TSTP Solution File: GRP777+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP777+1 : TPTP v8.1.0. Released v4.1.0.
% 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 11:21:02 EDT 2022
% Result : Theorem 1.30s 1.58s
% Output : Refutation 1.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP777+1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.12 % 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 07:28:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.30/1.58 ============================== Prover9 ===============================
% 1.30/1.58 Prover9 (32) version 2009-11A, November 2009.
% 1.30/1.58 Process 21579 was started by sandbox on n017.cluster.edu,
% 1.30/1.58 Mon Jun 13 07:28:38 2022
% 1.30/1.58 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21426_n017.cluster.edu".
% 1.30/1.58 ============================== end of head ===========================
% 1.30/1.58
% 1.30/1.58 ============================== INPUT =================================
% 1.30/1.58
% 1.30/1.58 % Reading from file /tmp/Prover9_21426_n017.cluster.edu
% 1.30/1.58
% 1.30/1.58 set(prolog_style_variables).
% 1.30/1.58 set(auto2).
% 1.30/1.58 % set(auto2) -> set(auto).
% 1.30/1.58 % set(auto) -> set(auto_inference).
% 1.30/1.58 % set(auto) -> set(auto_setup).
% 1.30/1.58 % set(auto_setup) -> set(predicate_elim).
% 1.30/1.58 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.30/1.58 % set(auto) -> set(auto_limits).
% 1.30/1.58 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.30/1.58 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.30/1.58 % set(auto) -> set(auto_denials).
% 1.30/1.58 % set(auto) -> set(auto_process).
% 1.30/1.58 % set(auto2) -> assign(new_constants, 1).
% 1.30/1.58 % set(auto2) -> assign(fold_denial_max, 3).
% 1.30/1.58 % set(auto2) -> assign(max_weight, "200.000").
% 1.30/1.58 % set(auto2) -> assign(max_hours, 1).
% 1.30/1.58 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.30/1.58 % set(auto2) -> assign(max_seconds, 0).
% 1.30/1.58 % set(auto2) -> assign(max_minutes, 5).
% 1.30/1.58 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.30/1.58 % set(auto2) -> set(sort_initial_sos).
% 1.30/1.58 % set(auto2) -> assign(sos_limit, -1).
% 1.30/1.58 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.30/1.58 % set(auto2) -> assign(max_megs, 400).
% 1.30/1.58 % set(auto2) -> assign(stats, some).
% 1.30/1.58 % set(auto2) -> clear(echo_input).
% 1.30/1.58 % set(auto2) -> set(quiet).
% 1.30/1.58 % set(auto2) -> clear(print_initial_clauses).
% 1.30/1.58 % set(auto2) -> clear(print_given).
% 1.30/1.58 assign(lrs_ticks,-1).
% 1.30/1.58 assign(sos_limit,10000).
% 1.30/1.58 assign(order,kbo).
% 1.30/1.58 set(lex_order_vars).
% 1.30/1.58 clear(print_given).
% 1.30/1.58
% 1.30/1.58 % formulas(sos). % not echoed (10 formulas)
% 1.30/1.58
% 1.30/1.58 ============================== end of input ==========================
% 1.30/1.58
% 1.30/1.58 % From the command line: assign(max_seconds, 300).
% 1.30/1.58
% 1.30/1.58 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.30/1.58
% 1.30/1.58 % Formulas that are not ordinary clauses:
% 1.30/1.58 1 (all B all A difference(A,product(A,B)) = B) # label(sos01) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 2 (all B all A product(A,difference(A,B)) = B) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 3 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 4 (all B all A product(quotient(A,B),B) = A) # label(sos04) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 5 (all D all C all B all A product(product(A,B),product(C,D)) = product(product(A,C),product(B,D))) # label(sos05) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 6 (all A product(A,A) = A) # label(sos06) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 7 (all B all A product(product(product(A,B),B),product(B,product(B,A))) = B) # label(sos07) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 8 (all C all B all A bigC(A,B,C) = product(product(A,B),product(C,A))) # label(sos08) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 9 -(all X0 bigC(a,b,X0) = bigC(c,c,X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.30/1.58
% 1.30/1.58 ============================== end of process non-clausal formulas ===
% 1.30/1.58
% 1.30/1.58 ============================== PROCESS INITIAL CLAUSES ===============
% 1.30/1.58
% 1.30/1.58 ============================== PREDICATE ELIMINATION =================
% 1.30/1.58
% 1.30/1.58 ============================== end predicate elimination =============
% 1.30/1.58
% 1.30/1.58 Auto_denials:
% 1.30/1.58 % copying label goals to answer in negative clause
% 1.30/1.58
% 1.30/1.58 Term ordering decisions:
% 1.30/1.58 Function symbol KB weights: a=1. b=1. c=1. c1=1. product=1. difference=1. quotient=1. bigC=1.
% 1.30/1.58
% 1.30/1.58 ============================== end of process initial clauses ========
% 1.30/1.58
% 1.30/1.58 ============================== CLAUSES FOR SEARCH ====================
% 1.30/1.58
% 1.30/1.58 ============================== end of clauses for search =============
% 1.30/1.58
% 1.30/1.58 ============================== SEARCH ================================
% 1.30/1.58
% 1.30/1.58 % Starting search at 0.01 seconds.
% 1.30/1.58
% 1.30/1.58 ============================== PROOF =================================
% 1.30/1.58 % SZS status Theorem
% 1.30/1.58 % SZS output start Refutation
% 1.30/1.58
% 1.30/1.58 % Proof 1 at 0.61 (+ 0.02) seconds: goals.
% 1.30/1.58 % Length of proof is 92.
% 1.30/1.58 % Level of proof is 23.
% 1.30/1.58 % Maximum clause weight is 23.000.
% 1.30/1.58 % Given clauses 130.
% 1.30/1.58
% 1.30/1.58 1 (all B all A difference(A,product(A,B)) = B) # label(sos01) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 2 (all B all A product(A,difference(A,B)) = B) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 3 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 4 (all B all A product(quotient(A,B),B) = A) # label(sos04) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 5 (all D all C all B all A product(product(A,B),product(C,D)) = product(product(A,C),product(B,D))) # label(sos05) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 6 (all A product(A,A) = A) # label(sos06) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 7 (all B all A product(product(product(A,B),B),product(B,product(B,A))) = B) # label(sos07) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 8 (all C all B all A bigC(A,B,C) = product(product(A,B),product(C,A))) # label(sos08) # label(axiom) # label(non_clause). [assumption].
% 1.30/1.58 9 -(all X0 bigC(a,b,X0) = bigC(c,c,X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.30/1.58 10 product(A,A) = A # label(sos06) # label(axiom). [clausify(6)].
% 1.30/1.58 11 difference(A,product(A,B)) = B # label(sos01) # label(axiom). [clausify(1)].
% 1.30/1.58 12 product(A,difference(A,B)) = B # label(sos02) # label(axiom). [clausify(2)].
% 1.30/1.58 13 quotient(product(A,B),B) = A # label(sos03) # label(axiom). [clausify(3)].
% 1.30/1.58 14 product(quotient(A,B),B) = A # label(sos04) # label(axiom). [clausify(4)].
% 1.30/1.58 15 product(product(a,c),product(c,b)) = product(a,b) # label(sos09) # label(axiom). [assumption].
% 1.30/1.58 16 bigC(A,B,C) = product(product(A,B),product(C,A)) # label(sos08) # label(axiom). [clausify(8)].
% 1.30/1.58 17 product(product(product(A,B),B),product(B,product(B,A))) = B # label(sos07) # label(axiom). [clausify(7)].
% 1.30/1.58 18 product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) # label(sos05) # label(axiom). [clausify(5)].
% 1.30/1.58 19 bigC(c,c,c1) != bigC(a,b,c1) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(9)].
% 1.30/1.58 20 product(product(a,b),product(c1,a)) != product(c,product(c1,c)) # answer(goals). [copy(19),rewrite([16(4),10(3),16(9)]),flip(a)].
% 1.30/1.58 23 quotient(A,difference(B,A)) = B. [para(12(a,1),13(a,1,1))].
% 1.30/1.58 24 difference(quotient(A,B),A) = B. [para(14(a,1),11(a,1,2))].
% 1.30/1.58 25 difference(product(a,c),product(a,b)) = product(c,b). [para(15(a,1),11(a,1,2))].
% 1.30/1.58 27 difference(product(product(A,B),B),B) = product(B,product(B,A)). [para(17(a,1),11(a,1,2))].
% 1.30/1.58 30 quotient(A,product(A,product(A,B))) = product(product(B,A),A). [para(17(a,1),13(a,1,1))].
% 1.30/1.58 37 product(product(A,B),product(A,C)) = product(A,product(B,C)). [para(10(a,1),18(a,1,1)),flip(a)].
% 1.30/1.58 38 product(product(A,B),product(C,B)) = product(product(A,C),B). [para(10(a,1),18(a,1,2)),flip(a)].
% 1.30/1.58 40 product(product(A,B),product(difference(A,C),D)) = product(C,product(B,D)). [para(12(a,1),18(a,1,1)),flip(a)].
% 1.30/1.58 44 product(product(A,quotient(B,C)),product(D,C)) = product(product(A,D),B). [para(14(a,1),18(a,1,2)),flip(a)].
% 1.30/1.58 61 product(A,product(A,quotient(B,A))) = difference(product(B,A),A). [para(14(a,1),27(a,1,1,1)),flip(a)].
% 1.30/1.58 77 product(product(A,B),A) = product(A,product(B,A)). [para(10(a,1),37(a,1,2))].
% 1.30/1.58 80 product(A,product(difference(A,B),C)) = product(B,product(A,C)). [para(12(a,1),37(a,1,1)),flip(a)].
% 1.30/1.58 94 quotient(product(A,B),product(A,product(B,product(B,C)))) = product(A,product(product(C,B),B)). [para(37(a,1),30(a,1,2,2)),rewrite([37(5),37(8),37(9)])].
% 1.30/1.58 111 quotient(product(A,product(B,A)),A) = product(A,B). [para(77(a,1),13(a,1,1))].
% 1.30/1.58 121 quotient(product(A,B),A) = product(A,quotient(B,A)). [para(14(a,1),111(a,1,1,2))].
% 1.30/1.58 127 product(A,quotient(difference(A,B),A)) = quotient(B,A). [para(12(a,1),121(a,1,1)),flip(a)].
% 1.30/1.58 132 difference(product(A,quotient(B,A)),product(A,B)) = A. [para(121(a,1),24(a,1,1))].
% 1.30/1.58 136 quotient(difference(A,B),A) = difference(A,quotient(B,A)). [para(127(a,1),11(a,1,2)),flip(a)].
% 1.30/1.58 155 product(difference(A,quotient(B,A)),A) = difference(A,B). [para(136(a,1),14(a,1,1))].
% 1.30/1.58 156 difference(difference(A,quotient(B,A)),difference(A,B)) = A. [para(136(a,1),24(a,1,1))].
% 1.30/1.58 162 difference(A,product(B,A)) = product(difference(A,B),A). [para(13(a,1),155(a,1,1,2)),flip(a)].
% 1.30/1.58 168 difference(product(difference(A,B),A),A) = product(A,quotient(B,A)). [para(155(a,1),27(a,1,1,1)),rewrite([12(6)])].
% 1.30/1.58 223 quotient(product(A,B),product(difference(B,A),B)) = B. [para(162(a,1),23(a,1,2))].
% 1.30/1.58 238 difference(product(difference(A,B),A),product(B,A)) = B. [para(223(a,1),155(a,1,1,2)),rewrite([168(3),40(5),14(2),10(1)]),flip(a)].
% 1.30/1.58 239 difference(product(A,quotient(B,A)),B) = product(difference(A,B),A). [para(223(a,1),156(a,1,1,2)),rewrite([168(3),238(6)])].
% 1.30/1.58 243 product(product(difference(A,B),A),B) = product(B,A). [para(238(a,1),12(a,1,2))].
% 1.30/1.58 245 difference(difference(A,B),B) = quotient(B,A). [para(14(a,1),238(a,1,2)),rewrite([155(3)])].
% 1.30/1.58 247 product(difference(A,B),A) = product(B,quotient(A,B)). [para(238(a,1),23(a,1,2)),rewrite([121(2)]),flip(a)].
% 1.30/1.58 252 quotient(A,product(difference(B,A),B)) = product(B,quotient(A,B)). [para(238(a,1),136(a,1,1)),rewrite([223(9),168(6)])].
% 1.30/1.58 273 product(difference(A,B),quotient(B,A)) = B. [para(245(a,1),12(a,1,2))].
% 1.30/1.58 275 quotient(product(A,B),product(A,quotient(B,A))) = B. [para(132(a,1),245(a,1,1)),rewrite([11(2)]),flip(a)].
% 1.30/1.58 308 product(product(A,quotient(B,A)),B) = product(B,quotient(B,A)). [para(24(a,1),243(a,1,1,1))].
% 1.30/1.58 335 difference(difference(A,B),product(B,quotient(A,B))) = A. [para(247(a,1),11(a,1,2))].
% 1.30/1.58 336 difference(A,product(difference(B,A),B)) = quotient(B,A). [para(247(a,2),11(a,1,2))].
% 1.30/1.58 355 product(A,product(difference(B,A),B)) = difference(product(B,A),A). [para(247(a,2),27(a,2,2)),rewrite([14(2)]),flip(a)].
% 1.30/1.58 357 quotient(A,product(A,B)) = product(A,quotient(A,B)). [para(247(a,1),30(a,2,1)),rewrite([12(2),308(5)])].
% 1.30/1.58 364 product(product(A,quotient(B,A)),difference(B,A)) = product(difference(B,A),A). [para(247(a,1),77(a,1,1)),rewrite([12(7)])].
% 1.30/1.58 377 difference(A,product(B,quotient(A,B))) = product(difference(A,difference(A,B)),A). [para(247(a,1),162(a,1,2))].
% 1.30/1.58 435 product(A,product(B,quotient(A,C))) = product(product(C,B),A). [para(273(a,1),40(a,1,2)),flip(a)].
% 1.30/1.58 453 difference(difference(product(A,B),B),product(B,A)) = product(A,B). [para(13(a,1),335(a,1,2,2))].
% 1.30/1.58 467 difference(product(A,B),B) = product(difference(A,B),B). [para(335(a,1),243(a,1,1,1)),rewrite([12(2),61(3),364(6)])].
% 1.30/1.58 471 difference(product(difference(A,B),B),product(B,A)) = product(A,B). [back_rewrite(453),rewrite([467(2)])].
% 1.30/1.58 480 product(A,product(difference(B,A),B)) = product(difference(B,A),A). [back_rewrite(355),rewrite([467(5)])].
% 1.30/1.58 490 product(A,product(A,quotient(B,A))) = product(difference(B,A),A). [back_rewrite(61),rewrite([467(5)])].
% 1.30/1.58 492 difference(product(A,B),product(B,A)) = product(A,quotient(A,B)). [para(11(a,1),336(a,1,2,1)),rewrite([357(5)])].
% 1.30/1.58 493 difference(A,product(B,quotient(A,B))) = quotient(quotient(A,B),A). [para(24(a,1),336(a,1,2,1))].
% 1.30/1.58 506 product(difference(A,difference(A,B)),A) = quotient(quotient(A,B),A). [back_rewrite(377),rewrite([493(3)]),flip(a)].
% 1.30/1.58 609 product(A,quotient(A,difference(A,B))) = quotient(A,B). [para(12(a,1),357(a,1,2)),flip(a)].
% 1.30/1.58 633 product(difference(quotient(A,B),B),B) = difference(A,B). [para(14(a,1),467(a,1,1)),flip(a)].
% 1.30/1.58 647 quotient(A,product(B,A)) = product(quotient(A,B),A). [para(467(a,1),245(a,1,1)),rewrite([467(3),245(2)]),flip(a)].
% 1.30/1.58 689 quotient(A,difference(A,B)) = difference(A,quotient(A,B)). [para(609(a,1),11(a,1,2)),flip(a)].
% 1.30/1.58 699 quotient(difference(A,B),B) = difference(quotient(A,B),B). [para(633(a,1),13(a,1,1))].
% 1.30/1.58 712 product(quotient(A,quotient(B,A)),A) = quotient(A,B). [para(245(a,1),633(a,2)),rewrite([699(2),245(3)])].
% 1.30/1.58 773 product(product(difference(A,B),C),B) = product(B,product(C,A)). [para(273(a,1),44(a,1,1)),flip(a)].
% 1.30/1.58 833 quotient(quotient(A,B),A) = quotient(A,quotient(B,A)). [para(336(a,1),689(a,1,2)),rewrite([252(5),493(5)]),flip(a)].
% 1.30/1.58 865 product(difference(A,difference(A,B)),A) = quotient(A,quotient(B,A)). [back_rewrite(506),rewrite([833(5)])].
% 1.30/1.58 1079 product(quotient(A,B),difference(A,B)) = product(B,A). [para(633(a,1),80(a,1,2)),rewrite([14(5)])].
% 1.30/1.58 1124 product(quotient(product(a,c),product(a,b)),product(c,b)) = product(a,product(b,c)). [para(25(a,1),1079(a,1,2)),rewrite([37(18)])].
% 1.30/1.58 1670 difference(product(A,quotient(A,B)),product(B,A)) = product(difference(A,B),B). [para(132(a,1),239(a,2,1)),rewrite([275(6),308(3),490(7)])].
% 1.30/1.58 2164 product(difference(A,product(B,C)),A) = product(C,quotient(A,B)). [para(435(a,1),11(a,1,2)),rewrite([162(3)])].
% 1.30/1.58 2723 difference(product(difference(product(A,quotient(B,C)),B),B),product(product(C,A),B)) = product(product(A,quotient(B,C)),B). [para(435(a,1),471(a,1,2))].
% 1.30/1.58 2789 product(difference(A,product(B,C)),product(B,C)) = product(product(B,C),product(C,quotient(A,B))). [para(480(a,1),38(a,2)),rewrite([2164(3),2164(6),38(7)]),flip(a)].
% 1.30/1.58 3899 product(A,quotient(product(B,C),A)) = product(difference(C,A),B). [para(773(a,1),13(a,1,1)),rewrite([121(3)])].
% 1.30/1.58 3907 product(product(difference(A,product(B,C)),B),C) = product(product(B,C),product(C,A)). [para(773(a,1),38(a,1)),flip(a)].
% 1.30/1.58 3938 product(product(difference(A,B),C),product(C,A)) = product(product(C,A),quotient(product(C,A),B)). [para(308(a,1),773(a,2)),rewrite([3899(3),3899(7),38(7),3907(6)])].
% 1.30/1.58 3954 product(difference(product(A,B),C),C) = product(C,product(difference(B,C),A)). [para(773(a,1),471(a,1,2)),rewrite([2789(6),23(4),3938(4),1670(7)])].
% 1.30/1.58 4096 product(product(A,quotient(B,C)),B) = product(B,quotient(B,product(C,A))). [back_rewrite(2723),rewrite([3954(4),24(2),492(5)]),flip(a)].
% 1.30/1.58 5367 quotient(product(A,B),product(A,C)) = product(A,quotient(B,C)). [para(865(a,1),94(a,2,2,1)),rewrite([12(4),12(3),712(6)])].
% 1.30/1.58 5481 product(product(a,c),c) = product(a,product(b,c)). [back_rewrite(1124),rewrite([5367(7),44(9)])].
% 1.30/1.58 5589 product(c,quotient(c,a)) = product(a,b). [para(5481(a,1),121(a,1,1)),rewrite([5367(9),13(6),647(11),38(12),4096(10),10(8)]),flip(a)].
% 1.30/1.58 5698 product(product(a,b),product(A,a)) = product(c,product(A,c)). [para(5589(a,1),44(a,1,1)),rewrite([77(10)])].
% 1.30/1.58 5699 $F # answer(goals). [resolve(5698,a,20,a)].
% 1.30/1.58
% 1.30/1.58 % SZS output end Refutation
% 1.30/1.58 ============================== end of proof ==========================
% 1.30/1.58
% 1.30/1.58 ============================== STATISTICS ============================
% 1.30/1.58
% 1.30/1.58 Given=130. Generated=15504. Kept=5688. proofs=1.
% 1.30/1.58 Usable=102. Sos=3336. Demods=2914. Limbo=18, Disabled=2241. Hints=0.
% 1.30/1.58 Megabytes=7.08.
% 1.30/1.58 User_CPU=0.61, System_CPU=0.02, Wall_clock=1.
% 1.30/1.58
% 1.30/1.58 ============================== end of statistics =====================
% 1.30/1.58
% 1.30/1.58 ============================== end of search =========================
% 1.30/1.58
% 1.30/1.58 THEOREM PROVED
% 1.30/1.58 % SZS status Theorem
% 1.30/1.58
% 1.30/1.58 Exiting with 1 proof.
% 1.30/1.58
% 1.30/1.58 Process 21579 exit (max_proofs) Mon Jun 13 07:28:39 2022
% 1.30/1.58 Prover9 interrupted
%------------------------------------------------------------------------------