TSTP Solution File: BOO012-2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO012-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 23:48:00 EDT 2022
% Result : Unsatisfiable 0.87s 1.16s
% Output : Refutation 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO012-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 15:52:12 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.87/1.16 ============================== Prover9 ===============================
% 0.87/1.16 Prover9 (32) version 2009-11A, November 2009.
% 0.87/1.16 Process 14509 was started by sandbox on n026.cluster.edu,
% 0.87/1.16 Wed Jun 1 15:52:12 2022
% 0.87/1.16 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_14356_n026.cluster.edu".
% 0.87/1.16 ============================== end of head ===========================
% 0.87/1.16
% 0.87/1.16 ============================== INPUT =================================
% 0.87/1.16
% 0.87/1.16 % Reading from file /tmp/Prover9_14356_n026.cluster.edu
% 0.87/1.16
% 0.87/1.16 set(prolog_style_variables).
% 0.87/1.16 set(auto2).
% 0.87/1.16 % set(auto2) -> set(auto).
% 0.87/1.16 % set(auto) -> set(auto_inference).
% 0.87/1.16 % set(auto) -> set(auto_setup).
% 0.87/1.16 % set(auto_setup) -> set(predicate_elim).
% 0.87/1.16 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.87/1.16 % set(auto) -> set(auto_limits).
% 0.87/1.16 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.87/1.16 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.87/1.16 % set(auto) -> set(auto_denials).
% 0.87/1.16 % set(auto) -> set(auto_process).
% 0.87/1.16 % set(auto2) -> assign(new_constants, 1).
% 0.87/1.16 % set(auto2) -> assign(fold_denial_max, 3).
% 0.87/1.16 % set(auto2) -> assign(max_weight, "200.000").
% 0.87/1.16 % set(auto2) -> assign(max_hours, 1).
% 0.87/1.16 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.87/1.16 % set(auto2) -> assign(max_seconds, 0).
% 0.87/1.16 % set(auto2) -> assign(max_minutes, 5).
% 0.87/1.16 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.87/1.16 % set(auto2) -> set(sort_initial_sos).
% 0.87/1.16 % set(auto2) -> assign(sos_limit, -1).
% 0.87/1.16 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.87/1.16 % set(auto2) -> assign(max_megs, 400).
% 0.87/1.16 % set(auto2) -> assign(stats, some).
% 0.87/1.16 % set(auto2) -> clear(echo_input).
% 0.87/1.16 % set(auto2) -> set(quiet).
% 0.87/1.16 % set(auto2) -> clear(print_initial_clauses).
% 0.87/1.16 % set(auto2) -> clear(print_given).
% 0.87/1.16 assign(lrs_ticks,-1).
% 0.87/1.16 assign(sos_limit,10000).
% 0.87/1.16 assign(order,kbo).
% 0.87/1.16 set(lex_order_vars).
% 0.87/1.16 clear(print_given).
% 0.87/1.16
% 0.87/1.16 % formulas(sos). % not echoed (15 formulas)
% 0.87/1.16
% 0.87/1.16 ============================== end of input ==========================
% 0.87/1.16
% 0.87/1.16 % From the command line: assign(max_seconds, 300).
% 0.87/1.16
% 0.87/1.16 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.87/1.16
% 0.87/1.16 % Formulas that are not ordinary clauses:
% 0.87/1.16
% 0.87/1.16 ============================== end of process non-clausal formulas ===
% 0.87/1.16
% 0.87/1.16 ============================== PROCESS INITIAL CLAUSES ===============
% 0.87/1.16
% 0.87/1.16 ============================== PREDICATE ELIMINATION =================
% 0.87/1.16
% 0.87/1.16 ============================== end predicate elimination =============
% 0.87/1.16
% 0.87/1.16 Auto_denials:
% 0.87/1.16 % copying label prove_inverse_is_an_involution to answer in negative clause
% 0.87/1.16
% 0.87/1.16 Term ordering decisions:
% 0.87/1.16
% 0.87/1.16 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.87/1.16 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. x=1. add=1. multiply=1. inverse=0.
% 0.87/1.16
% 0.87/1.16 ============================== end of process initial clauses ========
% 0.87/1.16
% 0.87/1.16 ============================== CLAUSES FOR SEARCH ====================
% 0.87/1.16
% 0.87/1.16 ============================== end of clauses for search =============
% 0.87/1.16
% 0.87/1.16 ============================== SEARCH ================================
% 0.87/1.16
% 0.87/1.16 % Starting search at 0.01 seconds.
% 0.87/1.16
% 0.87/1.16 ============================== PROOF =================================
% 0.87/1.16 % SZS status Unsatisfiable
% 0.87/1.16 % SZS output start Refutation
% 0.87/1.16
% 0.87/1.16 % Proof 1 at 0.14 (+ 0.01) seconds: prove_inverse_is_an_involution.
% 0.87/1.16 % Length of proof is 21.
% 0.87/1.16 % Level of proof is 6.
% 0.87/1.16 % Maximum clause weight is 13.000.
% 0.87/1.16 % Given clauses 70.
% 0.87/1.16
% 0.87/1.16 1 multiply(A,multiplicative_identity) = A # label(multiplicative_id1) # label(axiom). [assumption].
% 0.87/1.16 3 add(A,additive_identity) = A # label(additive_id1) # label(axiom). [assumption].
% 0.87/1.16 5 add(A,inverse(A)) = multiplicative_identity # label(additive_inverse1) # label(axiom). [assumption].
% 0.87/1.16 7 multiply(A,inverse(A)) = additive_identity # label(multiplicative_inverse1) # label(axiom). [assumption].
% 0.87/1.16 9 add(A,B) = add(B,A) # label(commutativity_of_add) # label(axiom). [assumption].
% 0.87/1.16 10 multiply(A,B) = multiply(B,A) # label(commutativity_of_multiply) # label(axiom). [assumption].
% 0.87/1.16 11 add(multiply(A,B),C) = multiply(add(A,C),add(B,C)) # label(distributivity1) # label(axiom). [assumption].
% 0.87/1.16 12 multiply(add(A,B),add(B,C)) = add(B,multiply(A,C)). [copy(11),rewrite([9(2)]),flip(a),rewrite([9(2)])].
% 0.87/1.16 13 add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)) # label(distributivity2) # label(axiom). [assumption].
% 0.87/1.16 14 multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)). [copy(13),flip(a)].
% 0.87/1.16 15 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distributivity3) # label(axiom). [assumption].
% 0.87/1.16 16 add(multiply(A,B),multiply(B,C)) = multiply(B,add(A,C)). [copy(15),rewrite([10(2)]),flip(a),rewrite([10(2)])].
% 0.87/1.16 19 inverse(inverse(x)) != x # label(prove_inverse_is_an_involution) # label(negated_conjecture) # answer(prove_inverse_is_an_involution). [assumption].
% 0.87/1.16 22 multiply(multiplicative_identity,add(A,inverse(B))) = add(inverse(B),multiply(B,A)). [para(5(a,1),12(a,1,1)),rewrite([9(3)])].
% 0.87/1.16 25 multiply(multiplicative_identity,add(A,B)) = add(A,multiply(B,inverse(A))). [para(5(a,1),14(a,1,1)),rewrite([10(5)])].
% 0.87/1.16 26 multiply(multiplicative_identity,add(A,B)) = add(A,B). [para(1(a,1),16(a,1,1)),rewrite([10(2),1(2)]),flip(a)].
% 0.87/1.16 39 add(A,multiply(B,inverse(A))) = add(A,B). [back_rewrite(25),rewrite([26(3)]),flip(a)].
% 0.87/1.16 40 add(inverse(A),multiply(B,A)) = add(B,inverse(A)). [back_rewrite(22),rewrite([26(4),10(4)]),flip(a)].
% 0.87/1.16 469 add(A,inverse(inverse(A))) = inverse(inverse(A)). [para(7(a,1),40(a,1,2)),rewrite([3(4)]),flip(a)].
% 0.87/1.16 545 inverse(inverse(A)) = A. [para(469(a,1),39(a,2)),rewrite([10(4),7(4),3(2)]),flip(a)].
% 0.87/1.16 546 $F # answer(prove_inverse_is_an_involution). [resolve(545,a,19,a)].
% 0.87/1.16
% 0.87/1.16 % SZS output end Refutation
% 0.87/1.16 ============================== end of proof ==========================
% 0.87/1.16
% 0.87/1.16 ============================== STATISTICS ============================
% 0.87/1.16
% 0.87/1.16 Given=70. Generated=3511. Kept=541. proofs=1.
% 0.87/1.16 Usable=58. Sos=294. Demods=349. Limbo=8, Disabled=195. Hints=0.
% 0.87/1.16 Megabytes=0.60.
% 0.87/1.16 User_CPU=0.14, System_CPU=0.01, Wall_clock=0.
% 0.87/1.16
% 0.87/1.16 ============================== end of statistics =====================
% 0.87/1.16
% 0.87/1.16 ============================== end of search =========================
% 0.87/1.16
% 0.87/1.16 THEOREM PROVED
% 0.87/1.16 % SZS status Unsatisfiable
% 0.87/1.16
% 0.87/1.16 Exiting with 1 proof.
% 0.87/1.16
% 0.87/1.16 Process 14509 exit (max_proofs) Wed Jun 1 15:52:12 2022
% 0.87/1.16 Prover9 interrupted
%------------------------------------------------------------------------------