TSTP Solution File: RNG001-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG001-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:39:07 EDT 2022
% Result : Unsatisfiable 1.07s 1.32s
% Output : Refutation 1.07s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n017.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 : Mon May 30 15:26:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.07/1.32 ============================== Prover9 ===============================
% 1.07/1.32 Prover9 (32) version 2009-11A, November 2009.
% 1.07/1.32 Process 8327 was started by sandbox2 on n017.cluster.edu,
% 1.07/1.32 Mon May 30 15:26:11 2022
% 1.07/1.32 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8174_n017.cluster.edu".
% 1.07/1.32 ============================== end of head ===========================
% 1.07/1.32
% 1.07/1.32 ============================== INPUT =================================
% 1.07/1.32
% 1.07/1.32 % Reading from file /tmp/Prover9_8174_n017.cluster.edu
% 1.07/1.32
% 1.07/1.32 set(prolog_style_variables).
% 1.07/1.32 set(auto2).
% 1.07/1.32 % set(auto2) -> set(auto).
% 1.07/1.32 % set(auto) -> set(auto_inference).
% 1.07/1.32 % set(auto) -> set(auto_setup).
% 1.07/1.32 % set(auto_setup) -> set(predicate_elim).
% 1.07/1.32 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.07/1.32 % set(auto) -> set(auto_limits).
% 1.07/1.32 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.07/1.32 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.07/1.32 % set(auto) -> set(auto_denials).
% 1.07/1.32 % set(auto) -> set(auto_process).
% 1.07/1.32 % set(auto2) -> assign(new_constants, 1).
% 1.07/1.32 % set(auto2) -> assign(fold_denial_max, 3).
% 1.07/1.32 % set(auto2) -> assign(max_weight, "200.000").
% 1.07/1.32 % set(auto2) -> assign(max_hours, 1).
% 1.07/1.32 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.07/1.32 % set(auto2) -> assign(max_seconds, 0).
% 1.07/1.32 % set(auto2) -> assign(max_minutes, 5).
% 1.07/1.32 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.07/1.32 % set(auto2) -> set(sort_initial_sos).
% 1.07/1.32 % set(auto2) -> assign(sos_limit, -1).
% 1.07/1.32 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.07/1.32 % set(auto2) -> assign(max_megs, 400).
% 1.07/1.32 % set(auto2) -> assign(stats, some).
% 1.07/1.32 % set(auto2) -> clear(echo_input).
% 1.07/1.32 % set(auto2) -> set(quiet).
% 1.07/1.32 % set(auto2) -> clear(print_initial_clauses).
% 1.07/1.32 % set(auto2) -> clear(print_given).
% 1.07/1.32 assign(lrs_ticks,-1).
% 1.07/1.32 assign(sos_limit,10000).
% 1.07/1.32 assign(order,kbo).
% 1.07/1.32 set(lex_order_vars).
% 1.07/1.32 clear(print_given).
% 1.07/1.32
% 1.07/1.32 % formulas(sos). % not echoed (18 formulas)
% 1.07/1.32
% 1.07/1.32 ============================== end of input ==========================
% 1.07/1.32
% 1.07/1.32 % From the command line: assign(max_seconds, 300).
% 1.07/1.32
% 1.07/1.32 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.07/1.32
% 1.07/1.32 % Formulas that are not ordinary clauses:
% 1.07/1.32
% 1.07/1.32 ============================== end of process non-clausal formulas ===
% 1.07/1.32
% 1.07/1.32 ============================== PROCESS INITIAL CLAUSES ===============
% 1.07/1.32
% 1.07/1.32 ============================== PREDICATE ELIMINATION =================
% 1.07/1.32
% 1.07/1.32 ============================== end predicate elimination =============
% 1.07/1.32
% 1.07/1.32 Auto_denials:
% 1.07/1.32 % copying label prove_a_times_0_is_0 to answer in negative clause
% 1.07/1.32
% 1.07/1.32 Term ordering decisions:
% 1.07/1.32
% 1.07/1.32 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (8).
% 1.07/1.32 Function symbol KB weights: additive_identity=1. a=1. add=1. multiply=1. additive_inverse=0.
% 1.07/1.32
% 1.07/1.32 ============================== end of process initial clauses ========
% 1.07/1.32
% 1.07/1.32 ============================== CLAUSES FOR SEARCH ====================
% 1.07/1.32
% 1.07/1.32 ============================== end of clauses for search =============
% 1.07/1.32
% 1.07/1.32 ============================== SEARCH ================================
% 1.07/1.32
% 1.07/1.32 % Starting search at 0.01 seconds.
% 1.07/1.32
% 1.07/1.32 ============================== PROOF =================================
% 1.07/1.32 % SZS status Unsatisfiable
% 1.07/1.32 % SZS output start Refutation
% 1.07/1.32
% 1.07/1.32 % Proof 1 at 0.30 (+ 0.01) seconds: prove_a_times_0_is_0.
% 1.07/1.32 % Length of proof is 25.
% 1.07/1.32 % Level of proof is 5.
% 1.07/1.32 % Maximum clause weight is 20.000.
% 1.07/1.32 % Given clauses 64.
% 1.07/1.32
% 1.07/1.32 1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom). [assumption].
% 1.07/1.32 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 1.07/1.32 3 sum(additive_inverse(A),A,additive_identity) # label(left_inverse) # label(axiom). [assumption].
% 1.07/1.32 4 sum(A,additive_inverse(A),additive_identity) # label(right_inverse) # label(axiom). [assumption].
% 1.07/1.32 5 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom). [assumption].
% 1.07/1.32 6 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 1.07/1.32 7 -product(a,additive_identity,additive_identity) # label(prove_a_times_0_is_0) # label(negated_conjecture) # answer(prove_a_times_0_is_0). [assumption].
% 1.07/1.32 8 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom). [assumption].
% 1.07/1.32 9 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 1.07/1.32 11 -sum(A,B,C) | -sum(B,D,E) | -sum(C,D,F) | sum(A,E,F) # label(associativity_of_addition1) # label(axiom). [assumption].
% 1.07/1.32 12 -sum(A,B,C) | -sum(B,D,E) | -sum(A,E,F) | sum(C,D,F) # label(associativity_of_addition2) # label(axiom). [assumption].
% 1.07/1.32 15 -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].
% 1.07/1.32 16 -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].
% 1.07/1.32 19 sum(A,B,add(B,A)). [hyper(8,a,6,a)].
% 1.07/1.32 22 add(A,additive_identity) = A. [hyper(9,a,6,a,b,2,a)].
% 1.07/1.32 23 add(additive_identity,A) = A. [hyper(9,a,6,a,b,1,a)].
% 1.07/1.32 43 sum(multiply(A,B),multiply(A,C),multiply(A,add(B,C))). [hyper(15,a,5,a,b,5,a,c,6,a,d,5,a)].
% 1.07/1.32 58 -sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity) # answer(prove_a_times_0_is_0). [ur(16,a,5,a,b,5,a,c,2,a,e,7,a)].
% 1.07/1.32 79 sum(add(A,B),additive_inverse(A),B). [hyper(12,a,19,a,b,4,a,c,19,a),rewrite([23(4)])].
% 1.07/1.32 115 add(A,B) = add(B,A). [hyper(9,a,6,a,b,19,a)].
% 1.07/1.32 209 -sum(additive_identity,multiply(a,additive_identity),additive_inverse(multiply(a,additive_identity))) # answer(prove_a_times_0_is_0). [ur(12,a,2,a,c,4,a,d,58,a)].
% 1.07/1.32 850 sum(additive_inverse(add(A,B)),B,additive_inverse(A)). [hyper(11,a,3,a,b,79,a,c,1,a)].
% 1.07/1.32 2480 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [hyper(9,a,6,a,b,43,a)].
% 1.07/1.32 2484 -sum(additive_inverse(multiply(a,A)),multiply(a,A),additive_identity) # answer(prove_a_times_0_is_0). [ur(12,b,43,a,c,850,a,d,209,a),rewrite([22(6),2480(6),115(3),22(3)])].
% 1.07/1.32 2485 $F # answer(prove_a_times_0_is_0). [resolve(2484,a,3,a)].
% 1.07/1.32
% 1.07/1.32 % SZS output end Refutation
% 1.07/1.32 ============================== end of proof ==========================
% 1.07/1.32
% 1.07/1.32 ============================== STATISTICS ============================
% 1.07/1.32
% 1.07/1.32 Given=64. Generated=11665. Kept=2484. proofs=1.
% 1.07/1.32 Usable=58. Sos=1406. Demods=15. Limbo=130, Disabled=907. Hints=0.
% 1.07/1.32 Megabytes=1.84.
% 1.07/1.32 User_CPU=0.30, System_CPU=0.01, Wall_clock=0.
% 1.07/1.32
% 1.07/1.32 ============================== end of statistics =====================
% 1.07/1.32
% 1.07/1.32 ============================== end of search =========================
% 1.07/1.32
% 1.07/1.32 THEOREM PROVED
% 1.07/1.32 % SZS status Unsatisfiable
% 1.07/1.32
% 1.07/1.32 Exiting with 1 proof.
% 1.07/1.32
% 1.07/1.32 Process 8327 exit (max_proofs) Mon May 30 15:26:11 2022
% 1.07/1.32 Prover9 interrupted
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