TSTP Solution File: RNG005-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG005-1 : 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 : Mon Jul 18 20:39:08 EDT 2022
% Result : Unsatisfiable 0.82s 1.12s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : RNG005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.05/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon May 30 05:46:29 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.82/1.12 ============================== Prover9 ===============================
% 0.82/1.12 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.12 Process 3228 was started by sandbox2 on n021.cluster.edu,
% 0.82/1.12 Mon May 30 05:46:30 2022
% 0.82/1.12 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3074_n021.cluster.edu".
% 0.82/1.12 ============================== end of head ===========================
% 0.82/1.12
% 0.82/1.12 ============================== INPUT =================================
% 0.82/1.12
% 0.82/1.12 % Reading from file /tmp/Prover9_3074_n021.cluster.edu
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% 0.82/1.12 set(prolog_style_variables).
% 0.82/1.12 set(auto2).
% 0.82/1.12 % set(auto2) -> set(auto).
% 0.82/1.12 % set(auto) -> set(auto_inference).
% 0.82/1.12 % set(auto) -> set(auto_setup).
% 0.82/1.12 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.12 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.12 % set(auto) -> set(auto_limits).
% 0.82/1.12 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.12 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.12 % set(auto) -> set(auto_denials).
% 0.82/1.12 % set(auto) -> set(auto_process).
% 0.82/1.12 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.12 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.12 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.12 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.12 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.12 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.12 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.12 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.12 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.12 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.12 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.12 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.12 % set(auto2) -> assign(stats, some).
% 0.82/1.12 % set(auto2) -> clear(echo_input).
% 0.82/1.12 % set(auto2) -> set(quiet).
% 0.82/1.12 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.12 % set(auto2) -> clear(print_given).
% 0.82/1.12 assign(lrs_ticks,-1).
% 0.82/1.12 assign(sos_limit,10000).
% 0.82/1.12 assign(order,kbo).
% 0.82/1.12 set(lex_order_vars).
% 0.82/1.12 clear(print_given).
% 0.82/1.12
% 0.82/1.12 % formulas(sos). % not echoed (20 formulas)
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% 0.82/1.12 ============================== end of input ==========================
% 0.82/1.12
% 0.82/1.12 % From the command line: assign(max_seconds, 300).
% 0.82/1.12
% 0.82/1.12 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.12
% 0.82/1.12 % Formulas that are not ordinary clauses:
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% 0.82/1.12 ============================== end of process non-clausal formulas ===
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% 0.82/1.12 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.82/1.12 ============================== PREDICATE ELIMINATION =================
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% 0.82/1.12 ============================== end predicate elimination =============
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% 0.82/1.12 Auto_denials:
% 0.82/1.12 % copying label prove_sum_is_additive_id to answer in negative clause
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% 0.82/1.12 Term ordering decisions:
% 0.82/1.12
% 0.82/1.12 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (11).
% 0.82/1.12 Function symbol KB weights: additive_identity=1. a=1. b=1. c=1. d=1. add=1. multiply=1. additive_inverse=0.
% 0.82/1.12
% 0.82/1.12 ============================== end of process initial clauses ========
% 0.82/1.12
% 0.82/1.12 ============================== CLAUSES FOR SEARCH ====================
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% 0.82/1.12 ============================== end of clauses for search =============
% 0.82/1.12
% 0.82/1.12 ============================== SEARCH ================================
% 0.82/1.12
% 0.82/1.12 % Starting search at 0.01 seconds.
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% 0.82/1.12 ============================== PROOF =================================
% 0.82/1.12 % SZS status Unsatisfiable
% 0.82/1.12 % SZS output start Refutation
% 0.82/1.12
% 0.82/1.12 % Proof 1 at 0.09 (+ 0.00) seconds: prove_sum_is_additive_id.
% 0.82/1.12 % Length of proof is 24.
% 0.82/1.12 % Level of proof is 4.
% 0.82/1.12 % Maximum clause weight is 20.000.
% 0.82/1.12 % Given clauses 53.
% 0.82/1.12
% 0.82/1.12 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 0.82/1.12 3 product(a,b,d) # label(a_times_b) # label(hypothesis). [assumption].
% 0.82/1.12 5 sum(A,additive_inverse(A),additive_identity) # label(right_inverse) # label(axiom). [assumption].
% 0.82/1.12 6 product(additive_inverse(a),b,c) # label(a_inverse_times_b) # label(hypothesis). [assumption].
% 0.82/1.12 7 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom). [assumption].
% 0.82/1.12 8 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 0.82/1.12 9 -sum(c,d,additive_identity) # label(prove_sum_is_additive_id) # label(negated_conjecture) # answer(prove_sum_is_additive_id). [assumption].
% 0.82/1.12 10 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom). [assumption].
% 0.82/1.12 11 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 0.82/1.12 12 -product(A,B,C) | -product(A,B,D) | C = D # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 0.82/1.12 13 -sum(A,B,C) | -sum(B,D,E) | -sum(C,D,F) | sum(A,E,F) # label(associativity_of_addition1) # label(axiom). [assumption].
% 0.82/1.12 14 -sum(A,B,C) | -sum(B,D,E) | -sum(A,E,F) | sum(C,D,F) # label(associativity_of_addition2) # label(axiom). [assumption].
% 0.82/1.12 19 -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].
% 0.82/1.12 21 sum(A,B,add(B,A)). [hyper(10,a,8,a)].
% 0.82/1.12 28 multiply(additive_inverse(a),b) = c. [hyper(12,a,7,a,b,6,a)].
% 0.82/1.12 29 multiply(a,b) = d. [hyper(12,a,7,a,b,3,a)].
% 0.82/1.12 31 sum(A,add(B,additive_inverse(add(A,B))),additive_identity). [hyper(13,a,8,a,b,8,a,c,5,a)].
% 0.82/1.12 42 -sum(add(c,d),additive_identity,additive_identity) # answer(prove_sum_is_additive_id). [ur(13,a,8,a,b,2,a,d,9,a)].
% 0.82/1.12 108 sum(c,multiply(additive_identity,b),c). [hyper(19,a,7,a,b,7,a,c,2,a,d,6,a),rewrite([28(4)])].
% 0.82/1.12 114 sum(d,c,multiply(additive_identity,b)). [hyper(19,a,7,a,b,6,a,c,5,a,d,7,a),rewrite([29(3)])].
% 0.82/1.12 201 add(A,B) = add(B,A). [hyper(11,a,8,a,b,21,a)].
% 0.82/1.12 462 -sum(add(c,d),A,A) # answer(prove_sum_is_additive_id). [ur(13,b,31,a,c,31,a,d,42,a)].
% 0.82/1.12 780 sum(add(c,d),multiply(additive_identity,b),multiply(additive_identity,b)). [hyper(14,a,8,a,b,108,a,c,114,a),rewrite([201(3)])].
% 0.82/1.12 781 $F # answer(prove_sum_is_additive_id). [resolve(780,a,462,a)].
% 0.82/1.12
% 0.82/1.12 % SZS output end Refutation
% 0.82/1.12 ============================== end of proof ==========================
% 0.82/1.12
% 0.82/1.12 ============================== STATISTICS ============================
% 0.82/1.12
% 0.82/1.12 Given=53. Generated=2475. Kept=780. proofs=1.
% 0.82/1.12 Usable=49. Sos=572. Demods=13. Limbo=4, Disabled=174. Hints=0.
% 0.82/1.12 Megabytes=0.55.
% 0.82/1.12 User_CPU=0.09, System_CPU=0.00, Wall_clock=0.
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% 0.82/1.12 ============================== end of statistics =====================
% 0.82/1.12
% 0.82/1.12 ============================== end of search =========================
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% 0.82/1.12 THEOREM PROVED
% 0.82/1.12 % SZS status Unsatisfiable
% 0.82/1.12
% 0.82/1.12 Exiting with 1 proof.
% 0.82/1.12
% 0.82/1.12 Process 3228 exit (max_proofs) Mon May 30 05:46:30 2022
% 0.82/1.12 Prover9 interrupted
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