TSTP Solution File: KLE022+4 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE022+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 02:21:47 EDT 2022
% Result : Theorem 0.75s 1.07s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE022+4 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n008.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 13:07:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.01 ============================== Prover9 ===============================
% 0.44/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.01 Process 20745 was started by sandbox2 on n008.cluster.edu,
% 0.44/1.01 Thu Jun 16 13:07:23 2022
% 0.44/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_20592_n008.cluster.edu".
% 0.44/1.01 ============================== end of head ===========================
% 0.44/1.01
% 0.44/1.01 ============================== INPUT =================================
% 0.44/1.01
% 0.44/1.01 % Reading from file /tmp/Prover9_20592_n008.cluster.edu
% 0.44/1.01
% 0.44/1.01 set(prolog_style_variables).
% 0.44/1.01 set(auto2).
% 0.44/1.01 % set(auto2) -> set(auto).
% 0.44/1.01 % set(auto) -> set(auto_inference).
% 0.44/1.01 % set(auto) -> set(auto_setup).
% 0.44/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.01 % set(auto) -> set(auto_limits).
% 0.44/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.01 % set(auto) -> set(auto_denials).
% 0.44/1.01 % set(auto) -> set(auto_process).
% 0.44/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.01 % set(auto2) -> assign(stats, some).
% 0.44/1.01 % set(auto2) -> clear(echo_input).
% 0.44/1.01 % set(auto2) -> set(quiet).
% 0.44/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.01 % set(auto2) -> clear(print_given).
% 0.44/1.01 assign(lrs_ticks,-1).
% 0.44/1.01 assign(sos_limit,10000).
% 0.44/1.01 assign(order,kbo).
% 0.44/1.01 set(lex_order_vars).
% 0.44/1.01 clear(print_given).
% 0.44/1.01
% 0.44/1.01 % formulas(sos). % not echoed (19 formulas)
% 0.44/1.01
% 0.44/1.01 ============================== end of input ==========================
% 0.44/1.01
% 0.44/1.01 % From the command line: assign(max_seconds, 300).
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.01
% 0.44/1.01 % Formulas that are not ordinary clauses:
% 0.44/1.01 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.44/1.01 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].
% 0.44/1.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 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].
% 0.75/1.07 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 19 -(all X0 all X1 (test(X1) -> leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) & leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.07
% 0.75/1.07 ============================== end of process non-clausal formulas ===
% 0.75/1.07
% 0.75/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.07
% 0.75/1.07 ============================== PREDICATE ELIMINATION =================
% 0.75/1.07 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.75/1.07 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.75/1.07 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.07 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 0.75/1.07 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.07 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.75/1.07 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.07 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.75/1.07 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.75/1.07 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 0.75/1.07 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 0.75/1.07 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 0.75/1.07 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 0.75/1.07 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.75/1.07 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.75/1.07 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.07 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.75/1.07 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 0.75/1.07
% 0.75/1.07 ============================== end predicate elimination =============
% 0.75/1.07
% 0.75/1.07 Auto_denials: (non-Horn, no changes).
% 0.75/1.07
% 0.75/1.07 Term ordering decisions:
% 0.75/1.07 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 0.75/1.07
% 0.75/1.07 ============================== end of process initial clauses ========
% 0.75/1.07
% 0.75/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.07
% 0.75/1.07 ============================== end of clauses for search =============
% 0.75/1.07
% 0.75/1.07 ============================== SEARCH ================================
% 0.75/1.07
% 0.75/1.07 % Starting search at 0.01 seconds.
% 0.75/1.07
% 0.75/1.07 ============================== PROOF =================================
% 0.75/1.07 % SZS status Theorem
% 0.75/1.07 % SZS output start Refutation
% 0.75/1.07
% 0.75/1.07 % Proof 1 at 0.07 (+ 0.01) seconds.
% 0.75/1.07 % Length of proof is 62.
% 0.75/1.07 % Level of proof is 12.
% 0.75/1.07 % Maximum clause weight is 17.000.
% 0.75/1.07 % Given clauses 121.
% 0.75/1.07
% 0.75/1.07 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 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].
% 0.75/1.07 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 19 -(all X0 all X1 (test(X1) -> leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) & leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.07 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.75/1.07 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.75/1.07 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.07 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.07 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.75/1.07 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.75/1.07 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.75/1.07 28 test(c2) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.75/1.07 29 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.75/1.07 30 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.75/1.07 31 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.75/1.07 32 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.75/1.07 33 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.75/1.07 36 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.75/1.07 40 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.75/1.07 41 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(40),flip(a)].
% 0.75/1.07 42 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.75/1.07 43 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(42),flip(a)].
% 0.75/1.07 44 -leq(c1,addition(multiplication(c1,c2),multiplication(c1,c(c2)))) | -leq(addition(multiplication(c1,c2),multiplication(c1,c(c2))),c1) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.75/1.07 45 -leq(c1,multiplication(c1,addition(c2,c(c2)))) | -leq(multiplication(c1,addition(c2,c(c2))),c1). [copy(44),rewrite([41(9),41(16)])].
% 0.75/1.07 47 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.75/1.07 48 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)].
% 0.75/1.07 49 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(48),flip(c)].
% 0.75/1.07 50 -test(A) | -test(B) | c(multiplication(A,B)) = addition(c(A),c(B)) # label(test_deMorgan2) # label(axiom). [clausify(18)].
% 0.75/1.07 51 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(A,B)). [copy(50),flip(c)].
% 0.75/1.07 53 multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.75/1.07 54 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.75/1.07 58 -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 0.75/1.07 59 -test(A) | c(A) != B | addition(A,B) = one. [copy(58),rewrite([36(4)])].
% 0.75/1.07 60 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.75/1.07 61 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.75/1.07 63 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(49,a,b),rewrite([30(5)])].
% 0.75/1.07 73 leq(A,A). [resolve(47,b,30,a)].
% 0.75/1.07 98 c(c2) != A | addition(A,c2) = one. [resolve(59,a,28,a),rewrite([36(5)])].
% 0.75/1.07 102 test(one). [resolve(61,c,29,a),rewrite([33(3),31(6)]),xx(a),xx(b)].
% 0.75/1.07 113 multiplication(c(c2),c(c2)) = c(c2). [resolve(63,a,28,a)].
% 0.75/1.07 124 addition(one,f1(one)) = one. [resolve(102,a,54,b)].
% 0.75/1.07 125 f1(one) = zero. [resolve(102,a,53,b),rewrite([31(4)])].
% 0.75/1.07 129 addition(zero,one) = one. [back_rewrite(124),rewrite([125(3),36(3)])].
% 0.75/1.07 130 -test(zero) | c(zero) = one. [para(125(a,1),60(a,1)),rewrite([125(4)]),unit_del(c,102)].
% 0.75/1.07 135 test(zero). [resolve(129,a,61,c),rewrite([31(3),33(6)]),xx(a),xx(b)].
% 0.75/1.07 137 c(zero) = one. [back_unit_del(130),unit_del(a,135)].
% 0.75/1.07 140 -test(A) | addition(one,c(A)) = one. [resolve(135,a,51,b),rewrite([137(4),36(4),33(6),137(6)])].
% 0.75/1.07 372 addition(one,c(c2)) = one. [resolve(140,a,28,a)].
% 0.75/1.07 374 addition(A,multiplication(c(c2),A)) = A. [para(372(a,1),43(a,2,1)),rewrite([32(2),32(6)])].
% 0.75/1.07 541 addition(c2,c(c2)) = one. [resolve(98,a,374,a(flip)),rewrite([113(7),30(5),36(4)])].
% 0.75/1.07 544 $F. [back_rewrite(45),rewrite([541(6),31(4),541(8),31(6)]),merge(b),unit_del(a,73)].
% 0.75/1.07
% 0.75/1.07 % SZS output end Refutation
% 0.75/1.07 ============================== end of proof ==========================
% 0.75/1.07
% 0.75/1.07 ============================== STATISTICS ============================
% 0.75/1.07
% 0.75/1.07 Given=121. Generated=1713. Kept=509. proofs=1.
% 0.75/1.07 Usable=110. Sos=315. Demods=165. Limbo=3, Disabled=117. Hints=0.
% 0.75/1.07 Megabytes=0.53.
% 0.75/1.07 User_CPU=0.07, System_CPU=0.01, Wall_clock=0.
% 0.75/1.07
% 0.75/1.07 ============================== end of statistics =====================
% 0.75/1.07
% 0.75/1.07 ============================== end of search =========================
% 0.75/1.07
% 0.75/1.07 THEOREM PROVED
% 0.75/1.07 % SZS status Theorem
% 0.75/1.07
% 0.75/1.07 Exiting with 1 proof.
% 0.75/1.07
% 0.75/1.07 Process 20745 exit (max_proofs) Thu Jun 16 13:07:23 2022
% 0.75/1.07 Prover9 interrupted
%------------------------------------------------------------------------------