TSTP Solution File: KLE113+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE113+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 02:22:17 EDT 2022
% Result : Theorem 0.73s 1.02s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : KLE113+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 11:05:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.01 ============================== Prover9 ===============================
% 0.43/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.01 Process 19254 was started by sandbox on n011.cluster.edu,
% 0.43/1.01 Thu Jun 16 11:05:52 2022
% 0.43/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19100_n011.cluster.edu".
% 0.43/1.01 ============================== end of head ===========================
% 0.43/1.01
% 0.43/1.01 ============================== INPUT =================================
% 0.43/1.01
% 0.43/1.01 % Reading from file /tmp/Prover9_19100_n011.cluster.edu
% 0.43/1.01
% 0.43/1.01 set(prolog_style_variables).
% 0.43/1.01 set(auto2).
% 0.43/1.01 % set(auto2) -> set(auto).
% 0.43/1.01 % set(auto) -> set(auto_inference).
% 0.43/1.01 % set(auto) -> set(auto_setup).
% 0.43/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.01 % set(auto) -> set(auto_limits).
% 0.43/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.01 % set(auto) -> set(auto_denials).
% 0.43/1.01 % set(auto) -> set(auto_process).
% 0.43/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.01 % set(auto2) -> assign(stats, some).
% 0.43/1.01 % set(auto2) -> clear(echo_input).
% 0.43/1.01 % set(auto2) -> set(quiet).
% 0.43/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.01 % set(auto2) -> clear(print_given).
% 0.43/1.01 assign(lrs_ticks,-1).
% 0.43/1.01 assign(sos_limit,10000).
% 0.43/1.01 assign(order,kbo).
% 0.43/1.01 set(lex_order_vars).
% 0.43/1.01 clear(print_given).
% 0.43/1.01
% 0.43/1.01 % formulas(sos). % not echoed (27 formulas)
% 0.43/1.01
% 0.43/1.01 ============================== end of input ==========================
% 0.43/1.01
% 0.43/1.01 % From the command line: assign(max_seconds, 300).
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.01
% 0.43/1.01 % Formulas that are not ordinary clauses:
% 0.43/1.01 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 14 (all X0 all X1 addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1))))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 18 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 27 -(all X0 forward_diamond(X0,zero) = zero) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.02
% 0.73/1.02 ============================== end of process non-clausal formulas ===
% 0.73/1.02
% 0.73/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.02
% 0.73/1.02 ============================== PREDICATE ELIMINATION =================
% 0.73/1.02 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 0.73/1.02 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 0.73/1.02
% 0.73/1.02 ============================== end predicate elimination =============
% 0.73/1.02
% 0.73/1.02 Auto_denials:
% 0.73/1.02 % copying label goals to answer in negative clause
% 0.73/1.02
% 0.73/1.02 Term ordering decisions:
% 0.73/1.02 Function symbol KB weights: zero=1. one=1. c1=1. multiplication=1. addition=1. backward_diamond=1. forward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. c=1. domain=1. codomain=1.
% 0.73/1.02
% 0.73/1.02 ============================== end of process initial clauses ========
% 0.73/1.02
% 0.73/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.02
% 0.73/1.02 ============================== end of clauses for search =============
% 0.73/1.02
% 0.73/1.02 ============================== SEARCH ================================
% 0.73/1.02
% 0.73/1.02 % Starting search at 0.01 seconds.
% 0.73/1.02
% 0.73/1.02 ============================== PROOF =================================
% 0.73/1.02 % SZS status Theorem
% 0.73/1.02 % SZS output start Refutation
% 0.73/1.02
% 0.73/1.02 % Proof 1 at 0.02 (+ 0.00) seconds: goals.
% 0.73/1.02 % Length of proof is 32.
% 0.73/1.02 % Level of proof is 6.
% 0.73/1.02 % Maximum clause weight is 13.000.
% 0.73/1.02 % Given clauses 33.
% 0.73/1.02
% 0.73/1.02 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 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].
% 0.73/1.02 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.02 27 -(all X0 forward_diamond(X0,zero) = zero) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.02 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 0.73/1.02 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 0.73/1.02 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 0.73/1.02 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 0.73/1.02 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 0.73/1.02 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 0.73/1.02 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 0.73/1.02 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 0.73/1.02 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 0.73/1.02 49 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 0.73/1.02 50 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(49),rewrite([37(2),37(5)])].
% 0.73/1.02 60 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 0.73/1.02 61 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(60),flip(a)].
% 0.73/1.02 68 forward_diamond(c1,zero) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 0.73/1.02 69 antidomain(antidomain(multiplication(c1,antidomain(antidomain(zero))))) != zero # answer(goals). [copy(68),rewrite([50(3)])].
% 0.73/1.02 70 antidomain(one) = zero. [para(36(a,1),32(a,1)),flip(a)].
% 0.73/1.02 76 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),61(a,2,2)),rewrite([34(3),42(3)])].
% 0.73/1.02 99 addition(zero,antidomain(zero)) = one. [para(70(a,1),44(a,1,1)),rewrite([70(3)])].
% 0.73/1.02 103 multiplication(A,antidomain(zero)) = A. [para(99(a,1),61(a,2,2)),rewrite([34(2),76(5),32(5)])].
% 0.73/1.02 111 antidomain(zero) = one. [para(103(a,1),33(a,1)),flip(a)].
% 0.73/1.02 114 $F # answer(goals). [back_rewrite(69),rewrite([111(3),70(3),34(3),111(2),70(2)]),xx(a)].
% 0.73/1.02
% 0.73/1.02 % SZS output end Refutation
% 0.73/1.02 ============================== end of proof ==========================
% 0.73/1.02
% 0.73/1.02 ============================== STATISTICS ============================
% 0.73/1.02
% 0.73/1.02 Given=33. Generated=353. Kept=70. proofs=1.
% 0.73/1.02 Usable=29. Sos=25. Demods=57. Limbo=3, Disabled=41. Hints=0.
% 0.73/1.02 Megabytes=0.12.
% 0.73/1.02 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.73/1.02
% 0.73/1.02 ============================== end of statistics =====================
% 0.73/1.02
% 0.73/1.02 ============================== end of search =========================
% 0.73/1.02
% 0.73/1.02 THEOREM PROVED
% 0.73/1.02 % SZS status Theorem
% 0.73/1.02
% 0.73/1.02 Exiting with 1 proof.
% 0.73/1.02
% 0.73/1.02 Process 19254 exit (max_proofs) Thu Jun 16 11:05:52 2022
% 0.73/1.02 Prover9 interrupted
%------------------------------------------------------------------------------