TSTP Solution File: BOO014-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO014-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 23:48:01 EDT 2022
% Result : Unsatisfiable 1.51s 1.78s
% Output : Refutation 1.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO014-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n021.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 : Wed Jun 1 16:54:31 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.51/1.78 ============================== Prover9 ===============================
% 1.51/1.78 Prover9 (32) version 2009-11A, November 2009.
% 1.51/1.78 Process 11916 was started by sandbox on n021.cluster.edu,
% 1.51/1.78 Wed Jun 1 16:54:31 2022
% 1.51/1.78 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11763_n021.cluster.edu".
% 1.51/1.78 ============================== end of head ===========================
% 1.51/1.78
% 1.51/1.78 ============================== INPUT =================================
% 1.51/1.78
% 1.51/1.78 % Reading from file /tmp/Prover9_11763_n021.cluster.edu
% 1.51/1.78
% 1.51/1.78 set(prolog_style_variables).
% 1.51/1.78 set(auto2).
% 1.51/1.78 % set(auto2) -> set(auto).
% 1.51/1.78 % set(auto) -> set(auto_inference).
% 1.51/1.78 % set(auto) -> set(auto_setup).
% 1.51/1.78 % set(auto_setup) -> set(predicate_elim).
% 1.51/1.78 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.51/1.78 % set(auto) -> set(auto_limits).
% 1.51/1.78 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.51/1.78 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.51/1.78 % set(auto) -> set(auto_denials).
% 1.51/1.78 % set(auto) -> set(auto_process).
% 1.51/1.78 % set(auto2) -> assign(new_constants, 1).
% 1.51/1.78 % set(auto2) -> assign(fold_denial_max, 3).
% 1.51/1.78 % set(auto2) -> assign(max_weight, "200.000").
% 1.51/1.78 % set(auto2) -> assign(max_hours, 1).
% 1.51/1.78 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.51/1.78 % set(auto2) -> assign(max_seconds, 0).
% 1.51/1.78 % set(auto2) -> assign(max_minutes, 5).
% 1.51/1.78 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.51/1.78 % set(auto2) -> set(sort_initial_sos).
% 1.51/1.78 % set(auto2) -> assign(sos_limit, -1).
% 1.51/1.78 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.51/1.78 % set(auto2) -> assign(max_megs, 400).
% 1.51/1.78 % set(auto2) -> assign(stats, some).
% 1.51/1.78 % set(auto2) -> clear(echo_input).
% 1.51/1.78 % set(auto2) -> set(quiet).
% 1.51/1.78 % set(auto2) -> clear(print_initial_clauses).
% 1.51/1.78 % set(auto2) -> clear(print_given).
% 1.51/1.78 assign(lrs_ticks,-1).
% 1.51/1.78 assign(sos_limit,10000).
% 1.51/1.78 assign(order,kbo).
% 1.51/1.78 set(lex_order_vars).
% 1.51/1.78 clear(print_given).
% 1.51/1.78
% 1.51/1.78 % formulas(sos). % not echoed (17 formulas)
% 1.51/1.78
% 1.51/1.78 ============================== end of input ==========================
% 1.51/1.78
% 1.51/1.78 % From the command line: assign(max_seconds, 300).
% 1.51/1.78
% 1.51/1.78 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.51/1.78
% 1.51/1.78 % Formulas that are not ordinary clauses:
% 1.51/1.78
% 1.51/1.78 ============================== end of process non-clausal formulas ===
% 1.51/1.78
% 1.51/1.78 ============================== PROCESS INITIAL CLAUSES ===============
% 1.51/1.78
% 1.51/1.78 ============================== PREDICATE ELIMINATION =================
% 1.51/1.78
% 1.51/1.78 ============================== end predicate elimination =============
% 1.51/1.78
% 1.51/1.78 Auto_denials:
% 1.51/1.78 % copying label prove_c_inverse_is_d to answer in negative clause
% 1.51/1.78
% 1.51/1.78 Term ordering decisions:
% 1.51/1.78
% 1.51/1.78 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 1.51/1.78 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. a=1. b=1. c=1. d=1. add=1. multiply=1. inverse=0.
% 1.51/1.78
% 1.51/1.78 ============================== end of process initial clauses ========
% 1.51/1.78
% 1.51/1.78 ============================== CLAUSES FOR SEARCH ====================
% 1.51/1.78
% 1.51/1.78 ============================== end of clauses for search =============
% 1.51/1.78
% 1.51/1.78 ============================== SEARCH ================================
% 1.51/1.78
% 1.51/1.78 % Starting search at 0.01 seconds.
% 1.51/1.78
% 1.51/1.78 ============================== PROOF =================================
% 1.51/1.78 % SZS status Unsatisfiable
% 1.51/1.78 % SZS output start Refutation
% 1.51/1.78
% 1.51/1.78 % Proof 1 at 0.75 (+ 0.02) seconds: prove_c_inverse_is_d.
% 1.51/1.78 % Length of proof is 78.
% 1.51/1.78 % Level of proof is 20.
% 1.51/1.78 % Maximum clause weight is 23.000.
% 1.51/1.78 % Given clauses 162.
% 1.51/1.78
% 1.51/1.78 1 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 1.51/1.78 3 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 1.51/1.78 5 add(a,b) = c # label(a_plus_b_is_c) # label(hypothesis). [assumption].
% 1.51/1.78 6 c = add(a,b). [copy(5),flip(a)].
% 1.51/1.78 7 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 1.51/1.78 9 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 1.51/1.78 11 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 1.51/1.78 12 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 1.51/1.78 13 multiply(inverse(a),inverse(b)) = d # label(a_inverse_times_b_inverse_is_d) # label(hypothesis). [assumption].
% 1.51/1.78 14 d = multiply(inverse(a),inverse(b)). [copy(13),flip(a)].
% 1.51/1.78 15 add(multiply(A,B),C) = multiply(add(A,C),add(B,C)) # label(distributivity1) # label(axiom). [assumption].
% 1.51/1.78 16 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [copy(15),rewrite([11(2)]),flip(a),rewrite([11(2)])].
% 1.51/1.78 17 add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)) # label(distributivity2) # label(axiom). [assumption].
% 1.51/1.78 18 multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)). [copy(17),flip(a)].
% 1.51/1.78 19 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distributivity3) # label(axiom). [assumption].
% 1.51/1.78 20 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [copy(19),rewrite([12(2)]),flip(a),rewrite([12(2)])].
% 1.51/1.78 21 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distributivity4) # label(axiom). [assumption].
% 1.51/1.78 22 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(21),flip(a)].
% 1.51/1.78 23 inverse(c) != d # label(prove_c_inverse_is_d) # label(negated_conjecture) # answer(prove_c_inverse_is_d). [assumption].
% 1.51/1.78 24 inverse(add(a,b)) != multiply(inverse(a),inverse(b)) # answer(prove_c_inverse_is_d). [copy(23),rewrite([6(1),14(5)])].
% 1.51/1.78 25 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(3(a,1),16(a,1,1)),rewrite([11(2),3(2)]),flip(a)].
% 1.51/1.78 26 multiply(A,add(B,A)) = add(A,multiply(B,additive_identity)). [para(3(a,1),16(a,1,2)),rewrite([12(2)])].
% 1.51/1.78 27 multiply(multiplicative_identity,add(A,inverse(B))) = add(inverse(B),multiply(B,A)). [para(7(a,1),16(a,1,1)),rewrite([11(3)])].
% 1.51/1.78 30 multiply(multiplicative_identity,add(A,B)) = add(A,multiply(B,inverse(A))). [para(7(a,1),18(a,1,1)),rewrite([12(5)])].
% 1.51/1.78 31 multiply(multiplicative_identity,add(A,B)) = add(A,B). [para(1(a,1),20(a,1,1)),rewrite([12(2),1(2)]),flip(a)].
% 1.51/1.78 32 multiply(A,add(B,multiplicative_identity)) = add(A,multiply(B,A)). [para(1(a,1),20(a,1,2)),rewrite([11(2)]),flip(a)].
% 1.51/1.78 33 multiply(inverse(A),add(A,B)) = multiply(B,inverse(A)). [para(9(a,1),20(a,1,1)),rewrite([12(3),25(4)]),flip(a)].
% 1.51/1.78 34 multiply(A,add(B,inverse(A))) = multiply(B,A). [para(9(a,1),20(a,1,2)),rewrite([11(3),25(3)]),flip(a)].
% 1.51/1.78 35 multiply(multiply(A,add(B,C)),add(D,multiply(A,C))) = add(multiply(A,C),multiply(D,multiply(A,B))). [para(20(a,1),16(a,1,1)),rewrite([11(4),12(7),12(8)])].
% 1.51/1.78 44 add(A,multiply(B,inverse(A))) = add(A,B). [back_rewrite(30),rewrite([31(3)]),flip(a)].
% 1.51/1.78 45 add(inverse(A),multiply(B,A)) = add(B,inverse(A)). [back_rewrite(27),rewrite([31(4),12(4)]),flip(a)].
% 1.51/1.78 52 add(additive_identity,add(A,B)) = add(A,B). [para(31(a,1),25(a,1,2)),rewrite([31(6)])].
% 1.51/1.78 54 add(additive_identity,multiplicative_identity) = multiplicative_identity. [para(7(a,1),52(a,1,2)),rewrite([7(5)])].
% 1.51/1.78 55 add(A,multiply(A,additive_identity)) = A. [para(54(a,1),20(a,2,2)),rewrite([12(2),1(4),11(3),1(5)])].
% 1.51/1.78 57 add(A,multiply(B,multiply(A,additive_identity))) = multiply(A,add(B,A)). [para(55(a,1),16(a,1,2)),rewrite([12(2)]),flip(a)].
% 1.51/1.78 59 multiply(additive_identity,additive_identity) = additive_identity. [para(55(a,1),25(a,1)),flip(a)].
% 1.51/1.78 68 add(multiply(A,B),add(B,multiply(C,additive_identity))) = multiply(B,add(A,add(B,C))). [para(26(a,1),20(a,1,2)),rewrite([11(6)])].
% 1.51/1.78 72 add(multiply(A,B),add(A,multiply(C,additive_identity))) = multiply(A,add(B,add(A,C))). [para(26(a,1),22(a,1,2)),rewrite([11(6)])].
% 1.51/1.78 78 multiply(A,A) = A. [para(59(a,1),16(a,2,2)),rewrite([11(2),3(2),3(2),3(3)])].
% 1.51/1.78 79 multiply(A,add(A,B)) = add(A,multiply(A,B)). [para(78(a,1),20(a,1,1)),flip(a)].
% 1.51/1.78 91 add(A,multiply(B,multiply(A,additive_identity))) = add(A,multiply(A,B)). [back_rewrite(57),rewrite([11(5),79(6)])].
% 1.51/1.78 92 multiply(multiplicative_identity,inverse(A)) = inverse(A). [para(9(a,1),32(a,2,2)),rewrite([33(4),3(6)])].
% 1.51/1.78 97 add(add(A,B),add(A,multiply(A,B))) = add(A,B). [para(32(a,1),18(a,1)),rewrite([79(3),1(6)])].
% 1.51/1.78 110 add(additive_identity,inverse(A)) = inverse(A). [para(92(a,1),25(a,1,2)),rewrite([92(6)])].
% 1.51/1.78 114 multiply(inverse(A),add(B,A)) = multiply(B,inverse(A)). [para(33(a,1),12(a,1)),rewrite([11(3),12(5)]),flip(a)].
% 1.51/1.78 119 multiply(inverse(multiply(A,B)),multiply(A,add(B,C))) = multiply(multiply(A,C),inverse(multiply(A,B))). [para(22(a,1),33(a,1,2))].
% 1.51/1.78 137 multiply(A,additive_identity) = additive_identity. [para(110(a,1),34(a,1,2)),rewrite([9(2),12(3)]),flip(a)].
% 1.51/1.78 140 add(A,multiply(A,B)) = A. [back_rewrite(91),rewrite([137(2),137(2),3(2)]),flip(a)].
% 1.51/1.78 145 multiply(A,add(B,add(A,C))) = A. [back_rewrite(72),rewrite([137(3),3(3),11(2),140(2)]),flip(a)].
% 1.51/1.78 146 add(A,multiply(B,A)) = A. [back_rewrite(68),rewrite([137(3),3(3),11(2),145(5)])].
% 1.51/1.78 148 add(A,add(A,B)) = add(A,B). [back_rewrite(97),rewrite([140(3),11(2)])].
% 1.51/1.78 155 multiply(A,add(B,A)) = A. [para(137(a,1),16(a,2,2)),rewrite([3(3),12(2),3(4)])].
% 1.51/1.78 173 multiply(A,multiply(B,add(C,A))) = multiply(B,A). [para(20(a,1),35(a,2)),rewrite([146(4),12(3),140(5),12(4)])].
% 1.51/1.78 183 multiply(multiply(A,B),add(C,multiply(A,multiply(B,D)))) = add(multiply(A,multiply(B,D)),multiply(C,multiply(A,B))). [para(140(a,1),35(a,1,1,2))].
% 1.51/1.78 193 multiply(A,multiply(A,B)) = multiply(A,B). [para(140(a,1),155(a,1,2)),rewrite([12(2)])].
% 1.51/1.78 474 add(A,inverse(inverse(A))) = inverse(inverse(A)). [para(9(a,1),45(a,1,2)),rewrite([3(4)]),flip(a)].
% 1.51/1.78 475 add(inverse(A),multiply(A,B)) = add(B,inverse(A)). [para(11(a,1),45(a,2)),rewrite([12(2),11(5)])].
% 1.51/1.78 492 add(A,inverse(multiply(A,B))) = multiplicative_identity. [para(193(a,1),45(a,1,2)),rewrite([11(4),7(4)]),flip(a)].
% 1.51/1.78 504 multiply(inverse(A),inverse(multiply(A,B))) = inverse(A). [para(492(a,1),33(a,1,2)),rewrite([1(3),12(5)]),flip(a)].
% 1.51/1.78 550 inverse(inverse(A)) = A. [para(474(a,1),44(a,2)),rewrite([12(4),9(4),3(2)]),flip(a)].
% 1.51/1.78 562 multiply(A,inverse(add(A,B))) = additive_identity. [para(148(a,1),114(a,1,2)),rewrite([12(4),9(4)]),flip(a)].
% 1.51/1.78 565 multiply(add(A,B),inverse(multiply(A,inverse(B)))) = multiply(B,inverse(multiply(A,inverse(B)))). [para(44(a,1),114(a,1,2)),rewrite([11(4),12(5)])].
% 1.51/1.78 567 multiply(add(A,inverse(B)),inverse(multiply(A,B))) = multiply(inverse(B),inverse(multiply(A,B))). [para(45(a,1),114(a,1,2)),rewrite([12(5)])].
% 1.51/1.78 631 multiply(A,inverse(multiply(B,inverse(A)))) = A. [para(33(a,1),504(a,1,2,1)),rewrite([550(2),550(6)])].
% 1.51/1.78 636 multiply(add(A,B),inverse(multiply(A,inverse(B)))) = B. [back_rewrite(565),rewrite([631(9)])].
% 1.51/1.78 742 multiply(multiply(A,inverse(B)),inverse(multiply(A,B))) = multiply(A,inverse(multiply(A,B))). [para(7(a,1),119(a,1,2,2)),rewrite([1(4),12(3)]),flip(a)].
% 1.51/1.78 743 multiply(inverse(A),multiply(B,add(C,A))) = multiply(multiply(C,B),inverse(A)). [para(16(a,1),119(a,1,2)),rewrite([12(2),155(2),33(4),12(5),12(7),155(7),12(7)]),flip(a)].
% 1.51/1.78 1009 multiply(multiply(A,B),multiply(B,C)) = multiply(C,multiply(A,B)). [para(146(a,1),173(a,1,2,2)),rewrite([12(2)])].
% 1.51/1.78 1733 add(inverse(A),inverse(add(A,B))) = inverse(A). [para(562(a,1),475(a,1,2)),rewrite([3(3),11(5)]),flip(a)].
% 1.51/1.78 1773 add(A,inverse(add(B,inverse(A)))) = A. [para(45(a,1),1733(a,1,2,1)),rewrite([550(2),550(6)])].
% 1.51/1.78 1815 multiply(inverse(A),inverse(multiply(B,A))) = inverse(A). [para(550(a,1),636(a,1,2,1,2)),rewrite([567(5)])].
% 1.51/1.78 1837 multiply(A,inverse(multiply(A,B))) = inverse(add(B,inverse(A))). [para(1773(a,1),636(a,1,1)),rewrite([550(4),34(3),12(1)])].
% 1.51/1.78 1874 multiply(multiply(A,inverse(B)),inverse(multiply(A,B))) = inverse(add(B,inverse(A))). [back_rewrite(742),rewrite([1837(8)])].
% 1.51/1.78 2369 multiply(A,multiply(B,C)) = multiply(C,multiply(A,B)). [para(20(a,1),183(a,2)),rewrite([146(5),1009(3),140(5),12(4)]),flip(a)].
% 1.51/1.78 2965 multiply(multiply(A,B),inverse(C)) = multiply(A,multiply(B,inverse(C))). [back_rewrite(743),rewrite([11(2),2369(4,R),12(3),33(3),12(4)]),flip(a)].
% 1.51/1.78 3065 inverse(add(A,inverse(B))) = multiply(B,inverse(A)). [back_rewrite(1874),rewrite([2965(5),1815(4)]),flip(a)].
% 1.51/1.78 3299 inverse(add(A,B)) = multiply(inverse(A),inverse(B)). [para(550(a,1),3065(a,1,1,2)),rewrite([12(5)])].
% 1.51/1.78 3300 $F # answer(prove_c_inverse_is_d). [resolve(3299,a,24,a)].
% 1.51/1.78
% 1.51/1.78 % SZS output end Refutation
% 1.51/1.78 ============================== end of proof ==========================
% 1.51/1.78
% 1.51/1.78 ============================== STATISTICS ============================
% 1.51/1.78
% 1.51/1.78 Given=162. Generated=22429. Kept=3292. proofs=1.
% 1.51/1.78 Usable=93. Sos=1150. Demods=1203. Limbo=5, Disabled=2060. Hints=0.
% 1.51/1.78 Megabytes=3.91.
% 1.51/1.78 User_CPU=0.76, System_CPU=0.02, Wall_clock=1.
% 1.51/1.78
% 1.51/1.78 ============================== end of statistics =====================
% 1.51/1.78
% 1.51/1.78 ============================== end of search =========================
% 1.51/1.78
% 1.51/1.78 THEOREM PROVED
% 1.51/1.78 % SZS status Unsatisfiable
% 1.51/1.78
% 1.51/1.78 Exiting with 1 proof.
% 1.51/1.78
% 1.51/1.78 Process 11916 exit (max_proofs) Wed Jun 1 16:54:32 2022
% 1.51/1.78 Prover9 interrupted
%------------------------------------------------------------------------------