TSTP Solution File: ROB022-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ROB022-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 : Mon Jul 18 20:55:31 EDT 2022
% Result : Unsatisfiable 0.92s 1.21s
% Output : Refutation 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ROB022-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n029.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 14:11:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.92/1.21 ============================== Prover9 ===============================
% 0.92/1.21 Prover9 (32) version 2009-11A, November 2009.
% 0.92/1.21 Process 12723 was started by sandbox2 on n029.cluster.edu,
% 0.92/1.21 Thu Jun 9 14:11:37 2022
% 0.92/1.21 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12570_n029.cluster.edu".
% 0.92/1.21 ============================== end of head ===========================
% 0.92/1.21
% 0.92/1.21 ============================== INPUT =================================
% 0.92/1.21
% 0.92/1.21 % Reading from file /tmp/Prover9_12570_n029.cluster.edu
% 0.92/1.21
% 0.92/1.21 set(prolog_style_variables).
% 0.92/1.21 set(auto2).
% 0.92/1.21 % set(auto2) -> set(auto).
% 0.92/1.21 % set(auto) -> set(auto_inference).
% 0.92/1.21 % set(auto) -> set(auto_setup).
% 0.92/1.21 % set(auto_setup) -> set(predicate_elim).
% 0.92/1.21 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.92/1.21 % set(auto) -> set(auto_limits).
% 0.92/1.21 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.92/1.21 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.92/1.21 % set(auto) -> set(auto_denials).
% 0.92/1.21 % set(auto) -> set(auto_process).
% 0.92/1.21 % set(auto2) -> assign(new_constants, 1).
% 0.92/1.21 % set(auto2) -> assign(fold_denial_max, 3).
% 0.92/1.21 % set(auto2) -> assign(max_weight, "200.000").
% 0.92/1.21 % set(auto2) -> assign(max_hours, 1).
% 0.92/1.21 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.92/1.21 % set(auto2) -> assign(max_seconds, 0).
% 0.92/1.21 % set(auto2) -> assign(max_minutes, 5).
% 0.92/1.21 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.92/1.21 % set(auto2) -> set(sort_initial_sos).
% 0.92/1.21 % set(auto2) -> assign(sos_limit, -1).
% 0.92/1.21 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.92/1.21 % set(auto2) -> assign(max_megs, 400).
% 0.92/1.21 % set(auto2) -> assign(stats, some).
% 0.92/1.21 % set(auto2) -> clear(echo_input).
% 0.92/1.21 % set(auto2) -> set(quiet).
% 0.92/1.21 % set(auto2) -> clear(print_initial_clauses).
% 0.92/1.21 % set(auto2) -> clear(print_given).
% 0.92/1.21 assign(lrs_ticks,-1).
% 0.92/1.21 assign(sos_limit,10000).
% 0.92/1.21 assign(order,kbo).
% 0.92/1.21 set(lex_order_vars).
% 0.92/1.21 clear(print_given).
% 0.92/1.21
% 0.92/1.21 % formulas(sos). % not echoed (5 formulas)
% 0.92/1.21
% 0.92/1.21 ============================== end of input ==========================
% 0.92/1.21
% 0.92/1.21 % From the command line: assign(max_seconds, 300).
% 0.92/1.21
% 0.92/1.21 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.92/1.21
% 0.92/1.21 % Formulas that are not ordinary clauses:
% 0.92/1.21
% 0.92/1.21 ============================== end of process non-clausal formulas ===
% 0.92/1.21
% 0.92/1.21 ============================== PROCESS INITIAL CLAUSES ===============
% 0.92/1.21
% 0.92/1.21 ============================== PREDICATE ELIMINATION =================
% 0.92/1.21
% 0.92/1.21 ============================== end predicate elimination =============
% 0.92/1.21
% 0.92/1.21 Auto_denials:
% 0.92/1.21 % copying label prove_huntingtons_axiom to answer in negative clause
% 0.92/1.21
% 0.92/1.21 Term ordering decisions:
% 0.92/1.21
% 0.92/1.21 % Assigning unary symbol negate kb_weight 0 and highest precedence (6).
% 0.92/1.21 Function symbol KB weights: c=1. a=1. b=1. add=1. negate=0.
% 0.92/1.21
% 0.92/1.21 ============================== end of process initial clauses ========
% 0.92/1.21
% 0.92/1.21 ============================== CLAUSES FOR SEARCH ====================
% 0.92/1.21
% 0.92/1.21 ============================== end of clauses for search =============
% 0.92/1.21
% 0.92/1.21 ============================== SEARCH ================================
% 0.92/1.21
% 0.92/1.21 % Starting search at 0.01 seconds.
% 0.92/1.21
% 0.92/1.21 ============================== PROOF =================================
% 0.92/1.21 % SZS status Unsatisfiable
% 0.92/1.21 % SZS output start Refutation
% 0.92/1.21
% 0.92/1.21 % Proof 1 at 0.24 (+ 0.01) seconds: prove_huntingtons_axiom.
% 0.92/1.21 % Length of proof is 71.
% 0.92/1.21 % Level of proof is 20.
% 0.92/1.21 % Maximum clause weight is 36.000.
% 0.92/1.21 % Given clauses 88.
% 0.92/1.21
% 0.92/1.21 1 add(c,negate(c)) = c # label(condition) # label(hypothesis). [assumption].
% 0.92/1.21 2 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 0.92/1.21 3 add(add(A,B),C) = add(A,add(B,C)) # label(associativity_of_add) # label(axiom). [assumption].
% 0.92/1.21 4 add(A,add(B,C)) = add(C,add(A,B)). [copy(3),rewrite([2(2)]),flip(a)].
% 0.92/1.21 5 negate(add(negate(add(A,B)),negate(add(A,negate(B))))) = A # label(robbins_axiom) # label(axiom). [assumption].
% 0.92/1.21 6 add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b # label(prove_huntingtons_axiom) # label(negated_conjecture) # answer(prove_huntingtons_axiom). [assumption].
% 0.92/1.21 7 negate(add(negate(c),negate(add(c,negate(negate(c)))))) = c. [para(1(a,1),5(a,1,1,1,1))].
% 0.92/1.21 8 negate(add(negate(c),negate(add(c,c)))) = c. [para(1(a,1),5(a,1,1,2,1)),rewrite([2(7)])].
% 0.92/1.21 9 negate(add(negate(add(A,B)),negate(add(B,negate(A))))) = B. [para(2(a,1),5(a,1,1,1,1))].
% 0.92/1.21 10 negate(add(negate(add(A,add(B,C))),negate(add(B,negate(add(A,C)))))) = B. [para(4(a,1),5(a,1,1,1,1)),rewrite([2(4)])].
% 0.92/1.21 12 negate(add(A,negate(add(negate(add(A,B)),negate(negate(add(A,negate(B)))))))) = negate(add(A,B)). [para(5(a,1),5(a,1,1,1))].
% 0.92/1.21 13 negate(add(negate(add(A,B)),negate(add(A,add(negate(add(B,C)),negate(add(B,negate(C)))))))) = A. [para(5(a,1),5(a,1,1,2,1,2)),rewrite([2(11)])].
% 0.92/1.21 17 negate(add(c,negate(add(c,add(negate(c),negate(negate(c))))))) = negate(c). [para(7(a,1),5(a,1,1,2)),rewrite([4(8,R),2(7),2(11)])].
% 0.92/1.21 19 negate(add(negate(add(A,c)),negate(add(A,add(negate(c),negate(add(c,c))))))) = A. [para(8(a,1),5(a,1,1,2,1,2)),rewrite([2(13)])].
% 0.92/1.21 20 negate(add(c,negate(add(c,c)))) = negate(c). [para(8(a,1),5(a,1,1,2)),rewrite([4(6),2(5),1(5),2(6)])].
% 0.92/1.21 23 negate(add(negate(c),negate(add(c,add(c,c))))) = c. [para(20(a,1),5(a,1,1,2)),rewrite([2(9)])].
% 0.92/1.21 26 negate(add(c,negate(add(c,add(c,c))))) = negate(c). [para(23(a,1),5(a,1,1,2)),rewrite([4(8,R),2(7),4(7),2(6),1(6),2(8)])].
% 0.92/1.21 31 negate(add(negate(add(A,add(B,C))),negate(add(add(A,C),negate(B))))) = add(A,C). [para(4(a,1),9(a,1,1,1,1)),rewrite([2(4),2(10)])].
% 0.92/1.21 32 negate(add(negate(add(A,add(B,C))),negate(add(add(A,B),negate(C))))) = add(A,B). [para(4(a,2),9(a,1,1,1,1))].
% 0.92/1.21 33 negate(add(negate(add(A,B)),negate(add(A,add(negate(add(C,B)),negate(add(B,negate(C)))))))) = A. [para(9(a,1),5(a,1,1,2,1,2)),rewrite([2(11)])].
% 0.92/1.21 38 negate(add(c,negate(add(negate(negate(c)),negate(add(c,c)))))) = negate(add(c,c)). [para(8(a,1),9(a,1,1,1)),rewrite([2(9)])].
% 0.92/1.21 39 negate(add(c,c)) = negate(c). [para(20(a,1),9(a,1,1,1)),rewrite([2(9),8(10),2(4),1(4)]),flip(a)].
% 0.92/1.21 41 negate(add(c,add(c,c))) = negate(c). [para(26(a,1),9(a,1,1,1)),rewrite([2(11),23(12),2(4),1(4)]),flip(a)].
% 0.92/1.21 43 negate(add(c,negate(add(negate(c),negate(negate(c)))))) = negate(c). [back_rewrite(38),rewrite([39(8),2(7),39(14)])].
% 0.92/1.21 44 negate(add(negate(add(A,c)),negate(add(A,add(negate(c),negate(c)))))) = A. [back_rewrite(19),rewrite([39(9)])].
% 0.92/1.21 45 negate(add(negate(c),negate(c))) = c. [back_rewrite(8),rewrite([39(6)])].
% 0.92/1.21 48 add(c,c) = c. [para(41(a,1),9(a,1,1,1)),rewrite([2(8),4(8),2(7),1(7),39(6),45(6)]),flip(a)].
% 0.92/1.21 56 negate(add(negate(add(A,c)),negate(add(c,negate(add(A,c)))))) = c. [para(48(a,1),10(a,1,1,1,1,2))].
% 0.92/1.21 59 negate(add(negate(c),negate(add(c,add(negate(c),negate(negate(c))))))) = c. [para(43(a,1),5(a,1,1,2)),rewrite([2(12)])].
% 0.92/1.21 61 negate(add(c,negate(add(c,negate(negate(c)))))) = negate(c). [para(4(a,1),17(a,1,1,2,1)),rewrite([1(8),2(6)])].
% 0.92/1.21 64 negate(add(negate(c),negate(add(c,add(c,add(negate(c),negate(negate(c)))))))) = c. [para(17(a,1),5(a,1,1,2)),rewrite([2(14)])].
% 0.92/1.21 65 negate(add(c,add(negate(c),negate(negate(c))))) = negate(c). [para(17(a,1),9(a,1,1,1)),rewrite([2(14),59(15),2(4),1(4)]),flip(a)].
% 0.92/1.21 68 negate(add(negate(c),negate(add(c,add(c,negate(negate(c))))))) = c. [para(61(a,1),5(a,1,1,2)),rewrite([2(11)])].
% 0.92/1.21 69 negate(add(c,negate(negate(c)))) = negate(c). [para(61(a,1),9(a,1,1,1)),rewrite([2(11),7(12),2(4),1(4)]),flip(a)].
% 0.92/1.21 70 negate(add(negate(c),negate(add(c,negate(negate(negate(c))))))) = c. [para(69(a,1),5(a,1,1,1))].
% 0.92/1.21 83 negate(add(c,negate(add(c,add(negate(c),negate(negate(negate(c)))))))) = negate(c). [para(70(a,1),5(a,1,1,2)),rewrite([4(9,R),2(8),2(12)])].
% 0.92/1.21 119 negate(add(c,add(c,add(negate(c),negate(negate(c)))))) = negate(c). [para(68(a,1),12(a,1,1,2,1,2,1)),rewrite([4(12,R),2(11),4(11,R),2(10),2(16),64(17),2(4),1(4),4(12,R),2(11),4(11,R),2(10)]),flip(a)].
% 0.92/1.21 126 negate(add(c,add(c,negate(negate(c))))) = negate(c). [para(4(a,1),119(a,1,1,2)),rewrite([1(8),2(6)])].
% 0.92/1.21 131 add(c,negate(negate(c))) = c. [para(126(a,1),9(a,1,1,1)),rewrite([2(10),4(10,R),2(9),65(11),45(6)]),flip(a)].
% 0.92/1.21 172 negate(add(c,negate(add(negate(add(A,c)),add(negate(add(B,negate(add(c,negate(add(A,c)))))),negate(add(negate(B),negate(add(c,negate(add(A,c))))))))))) = negate(add(A,c)). [para(56(a,1),13(a,1,1,1)),rewrite([2(11),2(20)])].
% 0.92/1.21 205 negate(add(negate(add(A,negate(add(B,c)))),negate(add(A,add(B,negate(add(B,add(add(negate(c),negate(c)),negate(add(B,c)))))))))) = A. [para(44(a,1),13(a,1,1,2,1,2,2)),rewrite([4(15,R),2(17)])].
% 0.92/1.21 228 negate(add(c,negate(add(c,negate(negate(negate(c))))))) = negate(c). [para(4(a,1),83(a,1,1,2,1)),rewrite([1(9),2(7)])].
% 0.92/1.21 280 negate(add(negate(c),negate(add(c,add(c,negate(negate(negate(c)))))))) = c. [para(228(a,1),5(a,1,1,2)),rewrite([2(12)])].
% 0.92/1.21 310 negate(add(negate(add(A,negate(c))),negate(add(A,add(c,negate(add(negate(c),negate(negate(add(c,add(c,negate(negate(negate(c)))))))))))))) = A. [para(280(a,1),13(a,1,1,2,1,2,1))].
% 0.92/1.21 314 add(A,negate(c)) = A. [para(1(a,1),31(a,1,1,1,1,2)),rewrite([2(9),4(9,R),44(12)]),flip(a)].
% 0.92/1.21 332 negate(negate(c)) = c. [para(65(a,1),31(a,1,1,1)),rewrite([131(7),131(7),314(5),131(8)])].
% 0.92/1.21 351 negate(add(negate(A),negate(add(A,c)))) = A. [back_rewrite(310),rewrite([314(3),332(9),314(9),48(7),332(7),2(6),314(6),314(5)])].
% 0.92/1.21 367 negate(add(negate(add(A,negate(add(B,c)))),negate(add(A,add(B,negate(add(B,add(negate(c),negate(add(B,c)))))))))) = A. [back_rewrite(205),rewrite([314(10)])].
% 0.92/1.21 377 negate(add(negate(A),negate(negate(A)))) = negate(c). [para(314(a,1),9(a,1,1,1,1)),rewrite([2(5),314(5)])].
% 0.92/1.21 379 negate(add(negate(A),negate(add(A,add(negate(B),negate(negate(B))))))) = A. [para(314(a,1),13(a,1,1,1,1)),rewrite([2(4),314(4),2(6),314(6)])].
% 0.92/1.21 396 negate(add(A,negate(A))) = negate(c). [para(5(a,1),377(a,1,1,1)),rewrite([5(7)])].
% 0.92/1.21 407 add(negate(A),negate(negate(A))) = c. [para(377(a,1),351(a,1,1,1)),rewrite([2(8),379(11)]),flip(a)].
% 0.92/1.21 432 negate(add(negate(c),negate(add(A,A)))) = A. [para(396(a,1),5(a,1,1,2)),rewrite([2(5)])].
% 0.92/1.21 459 add(A,negate(A)) = c. [para(5(a,1),407(a,1,1)),rewrite([5(7)])].
% 0.92/1.21 465 add(A,add(B,negate(A))) = add(B,c). [para(459(a,1),4(a,2,2)),rewrite([2(2)])].
% 0.92/1.21 467 add(A,add(negate(add(B,A)),negate(add(A,negate(B))))) = c. [para(9(a,1),459(a,1,2)),rewrite([2(7)])].
% 0.92/1.21 477 add(A,add(negate(A),negate(add(A,c)))) = c. [para(351(a,1),459(a,1,2)),rewrite([2(6)])].
% 0.92/1.21 481 negate(add(A,negate(add(A,A)))) = negate(c). [para(432(a,1),5(a,1,1,2)),rewrite([4(4),2(3),314(3),2(3)])].
% 0.92/1.21 522 negate(add(negate(A),negate(add(B,add(A,negate(add(B,B))))))) = A. [para(481(a,1),9(a,1,1,2,1,2)),rewrite([2(4),4(4,R),2(3),314(8),2(7)])].
% 0.92/1.21 534 add(A,negate(add(A,A))) = c. [para(481(a,1),351(a,1,1,1)),rewrite([2(7),4(7,R),2(6),522(10)]),flip(a)].
% 0.92/1.21 542 add(A,add(A,c)) = add(A,c). [para(534(a,1),465(a,1,2)),rewrite([2(3),4(3),2(2)])].
% 0.92/1.21 545 negate(add(negate(c),negate(add(A,c)))) = add(A,c). [para(542(a,1),9(a,1,1,1,1)),rewrite([2(7),4(7,R),465(7),48(6),2(6)])].
% 0.92/1.21 555 negate(add(negate(add(A,c)),negate(add(A,A)))) = add(A,A). [para(542(a,1),32(a,1,1,1,1)),rewrite([2(7),4(7),2(6),314(6)])].
% 0.92/1.21 570 add(c,negate(add(A,c))) = c. [para(477(a,1),4(a,1)),rewrite([459(6),2(6)]),flip(a)].
% 0.92/1.21 596 negate(add(A,c)) = negate(c). [back_rewrite(172),rewrite([570(9),314(7),570(11),314(9),459(8),2(6),570(6),459(4)]),flip(a)].
% 0.92/1.21 598 add(A,c) = c. [back_rewrite(545),rewrite([596(5),314(5),332(3)]),flip(a)].
% 0.92/1.21 599 negate(negate(A)) = A. [back_rewrite(367),rewrite([598(2),314(3),598(5),314(6),314(4),459(3),598(3),314(4)])].
% 0.92/1.21 605 add(A,A) = A. [back_rewrite(555),rewrite([598(2),432(6)]),flip(a)].
% 0.92/1.21 668 add(negate(add(A,B)),negate(add(B,negate(A)))) = negate(B). [para(605(a,1),33(a,1,1,2,1)),rewrite([2(7),467(7),9(9),2(3),314(3)]),flip(a)].
% 0.92/1.21 926 add(negate(add(A,negate(B))),negate(add(negate(A),negate(B)))) = B. [para(599(a,1),668(a,2)),rewrite([2(6)])].
% 0.92/1.21 927 $F # answer(prove_huntingtons_axiom). [resolve(926,a,6,a)].
% 0.92/1.21
% 0.92/1.21 % SZS output end Refutation
% 0.92/1.21 ============================== end of proof ==========================
% 0.92/1.21
% 0.92/1.21 ============================== STATISTICS ============================
% 0.92/1.21
% 0.92/1.21 Given=88. Generated=4393. Kept=925. proofs=1.
% 0.92/1.21 Usable=33. Sos=224. Demods=259. Limbo=3, Disabled=669. Hints=0.
% 0.92/1.21 Megabytes=1.09.
% 0.92/1.21 User_CPU=0.24, System_CPU=0.01, Wall_clock=1.
% 0.92/1.21
% 0.92/1.21 ============================== end of statistics =====================
% 0.92/1.21
% 0.92/1.21 ============================== end of search =========================
% 0.92/1.21
% 0.92/1.21 THEOREM PROVED
% 0.92/1.21 % SZS status Unsatisfiable
% 0.92/1.21
% 0.92/1.21 Exiting with 1 proof.
% 0.92/1.21
% 0.92/1.21 Process 12723 exit (max_proofs) Thu Jun 9 14:11:38 2022
% 0.92/1.21 Prover9 interrupted
%------------------------------------------------------------------------------