TSTP Solution File: RNG006-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:39:09 EDT 2022
% Result : Unsatisfiable 0.89s 1.14s
% Output : Refutation 0.89s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon May 30 19:07:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.89/1.14 ============================== Prover9 ===============================
% 0.89/1.14 Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.14 Process 12964 was started by sandbox on n029.cluster.edu,
% 0.89/1.14 Mon May 30 19:08:00 2022
% 0.89/1.14 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12811_n029.cluster.edu".
% 0.89/1.14 ============================== end of head ===========================
% 0.89/1.14
% 0.89/1.14 ============================== INPUT =================================
% 0.89/1.14
% 0.89/1.14 % Reading from file /tmp/Prover9_12811_n029.cluster.edu
% 0.89/1.14
% 0.89/1.14 set(prolog_style_variables).
% 0.89/1.14 set(auto2).
% 0.89/1.14 % set(auto2) -> set(auto).
% 0.89/1.14 % set(auto) -> set(auto_inference).
% 0.89/1.14 % set(auto) -> set(auto_setup).
% 0.89/1.14 % set(auto_setup) -> set(predicate_elim).
% 0.89/1.14 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.14 % set(auto) -> set(auto_limits).
% 0.89/1.14 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.14 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.14 % set(auto) -> set(auto_denials).
% 0.89/1.14 % set(auto) -> set(auto_process).
% 0.89/1.14 % set(auto2) -> assign(new_constants, 1).
% 0.89/1.14 % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.14 % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.14 % set(auto2) -> assign(max_hours, 1).
% 0.89/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.14 % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.14 % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.14 % set(auto2) -> set(sort_initial_sos).
% 0.89/1.14 % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.14 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.14 % set(auto2) -> assign(max_megs, 400).
% 0.89/1.14 % set(auto2) -> assign(stats, some).
% 0.89/1.14 % set(auto2) -> clear(echo_input).
% 0.89/1.14 % set(auto2) -> set(quiet).
% 0.89/1.14 % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.14 % set(auto2) -> clear(print_given).
% 0.89/1.14 assign(lrs_ticks,-1).
% 0.89/1.14 assign(sos_limit,10000).
% 0.89/1.14 assign(order,kbo).
% 0.89/1.14 set(lex_order_vars).
% 0.89/1.14 clear(print_given).
% 0.89/1.14
% 0.89/1.14 % formulas(sos). % not echoed (22 formulas)
% 0.89/1.14
% 0.89/1.14 ============================== end of input ==========================
% 0.89/1.14
% 0.89/1.14 % From the command line: assign(max_seconds, 300).
% 0.89/1.14
% 0.89/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.14
% 0.89/1.14 % Formulas that are not ordinary clauses:
% 0.89/1.14
% 0.89/1.14 ============================== end of process non-clausal formulas ===
% 0.89/1.14
% 0.89/1.14 ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.14
% 0.89/1.14 ============================== PREDICATE ELIMINATION =================
% 0.89/1.14
% 0.89/1.14 ============================== end predicate elimination =============
% 0.89/1.14
% 0.89/1.14 Auto_denials:
% 0.89/1.14 % copying label prove_a_times_bS_Ic_is_aPb_S__IaPc to answer in negative clause
% 0.89/1.14
% 0.89/1.14 Term ordering decisions:
% 0.89/1.14
% 0.89/1.14 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (14).
% 0.89/1.14 Function symbol KB weights: additive_identity=1. a=1. aPb=1. aPc=1. b=1. c=1. aPb_S_IaPc=1. bS_Ic=1. add=1. multiply=1. additive_inverse=0.
% 0.89/1.14
% 0.89/1.14 ============================== end of process initial clauses ========
% 0.89/1.14
% 0.89/1.14 ============================== CLAUSES FOR SEARCH ====================
% 0.89/1.14
% 0.89/1.14 ============================== end of clauses for search =============
% 0.89/1.14
% 0.89/1.14 ============================== SEARCH ================================
% 0.89/1.14
% 0.89/1.14 % Starting search at 0.01 seconds.
% 0.89/1.14
% 0.89/1.14 ============================== PROOF =================================
% 0.89/1.14 % SZS status Unsatisfiable
% 0.89/1.14 % SZS output start Refutation
% 0.89/1.14
% 0.89/1.14 % Proof 1 at 0.13 (+ 0.01) seconds: prove_a_times_bS_Ic_is_aPb_S__IaPc.
% 0.89/1.14 % Length of proof is 33.
% 0.89/1.14 % Level of proof is 5.
% 0.89/1.14 % Maximum clause weight is 20.000.
% 0.89/1.14 % Given clauses 78.
% 0.89/1.14
% 0.89/1.14 1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom). [assumption].
% 0.89/1.14 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 0.89/1.14 3 product(a,b,aPb) # label(a_times_b) # label(hypothesis). [assumption].
% 0.89/1.14 4 product(a,c,aPc) # label(a_times_c) # label(hypothesis). [assumption].
% 0.89/1.14 5 sum(additive_inverse(A),A,additive_identity) # label(left_inverse) # label(axiom). [assumption].
% 0.89/1.14 6 sum(A,additive_inverse(A),additive_identity) # label(right_inverse) # label(axiom). [assumption].
% 0.89/1.14 7 sum(b,additive_inverse(c),bS_Ic) # label(b_plus_inverse_c) # label(hypothesis). [assumption].
% 0.89/1.14 8 sum(aPb,additive_inverse(aPc),aPb_S_IaPc) # label(aPb_plus_IaPc) # label(hypothesis). [assumption].
% 0.89/1.14 9 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom). [assumption].
% 0.89/1.14 10 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 0.89/1.14 11 -product(a,bS_Ic,aPb_S_IaPc) # label(prove_a_times_bS_Ic_is_aPb_S__IaPc) # label(negated_conjecture) # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc). [assumption].
% 0.89/1.14 12 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom). [assumption].
% 0.89/1.14 13 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 0.89/1.14 14 -product(A,B,C) | -product(A,B,D) | C = D # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 0.89/1.14 15 -sum(A,B,C) | -sum(B,D,E) | -sum(C,D,F) | sum(A,E,F) # label(associativity_of_addition1) # label(axiom). [assumption].
% 0.89/1.14 16 -sum(A,B,C) | -sum(B,D,E) | -sum(A,E,F) | sum(C,D,F) # label(associativity_of_addition2) # label(axiom). [assumption].
% 0.89/1.14 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].
% 0.89/1.14 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].
% 0.89/1.14 24 sum(additive_inverse(aPc),aPb,aPb_S_IaPc). [hyper(12,a,8,a)].
% 0.89/1.14 30 add(A,additive_identity) = A. [hyper(13,a,10,a,b,2,a)].
% 0.89/1.14 31 add(additive_identity,A) = A. [hyper(13,a,10,a,b,1,a)].
% 0.89/1.14 33 multiply(a,c) = aPc. [hyper(14,a,9,a,b,4,a)].
% 0.89/1.14 34 multiply(a,b) = aPb. [hyper(14,a,9,a,b,3,a)].
% 0.89/1.14 50 sum(A,additive_identity,additive_inverse(additive_inverse(A))). [hyper(15,a,6,a,b,6,a,c,10,a),rewrite([31(5)])].
% 0.89/1.14 68 sum(bS_Ic,c,b). [hyper(16,a,7,a,b,5,a,c,10,a),rewrite([30(5)])].
% 0.89/1.14 92 sum(aPb,multiply(a,additive_identity),aPb). [hyper(19,a,9,a,b,9,a,c,2,a,d,3,a),rewrite([34(3)])].
% 0.89/1.14 135 -sum(multiply(a,bS_Ic),multiply(a,additive_identity),aPb_S_IaPc) # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc). [ur(20,a,9,a,b,9,a,c,2,a,e,11,a)].
% 0.89/1.14 364 sum(c,bS_Ic,b). [hyper(12,a,68,a)].
% 0.89/1.14 437 sum(aPc,multiply(a,bS_Ic),aPb). [hyper(19,a,9,a,b,9,a,c,364,a,d,3,a),rewrite([33(3)])].
% 0.89/1.14 909 additive_inverse(additive_inverse(A)) = A. [hyper(13,a,10,a,b,50,a),rewrite([30(2)]),flip(a)].
% 0.89/1.14 1101 -sum(additive_inverse(aPc),aPb,multiply(a,bS_Ic)) # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc). [ur(16,b,92,a,c,24,a,d,135,a)].
% 0.89/1.14 1222 -sum(aPc,multiply(a,bS_Ic),aPb) # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc). [ur(15,a,6,a,c,1,a,d,1101,a),rewrite([909(3)])].
% 0.89/1.14 1223 $F # answer(prove_a_times_bS_Ic_is_aPb_S__IaPc). [resolve(1222,a,437,a)].
% 0.89/1.14
% 0.89/1.14 % SZS output end Refutation
% 0.89/1.14 ============================== end of proof ==========================
% 0.89/1.14
% 0.89/1.14 ============================== STATISTICS ============================
% 0.89/1.14
% 0.89/1.14 Given=78. Generated=3292. Kept=1222. proofs=1.
% 0.89/1.14 Usable=76. Sos=798. Demods=20. Limbo=5, Disabled=364. Hints=0.
% 0.89/1.14 Megabytes=0.82.
% 0.89/1.14 User_CPU=0.13, System_CPU=0.01, Wall_clock=0.
% 0.89/1.14
% 0.89/1.14 ============================== end of statistics =====================
% 0.89/1.14
% 0.89/1.14 ============================== end of search =========================
% 0.89/1.14
% 0.89/1.14 THEOREM PROVED
% 0.89/1.14 % SZS status Unsatisfiable
% 0.89/1.14
% 0.89/1.14 Exiting with 1 proof.
% 0.89/1.14
% 0.89/1.14 Process 12964 exit (max_proofs) Mon May 30 19:08:00 2022
% 0.89/1.14 Prover9 interrupted
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