TSTP Solution File: GRP205-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP205-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 11:18:09 EDT 2022
% Result : Unsatisfiable 3.67s 3.94s
% Output : Refutation 3.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP205-1 : TPTP v8.1.0. Released v2.3.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 03:40:26 EDT 2022
% 0.14/0.35 % CPUTime :
% 3.67/3.94 ============================== Prover9 ===============================
% 3.67/3.94 Prover9 (32) version 2009-11A, November 2009.
% 3.67/3.94 Process 10711 was started by sandbox2 on n006.cluster.edu,
% 3.67/3.94 Tue Jun 14 03:40:27 2022
% 3.67/3.94 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10558_n006.cluster.edu".
% 3.67/3.94 ============================== end of head ===========================
% 3.67/3.94
% 3.67/3.94 ============================== INPUT =================================
% 3.67/3.94
% 3.67/3.94 % Reading from file /tmp/Prover9_10558_n006.cluster.edu
% 3.67/3.94
% 3.67/3.94 set(prolog_style_variables).
% 3.67/3.94 set(auto2).
% 3.67/3.94 % set(auto2) -> set(auto).
% 3.67/3.94 % set(auto) -> set(auto_inference).
% 3.67/3.94 % set(auto) -> set(auto_setup).
% 3.67/3.94 % set(auto_setup) -> set(predicate_elim).
% 3.67/3.94 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.67/3.94 % set(auto) -> set(auto_limits).
% 3.67/3.94 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.67/3.94 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.67/3.94 % set(auto) -> set(auto_denials).
% 3.67/3.94 % set(auto) -> set(auto_process).
% 3.67/3.94 % set(auto2) -> assign(new_constants, 1).
% 3.67/3.94 % set(auto2) -> assign(fold_denial_max, 3).
% 3.67/3.94 % set(auto2) -> assign(max_weight, "200.000").
% 3.67/3.94 % set(auto2) -> assign(max_hours, 1).
% 3.67/3.94 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.67/3.94 % set(auto2) -> assign(max_seconds, 0).
% 3.67/3.94 % set(auto2) -> assign(max_minutes, 5).
% 3.67/3.94 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.67/3.94 % set(auto2) -> set(sort_initial_sos).
% 3.67/3.94 % set(auto2) -> assign(sos_limit, -1).
% 3.67/3.94 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.67/3.94 % set(auto2) -> assign(max_megs, 400).
% 3.67/3.94 % set(auto2) -> assign(stats, some).
% 3.67/3.94 % set(auto2) -> clear(echo_input).
% 3.67/3.94 % set(auto2) -> set(quiet).
% 3.67/3.94 % set(auto2) -> clear(print_initial_clauses).
% 3.67/3.94 % set(auto2) -> clear(print_given).
% 3.67/3.94 assign(lrs_ticks,-1).
% 3.67/3.94 assign(sos_limit,10000).
% 3.67/3.94 assign(order,kbo).
% 3.67/3.94 set(lex_order_vars).
% 3.67/3.94 clear(print_given).
% 3.67/3.94
% 3.67/3.94 % formulas(sos). % not echoed (10 formulas)
% 3.67/3.94
% 3.67/3.94 ============================== end of input ==========================
% 3.67/3.94
% 3.67/3.94 % From the command line: assign(max_seconds, 300).
% 3.67/3.94
% 3.67/3.94 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.67/3.94
% 3.67/3.94 % Formulas that are not ordinary clauses:
% 3.67/3.94
% 3.67/3.94 ============================== end of process non-clausal formulas ===
% 3.67/3.94
% 3.67/3.94 ============================== PROCESS INITIAL CLAUSES ===============
% 3.67/3.94
% 3.67/3.94 ============================== PREDICATE ELIMINATION =================
% 3.67/3.94
% 3.67/3.94 ============================== end predicate elimination =============
% 3.67/3.94
% 3.67/3.94 Auto_denials:
% 3.67/3.94 % copying label prove_moufang4 to answer in negative clause
% 3.67/3.94
% 3.67/3.94 Term ordering decisions:
% 3.67/3.94 Function symbol KB weights: identity=1. x=1. y=1. z=1. multiply=1. left_division=1. right_division=1. left_inverse=1. right_inverse=1.
% 3.67/3.94
% 3.67/3.94 ============================== end of process initial clauses ========
% 3.67/3.94
% 3.67/3.94 ============================== CLAUSES FOR SEARCH ====================
% 3.67/3.94
% 3.67/3.94 ============================== end of clauses for search =============
% 3.67/3.94
% 3.67/3.94 ============================== SEARCH ================================
% 3.67/3.94
% 3.67/3.94 % Starting search at 0.01 seconds.
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=67.000, iters=3336
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=63.000, iters=3349
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=59.000, iters=3368
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=55.000, iters=3408
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=51.000, iters=3351
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=47.000, iters=3360
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=43.000, iters=3362
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=39.000, iters=3345
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=35.000, iters=3372
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=32.000, iters=3351
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=31.000, iters=3350
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=29.000, iters=3350
% 3.67/3.94
% 3.67/3.94 Low Water (keep): wt=27.000, iters=3343
% 3.67/3.94
% 3.67/3.94 ============================== PROOF =================================
% 3.67/3.94 % SZS status Unsatisfiable
% 3.67/3.94 % SZS output start Refutation
% 3.67/3.94
% 3.67/3.94 % Proof 1 at 2.88 (+ 0.05) seconds: prove_moufang4.
% 3.67/3.94 % Length of proof is 33.
% 3.67/3.94 % Level of proof is 12.
% 3.67/3.94 % Maximum clause weight is 15.000.
% 3.67/3.94 % Given clauses 289.
% 3.67/3.94
% 3.67/3.94 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 3.67/3.94 2 multiply(A,identity) = A # label(right_identity) # label(axiom). [assumption].
% 3.67/3.94 3 multiply(A,right_inverse(A)) = identity # label(right_inverse) # label(axiom). [assumption].
% 3.67/3.94 4 multiply(left_inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 3.67/3.94 5 multiply(A,left_division(A,B)) = B # label(multiply_left_division) # label(axiom). [assumption].
% 3.67/3.94 6 left_division(A,multiply(A,B)) = B # label(left_division_multiply) # label(axiom). [assumption].
% 3.67/3.94 7 multiply(right_division(A,B),B) = A # label(multiply_right_division) # label(axiom). [assumption].
% 3.67/3.94 8 right_division(multiply(A,B),B) = A # label(right_division_multiply) # label(axiom). [assumption].
% 3.67/3.94 9 multiply(multiply(multiply(A,B),A),C) = multiply(A,multiply(B,multiply(A,C))) # label(moufang3) # label(axiom). [assumption].
% 3.67/3.94 10 multiply(x,multiply(multiply(y,z),x)) != multiply(multiply(x,y),multiply(z,x)) # label(prove_moufang4) # label(negated_conjecture) # answer(prove_moufang4). [assumption].
% 3.67/3.94 11 multiply(multiply(x,y),multiply(z,x)) != multiply(x,multiply(multiply(y,z),x)) # answer(prove_moufang4). [copy(10),flip(a)].
% 3.67/3.94 15 left_division(A,A) = identity. [para(2(a,1),6(a,1,2))].
% 3.67/3.94 16 left_division(A,identity) = right_inverse(A). [para(3(a,1),6(a,1,2))].
% 3.67/3.94 17 right_inverse(left_inverse(A)) = A. [para(4(a,1),6(a,1,2)),rewrite([16(3)])].
% 3.67/3.94 26 multiply(multiply(A,B),A) = multiply(A,multiply(B,A)). [para(9(a,1),2(a,1)),rewrite([2(2)]),flip(a)].
% 3.67/3.94 30 multiply(left_inverse(A),multiply(A,multiply(left_inverse(A),B))) = multiply(left_inverse(A),B). [para(4(a,1),9(a,1,1,1)),rewrite([1(3)]),flip(a)].
% 3.67/3.94 34 multiply(A,multiply(left_division(A,B),multiply(A,C))) = multiply(multiply(B,A),C). [para(5(a,1),9(a,1,1,1)),flip(a)].
% 3.67/3.94 40 right_division(multiply(A,multiply(B,multiply(A,C))),C) = multiply(A,multiply(B,A)). [para(9(a,1),8(a,1,1)),rewrite([26(6)])].
% 3.67/3.94 59 multiply(A,multiply(right_inverse(A),A)) = A. [para(3(a,1),26(a,1,1)),rewrite([1(2)]),flip(a)].
% 3.67/3.94 67 multiply(right_inverse(A),A) = identity. [para(59(a,1),6(a,1,2)),rewrite([15(1)]),flip(a)].
% 3.67/3.94 70 multiply(A,left_inverse(A)) = identity. [para(17(a,1),67(a,1,1))].
% 3.67/3.94 77 multiply(left_inverse(A),multiply(A,B)) = B. [para(5(a,1),30(a,1,2,2)),rewrite([5(7)])].
% 3.67/3.94 81 left_division(left_inverse(A),B) = multiply(A,B). [para(77(a,1),6(a,1,2))].
% 3.67/3.94 109 multiply(multiply(A,B),left_inverse(B)) = A. [para(70(a,1),34(a,1,2,2)),rewrite([2(3),5(2)]),flip(a)].
% 3.67/3.94 114 left_division(multiply(A,B),A) = left_inverse(B). [para(109(a,1),6(a,1,2))].
% 3.67/3.94 115 multiply(A,left_inverse(B)) = right_division(A,B). [para(7(a,1),109(a,1,1))].
% 3.67/3.94 116 right_division(A,left_inverse(B)) = multiply(A,B). [para(109(a,1),8(a,1,1))].
% 3.67/3.94 131 left_inverse(left_division(A,B)) = left_division(B,A). [para(5(a,1),114(a,1,1)),flip(a)].
% 3.67/3.94 163 right_division(A,left_division(B,C)) = multiply(A,left_division(C,B)). [para(131(a,1),115(a,1,2)),flip(a)].
% 3.67/3.94 233 multiply(multiply(A,multiply(B,C)),left_division(C,A)) = multiply(A,multiply(B,A)). [para(5(a,1),40(a,1,1,2,2)),rewrite([163(4)])].
% 3.67/3.94 3164 multiply(multiply(A,B),left_division(C,A)) = multiply(A,multiply(right_division(B,C),A)). [para(7(a,1),233(a,1,1,2))].
% 3.67/3.94 14594 multiply(multiply(A,B),multiply(C,A)) = multiply(A,multiply(multiply(B,C),A)). [para(81(a,1),3164(a,1,2)),rewrite([116(5)])].
% 3.67/3.94 14595 $F # answer(prove_moufang4). [resolve(14594,a,11,a)].
% 3.67/3.94
% 3.67/3.94 % SZS output end Refutation
% 3.67/3.94 ============================== end of proof ==========================
% 3.67/3.94
% 3.67/3.94 ============================== STATISTICS ============================
% 3.67/3.94
% 3.67/3.94 Given=289. Generated=75329. Kept=14593. proofs=1.
% 3.67/3.94 Usable=218. Sos=8298. Demods=8516. Limbo=4, Disabled=6082. Hints=0.
% 3.67/3.94 Megabytes=17.99.
% 3.67/3.94 User_CPU=2.88, System_CPU=0.05, Wall_clock=3.
% 3.67/3.94
% 3.67/3.94 ============================== end of statistics =====================
% 3.67/3.94
% 3.67/3.94 ============================== end of search =========================
% 3.67/3.94
% 3.67/3.94 THEOREM PROVED
% 3.67/3.94 % SZS status Unsatisfiable
% 3.67/3.94
% 3.67/3.94 Exiting with 1 proof.
% 3.67/3.94
% 3.67/3.94 Process 10711 exit (max_proofs) Tue Jun 14 03:40:30 2022
% 3.67/3.94 Prover9 interrupted
%------------------------------------------------------------------------------