TSTP Solution File: KLE011+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE011+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 60.74s 61.05s
% Output : Refutation 60.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE011+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 10:27:42 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.42/0.98 ============================== Prover9 ===============================
% 0.42/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.98 Process 26726 was started by sandbox on n029.cluster.edu,
% 0.42/0.98 Thu Jun 16 10:27:43 2022
% 0.42/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26573_n029.cluster.edu".
% 0.42/0.98 ============================== end of head ===========================
% 0.42/0.98
% 0.42/0.98 ============================== INPUT =================================
% 0.42/0.98
% 0.42/0.98 % Reading from file /tmp/Prover9_26573_n029.cluster.edu
% 0.42/0.98
% 0.42/0.98 set(prolog_style_variables).
% 0.42/0.98 set(auto2).
% 0.42/0.98 % set(auto2) -> set(auto).
% 0.42/0.98 % set(auto) -> set(auto_inference).
% 0.42/0.98 % set(auto) -> set(auto_setup).
% 0.42/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.98 % set(auto) -> set(auto_limits).
% 0.42/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.98 % set(auto) -> set(auto_denials).
% 0.42/0.98 % set(auto) -> set(auto_process).
% 0.42/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.98 % set(auto2) -> assign(stats, some).
% 0.42/0.98 % set(auto2) -> clear(echo_input).
% 0.42/0.98 % set(auto2) -> set(quiet).
% 0.42/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.98 % set(auto2) -> clear(print_given).
% 0.42/0.98 assign(lrs_ticks,-1).
% 0.42/0.98 assign(sos_limit,10000).
% 0.42/0.98 assign(order,kbo).
% 0.42/0.98 set(lex_order_vars).
% 0.42/0.98 clear(print_given).
% 0.42/0.98
% 0.42/0.98 % formulas(sos). % not echoed (17 formulas)
% 0.42/0.98
% 0.42/0.98 ============================== end of input ==========================
% 0.42/0.98
% 0.42/0.98 % From the command line: assign(max_seconds, 300).
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.98
% 0.42/0.98 % Formulas that are not ordinary clauses:
% 0.42/0.98 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 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].
% 0.42/0.98 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 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].
% 0.42/0.98 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 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].
% 0.42/0.98 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].
% 0.42/0.98 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 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].
% 2.66/2.95 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 2.66/2.95 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 2.66/2.95 17 -(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].
% 2.66/2.95
% 2.66/2.95 ============================== end of process non-clausal formulas ===
% 2.66/2.95
% 2.66/2.95 ============================== PROCESS INITIAL CLAUSES ===============
% 2.66/2.95
% 2.66/2.95 ============================== PREDICATE ELIMINATION =================
% 2.66/2.95 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 2.66/2.95 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.66/2.95 20 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 2.66/2.95 21 test(A) | c(A) = zero # label(test_4) # label(axiom). [clausify(16)].
% 2.66/2.95 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 2.66/2.95 Derived: complement(f1(c2),c2). [resolve(18,a,19,a)].
% 2.66/2.95 Derived: complement(f1(c1),c1). [resolve(18,a,20,a)].
% 2.66/2.95 Derived: complement(f1(A),A) | c(A) = zero. [resolve(18,a,21,a)].
% 2.66/2.95 Derived: complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 2.66/2.95 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.66/2.95 Derived: c(c2) != A | complement(c2,A). [resolve(23,a,19,a)].
% 2.66/2.95 Derived: c(c1) != A | complement(c1,A). [resolve(23,a,20,a)].
% 2.66/2.95 Derived: c(A) != B | complement(A,B) | c(A) = zero. [resolve(23,a,21,a)].
% 2.66/2.95 Derived: c(A) != B | complement(A,B) | -complement(C,A). [resolve(23,a,22,a)].
% 2.66/2.95 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 2.66/2.95 Derived: c(c2) = A | -complement(c2,A). [resolve(24,a,19,a)].
% 2.66/2.95 Derived: c(c1) = A | -complement(c1,A). [resolve(24,a,20,a)].
% 2.66/2.95 Derived: c(A) = B | -complement(A,B) | c(A) = zero. [resolve(24,a,21,a)].
% 2.66/2.95 Derived: c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 2.66/2.95 25 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 2.66/2.95 26 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 2.66/2.95
% 2.66/2.95 ============================== end predicate elimination =============
% 2.66/2.95
% 2.66/2.95 Auto_denials: (non-Horn, no changes).
% 2.66/2.95
% 2.66/2.95 Term ordering decisions:
% 2.66/2.95 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 2.66/2.95
% 2.66/2.95 ============================== end of process initial clauses ========
% 2.66/2.95
% 2.66/2.95 ============================== CLAUSES FOR SEARCH ====================
% 2.66/2.95
% 2.66/2.95 ============================== end of clauses for search =============
% 2.66/2.95
% 2.66/2.95 ============================== SEARCH ================================
% 2.66/2.95
% 2.66/2.95 % Starting search at 0.01 seconds.
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=82.000, iters=3367
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=74.000, iters=3466
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=68.000, iters=3436
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=67.000, iters=3381
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=64.000, iters=3361
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=60.000, iters=3424
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=58.000, iters=3366
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=54.000, iters=3485
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=53.000, iters=3420
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=52.000, iters=3417
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=48.000, iters=3350
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=46.000, iters=3339
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=44.000, iters=3340
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=42.000, iters=3343
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=40.000, iters=3346
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=39.000, iters=3362
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=37.000, iters=3342
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=36.000, iters=3393
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=35.000, iters=3384
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=34.000, iters=3343
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=33.000, iters=3360
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=32.000, iters=3342
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=31.000, iters=3360
% 2.66/2.95
% 2.66/2.95 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 105 (0.00 of 1.60 sec).
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=30.000, iters=3407
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=29.000, iters=3390
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=28.000, iters=3360
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=27.000, iters=3466
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=26.000, iters=3336
% 2.66/2.95
% 2.66/2.95 Low Water (keep): wt=25.000, iters=3364
% 60.74/61.05
% 60.74/61.05 Low Water (keep): wt=24.000, iters=3338
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=5784, wt=107.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=5800, wt=88.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=5461, wt=85.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=5801, wt=82.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=5042, wt=81.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=5795, wt=80.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=5044, wt=79.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=5420, wt=75.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=6087, wt=74.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=5799, wt=72.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=6138, wt=68.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=6119, wt=67.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=5532, wt=66.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=6174, wt=64.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=11681, wt=21.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=11688, wt=18.000
% 60.74/61.05
% 60.74/61.05 Low Water (keep): wt=23.000, iters=3342
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=11808, wt=17.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=11848, wt=16.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=11862, wt=15.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=11894, wt=14.000
% 60.74/61.05
% 60.74/61.05 Low Water (displace): id=13098, wt=13.000
% 60.74/61.05
% 60.74/61.05 Low Water (keep): wt=22.000, iters=3333
% 60.74/61.05
% 60.74/61.05 Low Water (keep): wt=21.000, iters=3333
% 60.74/61.05
% 60.74/61.05 Low Water (keep): wt=20.000, iters=3338
% 60.74/61.05
% 60.74/61.05 Low Water (keep): wt=19.000, iters=3333
% 60.74/61.05
% 60.74/61.05 Low Water (keep): wt=18.000, iters=3345
% 60.74/61.05
% 60.74/61.05 Low Water (keep): wt=17.000, iters=3351
% 60.74/61.05
% 60.74/61.05 Low Water (keep): wt=16.000, iters=3333
% 60.74/61.05
% 60.74/61.05 ============================== PROOF =================================
% 60.74/61.05 % SZS status Theorem
% 60.74/61.05 % SZS output start Refutation
% 60.74/61.05
% 60.74/61.05 % Proof 1 at 58.67 (+ 1.41) seconds.
% 60.74/61.05 % Length of proof is 107.
% 60.74/61.05 % Level of proof is 14.
% 60.74/61.05 % Maximum clause weight is 21.000.
% 60.74/61.05 % Given clauses 3936.
% 60.74/61.05
% 60.74/61.05 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 60.74/61.05 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].
% 60.74/61.05 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 60.74/61.05 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 60.74/61.05 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].
% 60.74/61.05 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 60.74/61.05 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 60.74/61.05 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].
% 60.74/61.05 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].
% 60.74/61.05 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 60.74/61.05 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 60.74/61.05 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 60.74/61.05 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].
% 60.74/61.05 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 60.74/61.05 17 -(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].
% 60.74/61.05 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 60.74/61.05 19 test(c2) # label(goals) # label(negated_conjecture). [clausify(17)].
% 60.74/61.05 20 test(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 60.74/61.05 22 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 60.74/61.05 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 60.74/61.05 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 60.74/61.05 27 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 60.74/61.05 28 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 60.74/61.05 29 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 60.74/61.05 30 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 60.74/61.05 31 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 60.74/61.05 32 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 60.74/61.05 33 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 60.74/61.05 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 60.74/61.05 35 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(34),rewrite([33(2)]),flip(a)].
% 60.74/61.05 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 60.74/61.05 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 60.74/61.05 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(37),flip(a)].
% 60.74/61.05 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 60.74/61.05 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(39),flip(a)].
% 60.74/61.05 41 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(17)].
% 60.74/61.05 42 addition(multiplication(c(c1),c(c2)),addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c2,c(c2)),c1))) != one. [copy(41),rewrite([33(13),33(19)])].
% 60.74/61.05 44 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 60.74/61.05 45 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 60.74/61.05 46 -complement(A,B) | addition(A,B) = one. [copy(45),rewrite([33(2)])].
% 60.74/61.05 47 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 60.74/61.05 48 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(A,B) != one. [copy(47),rewrite([33(8)])].
% 60.74/61.05 49 complement(f1(c2),c2). [resolve(18,a,19,a)].
% 60.74/61.05 50 complement(f1(c1),c1). [resolve(18,a,20,a)].
% 60.74/61.05 52 complement(f1(A),A) | -complement(B,A). [resolve(18,a,22,a)].
% 60.74/61.05 53 c(c2) != A | complement(c2,A). [resolve(23,a,19,a)].
% 60.74/61.05 54 c(c1) != A | complement(c1,A). [resolve(23,a,20,a)].
% 60.74/61.05 60 c(A) = B | -complement(A,B) | -complement(C,A). [resolve(24,a,22,a)].
% 60.74/61.05 64 addition(A,addition(A,B)) = addition(A,B). [para(35(a,1),28(a,1)),rewrite([33(1),33(2),35(2,R),28(1),33(3)])].
% 60.74/61.05 65 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(27(a,1),38(a,2,2)),rewrite([31(3),33(3)])].
% 60.74/61.05 66 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(29(a,1),38(a,1,1)),rewrite([33(4)]),flip(a)].
% 60.74/61.05 67 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(30(a,1),40(a,1,1)),rewrite([33(4)]),flip(a)].
% 60.74/61.05 68 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(36(a,1),40(a,1,1)),rewrite([33(6)])].
% 60.74/61.05 72 complement(one,zero). [resolve(48,d,27,a),rewrite([29(6),31(9)]),xx(b),xx(c)].
% 60.74/61.05 77 addition(c2,f1(c2)) = one. [resolve(49,a,46,a),rewrite([33(4)])].
% 60.74/61.05 80 addition(c1,f1(c1)) = one. [resolve(50,a,46,a),rewrite([33(4)])].
% 60.74/61.05 86 complement(c2,c(c2)). [resolve(53,a,30,a(flip)),rewrite([30(5)])].
% 60.74/61.05 88 complement(c1,c(c1)). [resolve(54,a,30,a(flip)),rewrite([30(5)])].
% 60.74/61.05 101 c(zero) = A | -complement(zero,A). [resolve(72,a,60,c)].
% 60.74/61.05 104 addition(zero,one) = one. [resolve(72,a,46,a),rewrite([33(3)])].
% 60.74/61.05 108 addition(c2,c(c2)) = one. [resolve(86,a,46,a)].
% 60.74/61.05 109 multiplication(c2,c(c2)) = zero. [resolve(86,a,44,a)].
% 60.74/61.05 112 addition(c1,addition(multiplication(c(c1),c(c2)),multiplication(addition(c1,c(c1)),c2))) != one. [back_rewrite(42),rewrite([108(15),30(14),33(13),35(14,R),33(13)])].
% 60.74/61.05 115 complement(f1(c(c1)),c(c1)). [resolve(88,a,52,b)].
% 60.74/61.05 116 addition(c1,c(c1)) = one. [resolve(88,a,46,a)].
% 60.74/61.05 119 addition(c1,addition(c2,multiplication(c(c1),c(c2)))) != one. [back_rewrite(112),rewrite([116(10),30(9),33(8)])].
% 60.74/61.05 127 complement(zero,one). [resolve(104,a,48,d),rewrite([31(6),29(9)]),xx(b),xx(c)].
% 60.74/61.05 138 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))). [para(66(a,2),35(a,2,2)),rewrite([33(2)]),flip(a)].
% 60.74/61.05 166 addition(one,c2) = one. [para(77(a,1),64(a,1,2)),rewrite([33(3),77(7)])].
% 60.74/61.05 175 addition(A,multiplication(A,c2)) = A. [para(166(a,1),38(a,2,2)),rewrite([29(2),29(5)])].
% 60.74/61.05 176 addition(A,multiplication(c2,A)) = A. [para(166(a,1),40(a,2,1)),rewrite([30(2),30(5)])].
% 60.74/61.05 190 addition(one,c1) = one. [para(80(a,1),64(a,1,2)),rewrite([33(3),80(7)])].
% 60.74/61.05 239 multiplication(c2,addition(A,c(c2))) = multiplication(c2,A). [para(109(a,1),38(a,1,1)),rewrite([65(4),33(6)]),flip(a)].
% 60.74/61.05 240 multiplication(addition(A,c2),c(c2)) = multiplication(A,c(c2)). [para(109(a,1),40(a,1,1)),rewrite([65(5),33(5)]),flip(a)].
% 60.74/61.05 243 multiplication(addition(c2,multiplication(A,B)),c(c2)) = multiplication(A,multiplication(B,c(c2))). [para(109(a,1),68(a,1,2)),rewrite([33(6),65(6)]),flip(a)].
% 60.74/61.05 259 addition(c(c1),f1(c(c1))) = one. [resolve(115,a,46,a),rewrite([33(6)])].
% 60.74/61.05 328 c(zero) = one. [resolve(101,b,127,a)].
% 60.74/61.05 330 one = A | -complement(zero,A). [back_rewrite(101),rewrite([328(2)])].
% 60.74/61.05 333 -complement(zero,addition(c1,addition(c2,multiplication(c(c1),c(c2))))). [ur(330,a,119,a(flip))].
% 60.74/61.05 341 addition(zero,addition(c1,addition(c2,multiplication(c(c1),c(c2))))) != one. [ur(48,a,333,a,b,31,a,c,32,a)].
% 60.74/61.05 343 -complement(zero,addition(zero,addition(c1,addition(c2,multiplication(c(c1),c(c2)))))). [ur(330,a,341,a(flip))].
% 60.74/61.05 344 addition(A,addition(B,multiplication(A,c2))) = addition(A,B). [para(175(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 60.74/61.05 347 addition(A,addition(B,multiplication(c2,A))) = addition(A,B). [para(176(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 60.74/61.05 400 addition(one,c(c1)) = one. [para(259(a,1),64(a,1,2)),rewrite([33(4),259(10)])].
% 60.74/61.05 409 addition(A,multiplication(c(c1),A)) = A. [para(400(a,1),40(a,2,1)),rewrite([30(2),30(6)])].
% 60.74/61.05 496 addition(A,addition(B,multiplication(c(c1),A))) = addition(A,B). [para(409(a,1),35(a,2,2)),rewrite([33(4),33(6)])].
% 60.74/61.05 578 multiplication(c2,c2) = c2. [para(108(a,1),239(a,1,2)),rewrite([29(3)]),flip(a)].
% 60.74/61.05 583 multiplication(c2,multiplication(c2,A)) = multiplication(c2,A). [para(578(a,1),36(a,1,1)),flip(a)].
% 60.74/61.05 584 multiplication(c2,addition(A,c2)) = multiplication(c2,addition(A,one)). [para(578(a,1),38(a,1,1)),rewrite([66(4,R),33(7)]),flip(a)].
% 60.74/61.05 585 multiplication(addition(A,c2),c2) = multiplication(addition(A,one),c2). [para(578(a,1),40(a,1,1)),rewrite([67(4,R),33(6)]),flip(a)].
% 60.74/61.05 638 multiplication(c2,addition(A,multiplication(c2,B))) = multiplication(c2,addition(B,A)). [para(583(a,1),38(a,1,1)),rewrite([38(5),33(7)]),flip(a)].
% 60.74/61.05 1008 addition(multiplication(A,c(c2)),multiplication(addition(A,c2),B)) = multiplication(addition(A,c2),addition(B,c(c2))). [para(240(a,1),38(a,1,1)),rewrite([33(12)])].
% 60.74/61.05 1127 addition(A,multiplication(addition(A,B),c2)) = addition(A,multiplication(B,c2)). [para(40(a,1),344(a,1,2)),rewrite([33(1)])].
% 60.74/61.05 1133 addition(one,addition(c2,c(c1))) = one. [para(400(a,1),344(a,2)),rewrite([30(6),33(5)])].
% 60.74/61.05 7790 addition(c1,multiplication(c(c1),c2)) = addition(c1,c2). [para(116(a,1),1127(a,1,2,1)),rewrite([30(4)]),flip(a)].
% 60.74/61.05 7795 addition(one,multiplication(c(c1),c2)) = one. [para(400(a,1),1127(a,1,2,1)),rewrite([30(4),166(3)]),flip(a)].
% 60.74/61.05 7866 addition(A,multiplication(c(c1),multiplication(c2,A))) = A. [para(7795(a,1),40(a,2,1)),rewrite([30(2),36(5),30(8)])].
% 60.74/61.05 7957 multiplication(c2,addition(multiplication(c2,c1),multiplication(c(c1),c2))) = c2. [para(7790(a,1),638(a,2,2)),rewrite([33(9),584(15),33(14),190(14),29(13)])].
% 60.74/61.05 8017 multiplication(c(c1),addition(one,multiplication(c2,c(c1)))) = c(c1). [para(7866(a,1),66(a,2)),rewrite([33(8)])].
% 60.74/61.05 8275 addition(multiplication(c2,c1),multiplication(c(c1),c2)) = c2. [para(7957(a,1),67(a,2,2)),rewrite([33(3),166(3),30(10),33(18),496(18),66(13,R),33(12),190(12),29(11)])].
% 60.74/61.05 8278 addition(c(c1),multiplication(c2,c1)) = addition(c2,c(c1)). [para(8275(a,1),138(a,2,2)),rewrite([33(8),166(8),29(7),33(6),33(10)])].
% 60.74/61.05 8348 addition(c1,addition(c2,c(c1))) = one. [para(8278(a,1),347(a,1,2)),rewrite([116(10)])].
% 60.74/61.05 8374 addition(one,multiplication(c2,c(c1))) = one. [para(8017(a,1),67(a,2,2)),rewrite([33(4),400(4),30(8),33(15),347(15),33(10),400(10)])].
% 60.74/61.05 8375 multiplication(addition(c2,c(c1)),c(c2)) = multiplication(c(c1),c(c2)). [para(8017(a,1),243(a,1,1,2)),rewrite([8374(15),30(13)])].
% 60.74/61.05 23294 addition(multiplication(A,c(c2)),multiplication(addition(A,one),c2)) = addition(A,c2). [para(108(a,1),1008(a,2,2)),rewrite([585(7),29(12)])].
% 60.74/61.05 27824 addition(c2,multiplication(c(c1),c(c2))) = addition(c2,c(c1)). [para(8375(a,1),23294(a,1,1)),rewrite([33(11),1133(11),30(8),33(7),33(13),64(13)])].
% 60.74/61.05 27825 $F. [back_rewrite(343),rewrite([27824(10),8348(8),104(4)]),unit_del(a,127)].
% 60.74/61.05
% 60.74/61.05 % SZS output end Refutation
% 60.74/61.05 ============================== end of proof ==========================
% 60.74/61.05
% 60.74/61.05 ============================== STATISTICS ============================
% 60.74/61.05
% 60.74/61.05 Given=3936. Generated=2634923. Kept=27792. proofs=1.
% 60.74/61.05 Usable=3693. Sos=9980. Demods=1678. Limbo=1, Disabled=14155. Hints=0.
% 60.74/61.05 Megabytes=21.49.
% 60.74/61.05 User_CPU=58.67, System_CPU=1.41, Wall_clock=60.
% 60.74/61.05
% 60.74/61.05 ============================== end of statistics =====================
% 60.74/61.05
% 60.74/61.05 ============================== end of search =========================
% 60.74/61.05
% 60.74/61.05 THEOREM PROVED
% 60.74/61.05 % SZS status Theorem
% 60.74/61.05
% 60.74/61.05 Exiting with 1 proof.
% 60.74/61.05
% 60.74/61.05 Process 26726 exit (max_proofs) Thu Jun 16 10:28:43 2022
% 60.74/61.05 Prover9 interrupted
%------------------------------------------------------------------------------