TSTP Solution File: KLE078+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE078+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 02:22:07 EDT 2022
% Result : Theorem 0.93s 1.19s
% Output : Refutation 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KLE078+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n019.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 10:33:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.67/0.96 ============================== Prover9 ===============================
% 0.67/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.96 Process 30138 was started by sandbox2 on n019.cluster.edu,
% 0.67/0.96 Thu Jun 16 10:33:10 2022
% 0.67/0.96 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29985_n019.cluster.edu".
% 0.67/0.96 ============================== end of head ===========================
% 0.67/0.96
% 0.67/0.96 ============================== INPUT =================================
% 0.67/0.96
% 0.67/0.96 % Reading from file /tmp/Prover9_29985_n019.cluster.edu
% 0.67/0.96
% 0.67/0.96 set(prolog_style_variables).
% 0.67/0.96 set(auto2).
% 0.67/0.96 % set(auto2) -> set(auto).
% 0.67/0.96 % set(auto) -> set(auto_inference).
% 0.67/0.96 % set(auto) -> set(auto_setup).
% 0.67/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.96 % set(auto) -> set(auto_limits).
% 0.67/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.96 % set(auto) -> set(auto_denials).
% 0.67/0.96 % set(auto) -> set(auto_process).
% 0.67/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.96 % set(auto2) -> assign(stats, some).
% 0.67/0.96 % set(auto2) -> clear(echo_input).
% 0.67/0.96 % set(auto2) -> set(quiet).
% 0.67/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.96 % set(auto2) -> clear(print_given).
% 0.67/0.96 assign(lrs_ticks,-1).
% 0.67/0.96 assign(sos_limit,10000).
% 0.67/0.96 assign(order,kbo).
% 0.67/0.96 set(lex_order_vars).
% 0.67/0.96 clear(print_given).
% 0.67/0.96
% 0.67/0.96 % formulas(sos). % not echoed (18 formulas)
% 0.67/0.96
% 0.67/0.96 ============================== end of input ==========================
% 0.67/0.96
% 0.67/0.96 % From the command line: assign(max_seconds, 300).
% 0.67/0.96
% 0.67/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.96
% 0.67/0.96 % Formulas that are not ordinary clauses:
% 0.67/0.96 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 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].
% 0.67/0.96 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 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].
% 0.67/0.96 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 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].
% 0.67/0.96 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].
% 0.67/0.96 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 13 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 17 -(all X0 ((all X1 (addition(domain(X1),antidomain(X1)) = one & multiplication(domain(X1),antidomain(X1)) = zero)) -> domain(antidomain(X0)) = antidomain(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.93/1.19
% 0.93/1.19 ============================== end of process non-clausal formulas ===
% 0.93/1.19
% 0.93/1.19 ============================== PROCESS INITIAL CLAUSES ===============
% 0.93/1.19
% 0.93/1.19 ============================== PREDICATE ELIMINATION =================
% 0.93/1.19 18 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.93/1.19 19 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.93/1.19
% 0.93/1.19 ============================== end predicate elimination =============
% 0.93/1.19
% 0.93/1.19 Auto_denials:
% 0.93/1.19 % copying label goals to answer in negative clause
% 0.93/1.19
% 0.93/1.19 Term ordering decisions:
% 0.93/1.19 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. domain=1. antidomain=1.
% 0.93/1.19
% 0.93/1.19 ============================== end of process initial clauses ========
% 0.93/1.19
% 0.93/1.19 ============================== CLAUSES FOR SEARCH ====================
% 0.93/1.19
% 0.93/1.19 ============================== end of clauses for search =============
% 0.93/1.19
% 0.93/1.19 ============================== SEARCH ================================
% 0.93/1.19
% 0.93/1.19 % Starting search at 0.01 seconds.
% 0.93/1.19
% 0.93/1.19 ============================== PROOF =================================
% 0.93/1.19 % SZS status Theorem
% 0.93/1.19 % SZS output start Refutation
% 0.93/1.19
% 0.93/1.19 % Proof 1 at 0.22 (+ 0.01) seconds: goals.
% 0.93/1.19 % Length of proof is 64.
% 0.93/1.19 % Level of proof is 14.
% 0.93/1.19 % Maximum clause weight is 24.000.
% 0.93/1.19 % Given clauses 189.
% 0.93/1.19
% 0.93/1.19 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 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].
% 0.93/1.19 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 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].
% 0.93/1.19 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].
% 0.93/1.19 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 13 (all X0 addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 14 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 15 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 16 (all X0 all X1 domain(addition(X0,X1)) = addition(domain(X0),domain(X1))) # label(domain5) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 17 -(all X0 ((all X1 (addition(domain(X1),antidomain(X1)) = one & multiplication(domain(X1),antidomain(X1)) = zero)) -> domain(antidomain(X0)) = antidomain(X0))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.93/1.19 20 domain(zero) = zero # label(domain4) # label(axiom). [assumption].
% 0.93/1.19 21 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.93/1.19 23 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.93/1.19 24 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.93/1.19 25 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.93/1.19 26 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 0.93/1.19 27 addition(domain(A),one) = one # label(domain3) # label(axiom). [clausify(15)].
% 0.93/1.19 28 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.93/1.19 29 addition(domain(A),antidomain(A)) = one # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.93/1.19 30 multiplication(domain(A),antidomain(A)) = zero # label(goals) # label(negated_conjecture). [clausify(17)].
% 0.93/1.19 31 domain(multiplication(A,domain(B))) = domain(multiplication(A,B)) # label(domain2) # label(axiom). [clausify(14)].
% 0.93/1.19 32 domain(addition(A,B)) = addition(domain(A),domain(B)) # label(domain5) # label(axiom). [clausify(16)].
% 0.93/1.19 33 addition(domain(A),domain(B)) = domain(addition(A,B)). [copy(32),flip(a)].
% 0.93/1.19 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 0.93/1.19 37 multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)) # label(domain1) # label(axiom). [clausify(13)].
% 0.93/1.19 38 addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A). [copy(37),flip(a)].
% 0.93/1.19 39 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.93/1.19 40 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(39),flip(a)].
% 0.93/1.19 41 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 0.93/1.19 42 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(41),flip(a)].
% 0.93/1.19 43 antidomain(c1) != domain(antidomain(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 0.93/1.19 44 domain(antidomain(c1)) != antidomain(c1) # answer(goals). [copy(43),flip(a)].
% 0.93/1.19 45 addition(one,domain(A)) = one. [back_rewrite(27),rewrite([28(3)])].
% 0.93/1.19 46 domain(antidomain(c1)) = c_0. [new_symbol(44)].
% 0.93/1.19 47 antidomain(c1) != c_0 # answer(goals). [back_rewrite(44),rewrite([46(3)]),flip(a)].
% 0.93/1.19 50 addition(domain(multiplication(A,B)),antidomain(multiplication(A,domain(B)))) = one. [para(31(a,1),29(a,1,1))].
% 0.93/1.19 59 addition(multiplication(A,domain(B)),multiplication(domain(multiplication(A,B)),multiplication(A,domain(B)))) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))). [para(31(a,1),38(a,1,2,1)),rewrite([31(11)])].
% 0.93/1.19 62 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(21(a,1),40(a,2,2)),rewrite([25(3),28(3)])].
% 0.93/1.19 65 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(24(a,1),42(a,1,1)),rewrite([28(4)]),flip(a)].
% 0.93/1.19 70 multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))) = multiplication(A,domain(B)). [back_rewrite(59),rewrite([65(8,R),28(4),45(4),24(4)]),flip(a)].
% 0.93/1.19 73 addition(A,multiplication(domain(B),A)) = A. [para(45(a,1),42(a,2,1)),rewrite([24(2),24(5)])].
% 0.93/1.19 74 multiplication(domain(A),A) = A. [back_rewrite(38),rewrite([73(3)]),flip(a)].
% 0.93/1.19 79 addition(one,c_0) = one. [para(46(a,1),45(a,1,2))].
% 0.93/1.19 88 addition(A,multiplication(c_0,A)) = A. [para(79(a,1),42(a,2,1)),rewrite([24(2),24(5)])].
% 0.93/1.19 99 multiplication(addition(A,domain(B)),B) = addition(B,multiplication(A,B)). [para(74(a,1),42(a,1,1)),rewrite([28(4)]),flip(a)].
% 0.93/1.19 100 multiplication(c_0,antidomain(c1)) = antidomain(c1). [para(46(a,1),74(a,1,1))].
% 0.93/1.19 104 addition(zero,antidomain(multiplication(domain(A),domain(antidomain(A))))) = one. [para(30(a,1),50(a,1,1,1)),rewrite([20(2)])].
% 0.93/1.19 167 addition(zero,antidomain(A)) = antidomain(A). [para(30(a,1),73(a,1,2)),rewrite([28(3)])].
% 0.93/1.19 173 antidomain(multiplication(domain(A),domain(antidomain(A)))) = one. [back_rewrite(104),rewrite([167(7)])].
% 0.93/1.19 329 antidomain(multiplication(domain(c1),c_0)) = one. [para(46(a,1),173(a,1,1,2))].
% 0.93/1.19 336 domain(multiplication(domain(c1),c_0)) = zero. [para(329(a,1),30(a,1,2)),rewrite([23(7)])].
% 0.93/1.19 342 multiplication(domain(c1),c_0) = zero. [para(336(a,1),74(a,1,1)),rewrite([26(6)]),flip(a)].
% 0.93/1.19 343 multiplication(domain(c1),multiplication(c_0,A)) = zero. [para(342(a,1),36(a,1,1)),rewrite([26(2)]),flip(a)].
% 0.93/1.19 716 multiplication(domain(addition(A,B)),B) = B. [para(33(a,1),99(a,1,1)),rewrite([73(6)])].
% 0.93/1.19 751 multiplication(domain(A),multiplication(c_0,A)) = multiplication(c_0,A). [para(88(a,1),716(a,1,1,1))].
% 0.93/1.19 1112 multiplication(c_0,c1) = zero. [para(751(a,1),343(a,1))].
% 0.93/1.19 1125 multiplication(c_0,domain(c1)) = zero. [para(1112(a,1),70(a,1,1,1)),rewrite([20(2),26(6)]),flip(a)].
% 0.93/1.19 1127 multiplication(c_0,addition(A,domain(c1))) = multiplication(c_0,A). [para(1125(a,1),40(a,1,1)),rewrite([62(4),28(6)]),flip(a)].
% 0.93/1.19 1476 antidomain(c1) = c_0. [para(100(a,1),1127(a,2)),rewrite([28(6),29(6),23(3)]),flip(a)].
% 0.93/1.19 1477 $F # answer(goals). [resolve(1476,a,47,a)].
% 0.93/1.19
% 0.93/1.19 % SZS output end Refutation
% 0.93/1.19 ============================== end of proof ==========================
% 0.93/1.19
% 0.93/1.19 ============================== STATISTICS ============================
% 0.93/1.19
% 0.93/1.19 Given=189. Generated=10974. Kept=1451. proofs=1.
% 0.93/1.19 Usable=178. Sos=1111. Demods=1259. Limbo=4, Disabled=178. Hints=0.
% 0.93/1.19 Megabytes=1.73.
% 0.93/1.19 User_CPU=0.23, System_CPU=0.01, Wall_clock=0.
% 0.93/1.19
% 0.93/1.19 ============================== end of statistics =====================
% 0.93/1.19
% 0.93/1.19 ============================== end of search =========================
% 0.93/1.19
% 0.93/1.19 THEOREM PROVED
% 0.93/1.19 % SZS status Theorem
% 0.93/1.19
% 0.93/1.19 Exiting with 1 proof.
% 0.93/1.19
% 0.93/1.19 Process 30138 exit (max_proofs) Thu Jun 16 10:33:10 2022
% 0.93/1.19 Prover9 interrupted
%------------------------------------------------------------------------------