TSTP Solution File: KLE025+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE025+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 02:21:49 EDT 2022
% Result : Theorem 11.56s 11.92s
% Output : Refutation 11.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE025+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n028.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 09:51:11 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.40/1.07 ============================== Prover9 ===============================
% 0.40/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.40/1.07 Process 13988 was started by sandbox2 on n028.cluster.edu,
% 0.40/1.07 Thu Jun 16 09:51:12 2022
% 0.40/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13833_n028.cluster.edu".
% 0.40/1.07 ============================== end of head ===========================
% 0.40/1.07
% 0.40/1.07 ============================== INPUT =================================
% 0.40/1.07
% 0.40/1.07 % Reading from file /tmp/Prover9_13833_n028.cluster.edu
% 0.40/1.07
% 0.40/1.07 set(prolog_style_variables).
% 0.40/1.07 set(auto2).
% 0.40/1.07 % set(auto2) -> set(auto).
% 0.40/1.07 % set(auto) -> set(auto_inference).
% 0.40/1.07 % set(auto) -> set(auto_setup).
% 0.40/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.40/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.40/1.07 % set(auto) -> set(auto_limits).
% 0.40/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.40/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.40/1.07 % set(auto) -> set(auto_denials).
% 0.40/1.07 % set(auto) -> set(auto_process).
% 0.40/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.40/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.40/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.40/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.40/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.40/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.40/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.40/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.40/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.40/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.40/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.40/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.40/1.07 % set(auto2) -> assign(stats, some).
% 0.40/1.07 % set(auto2) -> clear(echo_input).
% 0.40/1.07 % set(auto2) -> set(quiet).
% 0.40/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.40/1.07 % set(auto2) -> clear(print_given).
% 0.40/1.07 assign(lrs_ticks,-1).
% 0.40/1.07 assign(sos_limit,10000).
% 0.40/1.07 assign(order,kbo).
% 0.40/1.07 set(lex_order_vars).
% 0.40/1.07 clear(print_given).
% 0.40/1.07
% 0.40/1.07 % formulas(sos). % not echoed (19 formulas)
% 0.40/1.07
% 0.40/1.07 ============================== end of input ==========================
% 0.40/1.07
% 0.40/1.07 % From the command line: assign(max_seconds, 300).
% 0.40/1.07
% 0.40/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.40/1.07
% 0.40/1.07 % Formulas that are not ordinary clauses:
% 0.40/1.07 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.07 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].
% 0.40/1.07 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.07 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.07 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].
% 0.40/1.07 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.07 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.07 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].
% 0.40/1.07 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].
% 0.40/1.07 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.07 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.07 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.07 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.07 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].
% 3.46/3.77 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 3.46/3.77 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 3.46/3.77 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].
% 3.46/3.77 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].
% 3.46/3.77 19 -(all X0 all X1 all X2 (test(X1) & test(X2) -> (multiplication(multiplication(X1,X0),c(X2)) = zero -> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.46/3.77
% 3.46/3.77 ============================== end of process non-clausal formulas ===
% 3.46/3.77
% 3.46/3.77 ============================== PROCESS INITIAL CLAUSES ===============
% 3.46/3.77
% 3.46/3.77 ============================== PREDICATE ELIMINATION =================
% 3.46/3.77 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 3.46/3.77 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 3.46/3.77 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 3.46/3.77 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 3.46/3.77 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 3.46/3.77 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 3.46/3.77 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 3.46/3.77 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 3.46/3.77 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 3.46/3.77 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 3.46/3.77 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 3.46/3.77 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 3.46/3.77 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 3.46/3.77 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 3.46/3.77 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 3.46/3.77 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 3.46/3.77 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 3.46/3.77 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 3.46/3.77 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 3.46/3.77 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 3.46/3.77
% 3.46/3.77 ============================== end predicate elimination =============
% 3.46/3.77
% 3.46/3.77 Auto_denials: (non-Horn, no changes).
% 3.46/3.77
% 3.46/3.77 Term ordering decisions:
% 3.46/3.77 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. c=1. f1=1.
% 3.46/3.77
% 3.46/3.77 ============================== end of process initial clauses ========
% 3.46/3.77
% 3.46/3.77 ============================== CLAUSES FOR SEARCH ====================
% 3.46/3.77
% 3.46/3.77 ============================== end of clauses for search =============
% 3.46/3.77
% 3.46/3.77 ============================== SEARCH ================================
% 3.46/3.77
% 3.46/3.77 % Starting search at 0.01 seconds.
% 3.46/3.77
% 3.46/3.77 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 102 (0.00 of 1.88 sec).
% 3.46/3.77
% 3.46/3.77 Low Water (keep): wt=51.000, iters=3429
% 3.46/3.77
% 3.46/3.77 Low Water (keep): wt=47.000, iters=3381
% 3.46/3.77
% 3.46/3.77 Low Water (keep): wt=43.000, iters=3370
% 3.46/3.77
% 3.46/3.77 Low Water (keep): wt=41.000, iters=3336
% 3.46/3.77
% 3.46/3.77 Low Water (keep): wt=40.000, iters=3427
% 3.46/3.77
% 3.46/3.77 Low Water (keep): wt=38.000, iters=3362
% 3.46/3.77
% 3.46/3.77 Low Water (keep): wt=36.000, iters=3363
% 3.46/3.77
% 3.46/3.77 Low Water (keep): wt=35.000, iters=3370
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% 3.46/3.77 Low Water (keep): wt=34.000, iters=3381
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% 3.46/3.77 Low Water (keep): wt=33.000, iters=3385
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% 3.46/3.77 Low Water (keep): wt=32.000, iters=3335
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% 3.46/3.77 Low Water (keep): wt=31.000, iters=3380
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% 3.46/3.77 Low Water (keep): wt=30.000, iters=3342
% 3.46/3.77
% 3.46/3.77 Low Water (keep): wt=29.000, iters=3336
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=28.000, iters=3339
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=27.000, iters=3370
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=26.000, iters=3348
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=25.000, iters=3350
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=24.000, iters=3391
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=23.000, iters=3338
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7900, wt=92.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7037, wt=85.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7972, wt=84.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7136, wt=83.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7036, wt=77.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=6655, wt=75.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=4721, wt=74.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7890, wt=73.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7906, wt=71.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=6372, wt=70.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7040, wt=69.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=6762, wt=68.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=6672, wt=67.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7843, wt=65.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7944, wt=64.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=5320, wt=63.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7945, wt=62.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=7889, wt=61.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=14341, wt=20.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=14924, wt=19.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=15062, wt=16.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=15072, wt=15.000
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=15078, wt=14.000
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=22.000, iters=3333
% 11.56/11.92
% 11.56/11.92 Low Water (displace): id=15802, wt=13.000
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=21.000, iters=3336
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=20.000, iters=3333
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=19.000, iters=3351
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=18.000, iters=3348
% 11.56/11.92
% 11.56/11.92 Low Water (keep): wt=17.000, iters=3335
% 11.56/11.92
% 11.56/11.92 ============================== PROOF =================================
% 11.56/11.92 % SZS status Theorem
% 11.56/11.92 % SZS output start Refutation
% 11.56/11.92
% 11.56/11.92 % Proof 1 at 10.57 (+ 0.25) seconds.
% 11.56/11.92 % Length of proof is 66.
% 11.56/11.92 % Level of proof is 12.
% 11.56/11.92 % Maximum clause weight is 17.000.
% 11.56/11.92 % Given clauses 1677.
% 11.56/11.92
% 11.56/11.92 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 11.56/11.92 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 11.56/11.92 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 11.56/11.92 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].
% 11.56/11.92 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 11.56/11.92 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 11.56/11.92 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].
% 11.56/11.92 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].
% 11.56/11.92 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 11.56/11.92 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 11.56/11.92 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].
% 11.56/11.92 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 11.56/11.92 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].
% 11.56/11.92 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].
% 11.56/11.92 19 -(all X0 all X1 all X2 (test(X1) & test(X2) -> (multiplication(multiplication(X1,X0),c(X2)) = zero -> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 11.56/11.92 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 11.56/11.92 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 11.56/11.92 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 11.56/11.92 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 11.56/11.92 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 11.56/11.92 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 11.56/11.92 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 11.56/11.92 31 test(c3) # label(goals) # label(negated_conjecture). [clausify(19)].
% 11.56/11.92 32 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 11.56/11.92 33 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 11.56/11.92 34 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 11.56/11.92 35 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 11.56/11.92 36 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 11.56/11.92 39 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 11.56/11.92 40 multiplication(multiplication(c2,c1),c(c3)) = zero # label(goals) # label(negated_conjecture). [clausify(19)].
% 11.56/11.92 43 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 11.56/11.92 44 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 11.56/11.92 45 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(44),flip(a)].
% 11.56/11.92 46 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 11.56/11.92 47 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(46),flip(a)].
% 11.56/11.92 48 multiplication(multiplication(c2,c1),c3) != multiplication(c2,c1) # label(goals) # label(negated_conjecture). [clausify(19)].
% 11.56/11.92 49 multiplication(c2,multiplication(c1,c3)) != multiplication(c2,c1). [copy(48),rewrite([43(5)])].
% 11.56/11.92 50 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)].
% 11.56/11.92 51 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(50),flip(c)].
% 11.56/11.92 52 -test(A) | -test(B) | c(multiplication(A,B)) = addition(c(A),c(B)) # label(test_deMorgan2) # label(axiom). [clausify(18)].
% 11.56/11.92 53 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(A,B)). [copy(52),flip(c)].
% 11.56/11.92 55 multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 11.56/11.92 56 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 11.56/11.92 60 -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 11.56/11.92 61 -test(A) | c(A) != B | addition(A,B) = one. [copy(60),rewrite([39(4)])].
% 11.56/11.92 62 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 11.56/11.92 63 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 11.56/11.92 65 multiplication(c2,multiplication(c1,c(c3))) = zero. [back_rewrite(40),rewrite([43(6)])].
% 11.56/11.92 66 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(51,a,b),rewrite([33(5)])].
% 11.56/11.92 71 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(32(a,1),45(a,2,2)),rewrite([36(3),39(3)])].
% 11.56/11.92 107 c(c3) != A | addition(A,c3) = one. [resolve(61,a,31,a),rewrite([39(5)])].
% 11.56/11.92 112 test(one). [resolve(63,c,32,a),rewrite([36(3),34(6)]),xx(a),xx(b)].
% 11.56/11.92 125 multiplication(c2,addition(A,multiplication(c1,c(c3)))) = multiplication(c2,A). [para(65(a,1),45(a,1,1)),rewrite([71(4),39(8)]),flip(a)].
% 11.56/11.92 128 multiplication(c(c3),c(c3)) = c(c3). [resolve(66,a,31,a)].
% 11.56/11.92 140 addition(one,f1(one)) = one. [resolve(112,a,56,b)].
% 11.56/11.92 141 f1(one) = zero. [resolve(112,a,55,b),rewrite([34(4)])].
% 11.56/11.92 145 addition(zero,one) = one. [back_rewrite(140),rewrite([141(3),39(3)])].
% 11.56/11.92 146 -test(zero) | c(zero) = one. [para(141(a,1),62(a,1)),rewrite([141(4)]),unit_del(c,112)].
% 11.56/11.92 147 test(zero). [resolve(145,a,63,c),rewrite([34(3),36(6)]),xx(a),xx(b)].
% 11.56/11.92 148 c(zero) = one. [back_unit_del(146),unit_del(a,147)].
% 11.56/11.92 151 -test(A) | addition(one,c(A)) = one. [resolve(147,a,53,b),rewrite([148(4),39(4),36(6),148(6)])].
% 11.56/11.92 494 addition(one,c(c3)) = one. [resolve(151,a,31,a)].
% 11.56/11.92 497 addition(A,multiplication(c(c3),A)) = A. [para(494(a,1),47(a,2,1)),rewrite([35(2),35(6)])].
% 11.56/11.92 921 addition(c3,c(c3)) = one. [resolve(107,a,497,a(flip)),rewrite([128(7),33(5),39(4)])].
% 11.56/11.92 1406 multiplication(c2,multiplication(c1,addition(A,c(c3)))) = multiplication(c2,multiplication(c1,A)). [para(45(a,1),125(a,1,2))].
% 11.56/11.92 23521 $F. [para(921(a,1),1406(a,1,2,2)),rewrite([34(4)]),flip(a),unit_del(a,49)].
% 11.56/11.92
% 11.56/11.92 % SZS output end Refutation
% 11.56/11.92 ============================== end of proof ==========================
% 11.56/11.92
% 11.56/11.92 ============================== STATISTICS ============================
% 11.56/11.92
% 11.56/11.92 Given=1677. Generated=252755. Kept=23484. proofs=1.
% 11.56/11.92 Usable=1356. Sos=9999. Demods=1910. Limbo=1, Disabled=12166. Hints=0.
% 11.56/11.92 Megabytes=20.02.
% 11.56/11.92 User_CPU=10.57, System_CPU=0.25, Wall_clock=11.
% 11.56/11.92
% 11.56/11.92 ============================== end of statistics =====================
% 11.56/11.92
% 11.56/11.92 ============================== end of search =========================
% 11.56/11.92
% 11.56/11.92 THEOREM PROVED
% 11.56/11.92 % SZS status Theorem
% 11.56/11.92
% 11.56/11.92 Exiting with 1 proof.
% 11.56/11.92
% 11.56/11.92 Process 13988 exit (max_proofs) Thu Jun 16 09:51:23 2022
% 11.56/11.92 Prover9 interrupted
%------------------------------------------------------------------------------