TSTP Solution File: RNG008-6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG008-6 : 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 : Mon Jul 18 20:39:10 EDT 2022
% Result : Unsatisfiable 2.79s 3.10s
% Output : Refutation 2.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG008-6 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % 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 : Mon May 30 16:12:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.79/3.10 ============================== Prover9 ===============================
% 2.79/3.10 Prover9 (32) version 2009-11A, November 2009.
% 2.79/3.10 Process 29344 was started by sandbox on n026.cluster.edu,
% 2.79/3.10 Mon May 30 16:12:26 2022
% 2.79/3.10 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29191_n026.cluster.edu".
% 2.79/3.10 ============================== end of head ===========================
% 2.79/3.10
% 2.79/3.10 ============================== INPUT =================================
% 2.79/3.10
% 2.79/3.10 % Reading from file /tmp/Prover9_29191_n026.cluster.edu
% 2.79/3.10
% 2.79/3.10 set(prolog_style_variables).
% 2.79/3.10 set(auto2).
% 2.79/3.10 % set(auto2) -> set(auto).
% 2.79/3.10 % set(auto) -> set(auto_inference).
% 2.79/3.10 % set(auto) -> set(auto_setup).
% 2.79/3.10 % set(auto_setup) -> set(predicate_elim).
% 2.79/3.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.79/3.10 % set(auto) -> set(auto_limits).
% 2.79/3.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.79/3.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.79/3.10 % set(auto) -> set(auto_denials).
% 2.79/3.10 % set(auto) -> set(auto_process).
% 2.79/3.10 % set(auto2) -> assign(new_constants, 1).
% 2.79/3.10 % set(auto2) -> assign(fold_denial_max, 3).
% 2.79/3.10 % set(auto2) -> assign(max_weight, "200.000").
% 2.79/3.10 % set(auto2) -> assign(max_hours, 1).
% 2.79/3.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.79/3.10 % set(auto2) -> assign(max_seconds, 0).
% 2.79/3.10 % set(auto2) -> assign(max_minutes, 5).
% 2.79/3.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.79/3.10 % set(auto2) -> set(sort_initial_sos).
% 2.79/3.10 % set(auto2) -> assign(sos_limit, -1).
% 2.79/3.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.79/3.10 % set(auto2) -> assign(max_megs, 400).
% 2.79/3.10 % set(auto2) -> assign(stats, some).
% 2.79/3.10 % set(auto2) -> clear(echo_input).
% 2.79/3.10 % set(auto2) -> set(quiet).
% 2.79/3.10 % set(auto2) -> clear(print_initial_clauses).
% 2.79/3.10 % set(auto2) -> clear(print_given).
% 2.79/3.10 assign(lrs_ticks,-1).
% 2.79/3.10 assign(sos_limit,10000).
% 2.79/3.10 assign(order,kbo).
% 2.79/3.10 set(lex_order_vars).
% 2.79/3.10 clear(print_given).
% 2.79/3.10
% 2.79/3.10 % formulas(sos). % not echoed (22 formulas)
% 2.79/3.10
% 2.79/3.10 ============================== end of input ==========================
% 2.79/3.10
% 2.79/3.10 % From the command line: assign(max_seconds, 300).
% 2.79/3.10
% 2.79/3.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.79/3.10
% 2.79/3.10 % Formulas that are not ordinary clauses:
% 2.79/3.10
% 2.79/3.10 ============================== end of process non-clausal formulas ===
% 2.79/3.10
% 2.79/3.10 ============================== PROCESS INITIAL CLAUSES ===============
% 2.79/3.10
% 2.79/3.10 ============================== PREDICATE ELIMINATION =================
% 2.79/3.10
% 2.79/3.10 ============================== end predicate elimination =============
% 2.79/3.10
% 2.79/3.10 Auto_denials:
% 2.79/3.10 % copying label prove_b_times_a_is_c to answer in negative clause
% 2.79/3.10
% 2.79/3.10 Term ordering decisions:
% 2.79/3.10
% 2.79/3.10 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (10).
% 2.79/3.10 Function symbol KB weights: additive_identity=1. a=1. b=1. c=1. add=1. multiply=1. additive_inverse=0.
% 2.79/3.10
% 2.79/3.10 ============================== end of process initial clauses ========
% 2.79/3.10
% 2.79/3.10 ============================== CLAUSES FOR SEARCH ====================
% 2.79/3.10
% 2.79/3.10 ============================== end of clauses for search =============
% 2.79/3.10
% 2.79/3.10 ============================== SEARCH ================================
% 2.79/3.10
% 2.79/3.10 % Starting search at 0.01 seconds.
% 2.79/3.10
% 2.79/3.10 Low Water (keep): wt=27.000, iters=3342
% 2.79/3.10
% 2.79/3.10 Low Water (keep): wt=23.000, iters=3359
% 2.79/3.10
% 2.79/3.10 Low Water (keep): wt=21.000, iters=3427
% 2.79/3.10
% 2.79/3.10 Low Water (keep): wt=19.000, iters=3421
% 2.79/3.10
% 2.79/3.10 Low Water (keep): wt=18.000, iters=3345
% 2.79/3.10
% 2.79/3.10 Low Water (keep): wt=17.000, iters=3336
% 2.79/3.10
% 2.79/3.10 Low Water (keep): wt=16.000, iters=3337
% 2.79/3.10
% 2.79/3.10 Low Water (keep): wt=15.000, iters=3400
% 2.79/3.10
% 2.79/3.10 Low Water (keep): wt=14.000, iters=3529
% 2.79/3.10
% 2.79/3.10 ============================== PROOF =================================
% 2.79/3.10 % SZS status Unsatisfiable
% 2.79/3.10 % SZS output start Refutation
% 2.79/3.10
% 2.79/3.10 % Proof 1 at 2.03 (+ 0.06) seconds: prove_b_times_a_is_c.
% 2.79/3.10 % Length of proof is 52.
% 2.79/3.10 % Level of proof is 10.
% 2.79/3.10 % Maximum clause weight is 20.000.
% 2.79/3.10 % Given clauses 176.
% 2.79/3.10
% 2.79/3.10 1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom). [assumption].
% 2.79/3.10 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 2.79/3.10 3 product(A,additive_identity,additive_identity) # label(x_times_identity_x_is_identity) # label(axiom). [assumption].
% 2.79/3.10 4 product(additive_identity,A,additive_identity) # label(identity_times_x_is_identity) # label(axiom). [assumption].
% 2.79/3.10 5 product(A,A,A) # label(x_squared_is_x) # label(hypothesis). [assumption].
% 2.79/3.10 6 product(a,b,c) # label(a_times_b_is_c) # label(hypothesis). [assumption].
% 2.79/3.10 7 sum(additive_inverse(A),A,additive_identity) # label(left_inverse) # label(axiom). [assumption].
% 2.79/3.10 8 sum(A,additive_inverse(A),additive_identity) # label(right_inverse) # label(axiom). [assumption].
% 2.79/3.10 9 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom). [assumption].
% 2.79/3.10 10 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 2.79/3.10 11 -product(b,a,c) # label(prove_b_times_a_is_c) # label(negated_conjecture) # answer(prove_b_times_a_is_c). [assumption].
% 2.79/3.10 12 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom). [assumption].
% 2.79/3.10 13 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 2.79/3.10 14 -product(A,B,C) | -product(A,B,D) | C = D # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 2.79/3.10 15 -sum(A,B,C) | -sum(B,D,E) | -sum(C,D,F) | sum(A,E,F) # label(associativity_of_addition1) # label(axiom). [assumption].
% 2.79/3.10 16 -sum(A,B,C) | -sum(B,D,E) | -sum(A,E,F) | sum(C,D,F) # label(associativity_of_addition2) # label(axiom). [assumption].
% 2.79/3.10 19 -product(A,B,C) | -product(A,D,E) | -sum(B,D,F) | -product(A,F,V6) | sum(C,E,V6) # label(distributivity1) # label(axiom). [assumption].
% 2.79/3.10 20 -product(A,B,C) | -product(A,D,E) | -sum(B,D,F) | -sum(C,E,V6) | product(A,F,V6) # label(distributivity2) # label(axiom). [assumption].
% 2.79/3.10 21 -product(A,B,C) | -product(D,B,E) | -sum(A,D,F) | -product(F,B,V6) | sum(C,E,V6) # label(distributivity3) # label(axiom). [assumption].
% 2.79/3.10 22 -product(A,B,C) | -product(D,B,E) | -sum(A,D,F) | -sum(C,E,V6) | product(F,B,V6) # label(distributivity4) # label(axiom). [assumption].
% 2.79/3.10 23 sum(A,B,add(B,A)). [hyper(12,a,10,a)].
% 2.79/3.10 26 add(A,additive_identity) = A. [hyper(13,a,10,a,b,2,a)].
% 2.79/3.10 27 add(additive_identity,A) = A. [hyper(13,a,10,a,b,1,a)].
% 2.79/3.10 28 additive_inverse(additive_identity) = additive_identity. [hyper(13,a,8,a,b,1,a),flip(a)].
% 2.79/3.10 31 multiply(additive_identity,A) = additive_identity. [hyper(14,a,9,a,b,4,a)].
% 2.79/3.10 32 multiply(A,additive_identity) = additive_identity. [hyper(14,a,9,a,b,3,a)].
% 2.79/3.10 38 sum(A,additive_identity,additive_inverse(additive_inverse(A))). [hyper(15,a,8,a,b,8,a,c,10,a),rewrite([27(5)])].
% 2.79/3.10 39 sum(additive_inverse(A),add(A,B),B). [hyper(15,a,7,a,b,10,a,c,10,a),rewrite([27(4)])].
% 2.79/3.10 41 sum(add(A,B),C,add(A,add(B,C))). [hyper(16,a,10,a,b,10,a,c,10,a)].
% 2.79/3.10 44 sum(add(A,additive_inverse(B)),B,A). [hyper(16,a,10,a,b,7,a,c,10,a),rewrite([26(4)])].
% 2.79/3.10 77 sum(multiply(A,additive_inverse(A)),A,additive_identity). [hyper(19,a,9,a,b,5,a,c,7,a,d,9,a),rewrite([32(4)])].
% 2.79/3.10 99 product(A,add(A,B),add(A,multiply(A,B))). [hyper(20,a,5,a,b,9,a,c,10,a,d,10,a)].
% 2.79/3.10 104 -sum(multiply(b,a),additive_identity,c) # answer(prove_b_times_a_is_c). [ur(20,a,9,a,b,9,a,c,2,a,e,11,a),rewrite([32(6)])].
% 2.79/3.10 114 sum(multiply(additive_inverse(A),A),A,additive_identity). [hyper(21,a,9,a,b,5,a,c,7,a,d,9,a),rewrite([31(4)])].
% 2.79/3.10 173 sum(add(A,B),additive_inverse(A),B). [hyper(16,a,23,a,b,8,a,c,23,a),rewrite([27(4)])].
% 2.79/3.10 198 sum(A,add(B,additive_inverse(A)),B). [hyper(15,a,8,a,b,23,a,c,23,a),rewrite([26(4)])].
% 2.79/3.10 209 add(A,B) = add(B,A). [hyper(13,a,10,a,b,23,a)].
% 2.79/3.10 226 -sum(additive_identity,c,multiply(b,a)) # answer(prove_b_times_a_is_c). [ur(16,b,2,a,c,1,a,d,104,a)].
% 2.79/3.10 497 additive_inverse(additive_inverse(A)) = A. [hyper(13,a,10,a,b,38,a),rewrite([26(2)]),flip(a)].
% 2.79/3.10 566 -sum(A,c,add(A,multiply(b,a))) # answer(prove_b_times_a_is_c). [ur(16,a,39,a,c,39,a,d,226,a),rewrite([26(2)])].
% 2.79/3.10 960 add(A,add(B,C)) = add(C,add(A,B)). [hyper(13,a,10,a,b,41,a),rewrite([209(2)]),flip(a)].
% 2.79/3.10 3303 sum(additive_identity,A,multiply(additive_inverse(A),A)). [hyper(16,a,77,a,b,39,a,c,2,a),rewrite([26(3),497(4)])].
% 2.79/3.10 5251 add(A,add(B,additive_inverse(A))) = B. [hyper(13,a,41,a,b,173,a)].
% 2.79/3.10 9106 -product(a,add(a,b),add(a,multiply(b,a))) # answer(prove_b_times_a_is_c). [ur(19,a,5,a,b,6,a,c,10,a,e,566,a)].
% 2.79/3.10 11077 sum(additive_inverse(multiply(additive_inverse(A),A)),additive_identity,multiply(additive_inverse(A),A)). [hyper(15,a,7,a,b,114,a,c,3303,a)].
% 2.79/3.10 11131 multiply(additive_inverse(A),A) = A. [hyper(13,a,198,a,b,3303,a),rewrite([28(2),26(2),28(3),26(3)]),flip(a)].
% 2.79/3.10 11140 sum(additive_inverse(A),additive_identity,A). [back_rewrite(11077),rewrite([11131(2),11131(4)])].
% 2.79/3.10 11829 sum(add(A,B),A,B). [hyper(15,a,173,a,b,11140,a,c,44,a),rewrite([28(2),26(2)])].
% 2.79/3.10 11862 additive_inverse(A) = A. [hyper(13,a,10,a,b,11140,a),rewrite([26(3)])].
% 2.79/3.10 12981 add(A,add(A,B)) = B. [back_rewrite(5251),rewrite([11862(1),209(1)])].
% 2.79/3.10 16072 product(A,add(A,B),add(A,multiply(B,A))). [hyper(22,a,5,a,b,99,a,c,11829,a,d,41,a),rewrite([209(1),960(5,R),209(4),12981(4)])].
% 2.79/3.10 16073 $F # answer(prove_b_times_a_is_c). [resolve(16072,a,9106,a)].
% 2.79/3.10
% 2.79/3.10 % SZS output end Refutation
% 2.79/3.10 ============================== end of proof ==========================
% 2.79/3.10
% 2.79/3.10 ============================== STATISTICS ============================
% 2.79/3.10
% 2.79/3.10 Given=176. Generated=87268. Kept=16072. proofs=1.
% 2.79/3.10 Usable=99. Sos=4204. Demods=29. Limbo=19, Disabled=11771. Hints=0.
% 2.79/3.10 Megabytes=10.32.
% 2.79/3.10 User_CPU=2.03, System_CPU=0.06, Wall_clock=2.
% 2.79/3.10
% 2.79/3.10 ============================== end of statistics =====================
% 2.79/3.10
% 2.79/3.10 ============================== end of search =========================
% 2.79/3.10
% 2.79/3.10 THEOREM PROVED
% 2.79/3.10 % SZS status Unsatisfiable
% 2.79/3.10
% 2.79/3.10 Exiting with 1 proof.
% 2.79/3.10
% 2.79/3.10 Process 29344 exit (max_proofs) Mon May 30 16:12:28 2022
% 2.79/3.10 Prover9 interrupted
%------------------------------------------------------------------------------