TSTP Solution File: KLE024+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE024+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 02:21:48 EDT 2022
% Result : Theorem 2.63s 2.91s
% Output : Refutation 2.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE024+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n009.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 13:35:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.00 ============================== Prover9 ===============================
% 0.44/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.00 Process 25039 was started by sandbox on n009.cluster.edu,
% 0.44/1.00 Thu Jun 16 13:35:38 2022
% 0.44/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24886_n009.cluster.edu".
% 0.44/1.00 ============================== end of head ===========================
% 0.44/1.00
% 0.44/1.00 ============================== INPUT =================================
% 0.44/1.00
% 0.44/1.00 % Reading from file /tmp/Prover9_24886_n009.cluster.edu
% 0.44/1.00
% 0.44/1.00 set(prolog_style_variables).
% 0.44/1.00 set(auto2).
% 0.44/1.00 % set(auto2) -> set(auto).
% 0.44/1.00 % set(auto) -> set(auto_inference).
% 0.44/1.00 % set(auto) -> set(auto_setup).
% 0.44/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.00 % set(auto) -> set(auto_limits).
% 0.44/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.00 % set(auto) -> set(auto_denials).
% 0.44/1.00 % set(auto) -> set(auto_process).
% 0.44/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.00 % set(auto2) -> assign(stats, some).
% 0.44/1.00 % set(auto2) -> clear(echo_input).
% 0.44/1.00 % set(auto2) -> set(quiet).
% 0.44/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.00 % set(auto2) -> clear(print_given).
% 0.44/1.00 assign(lrs_ticks,-1).
% 0.44/1.00 assign(sos_limit,10000).
% 0.44/1.00 assign(order,kbo).
% 0.44/1.00 set(lex_order_vars).
% 0.44/1.00 clear(print_given).
% 0.44/1.00
% 0.44/1.00 % formulas(sos). % not echoed (19 formulas)
% 0.44/1.00
% 0.44/1.00 ============================== end of input ==========================
% 0.44/1.00
% 0.44/1.00 % From the command line: assign(max_seconds, 300).
% 0.44/1.00
% 0.44/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.00
% 0.44/1.00 % Formulas that are not ordinary clauses:
% 0.44/1.00 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 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].
% 0.44/1.00 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 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].
% 0.44/1.00 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 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].
% 0.44/1.00 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].
% 0.44/1.00 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 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].
% 2.31/2.64 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.31/2.64 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.31/2.64 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].
% 2.31/2.64 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].
% 2.31/2.64 19 -(all X0 all X1 all X2 (test(X1) & test(X2) -> (addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) -> multiplication(multiplication(X1,X0),c(X2)) = zero))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.31/2.64
% 2.31/2.64 ============================== end of process non-clausal formulas ===
% 2.31/2.64
% 2.31/2.64 ============================== PROCESS INITIAL CLAUSES ===============
% 2.31/2.64
% 2.31/2.64 ============================== PREDICATE ELIMINATION =================
% 2.31/2.64 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.31/2.64 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.31/2.64 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.31/2.64 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 2.31/2.64 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.31/2.64 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 2.31/2.64 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 2.31/2.64 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 2.31/2.64 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.31/2.64 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 2.31/2.64 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 2.31/2.64 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 2.31/2.64 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 2.31/2.64 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.31/2.64 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 2.31/2.64 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 2.31/2.64 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 2.31/2.64 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 2.31/2.64 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.31/2.64 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.31/2.64
% 2.31/2.64 ============================== end predicate elimination =============
% 2.31/2.64
% 2.31/2.64 Auto_denials: (non-Horn, no changes).
% 2.31/2.64
% 2.31/2.64 Term ordering decisions:
% 2.31/2.64 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. c=1. f1=1.
% 2.31/2.64
% 2.31/2.64 ============================== end of process initial clauses ========
% 2.31/2.64
% 2.31/2.64 ============================== CLAUSES FOR SEARCH ====================
% 2.31/2.64
% 2.31/2.64 ============================== end of clauses for search =============
% 2.31/2.64
% 2.31/2.64 ============================== SEARCH ================================
% 2.31/2.64
% 2.31/2.64 % Starting search at 0.01 seconds.
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=73.000, iters=3363
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=71.000, iters=3352
% 2.31/2.64
% 2.31/2.64 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 104 (0.00 of 1.14 sec).
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=56.000, iters=3383
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=54.000, iters=3366
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=50.000, iters=3425
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=43.000, iters=3390
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=41.000, iters=3411
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=40.000, iters=3377
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=39.000, iters=3393
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=38.000, iters=3350
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=37.000, iters=3399
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=35.000, iters=3362
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=34.000, iters=3352
% 2.31/2.64
% 2.31/2.64 Low Water (keep): wt=33.000, iters=3344
% 2.63/2.91
% 2.63/2.91 Low Water (keep): wt=31.000, iters=3388
% 2.63/2.91
% 2.63/2.91 Low Water (keep): wt=30.000, iters=3352
% 2.63/2.91
% 2.63/2.91 Low Water (keep): wt=29.000, iters=3412
% 2.63/2.91
% 2.63/2.91 Low Water (keep): wt=27.000, iters=3347
% 2.63/2.91
% 2.63/2.91 Low Water (keep): wt=26.000, iters=3348
% 2.63/2.91
% 2.63/2.91 Low Water (keep): wt=25.000, iters=3370
% 2.63/2.91
% 2.63/2.91 ============================== PROOF =================================
% 2.63/2.91 % SZS status Theorem
% 2.63/2.91 % SZS output start Refutation
% 2.63/2.91
% 2.63/2.91 % Proof 1 at 1.87 (+ 0.05) seconds.
% 2.63/2.91 % Length of proof is 67.
% 2.63/2.91 % Level of proof is 14.
% 2.63/2.91 % Maximum clause weight is 17.000.
% 2.63/2.91 % Given clauses 687.
% 2.63/2.91
% 2.63/2.91 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.91 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.91 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.91 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].
% 2.63/2.91 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.91 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.91 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].
% 2.63/2.91 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].
% 2.63/2.91 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.91 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.91 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.91 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].
% 2.63/2.91 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.63/2.91 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].
% 2.63/2.91 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].
% 2.63/2.91 19 -(all X0 all X1 all X2 (test(X1) & test(X2) -> (addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) -> multiplication(multiplication(X1,X0),c(X2)) = zero))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.63/2.91 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.63/2.91 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.63/2.91 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 2.63/2.91 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 2.63/2.91 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.63/2.91 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.63/2.91 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 2.63/2.91 30 test(c2) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.63/2.91 32 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 2.63/2.91 33 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 2.63/2.91 34 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 2.63/2.91 35 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 2.63/2.91 36 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 2.63/2.91 37 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 2.63/2.91 39 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 2.63/2.91 42 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 2.63/2.91 43 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 2.63/2.91 44 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(43),flip(a)].
% 2.63/2.91 45 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 2.63/2.91 46 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(45),flip(a)].
% 2.63/2.91 47 multiplication(c(c2),c1) = addition(multiplication(c1,c(c3)),multiplication(c(c2),c1)) # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.63/2.91 48 addition(multiplication(c1,c(c3)),multiplication(c(c2),c1)) = multiplication(c(c2),c1). [copy(47),flip(a)].
% 2.63/2.91 49 multiplication(multiplication(c2,c1),c(c3)) != zero # label(goals) # label(negated_conjecture). [clausify(19)].
% 2.63/2.91 50 multiplication(c2,multiplication(c1,c(c3))) != zero. [copy(49),rewrite([42(6)])].
% 2.63/2.91 51 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)].
% 2.63/2.91 52 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(51),flip(c)].
% 2.63/2.91 53 -test(A) | -test(B) | c(multiplication(A,B)) = addition(c(A),c(B)) # label(test_deMorgan2) # label(axiom). [clausify(18)].
% 2.63/2.91 54 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(A,B)). [copy(53),flip(c)].
% 2.63/2.91 56 multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 2.63/2.91 57 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 2.63/2.91 60 -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 2.63/2.91 63 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 2.63/2.91 64 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 2.63/2.91 66 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(52,a,b),rewrite([33(5)])].
% 2.63/2.91 71 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(32(a,1),44(a,2,2)),rewrite([36(3),39(3)])].
% 2.63/2.91 106 c(c2) != A | multiplication(c2,A) = zero. [resolve(60,a,30,a)].
% 2.63/2.91 114 test(one). [resolve(64,c,32,a),rewrite([36(3),34(6)]),xx(a),xx(b)].
% 2.63/2.91 129 multiplication(c(c2),c(c2)) = c(c2). [resolve(66,a,30,a)].
% 2.63/2.91 140 addition(one,f1(one)) = one. [resolve(114,a,57,b)].
% 2.63/2.91 141 f1(one) = zero. [resolve(114,a,56,b),rewrite([34(4)])].
% 2.63/2.91 145 addition(zero,one) = one. [back_rewrite(140),rewrite([141(3),39(3)])].
% 2.63/2.91 146 -test(zero) | c(zero) = one. [para(141(a,1),63(a,1)),rewrite([141(4)]),unit_del(c,114)].
% 2.63/2.91 147 test(zero). [resolve(145,a,64,c),rewrite([34(3),36(6)]),xx(a),xx(b)].
% 2.63/2.91 148 c(zero) = one. [back_unit_del(146),unit_del(a,147)].
% 2.63/2.91 151 -test(A) | addition(one,c(A)) = one. [resolve(147,a,54,b),rewrite([148(4),39(4),36(6),148(6)])].
% 2.63/2.91 492 addition(one,c(c2)) = one. [resolve(151,a,30,a)].
% 2.63/2.91 504 addition(A,multiplication(c(c2),A)) = A. [para(492(a,1),46(a,2,1)),rewrite([35(2),35(6)])].
% 2.63/2.91 900 multiplication(c2,c(c2)) = zero. [resolve(106,a,504,a(flip)),rewrite([129(8),33(6)])].
% 2.63/2.91 908 multiplication(c2,multiplication(c(c2),A)) = zero. [para(900(a,1),42(a,1,1)),rewrite([37(2)]),flip(a)].
% 2.63/2.91 913 multiplication(c2,addition(A,multiplication(c(c2),B))) = multiplication(c2,A). [para(908(a,1),44(a,1,1)),rewrite([71(4),39(7)]),flip(a)].
% 2.63/2.91 13300 $F. [para(48(a,1),913(a,1,2)),rewrite([908(6)]),flip(a),unit_del(a,50)].
% 2.63/2.91
% 2.63/2.91 % SZS output end Refutation
% 2.63/2.91 ============================== end of proof ==========================
% 2.63/2.91
% 2.63/2.91 ============================== STATISTICS ============================
% 2.63/2.91
% 2.63/2.91 Given=687. Generated=60034. Kept=13262. proofs=1.
% 2.63/2.91 Usable=396. Sos=8930. Demods=1689. Limbo=3, Disabled=3971. Hints=0.
% 2.63/2.91 Megabytes=14.32.
% 2.63/2.91 User_CPU=1.87, System_CPU=0.05, Wall_clock=2.
% 2.63/2.91
% 2.63/2.91 ============================== end of statistics =====================
% 2.63/2.91
% 2.63/2.91 ============================== end of search =========================
% 2.63/2.91
% 2.63/2.91 THEOREM PROVED
% 2.63/2.91 % SZS status Theorem
% 2.63/2.91
% 2.63/2.91 Exiting with 1 proof.
% 2.63/2.91
% 2.63/2.91 Process 25039 exit (max_proofs) Thu Jun 16 13:35:40 2022
% 2.63/2.91 Prover9 interrupted
%------------------------------------------------------------------------------