100 c(c2) != A | multiplication(A,c2) = zero. [resolve(57,a,30,a)].
% 2.26/2.54 102 c(c1) != A | multiplication(c1,A) = zero. [resolve(58,a,31,a)].
% 2.26/2.54 103 c(c2) != A | multiplication(c2,A) = zero. [resolve(58,a,30,a)].
% 2.26/2.54 105 c(c1) != A | addition(A,c1) = one. [resolve(60,a,31,a),rewrite([39(5)])].
% 2.26/2.54 106 c(c2) != A | addition(A,c2) = one. [resolve(60,a,30,a),rewrite([39(5)])].
% 2.26/2.54 110 test(one). [resolve(62,c,32,a),rewrite([36(3),34(6)]),xx(a),xx(b)].
% 2.26/2.54 111 one != A | test(A). [para(32(a,1),62(c,1)),rewrite([36(2),37(5)]),flip(c),xx(a),xx(b)].
% 2.26/2.54 123 multiplication(c(c1),c(c1)) = c(c1). [resolve(64,a,31,a)].
% 2.26/2.54 124 multiplication(c(c2),c(c2)) = c(c2). [resolve(64,a,30,a)].
% 2.26/2.54 135 addition(one,f1(one)) = one. [resolve(110,a,55,b)].
% 2.26/2.54 136 f1(one) = zero. [resolve(110,a,54,b),rewrite([34(4)])].
% 2.26/2.54 140 addition(zero,one) = one. [back_rewrite(135),rewrite([136(3),39(3)])].
% 2.26/2.54 141 -test(zero) | c(zero) = one. [para(136(a,1),61(a,1)),rewrite([136(4)]),unit_del(c,110)].
% 2.26/2.54 142 test(zero). [resolve(140,a,62,c),rewrite([34(3),36(6)]),xx(a),xx(b)].
% 2.26/2.54 143 c(zero) = one. [back_unit_del(141),unit_del(a,142)].
% 2.26/2.54 146 -test(A) | addition(one,c(A)) = one. [resolve(142,a,52,b),rewrite([143(4),39(4),36(6),143(6)])].
% 2.26/2.54 148 multiplication(c1,addition(A,f1(c1))) = multiplication(c1,A). [para(87(a,1),44(a,1,1)),rewrite([69(4),39(6)]),flip(a)].
% 2.26/2.54 162 addition(zero,c1) = c1. [para(87(a,1),70(a,2,2)),rewrite([39(5),148(6),34(3),39(4)]),flip(a)].
% 2.26/2.54 165 multiplication(c2,addition(A,f1(c2))) = multiplication(c2,A). [para(88(a,1),44(a,1,1)),rewrite([69(4),39(6)]),flip(a)].
% 2.26/2.54 167 addition(zero,c2) = c2. [para(88(a,1),70(a,2,2)),rewrite([39(5),165(6),34(3),39(4)]),flip(a)].
% 2.26/2.54 192 addition(one,c2) = one. [para(94(a,1),68(a,1,2)),rewrite([39(3),94(7)])].
% 2.26/2.54 198 multiplication(addition(c1,multiplication(A,B)),f1(c1)) = multiplication(A,multiplication(B,f1(c1))). [para(87(a,1),72(a,1,2)),rewrite([39(6),69(6)]),flip(a)].
% 2.26/2.54 214 addition(A,multiplication(c2,A)) = A. [para(192(a,1),46(a,2,1)),rewrite([35(2),35(5)])].
% 2.26/2.54 215 test(c(c1)). [resolve(96,a,35,a(flip)),rewrite([35(4)])].
% 2.26/2.54 219 multiplication(A,c(c1)) != zero | multiplication(c(c1),A) != zero | addition(A,c(c1)) != one | c(c(c1)) = A. [resolve(215,a,63,d)].
% 2.26/2.54 223 c(c(c1)) != A | test(A). [resolve(215,a,56,a)].
% 2.26/2.54 256 test(c(c2)). [resolve(97,a,35,a(flip)),rewrite([35(4)])].
% 2.26/2.54 257 test(addition(zero,c(c2))). [resolve(97,a,32,a(flip)),rewrite([39(4)])].
% 2.26/2.54 259 multiplication(c(c(c2)),c(c(c2))) = c(c(c2)). [resolve(256,a,64,a)].
% 2.26/2.54 260 multiplication(A,c(c2)) != zero | multiplication(c(c2),A) != zero | addition(A,c(c2)) != one | c(c(c2)) = A. [resolve(256,a,63,d)].
% 2.26/2.54 264 c(c(c2)) != A | test(A). [resolve(256,a,56,a)].
% 2.26/2.54 295 multiplication(c(A),c(c1)) = c(addition(A,c1)) | c(A) = zero. [resolve(74,a,31,a),rewrite([39(6)])].
% 2.26/2.54 343 multiplication(c(c1),c(c2)) = c(addition(c1,c2)). [resolve(75,a,30,a),rewrite([39(8)])].
% 2.26/2.54 344 addition(c(addition(c1,c2)),addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c2,c(c2)),c1))) != one. [back_rewrite(48),rewrite([343(5)])].
% 2.26/2.54 350 multiplication(c(c2),c(c1)) = c(addition(c1,c2)). [resolve(76,a,31,a)].
% 2.26/2.54 359 multiplication(c(addition(zero,c(c2))),c(c1)) = c(addition(zero,addition(c1,c(c2)))). [resolve(78,a,257,a),rewrite([39(14),41(14,R),39(13)])].
% 2.26/2.54 360 multiplication(c(c(c2)),c(c1)) = c(addition(c1,c(c2))). [resolve(78,a,256,a),rewrite([39(10)])].
% 2.26/2.54 363 test(c(c(c1))). [resolve(223,a,214,a(flip)),rewrite([214(9)])].
% 2.26/2.54 368 multiplication(c(c1),c(c(c(c1)))) = c(addition(c1,c(c(c1)))). [resolve(363,a,75,a),rewrite([39(12)])].
% 2.26/2.54 404 test(c(c(c2))). [resolve(264,a,214,a(flip)),rewrite([214(9)])].
% 2.26/2.54 415 multiplication(c(c2),c(c(c(c2)))) = c(addition(c2,c(c(c2)))). [resolve(404,a,76,a),rewrite([39(12)])].
% 2.26/2.54 453 multiplication(c(c1),multiplication(c(c1),A)) = multiplication(c(c1),A). [para(123(a,1),42(a,1,1)),flip(a)].
% 2.26/2.54 470 addition(c(A),c(B)) = c(multiplication(B,A)) | c(B) = zero | c(A) = zero. [resolve(80,a,38,a)].
% 2.26/2.54 476 addition(zero,c(c2)) = c(c2). [para(124(a,1),69(a,1,2)),rewrite([124(9)])].
% 2.26/2.54 480 c(addition(zero,addition(c1,c(c2)))) = c(addition(c1,c(c2))). [back_rewrite(359),rewrite([476(4),360(6)]),flip(a)].
% 2.26/2.54 482 addition(one,c(c(c(c2)))) = one. [resolve(146,a,404,a)].
% 2.26/2.54 484 addition(one,c(c(c(c1)))) = one. [resolve(146,a,363,a)].
% 2.26/2.54 487 addition(one,c(c1)) = one. [resolve(146,a,31,a)].
% 2.26/2.54 488 addition(one,c(c2)) = one. [resolve(146,a,30,a)].
% 2.26/2.54 490 addition(A,multiplication(c(c1),A)) = A. [para(487(a,1),46(a,2,1)),rewrite([35(2),35(6)])].
% 2.26/2.54 500 addition(A,multiplication(c(c2),A)) = A. [para(488(a,1),46(a,2,1)),rewrite([35(2),35(6)])].
% 2.26/2.54 704 addition(A,multiplication(A,c(c(c(c2))))) = A. [para(482(a,1),44(a,2,2)),rewrite([34(2),34(8)])].
% 2.26/2.54 706 addition(A,multiplication(A,c(c(c(c1))))) = A. [para(484(a,1),44(a,2,2)),rewrite([34(2),34(8)])].
% 2.26/2.54 803 multiplication(c(c1),c1) = zero. [resolve(99,a,490,a(flip)),rewrite([123(7),33(5)])].
% 2.26/2.54 809 multiplication(c(c1),addition(A,c1)) = multiplication(c(c1),A). [para(803(a,1),44(a,1,1)),rewrite([69(5),39(7)]),flip(a)].
% 2.26/2.54 852 multiplication(c(c2),c2) = zero. [resolve(100,a,500,a(flip)),rewrite([124(7),33(5)])].
% 2.26/2.54 885 multiplication(c1,c(c1)) = zero. [resolve(102,a,490,a(flip)),rewrite([123(8),33(6)])].
% 2.26/2.54 895 multiplication(c2,c(c2)) = zero. [resolve(103,a,500,a(flip)),rewrite([124(8),33(6)])].
% 2.26/2.54 913 addition(c1,c(c1)) = one. [resolve(105,a,490,a(flip)),rewrite([123(7),33(5),39(4)])].
% 2.26/2.54 917 addition(c2,addition(c(addition(c1,c2)),multiplication(addition(c2,c(c2)),c1))) != one. [back_rewrite(344),rewrite([913(8),35(7),41(13,R),39(12)])].
% 2.26/2.54 919 addition(c2,c(c2)) = one. [resolve(106,a,500,a(flip)),rewrite([124(7),33(5),39(4)])].
% 2.26/2.54 921 addition(c1,addition(c2,c(addition(c1,c2)))) != one. [back_rewrite(917),rewrite([919(9),35(8),39(7),41(8,R),39(7)])].
% 2.26/2.54 927 addition(addition(c1,c2),c(addition(c1,c2))) != one. [para(41(a,1),921(a,1)),rewrite([39(8)])].
% 2.26/2.54 928 -test(addition(c1,c2)). [ur(60,b,xx,c,927,a)].
% 2.26/2.54 929 c(addition(c1,c2)) = zero. [resolve(928,a,38,a)].
% 2.26/2.54 935 addition(c1,c2) != one. [ur(111,b,928,a),flip(a)].
% 2.26/2.54 946 multiplication(c(c2),c(c1)) = zero. [back_rewrite(350),rewrite([929(9)])].
% 2.26/2.54 950 multiplication(addition(A,c(c2)),c(c1)) = multiplication(A,c(c1)). [para(946(a,1),46(a,1,1)),rewrite([69(5),39(6)]),flip(a)].
% 2.26/2.54 1501 multiplication(c2,c2) = c2. [para(94(a,1),165(a,1,2)),rewrite([34(3)]),flip(a)].
% 2.26/2.54 1508 multiplication(c2,multiplication(c2,A)) = multiplication(c2,A). [para(1501(a,1),42(a,1,1)),flip(a)].
% 2.26/2.54 1847 test(addition(c(c2),c(addition(c2,c(c(c2)))))). [resolve(704,a,97,a(flip)),rewrite([415(9)])].
% 2.26/2.54 1863 test(addition(c(c1),c(addition(c1,c(c(c1)))))). [resolve(706,a,96,a(flip)),rewrite([368(9)])].
% 2.26/2.54 2763 c(addition(c(c2),c(addition(c2,c(c(c2)))))) != addition(c1,c2). [ur(56,a,1847,a,c,928,a)].
% 2.26/2.54 2853 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(1863,a,85,a),rewrite([39(13)])].
% 2.26/2.54 2856 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(1863,a,82,a),rewrite([39(13),2853(13)])].
% 2.26/2.54 2880 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(2853),rewrite([2856(25)])].
% 2.26/2.54 3178 multiplication(c(c(c2)),multiplication(c(c(c2)),A)) = multiplication(c(c(c2)),A). [para(259(a,1),42(a,1,1)),flip(a)].
% 2.26/2.54 4444 multiplication(c(c1),f1(c1)) = f1(c1). [para(123(a,1),198(a,1,1,2)),rewrite([913(4),35(4),453(10)]),flip(a)].
% 2.26/2.54 4454 multiplication(addition(c1,c2),f1(c1)) = multiplication(c2,f1(c1)). [para(1501(a,1),198(a,1,1,2)),rewrite([1508(12)])].
% 2.26/2.54 4463 multiplication(addition(c1,c(c(c2))),f1(c1)) = multiplication(c(c(c2)),f1(c1)). [para(259(a,1),198(a,1,1,2)),rewrite([3178(18)])].
% 2.26/2.54 5966 c(c(c1)) = c1. [resolve(219,c,913,a),rewrite([885(4),803(7)]),xx(a),xx(b)].
% 2.26/2.54 5976 c(multiplication(c2,c(c1))) = addition(c1,c(c2)). [back_rewrite(2880),rewrite([5966(8),33(7),33(7),5966(5),39(4),5966(11),33(10),33(10)]),flip(a)].
% 2.26/2.54 7266 f1(c1) = c(c1). [para(4444(a,1),809(a,2)),rewrite([39(6),93(6),34(4)]),flip(a)].
% 2.26/2.54 7521 multiplication(addition(c1,c(c(c2))),c(c1)) = c(addition(c1,c(c2))). [back_rewrite(4463),rewrite([7266(7),7266(13),360(14)])].
% 2.26/2.54 7527 multiplication(addition(c1,c2),c(c1)) = multiplication(c2,c(c1)). [back_rewrite(4454),rewrite([7266(5),7266(9)])].
% 2.26/2.54 7615 c(c(c2)) = c2. [resolve(260,c,919,a),rewrite([895(4),852(7)]),xx(a),xx(b)].
% 2.26/2.54 7622 c(addition(c1,c(c2))) = multiplication(c2,c(c1)). [back_rewrite(7521),rewrite([7615(4),7527(6)]),flip(a)].
% 2.26/2.54 7629 addition(c1,c2) != c2. [back_rewrite(2763),rewrite([7615(6),33(5),33(5),7615(3)]),flip(a)].
% 2.26/2.54 7643 c(addition(zero,addition(c1,c(c2)))) = multiplication(c2,c(c1)). [back_rewrite(480),rewrite([7622(12)])].
% 2.26/2.54 7911 c(addition(c1,multiplication(c2,c(c1)))) = zero | addition(c1,c(c2)) = zero. [para(5976(a,1),295(a,1,1)),rewrite([950(7),885(4),39(7),5976(14)]),flip(a)].
% 2.26/2.54 8852 c2 = zero | c1 = zero. [para(946(a,1),470(a,2,1)),rewrite([5966(3),7615(4),143(5),7615(8),5966(11)]),unit_del(a,935)].
% 2.26/2.54 8963 c1 = zero. [para(8852(a,1),928(a,1,2)),rewrite([39(6),162(6)]),unit_del(b,31)].
% 2.26/2.54 8998 c(c2) = zero. [back_rewrite(7911),rewrite([8963(1),8963(3),143(4),34(4),167(3),8963(5),476(8)]),merge(b)].
% 2.26/2.54 9000 c2 = one. [back_rewrite(7643),rewrite([8963(2),8998(4),33(4),33(3),143(2),8963(3),143(4),34(4)]),flip(a)].
% 2.26/2.54 9001 $F. [back_rewrite(7629),rewrite([8963(1),9000(2),140(3),9000(2)]),xx(a)].
% 2.26/2.54
% 2.26/2.54 % SZS output end Refutation
% 2.26/2.54 ============================== end of proof ==========================
% 2.26/2.54
% 2.26/2.54 ============================== STATISTICS ============================
% 2.26/2.54
% 2.26/2.54 Given=590. Generated=43726. Kept=8964. proofs=1.
% 2.26/2.54 Usable=318. Sos=4657. Demods=1393. Limbo=38, Disabled=3988. Hints=0.
% 2.26/2.54 Megabytes=9.94.
% 2.26/2.54 User_CPU=1.43, System_CPU=0.04, Wall_clock=2.
% 2.26/2.54
% 2.26/2.54 ============================== end of statistics =====================
% 2.26/2.54
% 2.26/2.54 ============================== end of search =========================
% 2.26/2.54
% 2.26/2.54 THEOREM PROVED
% 2.26/2.54 % SZS status Theorem
% 2.26/2.54
% 2.26/2.54 Exiting with 1 proof.
% 2.26/2.54
% 2.26/2.54 Process 16771 exit (max_proofs) Thu Jun 16 10:40:29 2022
% 2.26/2.54 Prover9 interrupted
%------------------------------------------------------------------------------