TSTP Solution File: GRP607-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP607-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 11:19:49 EDT 2022
% Result : Unsatisfiable 0.77s 1.04s
% Output : Refutation 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP607-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 10:20:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.77/1.04 ============================== Prover9 ===============================
% 0.77/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.77/1.04 Process 17691 was started by sandbox2 on n027.cluster.edu,
% 0.77/1.04 Tue Jun 14 10:20:04 2022
% 0.77/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17538_n027.cluster.edu".
% 0.77/1.04 ============================== end of head ===========================
% 0.77/1.04
% 0.77/1.04 ============================== INPUT =================================
% 0.77/1.04
% 0.77/1.04 % Reading from file /tmp/Prover9_17538_n027.cluster.edu
% 0.77/1.04
% 0.77/1.04 set(prolog_style_variables).
% 0.77/1.04 set(auto2).
% 0.77/1.04 % set(auto2) -> set(auto).
% 0.77/1.04 % set(auto) -> set(auto_inference).
% 0.77/1.04 % set(auto) -> set(auto_setup).
% 0.77/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.77/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.77/1.04 % set(auto) -> set(auto_limits).
% 0.77/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.77/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.77/1.04 % set(auto) -> set(auto_denials).
% 0.77/1.04 % set(auto) -> set(auto_process).
% 0.77/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.77/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.77/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.77/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.77/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.77/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.77/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.77/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.77/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.77/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.77/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.77/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.77/1.04 % set(auto2) -> assign(stats, some).
% 0.77/1.04 % set(auto2) -> clear(echo_input).
% 0.77/1.04 % set(auto2) -> set(quiet).
% 0.77/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.77/1.04 % set(auto2) -> clear(print_given).
% 0.77/1.04 assign(lrs_ticks,-1).
% 0.77/1.04 assign(sos_limit,10000).
% 0.77/1.04 assign(order,kbo).
% 0.77/1.04 set(lex_order_vars).
% 0.77/1.04 clear(print_given).
% 0.77/1.04
% 0.77/1.04 % formulas(sos). % not echoed (3 formulas)
% 0.77/1.04
% 0.77/1.04 ============================== end of input ==========================
% 0.77/1.04
% 0.77/1.04 % From the command line: assign(max_seconds, 300).
% 0.77/1.04
% 0.77/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.77/1.04
% 0.77/1.04 % Formulas that are not ordinary clauses:
% 0.77/1.04
% 0.77/1.04 ============================== end of process non-clausal formulas ===
% 0.77/1.04
% 0.77/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.77/1.04
% 0.77/1.04 ============================== PREDICATE ELIMINATION =================
% 0.77/1.04
% 0.77/1.04 ============================== end predicate elimination =============
% 0.77/1.04
% 0.77/1.04 Auto_denials:
% 0.77/1.04 % copying label prove_these_axioms_3 to answer in negative clause
% 0.77/1.04
% 0.77/1.04 Term ordering decisions:
% 0.77/1.04
% 0.77/1.04 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.77/1.04 Function symbol KB weights: a3=1. b3=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.77/1.04
% 0.77/1.04 ============================== end of process initial clauses ========
% 0.77/1.04
% 0.77/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.77/1.04
% 0.77/1.04 ============================== end of clauses for search =============
% 0.77/1.04
% 0.77/1.04 ============================== SEARCH ================================
% 0.77/1.04
% 0.77/1.04 % Starting search at 0.01 seconds.
% 0.77/1.04
% 0.77/1.04 ============================== PROOF =================================
% 0.77/1.04 % SZS status Unsatisfiable
% 0.77/1.04 % SZS output start Refutation
% 0.77/1.04
% 0.77/1.04 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms_3.
% 0.77/1.04 % Length of proof is 47.
% 0.77/1.04 % Level of proof is 20.
% 0.77/1.04 % Maximum clause weight is 35.000.
% 0.77/1.04 % Given clauses 22.
% 0.77/1.04
% 0.77/1.04 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 0.77/1.04 2 double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = B # label(single_axiom) # label(axiom). [assumption].
% 0.77/1.04 3 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3). [assumption].
% 0.77/1.04 4 inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) # answer(prove_these_axioms_3). [copy(3),rewrite([1(3),1(6),1(11),1(13)]),flip(a)].
% 0.77/1.04 5 double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),inverse(double_divide(inverse(D),B)))),C) = D. [para(2(a,1),2(a,1,1,1,2,1,2))].
% 0.77/1.04 6 double_divide(A,inverse(double_divide(inverse(B),double_divide(A,double_divide(C,D))))) = double_divide(inverse(double_divide(C,inverse(B))),D). [para(2(a,1),2(a,1,1,1,2,1)),flip(a)].
% 0.77/1.04 10 double_divide(inverse(A),inverse(double_divide(inverse(B),A))) = B. [para(2(a,1),5(a,1,1,1))].
% 0.77/1.04 11 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),inverse(double_divide(inverse(D),B)))),inverse(double_divide(inverse(E),D)))),inverse(double_divide(inverse(F),E)))),C) = F. [para(5(a,1),5(a,1,1,1,1,1,2,1,2))].
% 0.77/1.04 14 double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = double_divide(inverse(C),inverse(B)). [para(2(a,1),10(a,1,2,1)),flip(a)].
% 0.77/1.04 17 double_divide(inverse(double_divide(inverse(A),inverse(B))),inverse(double_divide(inverse(C),B))) = double_divide(inverse(A),inverse(C)). [para(5(a,1),10(a,1,2,1)),rewrite([14(8)]),flip(a)].
% 0.77/1.04 18 double_divide(inverse(inverse(double_divide(inverse(A),B))),inverse(A)) = B. [para(10(a,1),10(a,1,2,1))].
% 0.77/1.04 20 double_divide(inverse(double_divide(inverse(A),inverse(B))),A) = B. [back_rewrite(11),rewrite([14(5),17(8),17(8),17(8)])].
% 0.77/1.04 21 double_divide(inverse(double_divide(A,inverse(B))),C) = double_divide(inverse(double_divide(A,C)),inverse(B)). [back_rewrite(6),rewrite([14(6)]),flip(a)].
% 0.77/1.04 22 double_divide(inverse(A),double_divide(inverse(inverse(B)),inverse(A))) = B. [para(20(a,1),20(a,1,1,1))].
% 0.77/1.04 23 inverse(double_divide(inverse(A),B)) = double_divide(inverse(inverse(A)),inverse(B)). [para(18(a,1),10(a,1,2,1)),flip(a)].
% 0.77/1.04 24 double_divide(double_divide(inverse(inverse(A)),inverse(inverse(B))),A) = B. [back_rewrite(20),rewrite([23(4)])].
% 0.77/1.04 28 double_divide(A,double_divide(inverse(inverse(B)),inverse(double_divide(A,C)))) = double_divide(inverse(C),inverse(B)). [back_rewrite(14),rewrite([23(4)])].
% 0.77/1.04 31 inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(inverse(double_divide(c3,b3))),inverse(a3)) # answer(prove_these_axioms_3). [back_rewrite(4),rewrite([23(7)]),flip(a)].
% 0.77/1.04 41 double_divide(double_divide(inverse(inverse(A)),inverse(inverse(B))),C) = double_divide(double_divide(inverse(inverse(A)),inverse(C)),inverse(B)). [para(23(a,1),21(a,1,1)),rewrite([23(9)])].
% 0.77/1.04 42 double_divide(double_divide(double_divide(inverse(inverse(inverse(A))),inverse(inverse(B))),inverse(inverse(C))),double_divide(inverse(A),B)) = C. [para(23(a,1),24(a,1,1,1,1)),rewrite([23(5)])].
% 0.77/1.04 47 double_divide(double_divide(inverse(inverse(inverse(A))),inverse(inverse(B))),inverse(C)) = double_divide(inverse(B),double_divide(inverse(inverse(C)),inverse(A))). [para(22(a,1),28(a,1,2,2,1)),rewrite([23(11)]),flip(a)].
% 0.77/1.04 49 double_divide(inverse(double_divide(A,inverse(B))),double_divide(inverse(inverse(C)),inverse(double_divide(A,D)))) = double_divide(double_divide(inverse(inverse(D)),inverse(inverse(C))),inverse(B)). [para(28(a,1),21(a,2,1,1)),rewrite([23(13)])].
% 0.77/1.04 53 double_divide(A,double_divide(inverse(B),double_divide(inverse(inverse(double_divide(A,C))),inverse(D)))) = double_divide(inverse(C),double_divide(inverse(inverse(D)),inverse(B))). [para(23(a,1),28(a,1,2,1,1)),rewrite([23(5),47(9),23(12)])].
% 0.77/1.04 55 double_divide(inverse(double_divide(A,B)),double_divide(inverse(inverse(C)),inverse(D))) = double_divide(A,double_divide(inverse(inverse(C)),double_divide(inverse(inverse(B)),inverse(inverse(D))))). [para(28(a,1),28(a,1,2,2,1)),rewrite([23(6),23(15),47(18)]),flip(a)].
% 0.77/1.04 59 double_divide(double_divide(inverse(A),double_divide(inverse(inverse(inverse(B))),inverse(C))),double_divide(inverse(C),A)) = B. [back_rewrite(42),rewrite([47(9)])].
% 0.77/1.04 61 double_divide(A,double_divide(inverse(inverse(B)),double_divide(inverse(inverse(inverse(C))),inverse(inverse(double_divide(A,D)))))) = double_divide(double_divide(inverse(inverse(D)),inverse(inverse(B))),inverse(C)). [back_rewrite(49),rewrite([55(9)])].
% 0.77/1.04 64 double_divide(inverse(A),double_divide(inverse(B),B)) = A. [para(22(a,1),59(a,1,1))].
% 0.77/1.04 84 double_divide(A,double_divide(inverse(inverse(B)),A)) = B. [para(64(a,1),59(a,1,1))].
% 0.77/1.04 89 double_divide(double_divide(inverse(A),A),inverse(B)) = B. [para(64(a,1),84(a,1,2))].
% 0.77/1.04 91 double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(A)). [para(89(a,1),21(a,2,1,1)),rewrite([89(4)])].
% 0.77/1.04 94 double_divide(double_divide(inverse(A),A),double_divide(inverse(B),inverse(inverse(C)))) = double_divide(inverse(C),B). [para(23(a,1),89(a,1,2)),rewrite([91(6)])].
% 0.77/1.04 95 double_divide(inverse(A),inverse(inverse(B))) = double_divide(inverse(A),B). [para(89(a,1),28(a,1,2,2,1)),rewrite([91(6),94(7),91(6)]),flip(a)].
% 0.77/1.04 118 double_divide(A,double_divide(inverse(inverse(B)),double_divide(inverse(inverse(inverse(C))),double_divide(A,D)))) = double_divide(double_divide(inverse(inverse(B)),D),inverse(C)). [back_rewrite(61),rewrite([95(9),91(14),95(14)])].
% 0.77/1.04 124 double_divide(A,double_divide(inverse(B),double_divide(inverse(C),double_divide(A,D)))) = double_divide(inverse(D),double_divide(inverse(B),C)). [back_rewrite(53),rewrite([91(6),95(6),91(11),95(11)])].
% 0.77/1.04 128 double_divide(double_divide(inverse(inverse(A)),B),C) = double_divide(double_divide(inverse(C),A),inverse(B)). [back_rewrite(41),rewrite([95(5),91(8),95(8)])].
% 0.77/1.04 133 inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(a3),double_divide(c3,b3)) # answer(prove_these_axioms_3). [back_rewrite(31),rewrite([91(15),95(15)])].
% 0.77/1.04 137 inverse(double_divide(inverse(A),B)) = double_divide(inverse(B),A). [back_rewrite(23),rewrite([91(7),95(7)])].
% 0.77/1.04 143 double_divide(double_divide(inverse(inverse(A)),B),A) = B. [back_rewrite(24),rewrite([95(5)])].
% 0.77/1.04 148 double_divide(double_divide(inverse(inverse(A)),B),inverse(C)) = double_divide(inverse(B),double_divide(inverse(inverse(A)),C)). [back_rewrite(118),rewrite([124(9),95(6)]),flip(a)].
% 0.77/1.04 158 inverse(inverse(A)) = A. [para(143(a,1),89(a,1))].
% 0.77/1.04 166 double_divide(double_divide(A,B),inverse(C)) = double_divide(inverse(B),double_divide(A,C)). [back_rewrite(148),rewrite([158(2),158(6)])].
% 0.77/1.04 172 double_divide(double_divide(A,B),C) = double_divide(inverse(A),double_divide(inverse(C),B)). [back_rewrite(128),rewrite([158(2),166(6)])].
% 0.77/1.04 193 double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(C),double_divide(A,B)). [back_rewrite(166),rewrite([172(3),158(3)])].
% 0.77/1.04 200 double_divide(inverse(A),B) = double_divide(B,inverse(A)). [para(158(a,1),91(a,1,1)),rewrite([158(5)]),flip(a)].
% 0.77/1.04 217 inverse(double_divide(A,inverse(B))) = double_divide(B,inverse(A)). [back_rewrite(137),rewrite([200(2),200(5)])].
% 0.77/1.04 221 double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(inverse(a3),double_divide(c3,b3)) # answer(prove_these_axioms_3). [back_rewrite(133),rewrite([217(7),200(6,R)])].
% 0.77/1.04 222 $F # answer(prove_these_axioms_3). [resolve(221,a,193,a)].
% 0.77/1.04
% 0.77/1.04 % SZS output end Refutation
% 0.77/1.04 ============================== end of proof ==========================
% 0.77/1.04
% 0.77/1.04 ============================== STATISTICS ============================
% 0.77/1.04
% 0.77/1.04 Given=22. Generated=365. Kept=220. proofs=1.
% 0.77/1.04 Usable=2. Sos=26. Demods=24. Limbo=4, Disabled=190. Hints=0.
% 0.77/1.04 Megabytes=0.18.
% 0.77/1.04 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.77/1.04
% 0.77/1.04 ============================== end of statistics =====================
% 0.77/1.04
% 0.77/1.04 ============================== end of search =========================
% 0.77/1.04
% 0.77/1.04 THEOREM PROVED
% 0.77/1.04 % SZS status Unsatisfiable
% 0.77/1.04
% 0.77/1.04 Exiting with 1 proof.
% 0.77/1.04
% 0.77/1.04 Process 17691 exit (max_proofs) Tue Jun 14 10:20:04 2022
% 0.77/1.04 Prover9 interrupted
%------------------------------------------------------------------------------