TSTP Solution File: GRP510-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP510-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 : Sat Jul 16 11:19:24 EDT 2022
% Result : Unsatisfiable 0.42s 0.97s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP510-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n017.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 : Mon Jun 13 09:49:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.97 ============================== Prover9 ===============================
% 0.42/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.97 Process 18469 was started by sandbox on n017.cluster.edu,
% 0.42/0.97 Mon Jun 13 09:49:38 2022
% 0.42/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18316_n017.cluster.edu".
% 0.42/0.97 ============================== end of head ===========================
% 0.42/0.97
% 0.42/0.97 ============================== INPUT =================================
% 0.42/0.97
% 0.42/0.97 % Reading from file /tmp/Prover9_18316_n017.cluster.edu
% 0.42/0.97
% 0.42/0.97 set(prolog_style_variables).
% 0.42/0.97 set(auto2).
% 0.42/0.97 % set(auto2) -> set(auto).
% 0.42/0.97 % set(auto) -> set(auto_inference).
% 0.42/0.97 % set(auto) -> set(auto_setup).
% 0.42/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.97 % set(auto) -> set(auto_limits).
% 0.42/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.97 % set(auto) -> set(auto_denials).
% 0.42/0.97 % set(auto) -> set(auto_process).
% 0.42/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.97 % set(auto2) -> assign(stats, some).
% 0.42/0.97 % set(auto2) -> clear(echo_input).
% 0.42/0.97 % set(auto2) -> set(quiet).
% 0.42/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.97 % set(auto2) -> clear(print_given).
% 0.42/0.97 assign(lrs_ticks,-1).
% 0.42/0.97 assign(sos_limit,10000).
% 0.42/0.97 assign(order,kbo).
% 0.42/0.97 set(lex_order_vars).
% 0.42/0.97 clear(print_given).
% 0.42/0.97
% 0.42/0.97 % formulas(sos). % not echoed (2 formulas)
% 0.42/0.97
% 0.42/0.97 ============================== end of input ==========================
% 0.42/0.97
% 0.42/0.97 % From the command line: assign(max_seconds, 300).
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.97
% 0.42/0.97 % Formulas that are not ordinary clauses:
% 0.42/0.97
% 0.42/0.97 ============================== end of process non-clausal formulas ===
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.97
% 0.42/0.97 ============================== PREDICATE ELIMINATION =================
% 0.42/0.97
% 0.42/0.97 ============================== end predicate elimination =============
% 0.42/0.97
% 0.42/0.97 Auto_denials:
% 0.42/0.97 % copying label prove_these_axioms_2 to answer in negative clause
% 0.42/0.97
% 0.42/0.97 Term ordering decisions:
% 0.42/0.97
% 0.42/0.97 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 0.42/0.97 Function symbol KB weights: a2=1. b2=1. multiply=1. inverse=0.
% 0.42/0.97
% 0.42/0.97 ============================== end of process initial clauses ========
% 0.42/0.97
% 0.42/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.42/0.97
% 0.42/0.97 ============================== end of clauses for search =============
% 0.42/0.97
% 0.42/0.97 ============================== SEARCH ================================
% 0.42/0.97
% 0.42/0.97 % Starting search at 0.01 seconds.
% 0.42/0.97
% 0.42/0.97 ============================== PROOF =================================
% 0.42/0.97 % SZS status Unsatisfiable
% 0.42/0.97 % SZS output start Refutation
% 0.42/0.97
% 0.42/0.97 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms_2.
% 0.42/0.97 % Length of proof is 38.
% 0.42/0.97 % Level of proof is 17.
% 0.42/0.97 % Maximum clause weight is 23.000.
% 0.42/0.97 % Given clauses 20.
% 0.42/0.97
% 0.42/0.97 1 multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.42/0.97 2 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 0.42/0.97 3 multiply(multiply(A,B),inverse(multiply(multiply(multiply(C,A),D),B))) = inverse(multiply(C,D)). [para(1(a,1),1(a,1,1,1))].
% 0.42/0.97 4 multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) = C. [para(1(a,1),1(a,1,1))].
% 0.42/0.97 10 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(multiply(C,D),inverse(multiply(B,D))). [para(1(a,1),3(a,1,2,1,1)),flip(a)].
% 0.42/0.97 11 multiply(multiply(A,inverse(multiply(B,C))),inverse(A)) = inverse(multiply(B,C)). [para(1(a,1),3(a,1,2,1))].
% 0.42/0.97 15 multiply(A,inverse(multiply(B,inverse(multiply(multiply(C,multiply(B,D)),inverse(multiply(C,A))))))) = D. [para(4(a,1),1(a,1,1))].
% 0.42/0.97 19 inverse(multiply(A,inverse(multiply(multiply(B,multiply(A,C)),inverse(multiply(B,D)))))) = multiply(multiply(C,E),inverse(multiply(D,E))). [para(4(a,1),3(a,1,2,1,1)),flip(a)].
% 0.42/0.97 21 inverse(multiply(A,multiply(B,inverse(multiply(multiply(A,B),C))))) = C. [para(4(a,1),3(a,1)),flip(a)].
% 0.42/0.97 24 multiply(inverse(multiply(multiply(A,B),inverse(multiply(A,C)))),inverse(multiply(C,inverse(multiply(B,D))))) = D. [para(4(a,1),4(a,1,2,1,1))].
% 0.42/0.97 25 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))). [para(4(a,1),4(a,1,2,1,2,1)),flip(a)].
% 0.42/0.97 26 multiply(multiply(multiply(A,B),multiply(C,inverse(multiply(multiply(A,C),D)))),D) = B. [para(21(a,1),1(a,1,2))].
% 0.42/0.97 27 inverse(multiply(multiply(multiply(A,B),C),multiply(inverse(multiply(A,C)),inverse(multiply(B,D))))) = D. [para(1(a,1),21(a,1,1,2,2,1,1))].
% 0.42/0.97 28 inverse(multiply(multiply(A,B),multiply(C,inverse(B)))) = inverse(multiply(A,C)). [para(1(a,1),21(a,1,1,2,2,1))].
% 0.42/0.97 31 inverse(multiply(multiply(multiply(A,B),C),D)) = inverse(multiply(B,multiply(D,inverse(inverse(multiply(A,C)))))). [para(3(a,1),21(a,1,1,2,2,1)),flip(a)].
% 0.42/0.97 35 inverse(multiply(multiply(A,multiply(B,C)),inverse(multiply(A,D)))) = inverse(multiply(B,multiply(C,inverse(D)))). [para(4(a,1),21(a,1,1,2,2,1)),flip(a)].
% 0.42/0.97 39 inverse(multiply(A,inverse(multiply(A,B)))) = B. [back_rewrite(27),rewrite([31(9),11(9)])].
% 0.42/0.97 49 multiply(multiply(A,B),inverse(multiply(C,B))) = multiply(A,inverse(C)). [back_rewrite(19),rewrite([35(6),39(6)]),flip(a)].
% 0.42/0.97 50 multiply(A,multiply(B,inverse(A))) = B. [back_rewrite(15),rewrite([35(6),39(6)])].
% 0.42/0.97 52 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(C,inverse(B)). [back_rewrite(10),rewrite([49(9)])].
% 0.42/0.97 53 multiply(multiply(A,B),inverse(A)) = B. [back_rewrite(1),rewrite([49(5)])].
% 0.42/0.97 60 inverse(multiply(A,multiply(B,inverse(C)))) = multiply(C,inverse(multiply(A,B))). [back_rewrite(35),rewrite([52(6)]),flip(a)].
% 0.42/0.97 61 multiply(A,inverse(multiply(multiply(B,A),inverse(C)))) = multiply(C,inverse(B)). [back_rewrite(25),rewrite([52(5)]),flip(a)].
% 0.42/0.97 62 multiply(multiply(A,inverse(B)),inverse(multiply(A,inverse(multiply(B,C))))) = C. [back_rewrite(24),rewrite([52(5)])].
% 0.42/0.97 64 multiply(A,inverse(multiply(multiply(B,A),C))) = inverse(multiply(B,C)). [back_rewrite(28),rewrite([60(5)])].
% 0.42/0.97 65 inverse(multiply(A,inverse(B))) = multiply(B,inverse(A)). [back_rewrite(61),rewrite([64(5)])].
% 0.42/0.97 67 multiply(multiply(multiply(A,B),inverse(multiply(A,C))),C) = B. [back_rewrite(26),rewrite([64(5)])].
% 0.42/0.97 68 multiply(multiply(A,inverse(B)),multiply(multiply(B,C),inverse(A))) = C. [back_rewrite(62),rewrite([65(6)])].
% 0.42/0.97 69 multiply(multiply(A,B),inverse(multiply(A,C))) = multiply(B,inverse(C)). [back_rewrite(52),rewrite([65(5)])].
% 0.42/0.97 70 multiply(multiply(A,inverse(B)),B) = A. [back_rewrite(67),rewrite([69(4)])].
% 0.42/0.97 99 inverse(inverse(A)) = A. [para(70(a,1),53(a,1)),flip(a)].
% 0.42/0.97 100 multiply(A,B) = multiply(B,A). [para(53(a,1),70(a,1,1))].
% 0.42/0.97 114 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(53),rewrite([100(3)])].
% 0.42/0.97 115 multiply(a2,multiply(b2,inverse(b2))) != a2 # answer(prove_these_axioms_2). [back_rewrite(2),rewrite([100(4),100(6)])].
% 0.42/0.97 122 multiply(multiply(A,B),multiply(C,inverse(A))) = multiply(B,C). [para(114(a,1),68(a,1,2,1)),rewrite([99(2)])].
% 0.42/0.97 139 multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)). [para(114(a,1),122(a,1,1)),rewrite([99(2),100(3),100(4)])].
% 0.42/0.97 155 multiply(A,multiply(B,inverse(B))) = A. [para(139(a,1),50(a,1))].
% 0.42/0.97 156 $F # answer(prove_these_axioms_2). [resolve(155,a,115,a)].
% 0.42/0.97
% 0.42/0.97 % SZS output end Refutation
% 0.42/0.97 ============================== end of proof ==========================
% 0.42/0.97
% 0.42/0.97 ============================== STATISTICS ============================
% 0.42/0.97
% 0.42/0.97 Given=20. Generated=341. Kept=155. proofs=1.
% 0.42/0.97 Usable=8. Sos=16. Demods=23. Limbo=0, Disabled=132. Hints=0.
% 0.42/0.97 Megabytes=0.15.
% 0.42/0.97 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.42/0.97
% 0.42/0.97 ============================== end of statistics =====================
% 0.42/0.97
% 0.42/0.97 ============================== end of search =========================
% 0.42/0.97
% 0.42/0.97 THEOREM PROVED
% 0.42/0.97 % SZS status Unsatisfiable
% 0.42/0.97
% 0.42/0.97 Exiting with 1 proof.
% 0.42/0.97
% 0.42/0.97 Process 18469 exit (max_proofs) Mon Jun 13 09:49:38 2022
% 0.42/0.97 Prover9 interrupted
%------------------------------------------------------------------------------