TSTP Solution File: BOO025-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO025-1 : TPTP v8.1.0. Released v2.2.0.
% 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 : Thu Jul 14 23:48:03 EDT 2022
% Result : Unsatisfiable 0.66s 1.01s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO025-1 : TPTP v8.1.0. Released v2.2.0.
% 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 : Wed Jun 1 16:00:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.66/1.01 ============================== Prover9 ===============================
% 0.66/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.66/1.01 Process 21406 was started by sandbox2 on n017.cluster.edu,
% 0.66/1.01 Wed Jun 1 16:00:57 2022
% 0.66/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21253_n017.cluster.edu".
% 0.66/1.01 ============================== end of head ===========================
% 0.66/1.01
% 0.66/1.01 ============================== INPUT =================================
% 0.66/1.01
% 0.66/1.01 % Reading from file /tmp/Prover9_21253_n017.cluster.edu
% 0.66/1.01
% 0.66/1.01 set(prolog_style_variables).
% 0.66/1.01 set(auto2).
% 0.66/1.01 % set(auto2) -> set(auto).
% 0.66/1.01 % set(auto) -> set(auto_inference).
% 0.66/1.01 % set(auto) -> set(auto_setup).
% 0.66/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.66/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.66/1.01 % set(auto) -> set(auto_limits).
% 0.66/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.66/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.66/1.01 % set(auto) -> set(auto_denials).
% 0.66/1.01 % set(auto) -> set(auto_process).
% 0.66/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.66/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.66/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.66/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.66/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.66/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.66/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.66/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.66/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.66/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.66/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.66/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.66/1.01 % set(auto2) -> assign(stats, some).
% 0.66/1.01 % set(auto2) -> clear(echo_input).
% 0.66/1.01 % set(auto2) -> set(quiet).
% 0.66/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.66/1.01 % set(auto2) -> clear(print_given).
% 0.66/1.01 assign(lrs_ticks,-1).
% 0.66/1.01 assign(sos_limit,10000).
% 0.66/1.01 assign(order,kbo).
% 0.66/1.01 set(lex_order_vars).
% 0.66/1.01 clear(print_given).
% 0.66/1.01
% 0.66/1.01 % formulas(sos). % not echoed (8 formulas)
% 0.66/1.01
% 0.66/1.01 ============================== end of input ==========================
% 0.66/1.01
% 0.66/1.01 % From the command line: assign(max_seconds, 300).
% 0.66/1.01
% 0.66/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.66/1.01
% 0.66/1.01 % Formulas that are not ordinary clauses:
% 0.66/1.01
% 0.66/1.01 ============================== end of process non-clausal formulas ===
% 0.66/1.01
% 0.66/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.66/1.01
% 0.66/1.01 ============================== PREDICATE ELIMINATION =================
% 0.66/1.01
% 0.66/1.01 ============================== end predicate elimination =============
% 0.66/1.01
% 0.66/1.01 Auto_denials:
% 0.66/1.01 % copying label prove_equal_identity to answer in negative clause
% 0.66/1.01
% 0.66/1.01 Term ordering decisions:
% 0.66/1.01
% 0.66/1.01 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.66/1.01 Function symbol KB weights: n1=1. a=1. b=1. multiply=1. add=1. pixley=1. inverse=0.
% 0.66/1.01
% 0.66/1.01 ============================== end of process initial clauses ========
% 0.66/1.01
% 0.66/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.66/1.01
% 0.66/1.01 ============================== end of clauses for search =============
% 0.66/1.01
% 0.66/1.01 ============================== SEARCH ================================
% 0.66/1.01
% 0.66/1.01 % Starting search at 0.01 seconds.
% 0.66/1.01
% 0.66/1.01 ============================== PROOF =================================
% 0.66/1.01 % SZS status Unsatisfiable
% 0.66/1.01 % SZS output start Refutation
% 0.66/1.01
% 0.66/1.01 % Proof 1 at 0.03 (+ 0.00) seconds: prove_equal_identity.
% 0.66/1.01 % Length of proof is 72.
% 0.66/1.01 % Level of proof is 31.
% 0.66/1.01 % Maximum clause weight is 20.000.
% 0.66/1.01 % Given clauses 52.
% 0.66/1.01
% 0.66/1.01 1 add(A,inverse(A)) = n1 # label(additive_inverse) # label(axiom). [assumption].
% 0.66/1.01 2 pixley(A,A,B) = B # label(pixley1) # label(axiom). [assumption].
% 0.66/1.01 3 pixley(A,B,B) = A # label(pixley2) # label(axiom). [assumption].
% 0.66/1.01 4 pixley(A,B,A) = A # label(pixley3) # label(axiom). [assumption].
% 0.66/1.01 5 multiply(add(A,B),B) = B # label(multiply_add) # label(axiom). [assumption].
% 0.66/1.01 6 multiply(A,add(B,C)) = add(multiply(B,A),multiply(C,A)) # label(multiply_add_property) # label(axiom). [assumption].
% 0.66/1.01 7 add(multiply(A,B),multiply(C,B)) = multiply(B,add(A,C)). [copy(6),flip(a)].
% 0.66/1.01 8 pixley(A,B,C) = add(multiply(A,inverse(B)),add(multiply(A,C),multiply(inverse(B),C))) # label(pixley_defn) # label(axiom). [assumption].
% 0.66/1.01 9 pixley(A,B,C) = add(multiply(A,inverse(B)),multiply(C,add(A,inverse(B)))). [copy(8),rewrite([7(7)])].
% 0.66/1.01 10 multiply(b,inverse(b)) != multiply(a,inverse(a)) # label(prove_equal_identity) # label(negated_conjecture) # answer(prove_equal_identity). [assumption].
% 0.66/1.01 11 add(multiply(A,inverse(B)),multiply(A,add(A,inverse(B)))) = A. [back_rewrite(4),rewrite([9(1)])].
% 0.66/1.01 12 add(multiply(A,inverse(B)),multiply(B,add(A,inverse(B)))) = A. [back_rewrite(3),rewrite([9(1)])].
% 0.66/1.01 13 add(multiply(A,inverse(A)),multiply(B,n1)) = B. [back_rewrite(2),rewrite([9(1),1(4)])].
% 0.66/1.01 14 multiply(n1,inverse(A)) = inverse(A). [para(1(a,1),5(a,1,1))].
% 0.66/1.01 15 multiply(multiply(A,add(B,C)),multiply(C,A)) = multiply(C,A). [para(7(a,1),5(a,1,1))].
% 0.66/1.01 16 multiply(A,add(add(B,A),C)) = add(A,multiply(C,A)). [para(5(a,1),7(a,1,1)),flip(a)].
% 0.66/1.01 17 multiply(A,add(B,add(C,A))) = add(multiply(B,A),A). [para(5(a,1),7(a,1,2)),flip(a)].
% 0.66/1.01 21 multiply(A,multiply(B,add(A,inverse(B)))) = multiply(B,add(A,inverse(B))). [para(12(a,1),5(a,1,1))].
% 0.66/1.01 23 multiply(A,multiply(A,n1)) = multiply(A,n1). [para(13(a,1),5(a,1,1))].
% 0.66/1.01 24 add(multiply(A,inverse(A)),n1) = add(B,n1). [para(5(a,1),13(a,1,2))].
% 0.66/1.01 25 add(multiply(A,inverse(A)),n1) = c_0. [new_symbol(24)].
% 0.66/1.01 26 add(A,n1) = c_0. [back_rewrite(24),rewrite([25(4)]),flip(a)].
% 0.66/1.01 28 add(multiply(A,inverse(B)),inverse(B)) = multiply(inverse(B),c_0). [para(14(a,1),7(a,1,2)),rewrite([26(7)])].
% 0.66/1.01 31 add(inverse(n1),multiply(A,n1)) = A. [para(14(a,1),13(a,1,1))].
% 0.66/1.01 32 multiply(c_0,n1) = n1. [para(26(a,1),5(a,1,1))].
% 0.66/1.01 34 multiply(n1,add(A,c_0)) = c_0. [para(32(a,1),7(a,1,2)),rewrite([26(4)]),flip(a)].
% 0.66/1.01 36 add(multiply(A,add(B,c_0)),c_0) = c_0. [para(34(a,1),7(a,1,2)),rewrite([26(9),5(9)])].
% 0.66/1.01 45 multiply(multiply(inverse(A),c_0),inverse(A)) = inverse(A). [para(14(a,1),15(a,1,2)),rewrite([26(3),14(8)])].
% 0.66/1.01 47 multiply(c_0,c_0) = c_0. [para(34(a,1),15(a,1,2)),rewrite([26(4),5(4),34(7)])].
% 0.66/1.01 49 add(multiply(A,c_0),c_0) = multiply(c_0,add(A,c_0)). [para(47(a,1),7(a,1,2))].
% 0.66/1.01 55 multiply(n1,c_0) = c_0. [para(36(a,1),34(a,1,2))].
% 0.66/1.01 58 multiply(c_0,add(A,c_0)) = c_0. [para(36(a,1),36(a,1,1,2)),rewrite([49(4)])].
% 0.66/1.01 59 add(multiply(A,c_0),c_0) = c_0. [back_rewrite(49),rewrite([58(8)])].
% 0.66/1.01 68 multiply(inverse(A),c_0) = add(inverse(A),inverse(A)). [para(14(a,1),16(a,2,2)),rewrite([26(5)])].
% 0.66/1.01 69 add(A,multiply(n1,A)) = multiply(A,c_0). [para(26(a,1),16(a,1,2)),flip(a)].
% 0.66/1.01 80 multiply(multiply(n1,n1),c_0) = c_0. [para(23(a,1),69(a,1,2)),rewrite([7(7),26(4),55(3)]),flip(a)].
% 0.66/1.01 85 multiply(c_0,add(A,multiply(n1,n1))) = c_0. [para(80(a,1),7(a,1,2)),rewrite([59(4)]),flip(a)].
% 0.66/1.01 94 c_0 = n1. [para(13(a,1),85(a,1,2)),rewrite([32(3)]),flip(a)].
% 0.66/1.01 101 add(A,multiply(n1,A)) = multiply(A,n1). [back_rewrite(69),rewrite([94(4)])].
% 0.66/1.01 102 multiply(inverse(A),n1) = add(inverse(A),inverse(A)). [back_rewrite(68),rewrite([94(2)])].
% 0.66/1.01 104 multiply(multiply(inverse(A),n1),inverse(A)) = inverse(A). [back_rewrite(45),rewrite([94(2)])].
% 0.66/1.01 106 add(multiply(A,inverse(B)),inverse(B)) = multiply(inverse(B),n1). [back_rewrite(28),rewrite([94(6)])].
% 0.66/1.01 107 add(A,n1) = n1. [back_rewrite(26),rewrite([94(3)])].
% 0.66/1.01 108 add(add(inverse(A),inverse(A)),multiply(B,n1)) = multiply(n1,add(inverse(A),B)). [para(102(a,1),7(a,1,1))].
% 0.66/1.01 109 add(multiply(A,n1),add(inverse(B),inverse(B))) = multiply(n1,add(A,inverse(B))). [para(102(a,1),7(a,1,2))].
% 0.66/1.01 112 add(multiply(inverse(A),inverse(A)),multiply(inverse(A),n1)) = inverse(A). [para(102(a,2),11(a,1,2,2)),rewrite([23(8)])].
% 0.66/1.01 115 add(inverse(n1),add(inverse(A),inverse(A))) = inverse(A). [para(102(a,1),31(a,1,2))].
% 0.66/1.01 124 add(inverse(A),multiply(multiply(inverse(A),n1),add(multiply(inverse(A),n1),inverse(A)))) = multiply(inverse(A),n1). [para(104(a,1),11(a,1,1))].
% 0.66/1.01 135 multiply(inverse(A),inverse(A)) = multiply(inverse(A),n1). [para(115(a,1),17(a,1,2)),rewrite([106(9)])].
% 0.66/1.01 137 add(multiply(A,inverse(B)),multiply(inverse(B),n1)) = multiply(inverse(B),add(A,inverse(B))). [para(135(a,1),7(a,1,2))].
% 0.66/1.01 147 multiply(inverse(A),multiply(inverse(A),inverse(A))) = multiply(inverse(A),n1). [para(135(a,2),23(a,1,2))].
% 0.66/1.01 151 add(inverse(A),inverse(A)) = multiply(inverse(A),inverse(A)). [para(135(a,2),101(a,2)),rewrite([14(4)])].
% 0.66/1.01 153 multiply(inverse(A),n1) = inverse(A). [back_rewrite(112),rewrite([137(7),151(4),147(5)])].
% 0.66/1.01 155 multiply(inverse(A),inverse(A)) = inverse(A). [back_rewrite(124),rewrite([153(4),153(5),151(5),147(6),153(4),151(3),153(6)])].
% 0.66/1.01 163 add(inverse(n1),inverse(A)) = inverse(A). [back_rewrite(115),rewrite([151(5),155(5)])].
% 0.66/1.01 165 add(multiply(A,n1),inverse(B)) = multiply(n1,add(A,inverse(B))). [back_rewrite(109),rewrite([151(5),155(5)])].
% 0.66/1.01 166 add(inverse(A),multiply(B,n1)) = multiply(n1,add(inverse(A),B)). [back_rewrite(108),rewrite([151(3),155(3)])].
% 0.66/1.01 173 inverse(inverse(n1)) = n1. [para(163(a,1),1(a,1))].
% 0.66/1.01 175 multiply(inverse(A),add(inverse(n1),A)) = inverse(n1). [para(163(a,1),12(a,1,2,2)),rewrite([7(7)])].
% 0.66/1.01 186 multiply(n1,add(A,A)) = A. [para(173(a,1),11(a,1,1,2)),rewrite([173(5),107(4),7(5)])].
% 0.66/1.01 187 multiply(n1,add(A,inverse(n1))) = A. [para(173(a,1),12(a,1,1,2)),rewrite([173(7),107(6),153(6),165(5)])].
% 0.66/1.01 188 multiply(A,inverse(n1)) = inverse(n1). [para(173(a,1),21(a,1,2,2,2)),rewrite([107(4),153(4),173(8),107(7),153(7)])].
% 0.66/1.01 191 multiply(n1,multiply(A,add(B,B))) = multiply(B,A). [para(7(a,1),186(a,1,2))].
% 0.66/1.01 196 add(inverse(n1),A) = A. [para(188(a,1),12(a,1,1)),rewrite([187(7)])].
% 0.66/1.01 197 multiply(n1,A) = A. [para(188(a,1),13(a,1,1)),rewrite([166(5),196(4)])].
% 0.66/1.01 199 multiply(inverse(A),A) = inverse(n1). [back_rewrite(175),rewrite([196(4)])].
% 0.66/1.01 200 multiply(A,add(B,B)) = multiply(B,A). [back_rewrite(191),rewrite([197(4)])].
% 0.66/1.01 202 multiply(A,n1) = A. [back_rewrite(186),rewrite([200(3)])].
% 0.66/1.01 205 add(A,A) = A. [back_rewrite(101),rewrite([197(2),202(3)])].
% 0.66/1.01 221 multiply(A,B) = multiply(B,A). [back_rewrite(200),rewrite([205(1)])].
% 0.66/1.01 244 multiply(A,inverse(A)) = inverse(n1). [back_rewrite(199),rewrite([221(2)])].
% 0.66/1.01 254 $F # answer(prove_equal_identity). [back_rewrite(10),rewrite([244(4),244(6)]),xx(a)].
% 0.66/1.01
% 0.66/1.01 % SZS output end Refutation
% 0.66/1.01 ============================== end of proof ==========================
% 0.66/1.01
% 0.66/1.01 ============================== STATISTICS ============================
% 0.66/1.01
% 0.66/1.01 Given=52. Generated=835. Kept=251. proofs=1.
% 0.66/1.01 Usable=12. Sos=32. Demods=50. Limbo=10, Disabled=205. Hints=0.
% 0.66/1.01 Megabytes=0.20.
% 0.66/1.01 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.66/1.01
% 0.66/1.01 ============================== end of statistics =====================
% 0.66/1.01
% 0.66/1.01 ============================== end of search =========================
% 0.66/1.01
% 0.66/1.01 THEOREM PROVED
% 0.66/1.01 % SZS status Unsatisfiable
% 0.66/1.01
% 0.66/1.01 Exiting with 1 proof.
% 0.66/1.01
% 0.66/1.01 Process 21406 exit (max_proofs) Wed Jun 1 16:00:57 2022
% 0.66/1.01 Prover9 interrupted
%------------------------------------------------------------------------------