TSTP Solution File: KLE007+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE007+3 : 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 02:21:39 EDT 2022
% Result : Theorem 0.82s 1.09s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE007+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 11:55:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/0.98 ============================== Prover9 ===============================
% 0.43/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.98 Process 2473 was started by sandbox2 on n009.cluster.edu,
% 0.43/0.98 Thu Jun 16 11:55:23 2022
% 0.43/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2320_n009.cluster.edu".
% 0.43/0.98 ============================== end of head ===========================
% 0.43/0.98
% 0.43/0.98 ============================== INPUT =================================
% 0.43/0.98
% 0.43/0.98 % Reading from file /tmp/Prover9_2320_n009.cluster.edu
% 0.43/0.98
% 0.43/0.98 set(prolog_style_variables).
% 0.43/0.98 set(auto2).
% 0.43/0.98 % set(auto2) -> set(auto).
% 0.43/0.98 % set(auto) -> set(auto_inference).
% 0.43/0.98 % set(auto) -> set(auto_setup).
% 0.43/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.98 % set(auto) -> set(auto_limits).
% 0.43/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.98 % set(auto) -> set(auto_denials).
% 0.43/0.98 % set(auto) -> set(auto_process).
% 0.43/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.98 % set(auto2) -> assign(stats, some).
% 0.43/0.98 % set(auto2) -> clear(echo_input).
% 0.43/0.98 % set(auto2) -> set(quiet).
% 0.43/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.98 % set(auto2) -> clear(print_given).
% 0.43/0.98 assign(lrs_ticks,-1).
% 0.43/0.98 assign(sos_limit,10000).
% 0.43/0.98 assign(order,kbo).
% 0.43/0.98 set(lex_order_vars).
% 0.43/0.98 clear(print_given).
% 0.43/0.98
% 0.43/0.98 % formulas(sos). % not echoed (19 formulas)
% 0.43/0.98
% 0.43/0.98 ============================== end of input ==========================
% 0.43/0.98
% 0.43/0.98 % From the command line: assign(max_seconds, 300).
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.98
% 0.43/0.98 % Formulas that are not ordinary clauses:
% 0.43/0.98 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 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].
% 0.43/0.98 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 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].
% 0.43/0.98 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 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].
% 0.43/0.98 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].
% 0.43/0.98 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 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].
% 0.82/1.09 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 19 -(all X0 all X1 (test(X1) & test(X0) -> one = addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.09
% 0.82/1.09 ============================== end of process non-clausal formulas ===
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.09
% 0.82/1.09 ============================== PREDICATE ELIMINATION =================
% 0.82/1.09 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.82/1.09 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.82/1.09 22 -complement(A,B) | multiplication(B,A) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.82/1.09 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,a,20,b)].
% 0.82/1.09 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.82/1.09 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.82/1.09 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.82/1.09 Derived: addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.82/1.09 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.82/1.09 Derived: -test(A) | c(A) != B | test(B). [resolve(25,c,21,b)].
% 0.82/1.09 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(25,c,22,a)].
% 0.82/1.09 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(25,c,23,a)].
% 0.82/1.09 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 0.82/1.09 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.82/1.09 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.82/1.09 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.82/1.09 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.82/1.09 Derived: multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | -test(B) | c(B) = A. [resolve(27,a,26,c)].
% 0.82/1.09 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.82/1.09 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.82/1.09
% 0.82/1.09 ============================== end predicate elimination =============
% 0.82/1.09
% 0.82/1.09 Auto_denials: (non-Horn, no changes).
% 0.82/1.09
% 0.82/1.09 Term ordering decisions:
% 0.82/1.09 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 0.82/1.09
% 0.82/1.09 ============================== end of process initial clauses ========
% 0.82/1.09
% 0.82/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.09
% 0.82/1.09 ============================== end of clauses for search =============
% 0.82/1.09
% 0.82/1.09 ============================== SEARCH ================================
% 0.82/1.09
% 0.82/1.09 % Starting search at 0.01 seconds.
% 0.82/1.09
% 0.82/1.09 ============================== PROOF =================================
% 0.82/1.09 % SZS status Theorem
% 0.82/1.09 % SZS output start Refutation
% 0.82/1.09
% 0.82/1.09 % Proof 1 at 0.12 (+ 0.01) seconds.
% 0.82/1.09 % Length of proof is 65.
% 0.82/1.09 % Level of proof is 13.
% 0.82/1.09 % Maximum clause weight is 17.000.
% 0.82/1.09 % Given clauses 156.
% 0.82/1.09
% 0.82/1.09 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 19 -(all X0 all X1 (test(X1) & test(X0) -> one = addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.09 20 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom). [clausify(13)].
% 0.82/1.09 21 test(A) | -complement(B,A) # label(test_1) # label(axiom). [clausify(13)].
% 0.82/1.09 23 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom). [clausify(14)].
% 0.82/1.09 24 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom). [clausify(14)].
% 0.82/1.09 25 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.82/1.09 26 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom). [clausify(15)].
% 0.82/1.09 27 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom). [clausify(14)].
% 0.82/1.09 30 test(c2) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.82/1.09 31 test(c1) # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.82/1.09 32 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.82/1.09 33 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 0.82/1.09 34 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.82/1.09 35 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.82/1.09 36 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.82/1.09 39 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.82/1.09 43 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.82/1.09 44 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(43),flip(a)].
% 0.82/1.09 45 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.82/1.09 46 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(45),flip(a)].
% 0.82/1.09 47 addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c1,c(c1)),c(c2))) != one # label(goals) # label(negated_conjecture). [clausify(19)].
% 0.82/1.09 48 multiplication(addition(c1,c(c1)),addition(c2,c(c2))) != one. [copy(47),rewrite([44(14)])].
% 0.82/1.09 49 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)].
% 0.82/1.09 50 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(49),flip(c)].
% 0.82/1.09 51 -test(A) | -test(B) | c(multiplication(A,B)) = addition(c(A),c(B)) # label(test_deMorgan2) # label(axiom). [clausify(18)].
% 0.82/1.09 52 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(A,B)). [copy(51),flip(c)].
% 0.82/1.09 54 multiplication(f1(A),A) = zero | -test(A). [resolve(23,a,20,b)].
% 0.82/1.09 55 addition(A,f1(A)) = one | -test(A). [resolve(24,a,20,b)].
% 0.82/1.09 59 -test(A) | c(A) != B | addition(B,A) = one. [resolve(25,c,24,a)].
% 0.82/1.09 60 -test(A) | c(A) != B | addition(A,B) = one. [copy(59),rewrite([39(4)])].
% 0.82/1.09 61 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(26,c,20,b)].
% 0.82/1.09 62 multiplication(A,B) != zero | multiplication(B,A) != zero | addition(A,B) != one | test(A). [resolve(27,a,21,b)].
% 0.82/1.09 64 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(50,a,b),rewrite([33(5)])].
% 0.82/1.09 105 c(c1) != A | addition(A,c1) = one. [resolve(60,a,31,a),rewrite([39(5)])].
% 0.82/1.09 106 c(c2) != A | addition(A,c2) = one. [resolve(60,a,30,a),rewrite([39(5)])].
% 0.82/1.09 110 test(one). [resolve(62,c,32,a),rewrite([36(3),34(6)]),xx(a),xx(b)].
% 0.82/1.09 123 multiplication(c(c1),c(c1)) = c(c1). [resolve(64,a,31,a)].
% 0.82/1.09 124 multiplication(c(c2),c(c2)) = c(c2). [resolve(64,a,30,a)].
% 0.82/1.09 135 addition(one,f1(one)) = one. [resolve(110,a,55,b)].
% 0.82/1.09 136 f1(one) = zero. [resolve(110,a,54,b),rewrite([34(4)])].
% 0.82/1.09 140 addition(zero,one) = one. [back_rewrite(135),rewrite([136(3),39(3)])].
% 0.82/1.09 141 -test(zero) | c(zero) = one. [para(136(a,1),61(a,1)),rewrite([136(4)]),unit_del(c,110)].
% 0.82/1.09 142 test(zero). [resolve(140,a,62,c),rewrite([34(3),36(6)]),xx(a),xx(b)].
% 0.82/1.09 143 c(zero) = one. [back_unit_del(141),unit_del(a,142)].
% 0.82/1.09 146 -test(A) | addition(one,c(A)) = one. [resolve(142,a,52,b),rewrite([143(4),39(4),36(6),143(6)])].
% 0.82/1.09 486 addition(one,c(c1)) = one. [resolve(146,a,31,a)].
% 0.82/1.09 487 addition(one,c(c2)) = one. [resolve(146,a,30,a)].
% 0.82/1.09 489 addition(A,multiplication(c(c1),A)) = A. [para(486(a,1),46(a,2,1)),rewrite([35(2),35(6)])].
% 0.82/1.09 499 addition(A,multiplication(c(c2),A)) = A. [para(487(a,1),46(a,2,1)),rewrite([35(2),35(6)])].
% 0.82/1.09 912 addition(c1,c(c1)) = one. [resolve(105,a,489,a(flip)),rewrite([123(7),33(5),39(4)])].
% 0.82/1.09 917 addition(c2,c(c2)) != one. [back_rewrite(48),rewrite([912(4),35(6)])].
% 0.82/1.09 918 $F. [resolve(106,a,499,a(flip)),rewrite([124(7),33(5),39(4)]),unit_del(a,917)].
% 0.82/1.09
% 0.82/1.09 % SZS output end Refutation
% 0.82/1.09 ============================== end of proof ==========================
% 0.82/1.09
% 0.82/1.09 ============================== STATISTICS ============================
% 0.82/1.09
% 0.82/1.09 Given=156. Generated=2634. Kept=881. proofs=1.
% 0.82/1.09 Usable=145. Sos=597. Demods=367. Limbo=0, Disabled=176. Hints=0.
% 0.82/1.09 Megabytes=0.87.
% 0.82/1.09 User_CPU=0.12, System_CPU=0.01, Wall_clock=0.
% 0.82/1.09
% 0.82/1.09 ============================== end of statistics =====================
% 0.82/1.09
% 0.82/1.09 ============================== end of search =========================
% 0.82/1.09
% 0.82/1.09 THEOREM PROVED
% 0.82/1.09 % SZS status Theorem
% 0.82/1.09
% 0.82/1.09 Exiting with 1 proof.
% 0.82/1.09
% 0.82/1.09 Process 2473 exit (max_proofs) Thu Jun 16 11:55:23 2022
% 0.82/1.09 Prover9 interrupted
%------------------------------------------------------------------------------