TSTP Solution File: BOO012-3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO012-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 0.95s 1.22s
% Output : Refutation 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO012-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 1 16:36:15 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.95/1.22 ============================== Prover9 ===============================
% 0.95/1.22 Prover9 (32) version 2009-11A, November 2009.
% 0.95/1.22 Process 31876 was started by sandbox on n029.cluster.edu,
% 0.95/1.22 Wed Jun 1 16:36:16 2022
% 0.95/1.22 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31723_n029.cluster.edu".
% 0.95/1.22 ============================== end of head ===========================
% 0.95/1.22
% 0.95/1.22 ============================== INPUT =================================
% 0.95/1.22
% 0.95/1.22 % Reading from file /tmp/Prover9_31723_n029.cluster.edu
% 0.95/1.22
% 0.95/1.22 set(prolog_style_variables).
% 0.95/1.22 set(auto2).
% 0.95/1.22 % set(auto2) -> set(auto).
% 0.95/1.22 % set(auto) -> set(auto_inference).
% 0.95/1.22 % set(auto) -> set(auto_setup).
% 0.95/1.22 % set(auto_setup) -> set(predicate_elim).
% 0.95/1.22 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.95/1.22 % set(auto) -> set(auto_limits).
% 0.95/1.22 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.95/1.22 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.95/1.22 % set(auto) -> set(auto_denials).
% 0.95/1.22 % set(auto) -> set(auto_process).
% 0.95/1.22 % set(auto2) -> assign(new_constants, 1).
% 0.95/1.22 % set(auto2) -> assign(fold_denial_max, 3).
% 0.95/1.22 % set(auto2) -> assign(max_weight, "200.000").
% 0.95/1.22 % set(auto2) -> assign(max_hours, 1).
% 0.95/1.22 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.95/1.22 % set(auto2) -> assign(max_seconds, 0).
% 0.95/1.22 % set(auto2) -> assign(max_minutes, 5).
% 0.95/1.22 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.95/1.22 % set(auto2) -> set(sort_initial_sos).
% 0.95/1.22 % set(auto2) -> assign(sos_limit, -1).
% 0.95/1.22 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.95/1.22 % set(auto2) -> assign(max_megs, 400).
% 0.95/1.22 % set(auto2) -> assign(stats, some).
% 0.95/1.22 % set(auto2) -> clear(echo_input).
% 0.95/1.22 % set(auto2) -> set(quiet).
% 0.95/1.22 % set(auto2) -> clear(print_initial_clauses).
% 0.95/1.22 % set(auto2) -> clear(print_given).
% 0.95/1.22 assign(lrs_ticks,-1).
% 0.95/1.22 assign(sos_limit,10000).
% 0.95/1.22 assign(order,kbo).
% 0.95/1.22 set(lex_order_vars).
% 0.95/1.22 clear(print_given).
% 0.95/1.22
% 0.95/1.22 % formulas(sos). % not echoed (35 formulas)
% 0.95/1.22
% 0.95/1.22 ============================== end of input ==========================
% 0.95/1.22
% 0.95/1.22 % From the command line: assign(max_seconds, 300).
% 0.95/1.22
% 0.95/1.22 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.95/1.22
% 0.95/1.22 % Formulas that are not ordinary clauses:
% 0.95/1.22
% 0.95/1.22 ============================== end of process non-clausal formulas ===
% 0.95/1.22
% 0.95/1.22 ============================== PROCESS INITIAL CLAUSES ===============
% 0.95/1.22
% 0.95/1.22 ============================== PREDICATE ELIMINATION =================
% 0.95/1.22
% 0.95/1.22 ============================== end predicate elimination =============
% 0.95/1.22
% 0.95/1.22 Auto_denials:
% 0.95/1.22 % copying label prove_inverse_is_an_involution to answer in negative clause
% 0.95/1.22
% 0.95/1.22 Term ordering decisions:
% 0.95/1.22
% 0.95/1.22 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 0.95/1.22 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. x=1. add=1. multiply=1. inverse=0.
% 0.95/1.22
% 0.95/1.22 ============================== end of process initial clauses ========
% 0.95/1.22
% 0.95/1.22 ============================== CLAUSES FOR SEARCH ====================
% 0.95/1.22
% 0.95/1.22 ============================== end of clauses for search =============
% 0.95/1.22
% 0.95/1.22 ============================== SEARCH ================================
% 0.95/1.22
% 0.95/1.22 % Starting search at 0.01 seconds.
% 0.95/1.22
% 0.95/1.22 ============================== PROOF =================================
% 0.95/1.22 % SZS status Unsatisfiable
% 0.95/1.22 % SZS output start Refutation
% 0.95/1.22
% 0.95/1.22 % Proof 1 at 0.20 (+ 0.02) seconds: prove_inverse_is_an_involution.
% 0.95/1.22 % Length of proof is 15.
% 0.95/1.22 % Level of proof is 3.
% 0.95/1.22 % Maximum clause weight is 20.000.
% 0.95/1.22 % Given clauses 36.
% 0.95/1.22
% 0.95/1.22 1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom). [assumption].
% 0.95/1.22 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 0.95/1.22 10 sum(A,inverse(A),multiplicative_identity) # label(additive_inverse2) # label(axiom). [assumption].
% 0.95/1.22 11 product(inverse(A),A,additive_identity) # label(multiplicative_inverse1) # label(axiom). [assumption].
% 0.95/1.22 12 product(A,inverse(A),additive_identity) # label(multiplicative_inverse2) # label(axiom). [assumption].
% 0.95/1.22 13 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 0.95/1.22 17 inverse(inverse(x)) != x # label(prove_inverse_is_an_involution) # label(negated_conjecture) # answer(prove_inverse_is_an_involution). [assumption].
% 0.95/1.22 22 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 0.95/1.22 31 -sum(A,B,C) | -sum(A,D,E) | -product(B,D,F) | -product(C,E,V6) | sum(A,F,V6) # label(distributivity6) # label(axiom). [assumption].
% 0.95/1.22 32 -sum(A,B,C) | -sum(D,B,E) | -product(A,D,F) | -sum(F,B,V6) | product(C,E,V6) # label(distributivity7) # label(axiom). [assumption].
% 0.95/1.22 47 add(additive_identity,A) = A. [hyper(22,a,13,a,b,1,a)].
% 0.95/1.22 53 -sum(x,additive_identity,inverse(inverse(x))) # answer(prove_inverse_is_an_involution). [ur(22,b,2,a,c,17,a)].
% 0.95/1.22 286 product(add(A,inverse(inverse(A))),multiplicative_identity,inverse(inverse(A))). [hyper(32,a,13,a,b,10,a,c,12,a,d,13,a),rewrite([47(8)])].
% 0.95/1.22 428 -product(add(x,inverse(inverse(x))),multiplicative_identity,inverse(inverse(x))) # answer(prove_inverse_is_an_involution). [ur(31,a,13,a,b,10,a,c,11,a,e,53,a)].
% 0.95/1.22 429 $F # answer(prove_inverse_is_an_involution). [resolve(428,a,286,a)].
% 0.95/1.22
% 0.95/1.22 % SZS output end Refutation
% 0.95/1.22 ============================== end of proof ==========================
% 0.95/1.22
% 0.95/1.22 ============================== STATISTICS ============================
% 0.95/1.22
% 0.95/1.22 Given=36. Generated=10285. Kept=428. proofs=1.
% 0.95/1.22 Usable=36. Sos=355. Demods=19. Limbo=5, Disabled=66. Hints=0.
% 0.95/1.22 Megabytes=0.33.
% 0.95/1.22 User_CPU=0.20, System_CPU=0.02, Wall_clock=0.
% 0.95/1.22
% 0.95/1.22 ============================== end of statistics =====================
% 0.95/1.22
% 0.95/1.22 ============================== end of search =========================
% 0.95/1.22
% 0.95/1.22 THEOREM PROVED
% 0.95/1.22 % SZS status Unsatisfiable
% 0.95/1.22
% 0.95/1.22 Exiting with 1 proof.
% 0.95/1.22
% 0.95/1.22 Process 31876 exit (max_proofs) Wed Jun 1 16:36:16 2022
% 0.95/1.22 Prover9 interrupted
%------------------------------------------------------------------------------