TSTP Solution File: KLE026+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE026+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 02:21:49 EDT 2022
% Result : Theorem 0.43s 1.02s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE026+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 600
% 0.17/0.33 % DateTime : Thu Jun 16 14:21:37 EDT 2022
% 0.17/0.33 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 25370 was started by sandbox on n009.cluster.edu,
% 0.43/0.99 Thu Jun 16 14:21:38 2022
% 0.43/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25217_n009.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_25217_n009.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (19 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.43/0.99 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/1.02 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 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].
% 0.43/1.02 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].
% 0.43/1.02 19 -(all X0 all X1 all X2 (test(X1) & test(X2) -> (multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) -> leq(multiplication(X1,X0),multiplication(X0,X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.02
% 0.43/1.02 ============================== end of process non-clausal formulas ===
% 0.43/1.02
% 0.43/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.02
% 0.43/1.02 ============================== PREDICATE ELIMINATION =================
% 0.43/1.02 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.43/1.02 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.43/1.02 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 0.43/1.02 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.43/1.02 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.43/1.02 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.43/1.02 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 0.43/1.02 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 0.43/1.02 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 0.43/1.02 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 0.43/1.02 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.43/1.02 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.43/1.02 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.43/1.02 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 0.43/1.02
% 0.43/1.02 ============================== end predicate elimination =============
% 0.43/1.02
% 0.43/1.02 Auto_denials: (non-Horn, no changes).
% 0.43/1.02
% 0.43/1.02 Term ordering decisions:
% 0.43/1.02 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. c=1. f1=1.
% 0.43/1.02
% 0.43/1.02 ============================== end of process initial clauses ========
% 0.43/1.02
% 0.43/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.43/1.02
% 0.43/1.02 ============================== end of clauses for search =============
% 0.43/1.02
% 0.43/1.02 ============================== SEARCH ================================
% 0.43/1.02
% 0.43/1.02 % Starting search at 0.02 seconds.
% 0.43/1.02
% 0.43/1.02 ============================== PROOF =================================
% 0.43/1.02 % SZS status Theorem
% 0.43/1.02 % SZS output start Refutation
% 0.43/1.02
% 0.43/1.02 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.43/1.02 % Length of proof is 34.
% 0.43/1.02 % Level of proof is 6.
% 0.43/1.02 % Maximum clause weight is 15.000.
% 0.43/1.02 % Given clauses 64.
% 0.43/1.02
% 0.43/1.02 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 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].
% 0.43/1.02 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 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].
% 0.43/1.02 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 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].
% 0.43/1.02 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 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].
% 0.43/1.02 19 -(all X0 all X1 all X2 (test(X1) & test(X2) -> (multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) -> leq(multiplication(X1,X0),multiplication(X0,X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.02 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.43/1.02 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.43/1.02 28 test(c2) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.43/1.02 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.43/1.02 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.43/1.02 37 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.43/1.02 38 multiplication(multiplication(c2,c1),c3) = multiplication(c2,c1) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.43/1.02 39 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 0.43/1.02 40 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(39),rewrite([37(2)]),flip(a)].
% 0.43/1.02 41 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.43/1.02 44 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.43/1.02 45 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(44),flip(a)].
% 0.43/1.02 46 -leq(multiplication(c2,c1),multiplication(c1,c3)) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.43/1.02 48 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.43/1.02 55 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.43/1.02 64 multiplication(c2,multiplication(c1,c3)) = multiplication(c2,c1). [back_rewrite(38),rewrite([41(5)])].
% 0.43/1.02 69 addition(A,addition(A,B)) = addition(A,B). [para(40(a,1),31(a,1)),rewrite([37(1),37(2),40(2,R),31(1),37(3)])].
% 0.43/1.02 72 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(33(a,1),45(a,1,1)),rewrite([37(4)]),flip(a)].
% 0.43/1.02 76 addition(multiplication(c1,c3),multiplication(c2,c1)) != multiplication(c1,c3). [ur(48,a,46,a),rewrite([37(7)])].
% 0.43/1.02 100 addition(c2,f1(c2)) = one. [resolve(55,b,28,a)].
% 0.43/1.02 189 addition(multiplication(c1,c3),multiplication(c2,c1)) = multiplication(addition(one,c2),multiplication(c1,c3)). [para(64(a,1),72(a,2,2)),rewrite([37(3)]),flip(a)].
% 0.43/1.02 194 multiplication(addition(one,c2),multiplication(c1,c3)) != multiplication(c1,c3). [back_rewrite(76),rewrite([189(7)])].
% 0.43/1.02 256 addition(one,c2) = one. [para(100(a,1),69(a,1,2)),rewrite([37(3),100(7)])].
% 0.43/1.02 258 $F. [back_rewrite(194),rewrite([256(3),33(5)]),xx(a)].
% 0.43/1.02
% 0.43/1.02 % SZS output end Refutation
% 0.43/1.02 ============================== end of proof ==========================
% 0.43/1.02
% 0.43/1.02 ============================== STATISTICS ============================
% 0.43/1.02
% 0.43/1.02 Given=64. Generated=718. Kept=224. proofs=1.
% 0.43/1.02 Usable=60. Sos=149. Demods=90. Limbo=2, Disabled=51. Hints=0.
% 0.43/1.02 Megabytes=0.28.
% 0.43/1.02 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.43/1.02
% 0.43/1.02 ============================== end of statistics =====================
% 0.43/1.02
% 0.43/1.02 ============================== end of search =========================
% 0.43/1.02
% 0.43/1.02 THEOREM PROVED
% 0.43/1.02 % SZS status Theorem
% 0.43/1.02
% 0.43/1.02 Exiting with 1 proof.
% 0.43/1.02
% 0.43/1.02 Process 25370 exit (max_proofs) Thu Jun 16 14:21:38 2022
% 0.43/1.02 Prover9 interrupted
%------------------------------------------------------------------------------