TSTP Solution File: BOO074-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO074-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 : Thu Jul 14 23:48:07 EDT 2022
% Result : Unsatisfiable 0.98s 1.30s
% Output : Refutation 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : BOO074-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n023.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 : Wed Jun 1 22:40:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.98/1.30 ============================== Prover9 ===============================
% 0.98/1.30 Prover9 (32) version 2009-11A, November 2009.
% 0.98/1.30 Process 19178 was started by sandbox2 on n023.cluster.edu,
% 0.98/1.30 Wed Jun 1 22:40:11 2022
% 0.98/1.30 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19024_n023.cluster.edu".
% 0.98/1.30 ============================== end of head ===========================
% 0.98/1.30
% 0.98/1.30 ============================== INPUT =================================
% 0.98/1.30
% 0.98/1.30 % Reading from file /tmp/Prover9_19024_n023.cluster.edu
% 0.98/1.30
% 0.98/1.30 set(prolog_style_variables).
% 0.98/1.30 set(auto2).
% 0.98/1.30 % set(auto2) -> set(auto).
% 0.98/1.30 % set(auto) -> set(auto_inference).
% 0.98/1.30 % set(auto) -> set(auto_setup).
% 0.98/1.30 % set(auto_setup) -> set(predicate_elim).
% 0.98/1.30 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.98/1.30 % set(auto) -> set(auto_limits).
% 0.98/1.30 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.98/1.30 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.98/1.30 % set(auto) -> set(auto_denials).
% 0.98/1.30 % set(auto) -> set(auto_process).
% 0.98/1.30 % set(auto2) -> assign(new_constants, 1).
% 0.98/1.30 % set(auto2) -> assign(fold_denial_max, 3).
% 0.98/1.30 % set(auto2) -> assign(max_weight, "200.000").
% 0.98/1.30 % set(auto2) -> assign(max_hours, 1).
% 0.98/1.30 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.98/1.30 % set(auto2) -> assign(max_seconds, 0).
% 0.98/1.30 % set(auto2) -> assign(max_minutes, 5).
% 0.98/1.30 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.98/1.30 % set(auto2) -> set(sort_initial_sos).
% 0.98/1.30 % set(auto2) -> assign(sos_limit, -1).
% 0.98/1.30 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.98/1.30 % set(auto2) -> assign(max_megs, 400).
% 0.98/1.30 % set(auto2) -> assign(stats, some).
% 0.98/1.30 % set(auto2) -> clear(echo_input).
% 0.98/1.30 % set(auto2) -> set(quiet).
% 0.98/1.30 % set(auto2) -> clear(print_initial_clauses).
% 0.98/1.30 % set(auto2) -> clear(print_given).
% 0.98/1.30 assign(lrs_ticks,-1).
% 0.98/1.30 assign(sos_limit,10000).
% 0.98/1.30 assign(order,kbo).
% 0.98/1.30 set(lex_order_vars).
% 0.98/1.30 clear(print_given).
% 0.98/1.30
% 0.98/1.30 % formulas(sos). % not echoed (2 formulas)
% 0.98/1.30
% 0.98/1.30 ============================== end of input ==========================
% 0.98/1.30
% 0.98/1.30 % From the command line: assign(max_seconds, 300).
% 0.98/1.30
% 0.98/1.30 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.98/1.30
% 0.98/1.30 % Formulas that are not ordinary clauses:
% 0.98/1.30
% 0.98/1.30 ============================== end of process non-clausal formulas ===
% 0.98/1.30
% 0.98/1.30 ============================== PROCESS INITIAL CLAUSES ===============
% 0.98/1.30
% 0.98/1.30 ============================== PREDICATE ELIMINATION =================
% 0.98/1.30
% 0.98/1.30 ============================== end predicate elimination =============
% 0.98/1.30
% 0.98/1.30 Auto_denials:
% 0.98/1.30 % copying label huntinton_3 to answer in negative clause
% 0.98/1.30
% 0.98/1.30 Term ordering decisions:
% 0.98/1.30
% 0.98/1.30 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 0.98/1.30 Function symbol KB weights: a=1. b=1. add=1. inverse=0.
% 0.98/1.30
% 0.98/1.30 ============================== end of process initial clauses ========
% 0.98/1.30
% 0.98/1.30 ============================== CLAUSES FOR SEARCH ====================
% 0.98/1.30
% 0.98/1.30 ============================== end of clauses for search =============
% 0.98/1.30
% 0.98/1.30 ============================== SEARCH ================================
% 0.98/1.30
% 0.98/1.30 % Starting search at 0.01 seconds.
% 0.98/1.30
% 0.98/1.30 ============================== PROOF =================================
% 0.98/1.30 % SZS status Unsatisfiable
% 0.98/1.30 % SZS output start Refutation
% 0.98/1.30
% 0.98/1.30 % Proof 1 at 0.26 (+ 0.01) seconds: huntinton_3.
% 0.98/1.30 % Length of proof is 70.
% 0.98/1.30 % Level of proof is 26.
% 0.98/1.30 % Maximum clause weight is 49.000.
% 0.98/1.30 % Given clauses 93.
% 0.98/1.30
% 0.98/1.30 1 inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,D)))))))) = C # label(dn1) # label(axiom). [assumption].
% 0.98/1.30 2 add(inverse(add(inverse(a),b)),inverse(add(inverse(a),inverse(b)))) != a # label(huntinton_3) # label(negated_conjecture) # answer(huntinton_3). [assumption].
% 0.98/1.30 3 inverse(add(inverse(add(A,B)),inverse(add(inverse(add(inverse(add(C,D)),A)),inverse(add(inverse(B),inverse(add(B,E)))))))) = B. [para(1(a,1),1(a,1,1,1,1,1))].
% 0.98/1.30 4 inverse(add(A,inverse(add(inverse(add(B,C)),inverse(add(inverse(inverse(add(B,inverse(add(inverse(A),inverse(add(A,D))))))),inverse(add(inverse(add(B,inverse(add(inverse(A),inverse(add(A,D)))))),E)))))))) = inverse(add(B,inverse(add(inverse(A),inverse(add(A,D)))))). [para(1(a,1),1(a,1,1,1))].
% 0.98/1.30 16 inverse(add(inverse(add(A,inverse(A))),A)) = inverse(A). [para(1(a,1),3(a,1,1,2))].
% 0.98/1.30 20 inverse(add(inverse(A),inverse(add(A,inverse(add(inverse(A),inverse(add(A,B)))))))) = A. [para(16(a,1),1(a,1,1,1))].
% 0.98/1.30 25 inverse(add(inverse(add(A,B)),inverse(add(inverse(A),inverse(add(inverse(B),inverse(add(B,C)))))))) = B. [para(20(a,1),1(a,1,1,1,1,1))].
% 0.98/1.30 29 inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,C)))) = C. [para(20(a,1),1(a,1,1,2,1,2))].
% 0.98/1.30 56 inverse(add(inverse(add(A,B)),inverse(add(inverse(A),B)))) = B. [para(20(a,1),29(a,1,1,1,1,1))].
% 0.98/1.30 62 inverse(add(A,inverse(add(inverse(add(B,C)),inverse(add(B,A)))))) = inverse(add(B,A)). [para(29(a,1),29(a,1,1,1))].
% 0.98/1.30 63 inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(A,B)),C)),D)),inverse(add(A,C)))),C)) = inverse(add(A,C)). [para(29(a,1),29(a,1,1,2))].
% 0.98/1.30 66 inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(D,inverse(add(inverse(C),inverse(add(C,E)))))))))))) = C. [para(4(a,1),1(a,1,1,2,1,2,1,2))].
% 0.98/1.30 97 inverse(add(inverse(add(inverse(add(inverse(add(A,inverse(add(A,B)))),C)),A)),inverse(add(A,B)))) = A. [para(56(a,1),1(a,1,1,2))].
% 0.98/1.30 104 inverse(add(inverse(add(add(A,inverse(A)),A)),inverse(A))) = A. [para(16(a,1),56(a,1,1,2))].
% 0.98/1.30 114 inverse(add(inverse(add(A,B)),inverse(add(inverse(add(C,A)),B)))) = B. [para(56(a,1),29(a,1,1,1,1,1))].
% 0.98/1.30 115 inverse(add(A,inverse(add(B,inverse(add(inverse(B),A)))))) = inverse(add(inverse(B),A)). [para(56(a,1),29(a,1,1,1))].
% 0.98/1.30 141 inverse(add(A,inverse(add(add(A,inverse(A)),inverse(A))))) = inverse(A). [para(104(a,1),29(a,1,1,1))].
% 0.98/1.30 160 inverse(add(inverse(A),inverse(A))) = A. [para(141(a,1),20(a,1,1,2,1,2,1,2)),rewrite([115(9)])].
% 0.98/1.30 164 inverse(add(inverse(add(inverse(A),B)),inverse(add(A,B)))) = B. [para(141(a,1),29(a,1,1,1,1,1))].
% 0.98/1.30 181 add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,D))))))) = inverse(add(C,C)). [para(1(a,1),160(a,1,1,1)),rewrite([1(13)]),flip(a)].
% 0.98/1.30 184 add(inverse(add(A,inverse(A))),A) = A. [para(16(a,1),160(a,1,1,1)),rewrite([16(6),160(4)]),flip(a)].
% 0.98/1.30 191 inverse(add(inverse(add(inverse(add(inverse(A),B)),inverse(A))),A)) = inverse(A). [para(160(a,1),29(a,1,1,2))].
% 0.98/1.30 192 add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,C))) = inverse(add(C,C)). [para(29(a,1),160(a,1,1,1)),rewrite([29(8)]),flip(a)].
% 0.98/1.30 198 add(inverse(add(A,B)),inverse(add(inverse(A),B))) = inverse(add(B,B)). [para(56(a,1),160(a,1,1,1)),rewrite([56(7)]),flip(a)].
% 0.98/1.30 203 inverse(add(A,A)) = add(inverse(A),inverse(A)). [para(160(a,1),160(a,1,1,1)),rewrite([160(4)])].
% 0.98/1.30 208 add(inverse(inverse(A)),inverse(inverse(A))) = A. [back_rewrite(1),rewrite([181(12),203(2),203(4)])].
% 0.98/1.30 217 add(inverse(add(A,B)),inverse(add(inverse(A),B))) = add(inverse(B),inverse(B)). [back_rewrite(198),rewrite([203(8)])].
% 0.98/1.30 218 add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,C))) = add(inverse(C),inverse(C)). [back_rewrite(192),rewrite([203(9)])].
% 0.98/1.30 252 add(inverse(add(inverse(A),B)),inverse(add(A,B))) = add(inverse(B),inverse(B)). [para(164(a,1),208(a,1,1,1)),rewrite([164(8)]),flip(a)].
% 0.98/1.30 377 inverse(add(inverse(add(inverse(A),A)),inverse(A))) = A. [para(184(a,1),114(a,1,1,2,1))].
% 0.98/1.30 378 add(inverse(add(A,B)),inverse(add(inverse(add(C,A)),B))) = add(inverse(B),inverse(B)). [para(114(a,1),208(a,1,1,1)),rewrite([114(9)]),flip(a)].
% 0.98/1.30 405 add(inverse(add(inverse(A),A)),inverse(A)) = add(inverse(A),inverse(A)). [para(377(a,1),208(a,1,1,1)),rewrite([377(7)]),flip(a)].
% 0.98/1.30 411 add(inverse(add(A,B)),inverse(add(inverse(A),inverse(add(inverse(B),inverse(add(B,C))))))) = add(inverse(B),inverse(B)). [para(25(a,1),208(a,1,1,1)),rewrite([25(13)]),flip(a)].
% 0.98/1.30 416 inverse(add(inverse(add(A,add(B,B))),inverse(add(inverse(A),inverse(add(add(inverse(B),inverse(B)),inverse(add(add(B,B),C)))))))) = add(B,B). [para(203(a,1),25(a,1,1,2,1,2,1,1))].
% 0.98/1.30 426 add(inverse(add(A,add(inverse(A),inverse(A)))),A) = add(A,A). [para(25(a,1),405(a,1,1,1,1)),rewrite([411(11),411(16),203(9),208(10),411(17),203(10),208(11),411(17),203(10),208(11)])].
% 0.98/1.30 441 add(inverse(add(inverse(add(inverse(A),B)),inverse(A))),A) = A. [para(191(a,1),208(a,1,1,1)),rewrite([191(10),208(5)]),flip(a)].
% 0.98/1.30 443 add(inverse(A),inverse(A)) = inverse(A). [para(405(a,1),191(a,1,1,1,1)),rewrite([203(4),208(5),203(2)])].
% 0.98/1.30 444 add(A,A) = A. [para(191(a,1),426(a,1,1,1,2,1)),rewrite([441(7),441(8),443(3),441(10),184(4),441(7),441(7)]),flip(a)].
% 0.98/1.30 447 inverse(inverse(A)) = A. [back_rewrite(416),rewrite([444(1),444(6),444(5),411(11),444(3),444(3)])].
% 0.98/1.30 451 add(inverse(add(A,B)),inverse(add(inverse(add(C,A)),B))) = inverse(B). [back_rewrite(378),rewrite([444(10)])].
% 0.98/1.30 468 add(inverse(add(inverse(A),B)),inverse(add(A,B))) = inverse(B). [back_rewrite(252),rewrite([444(9)])].
% 0.98/1.30 474 add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,C))) = inverse(C). [back_rewrite(218),rewrite([444(10)])].
% 0.98/1.30 475 add(inverse(add(A,B)),inverse(add(inverse(A),B))) = inverse(B). [back_rewrite(217),rewrite([444(9)])].
% 0.98/1.30 749 add(inverse(add(inverse(add(A,B)),C)),inverse(add(B,C))) = inverse(C). [para(468(a,1),451(a,1,2,1,1,1)),rewrite([447(6)])].
% 0.98/1.30 776 inverse(add(A,add(B,A))) = inverse(add(B,A)). [para(444(a,1),62(a,1,1,2,1)),rewrite([447(3)])].
% 0.98/1.30 817 add(A,add(B,A)) = add(B,A). [para(776(a,1),447(a,1,1)),rewrite([447(3)]),flip(a)].
% 0.98/1.30 828 add(inverse(add(A,B)),inverse(B)) = inverse(B). [para(468(a,1),817(a,1,2)),rewrite([468(10)])].
% 0.98/1.30 829 add(inverse(add(A,inverse(B))),B) = B. [para(447(a,1),828(a,1,2)),rewrite([447(6)])].
% 0.98/1.30 863 inverse(add(add(A,B),B)) = inverse(add(A,B)). [para(828(a,1),63(a,1,1,1,1)),rewrite([447(3)])].
% 0.98/1.30 881 add(add(A,B),B) = add(A,B). [para(863(a,1),447(a,1,1)),rewrite([447(3)]),flip(a)].
% 0.98/1.30 885 add(inverse(A),inverse(add(B,A))) = inverse(A). [para(468(a,1),881(a,1,1)),rewrite([468(10)])].
% 0.98/1.30 886 add(A,inverse(add(B,inverse(A)))) = A. [para(447(a,1),885(a,1,1)),rewrite([447(6)])].
% 0.98/1.30 899 inverse(add(A,inverse(add(inverse(B),inverse(add(add(B,A),inverse(add(C,inverse(add(add(B,A),inverse(add(inverse(add(B,A)),D)))))))))))) = inverse(add(B,A)). [para(468(a,1),66(a,1,1,1,1)),rewrite([447(2),447(4),447(5)])].
% 0.98/1.30 932 add(A,inverse(add(inverse(B),inverse(add(B,A))))) = add(B,A). [para(468(a,1),474(a,1,1,1)),rewrite([447(2),447(9)])].
% 0.98/1.30 970 add(inverse(add(A,inverse(add(inverse(B),inverse(add(B,inverse(A))))))),inverse(add(B,inverse(A)))) = add(inverse(B),inverse(add(B,inverse(A)))). [para(932(a,1),475(a,1,2,1)),rewrite([447(19)])].
% 0.98/1.30 971 add(inverse(add(A,B)),inverse(add(inverse(add(C,B)),inverse(add(inverse(A),inverse(add(A,B))))))) = add(inverse(A),inverse(add(A,B))). [para(932(a,1),451(a,1,1,1)),rewrite([447(18)])].
% 0.98/1.30 972 add(inverse(add(A,inverse(add(inverse(B),inverse(add(B,inverse(add(C,A)))))))),inverse(add(B,inverse(add(C,A))))) = add(inverse(B),inverse(add(B,inverse(add(C,A))))). [para(932(a,1),451(a,1,2,1)),rewrite([447(22)])].
% 0.98/1.30 973 add(inverse(add(A,inverse(add(B,C)))),inverse(add(B,inverse(add(inverse(A),inverse(add(A,inverse(add(B,C))))))))) = add(inverse(A),inverse(add(A,inverse(add(B,C))))). [para(932(a,1),474(a,1,1,1)),rewrite([447(22)])].
% 0.98/1.30 1011 add(inverse(add(inverse(add(inverse(add(A,inverse(add(A,B)))),C)),A)),inverse(add(A,B))) = inverse(A). [para(97(a,1),447(a,1,1)),flip(a)].
% 0.98/1.30 1021 inverse(add(A,inverse(add(inverse(A),B)))) = inverse(A). [para(828(a,1),97(a,1,1,1,1)),rewrite([447(2)])].
% 0.98/1.30 1022 inverse(add(inverse(A),inverse(add(A,B)))) = A. [para(829(a,1),97(a,1,1,1,1))].
% 0.98/1.30 1031 add(inverse(A),B) = add(B,inverse(A)). [para(97(a,1),932(a,1,2,1,1)),rewrite([1011(11),1021(5),1011(13)]),flip(a)].
% 0.98/1.30 1037 add(inverse(add(A,B)),inverse(add(B,inverse(add(A,C))))) = inverse(B). [para(97(a,1),749(a,1,1,1,1)),rewrite([1031(5)])].
% 0.98/1.30 1056 inverse(add(A,B)) = inverse(add(B,A)). [back_rewrite(899),rewrite([1031(6),886(8),886(7),1022(5)])].
% 0.98/1.30 1084 add(inverse(add(A,B)),inverse(add(A,inverse(add(B,C))))) = add(inverse(A),inverse(add(A,inverse(add(B,C))))). [back_rewrite(973),rewrite([1022(11),1056(6),1031(7,R)])].
% 0.98/1.30 1085 add(inverse(A),inverse(add(A,inverse(add(B,C))))) = inverse(A). [back_rewrite(972),rewrite([1056(3),1022(7),1056(4),1037(7),1056(4)]),flip(a)].
% 0.98/1.30 1086 add(inverse(A),inverse(add(A,B))) = inverse(A). [back_rewrite(971),rewrite([1056(4),1022(9),1031(5),1084(7),1085(6)]),flip(a)].
% 0.98/1.30 1087 add(inverse(add(A,B)),inverse(add(B,inverse(A)))) = inverse(B). [back_rewrite(970),rewrite([1086(5),447(2),1086(11)])].
% 0.98/1.30 1095 add(A,B) = add(B,A). [back_rewrite(932),rewrite([1056(3),885(4),447(2)])].
% 0.98/1.30 1151 $F # answer(huntinton_3). [back_rewrite(2),rewrite([1095(4),1087(12),447(3)]),xx(a)].
% 0.98/1.30
% 0.98/1.30 % SZS output end Refutation
% 0.98/1.30 ============================== end of proof ==========================
% 0.98/1.30
% 0.98/1.30 ============================== STATISTICS ============================
% 0.98/1.30
% 0.98/1.30 Given=93. Generated=4152. Kept=1150. proofs=1.
% 0.98/1.30 Usable=7. Sos=15. Demods=142. Limbo=120, Disabled=1010. Hints=0.
% 0.98/1.30 Megabytes=1.58.
% 0.98/1.30 User_CPU=0.26, System_CPU=0.01, Wall_clock=1.
% 0.98/1.30
% 0.98/1.30 ============================== end of statistics =====================
% 0.98/1.30
% 0.98/1.30 ============================== end of search =========================
% 0.98/1.30
% 0.98/1.30 THEOREM PROVED
% 0.98/1.30 % SZS status Unsatisfiable
% 0.98/1.30
% 0.98/1.30 Exiting with 1 proof.
% 0.98/1.30
% 0.98/1.30 Process 19178 exit (max_proofs) Wed Jun 1 22:40:12 2022
% 0.98/1.30 Prover9 interrupted
%------------------------------------------------------------------------------