TSTP Solution File: RNG100+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG100+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 20:39:22 EDT 2022
% Result : Timeout 300.11s 300.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG100+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 16:03:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/1.02 ============================== Prover9 ===============================
% 0.45/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.02 Process 895 was started by sandbox2 on n027.cluster.edu,
% 0.45/1.02 Mon May 30 16:03:17 2022
% 0.45/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_731_n027.cluster.edu".
% 0.45/1.02 ============================== end of head ===========================
% 0.45/1.02
% 0.45/1.02 ============================== INPUT =================================
% 0.45/1.02
% 0.45/1.02 % Reading from file /tmp/Prover9_731_n027.cluster.edu
% 0.45/1.02
% 0.45/1.02 set(prolog_style_variables).
% 0.45/1.02 set(auto2).
% 0.45/1.02 % set(auto2) -> set(auto).
% 0.45/1.02 % set(auto) -> set(auto_inference).
% 0.45/1.02 % set(auto) -> set(auto_setup).
% 0.45/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.02 % set(auto) -> set(auto_limits).
% 0.45/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.02 % set(auto) -> set(auto_denials).
% 0.45/1.02 % set(auto) -> set(auto_process).
% 0.45/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.02 % set(auto2) -> assign(stats, some).
% 0.45/1.02 % set(auto2) -> clear(echo_input).
% 0.45/1.02 % set(auto2) -> set(quiet).
% 0.45/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.02 % set(auto2) -> clear(print_given).
% 0.45/1.02 assign(lrs_ticks,-1).
% 0.45/1.02 assign(sos_limit,10000).
% 0.45/1.02 assign(order,kbo).
% 0.45/1.02 set(lex_order_vars).
% 0.45/1.02 clear(print_given).
% 0.45/1.02
% 0.45/1.02 % formulas(sos). % not echoed (39 formulas)
% 0.45/1.02
% 0.45/1.02 ============================== end of input ==========================
% 0.45/1.02
% 0.45/1.02 % From the command line: assign(max_seconds, 300).
% 0.45/1.02
% 0.45/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.02
% 0.45/1.02 % Formulas that are not ordinary clauses:
% 0.45/1.02 1 (all W0 (aElement0(W0) -> $T)) # label(mElmSort) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 2 (all W0 (aElement0(W0) -> aElement0(smndt0(W0)))) # label(mSortsU) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 3 (all W0 all W1 (aElement0(W0) & aElement0(W1) -> aElement0(sdtpldt0(W0,W1)))) # label(mSortsB) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 4 (all W0 all W1 (aElement0(W0) & aElement0(W1) -> aElement0(sdtasdt0(W0,W1)))) # label(mSortsB_02) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 5 (all W0 all W1 (aElement0(W0) & aElement0(W1) -> sdtpldt0(W0,W1) = sdtpldt0(W1,W0))) # label(mAddComm) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 6 (all W0 all W1 all W2 (aElement0(W0) & aElement0(W1) & aElement0(W2) -> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)))) # label(mAddAsso) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 7 (all W0 (aElement0(W0) -> sdtpldt0(W0,sz00) = W0 & W0 = sdtpldt0(sz00,W0))) # label(mAddZero) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 8 (all W0 (aElement0(W0) -> sdtpldt0(W0,smndt0(W0)) = sz00 & sz00 = sdtpldt0(smndt0(W0),W0))) # label(mAddInvr) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 9 (all W0 all W1 (aElement0(W0) & aElement0(W1) -> sdtasdt0(W0,W1) = sdtasdt0(W1,W0))) # label(mMulComm) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 10 (all W0 all W1 all W2 (aElement0(W0) & aElement0(W1) & aElement0(W2) -> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)))) # label(mMulAsso) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 11 (all W0 (aElement0(W0) -> sdtasdt0(W0,sz10) = W0 & W0 = sdtasdt0(sz10,W0))) # label(mMulUnit) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 12 (all W0 all W1 all W2 (aElement0(W0) & aElement0(W1) & aElement0(W2) -> sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)))) # label(mAMDistr) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 13 (all W0 (aElement0(W0) -> sdtasdt0(smndt0(sz10),W0) = smndt0(W0) & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)))) # label(mMulMnOne) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 14 (all W0 (aElement0(W0) -> sdtasdt0(W0,sz00) = sz00 & sz00 = sdtasdt0(sz00,W0))) # label(mMulZero) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 15 (all W0 all W1 (aElement0(W0) & aElement0(W1) -> (sdtasdt0(W0,W1) = sz00 -> W0 = sz00 | W1 = sz00))) # label(mCancel) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 16 (all W0 (aSet0(W0) -> $T)) # label(mSetSort) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 17 (all W0 (aSet0(W0) -> (all W1 (aElementOf0(W1,W0) -> aElement0(W1))))) # label(mEOfElem) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 18 (all W0 all W1 (aSet0(W0) & aSet0(W1) -> ((all W2 (aElementOf0(W2,W0) -> aElementOf0(W2,W1))) & (all W2 (aElementOf0(W2,W1) -> aElementOf0(W2,W0))) -> W0 = W1))) # label(mSetEq) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 19 (all W0 all W1 (aSet0(W0) & aSet0(W1) -> (all W2 (W2 = sdtpldt1(W0,W1) <-> aSet0(W2) & (all W3 (aElementOf0(W3,W2) <-> (exists W4 exists W5 (aElementOf0(W4,W0) & aElementOf0(W5,W1) & sdtpldt0(W4,W5) = W3)))))))) # label(mDefSSum) # label(definition) # label(non_clause). [assumption].
% 0.45/1.03 20 (all W0 all W1 (aSet0(W0) & aSet0(W1) -> (all W2 (W2 = sdtasasdt0(W0,W1) <-> aSet0(W2) & (all W3 (aElementOf0(W3,W2) <-> aElementOf0(W3,W0) & aElementOf0(W3,W1))))))) # label(mDefSInt) # label(definition) # label(non_clause). [assumption].
% 0.45/1.03 21 (all W0 (aIdeal0(W0) <-> aSet0(W0) & (all W1 (aElementOf0(W1,W0) -> (all W2 (aElementOf0(W2,W0) -> aElementOf0(sdtpldt0(W1,W2),W0))) & (all W2 (aElement0(W2) -> aElementOf0(sdtasdt0(W2,W1),W0))))))) # label(mDefIdeal) # label(definition) # label(non_clause). [assumption].
% 0.45/1.03 22 (all W0 all W1 (aIdeal0(W0) & aIdeal0(W1) -> aIdeal0(sdtpldt1(W0,W1)))) # label(mIdeSum) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 23 (all W0 all W1 (aIdeal0(W0) & aIdeal0(W1) -> aIdeal0(sdtasasdt0(W0,W1)))) # label(mIdeInt) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 24 (all W0 all W1 all W2 (aElement0(W0) & aElement0(W1) & aIdeal0(W2) -> (sdteqdtlpzmzozddtrp0(W0,W1,W2) <-> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2)))) # label(mDefMod) # label(definition) # label(non_clause). [assumption].
% 0.45/1.03 25 (all W0 all W1 (aIdeal0(W0) & aIdeal0(W1) -> ((all W2 (aElement0(W2) -> aElementOf0(W2,sdtpldt1(W0,W1)))) -> (all W2 all W3 (aElement0(W2) & aElement0(W3) -> (exists W4 (aElement0(W4) & sdteqdtlpzmzozddtrp0(W4,W2,W0) & sdteqdtlpzmzozddtrp0(W4,W3,W1)))))))) # label(mChineseRemainder) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 26 (all W0 (aNaturalNumber0(W0) -> $T)) # label(mNatSort) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 27 (all W0 (aElement0(W0) & W0 != sz00 -> aNaturalNumber0(sbrdtbr0(W0)))) # label(mEucSort) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 28 (all W0 all W1 (aNaturalNumber0(W0) & aNaturalNumber0(W1) -> (iLess0(W0,W1) -> $T))) # label(mNatLess) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 29 (all W0 all W1 (aElement0(W0) & aElement0(W1) & W1 != sz00 -> (exists W2 exists W3 (aElement0(W2) & aElement0(W3) & W0 = sdtpldt0(sdtasdt0(W2,W1),W3) & (W3 != sz00 -> iLess0(sbrdtbr0(W3),sbrdtbr0(W1))))))) # label(mDivision) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 30 (all W0 all W1 (aElement0(W0) & aElement0(W1) -> (doDivides0(W0,W1) <-> (exists W2 (aElement0(W2) & sdtasdt0(W0,W2) = W1))))) # label(mDefDiv) # label(definition) # label(non_clause). [assumption].
% 0.45/1.03 31 (all W0 (aElement0(W0) -> (all W1 (aDivisorOf0(W1,W0) <-> aElement0(W1) & doDivides0(W1,W0))))) # label(mDefDvs) # label(definition) # label(non_clause). [assumption].
% 0.45/1.03 32 (all W0 all W1 (aElement0(W0) & aElement0(W1) -> (all W2 (aGcdOfAnd0(W2,W0,W1) <-> aDivisorOf0(W2,W0) & aDivisorOf0(W2,W1) & (all W3 (aDivisorOf0(W3,W0) & aDivisorOf0(W3,W1) -> doDivides0(W3,W2))))))) # label(mDefGCD) # label(definition) # label(non_clause). [assumption].
% 0.45/1.03 33 (all W0 all W1 (aElement0(W0) & aElement0(W1) -> (misRelativelyPrime0(W0,W1) <-> aGcdOfAnd0(sz10,W0,W1)))) # label(mDefRel) # label(definition) # label(non_clause). [assumption].
% 0.76/1.03 34 (all W0 (aElement0(W0) -> (all W1 (W1 = slsdtgt0(W0) <-> aSet0(W1) & (all W2 (aElementOf0(W2,W1) <-> (exists W3 (aElement0(W3) & sdtasdt0(W0,W3) = W2)))))))) # label(mDefPrIdeal) # label(definition) # label(non_clause). [assumption].
% 0.76/1.03
% 0.76/1.03 ============================== end of process non-clausal formulas ===
% 0.76/1.03
% 0.76/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.03
% 0.76/1.03 ============================== PREDICATE ELIMINATION =================
% 0.76/1.03 35 -aElement0(A) | -aElement0(B) | misRelativelyPrime0(A,B) | -aGcdOfAnd0(sz10,A,B) # label(mDefRel) # label(definition). [clausify(33)].
% 0.76/1.03 36 -aElement0(A) | -aElement0(B) | -misRelativelyPrime0(A,B) | aGcdOfAnd0(sz10,A,B) # label(mDefRel) # label(definition). [clausify(33)].
% 0.76/1.03 37 -aElement0(A) | -aElement0(B) | aGcdOfAnd0(C,A,B) | -aDivisorOf0(C,A) | -aDivisorOf0(C,B) | aDivisorOf0(f17(A,B,C),A) # label(mDefGCD) # label(definition). [clausify(32)].
% 0.76/1.03 38 -aElement0(A) | -aElement0(B) | -aGcdOfAnd0(C,A,B) | aDivisorOf0(C,A) # label(mDefGCD) # label(definition). [clausify(32)].
% 0.76/1.03 39 -aElement0(A) | -aElement0(B) | -aGcdOfAnd0(C,A,B) | aDivisorOf0(C,B) # label(mDefGCD) # label(definition). [clausify(32)].
% 0.76/1.03 40 -aElement0(A) | -aElement0(B) | -aGcdOfAnd0(C,A,B) | -aDivisorOf0(D,A) | -aDivisorOf0(D,B) | doDivides0(D,C) # label(mDefGCD) # label(definition). [clausify(32)].
% 0.76/1.03 Derived: -aElement0(A) | -aElement0(B) | -aDivisorOf0(C,A) | -aDivisorOf0(C,B) | aDivisorOf0(f17(A,B,C),A) | -aElement0(A) | -aElement0(B) | -aDivisorOf0(D,A) | -aDivisorOf0(D,B) | doDivides0(D,C). [resolve(37,c,40,c)].
% 0.76/1.03 41 -aElement0(A) | -aElement0(B) | aGcdOfAnd0(C,A,B) | -aDivisorOf0(C,A) | -aDivisorOf0(C,B) | aDivisorOf0(f17(A,B,C),B) # label(mDefGCD) # label(definition). [clausify(32)].
% 0.76/1.03 Derived: -aElement0(A) | -aElement0(B) | -aDivisorOf0(C,A) | -aDivisorOf0(C,B) | aDivisorOf0(f17(A,B,C),B) | -aElement0(A) | -aElement0(B) | -aDivisorOf0(D,A) | -aDivisorOf0(D,B) | doDivides0(D,C). [resolve(41,c,40,c)].
% 0.76/1.03 42 -aElement0(A) | -aElement0(B) | aGcdOfAnd0(C,A,B) | -aDivisorOf0(C,A) | -aDivisorOf0(C,B) | -doDivides0(f17(A,B,C),C) # label(mDefGCD) # label(definition). [clausify(32)].
% 0.76/1.03 Derived: -aElement0(A) | -aElement0(B) | -aDivisorOf0(C,A) | -aDivisorOf0(C,B) | -doDivides0(f17(A,B,C),C) | -aElement0(A) | -aElement0(B) | -aDivisorOf0(D,A) | -aDivisorOf0(D,B) | doDivides0(D,C). [resolve(42,c,40,c)].
% 0.76/1.03 43 -aElement0(A) | -aElement0(B) | -aIdeal0(C) | sdteqdtlpzmzozddtrp0(A,B,C) | -aElementOf0(sdtpldt0(A,smndt0(B)),C) # label(mDefMod) # label(definition). [clausify(24)].
% 0.76/1.03 44 -aElement0(A) | -aElement0(B) | -aIdeal0(C) | -sdteqdtlpzmzozddtrp0(A,B,C) | aElementOf0(sdtpldt0(A,smndt0(B)),C) # label(mDefMod) # label(definition). [clausify(24)].
% 0.76/1.03 45 -aIdeal0(A) | -aIdeal0(B) | aElement0(f12(A,B)) | -aElement0(C) | -aElement0(D) | sdteqdtlpzmzozddtrp0(f13(A,B,C,D),C,A) # label(mChineseRemainder) # label(axiom). [clausify(25)].
% 0.76/1.03 Derived: -aIdeal0(A) | -aIdeal0(B) | aElement0(f12(A,B)) | -aElement0(C) | -aElement0(D) | -aElement0(f13(A,B,C,D)) | -aElement0(C) | -aIdeal0(A) | aElementOf0(sdtpldt0(f13(A,B,C,D),smndt0(C)),A). [resolve(45,f,44,d)].
% 0.76/1.03 46 -aIdeal0(A) | -aIdeal0(B) | aElement0(f12(A,B)) | -aElement0(C) | -aElement0(D) | sdteqdtlpzmzozddtrp0(f13(A,B,C,D),D,B) # label(mChineseRemainder) # label(axiom). [clausify(25)].
% 0.76/1.03 Derived: -aIdeal0(A) | -aIdeal0(B) | aElement0(f12(A,B)) | -aElement0(C) | -aElement0(D) | -aElement0(f13(A,B,C,D)) | -aElement0(D) | -aIdeal0(B) | aElementOf0(sdtpldt0(f13(A,B,C,D),smndt0(D)),B). [resolve(46,f,44,d)].
% 0.76/1.03 47 -aIdeal0(A) | -aIdeal0(B) | -aElementOf0(f12(A,B),sdtpldt1(A,B)) | -aElement0(C) | -aElement0(D) | sdteqdtlpzmzozddtrp0(f13(A,B,C,D),C,A) # label(mChineseRemainder) # label(axiom). [clausify(25)].
% 0.76/1.03 Derived: -aIdeal0(A) | -aIdeal0(B) | -aElementOf0(f12(A,B),sdtpldt1(A,B)) | -aElement0(C) | -aElement0(D) | -aElement0(f13(A,B,C,D)) | -aElement0(C) | -aIdeal0(A) | aElementOf0(sdtpldt0(f13(A,B,C,D),smndt0(C)),A). [resolve(47,f,44,d)].
% 0.76/1.03 48 -aIdeal0(A) | -aIdeal0(B) | -aElementOf0(f12(A,B),sdtpldt1(A,Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------