TSTP Solution File: RNG007-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG007-1 : 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 20:39:09 EDT 2022
% Result : Unsatisfiable 1.00s 1.30s
% Output : Refutation 1.00s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n017.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 07:33:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.00/1.30 ============================== Prover9 ===============================
% 1.00/1.30 Prover9 (32) version 2009-11A, November 2009.
% 1.00/1.30 Process 31580 was started by sandbox2 on n017.cluster.edu,
% 1.00/1.30 Mon May 30 07:33:55 2022
% 1.00/1.30 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31427_n017.cluster.edu".
% 1.00/1.30 ============================== end of head ===========================
% 1.00/1.30
% 1.00/1.30 ============================== INPUT =================================
% 1.00/1.30
% 1.00/1.30 % Reading from file /tmp/Prover9_31427_n017.cluster.edu
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% 1.00/1.30 set(prolog_style_variables).
% 1.00/1.30 set(auto2).
% 1.00/1.30 % set(auto2) -> set(auto).
% 1.00/1.30 % set(auto) -> set(auto_inference).
% 1.00/1.30 % set(auto) -> set(auto_setup).
% 1.00/1.30 % set(auto_setup) -> set(predicate_elim).
% 1.00/1.30 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.00/1.30 % set(auto) -> set(auto_limits).
% 1.00/1.30 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.00/1.30 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.00/1.30 % set(auto) -> set(auto_denials).
% 1.00/1.30 % set(auto) -> set(auto_process).
% 1.00/1.30 % set(auto2) -> assign(new_constants, 1).
% 1.00/1.30 % set(auto2) -> assign(fold_denial_max, 3).
% 1.00/1.30 % set(auto2) -> assign(max_weight, "200.000").
% 1.00/1.30 % set(auto2) -> assign(max_hours, 1).
% 1.00/1.30 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.00/1.30 % set(auto2) -> assign(max_seconds, 0).
% 1.00/1.30 % set(auto2) -> assign(max_minutes, 5).
% 1.00/1.30 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.00/1.30 % set(auto2) -> set(sort_initial_sos).
% 1.00/1.30 % set(auto2) -> assign(sos_limit, -1).
% 1.00/1.30 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.00/1.30 % set(auto2) -> assign(max_megs, 400).
% 1.00/1.30 % set(auto2) -> assign(stats, some).
% 1.00/1.30 % set(auto2) -> clear(echo_input).
% 1.00/1.30 % set(auto2) -> set(quiet).
% 1.00/1.30 % set(auto2) -> clear(print_initial_clauses).
% 1.00/1.30 % set(auto2) -> clear(print_given).
% 1.00/1.30 assign(lrs_ticks,-1).
% 1.00/1.30 assign(sos_limit,10000).
% 1.00/1.30 assign(order,kbo).
% 1.00/1.30 set(lex_order_vars).
% 1.00/1.30 clear(print_given).
% 1.00/1.30
% 1.00/1.30 % formulas(sos). % not echoed (19 formulas)
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% 1.00/1.30 ============================== end of input ==========================
% 1.00/1.30
% 1.00/1.30 % From the command line: assign(max_seconds, 300).
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% 1.00/1.30 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
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% 1.00/1.30 % Formulas that are not ordinary clauses:
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% 1.00/1.30 ============================== end of process non-clausal formulas ===
% 1.00/1.30
% 1.00/1.30 ============================== PROCESS INITIAL CLAUSES ===============
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% 1.00/1.30 ============================== PREDICATE ELIMINATION =================
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% 1.00/1.30 ============================== end predicate elimination =============
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% 1.00/1.30 Auto_denials:
% 1.00/1.30 % copying label prove_a_plus_a_is_id to answer in negative clause
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% 1.00/1.30 Term ordering decisions:
% 1.00/1.30
% 1.00/1.30 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (8).
% 1.00/1.30 Function symbol KB weights: additive_identity=1. a=1. add=1. multiply=1. additive_inverse=0.
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% 1.00/1.30 ============================== end of process initial clauses ========
% 1.00/1.30
% 1.00/1.30 ============================== CLAUSES FOR SEARCH ====================
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% 1.00/1.30 ============================== end of clauses for search =============
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% 1.00/1.30 ============================== SEARCH ================================
% 1.00/1.30
% 1.00/1.30 % Starting search at 0.01 seconds.
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% 1.00/1.30 ============================== PROOF =================================
% 1.00/1.30 % SZS status Unsatisfiable
% 1.00/1.30 % SZS output start Refutation
% 1.00/1.30
% 1.00/1.30 % Proof 1 at 0.30 (+ 0.02) seconds: prove_a_plus_a_is_id.
% 1.00/1.30 % Length of proof is 39.
% 1.00/1.30 % Level of proof is 7.
% 1.00/1.30 % Maximum clause weight is 20.000.
% 1.00/1.30 % Given clauses 70.
% 1.00/1.30
% 1.00/1.30 1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom). [assumption].
% 1.00/1.30 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 1.00/1.30 3 product(A,A,A) # label(x_squared_is_x) # label(hypothesis). [assumption].
% 1.00/1.30 4 sum(additive_inverse(A),A,additive_identity) # label(left_inverse) # label(axiom). [assumption].
% 1.00/1.30 5 sum(A,additive_inverse(A),additive_identity) # label(right_inverse) # label(axiom). [assumption].
% 1.00/1.30 6 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom). [assumption].
% 1.00/1.30 7 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 1.00/1.30 8 -sum(a,a,additive_identity) # label(prove_a_plus_a_is_id) # label(negated_conjecture) # answer(prove_a_plus_a_is_id). [assumption].
% 1.00/1.30 9 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom). [assumption].
% 1.00/1.30 10 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 1.00/1.30 11 -product(A,B,C) | -product(A,B,D) | C = D # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 1.00/1.30 12 -sum(A,B,C) | -sum(B,D,E) | -sum(C,D,F) | sum(A,E,F) # label(associativity_of_addition1) # label(axiom). [assumption].
% 1.00/1.30 13 -sum(A,B,C) | -sum(B,D,E) | -sum(A,E,F) | sum(C,D,F) # label(associativity_of_addition2) # label(axiom). [assumption].
% 1.00/1.30 16 -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].
% 1.00/1.30 18 -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].
% 1.00/1.30 20 sum(A,B,add(B,A)). [hyper(9,a,7,a)].
% 1.00/1.30 21 add(A,additive_inverse(A)) = additive_identity. [hyper(10,a,7,a,b,5,a)].
% 1.00/1.30 23 add(A,additive_identity) = A. [hyper(10,a,7,a,b,2,a)].
% 1.00/1.30 24 add(additive_identity,A) = A. [hyper(10,a,7,a,b,1,a)].
% 1.00/1.30 25 additive_inverse(additive_identity) = additive_identity. [hyper(10,a,5,a,b,1,a),flip(a)].
% 1.00/1.30 26 multiply(A,A) = A. [hyper(11,a,6,a,b,3,a)].
% 1.00/1.30 28 sum(A,add(B,additive_inverse(add(A,B))),additive_identity). [hyper(12,a,7,a,b,7,a,c,5,a)].
% 1.00/1.30 32 sum(A,additive_identity,additive_inverse(additive_inverse(A))). [hyper(12,a,5,a,b,5,a,c,7,a),rewrite([24(5)])].
% 1.00/1.30 33 sum(additive_inverse(A),add(A,B),B). [hyper(12,a,4,a,b,7,a,c,7,a),rewrite([24(4)])].
% 1.00/1.30 49 -sum(additive_identity,a,additive_inverse(a)) # answer(prove_a_plus_a_is_id). [ur(13,a,2,a,c,5,a,d,8,a)].
% 1.00/1.30 66 sum(A,multiply(A,additive_identity),A). [hyper(16,a,6,a,b,6,a,c,2,a,d,3,a),rewrite([26(1)])].
% 1.00/1.30 73 sum(A,multiply(A,additive_inverse(A)),multiply(A,additive_identity)). [hyper(16,a,3,a,b,6,a,c,5,a,d,6,a)].
% 1.00/1.30 98 sum(A,multiply(additive_identity,A),A). [hyper(18,a,6,a,b,6,a,c,2,a,d,3,a),rewrite([26(1)])].
% 1.00/1.30 103 sum(multiply(additive_inverse(A),A),A,multiply(additive_identity,A)). [hyper(18,a,6,a,b,3,a,c,4,a,d,6,a)].
% 1.00/1.30 175 add(A,B) = add(B,A). [hyper(10,a,7,a,b,20,a)].
% 1.00/1.30 359 additive_inverse(additive_inverse(A)) = A. [hyper(10,a,7,a,b,32,a),rewrite([23(2)]),flip(a)].
% 1.00/1.30 383 sum(additive_identity,multiply(A,additive_identity),additive_identity). [hyper(13,a,7,a,b,66,a,c,4,a),rewrite([175(2),21(2)])].
% 1.00/1.30 683 sum(additive_identity,multiply(additive_identity,A),additive_identity). [hyper(13,a,33,a,b,98,a,c,28,a),rewrite([175(2),21(2),25(2),175(4),21(4),25(4),23(4)])].
% 1.00/1.30 906 multiply(A,additive_identity) = additive_identity. [hyper(10,a,1,a,b,383,a)].
% 1.00/1.30 918 sum(A,multiply(A,additive_inverse(A)),additive_identity). [back_rewrite(73),rewrite([906(4)])].
% 1.00/1.30 1266 multiply(additive_identity,A) = additive_identity. [hyper(10,a,1,a,b,683,a)].
% 1.00/1.30 1273 sum(multiply(additive_inverse(A),A),A,additive_identity). [back_rewrite(103),rewrite([1266(4)])].
% 1.00/1.30 2629 -sum(multiply(additive_inverse(a),a),a,additive_identity) # answer(prove_a_plus_a_is_id). [ur(13,a,918,a,c,2,a,d,49,a),rewrite([359(5)])].
% 1.00/1.30 2630 $F # answer(prove_a_plus_a_is_id). [resolve(2629,a,1273,a)].
% 1.00/1.30
% 1.00/1.30 % SZS output end Refutation
% 1.00/1.30 ============================== end of proof ==========================
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% 1.00/1.30 ============================== STATISTICS ============================
% 1.00/1.30
% 1.00/1.30 Given=70. Generated=14200. Kept=2629. proofs=1.
% 1.00/1.30 Usable=57. Sos=1419. Demods=15. Limbo=238, Disabled=933. Hints=0.
% 1.00/1.30 Megabytes=1.68.
% 1.00/1.30 User_CPU=0.30, System_CPU=0.02, Wall_clock=1.
% 1.00/1.30
% 1.00/1.30 ============================== end of statistics =====================
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% 1.00/1.30 ============================== end of search =========================
% 1.00/1.30
% 1.00/1.30 THEOREM PROVED
% 1.00/1.30 % SZS status Unsatisfiable
% 1.00/1.30
% 1.00/1.30 Exiting with 1 proof.
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% 1.00/1.30 Process 31580 exit (max_proofs) Mon May 30 07:33:56 2022
% 1.00/1.30 Prover9 interrupted
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