TSTP Solution File: RNG050+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG050+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 20:39:16 EDT 2022
% Result : Theorem 0.46s 1.07s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG050+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.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 15:49:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/1.04 ============================== Prover9 ===============================
% 0.46/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.04 Process 13722 was started by sandbox on n026.cluster.edu,
% 0.46/1.04 Mon May 30 15:49:26 2022
% 0.46/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13569_n026.cluster.edu".
% 0.46/1.04 ============================== end of head ===========================
% 0.46/1.04
% 0.46/1.04 ============================== INPUT =================================
% 0.46/1.04
% 0.46/1.04 % Reading from file /tmp/Prover9_13569_n026.cluster.edu
% 0.46/1.04
% 0.46/1.04 set(prolog_style_variables).
% 0.46/1.04 set(auto2).
% 0.46/1.04 % set(auto2) -> set(auto).
% 0.46/1.04 % set(auto) -> set(auto_inference).
% 0.46/1.04 % set(auto) -> set(auto_setup).
% 0.46/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.04 % set(auto) -> set(auto_limits).
% 0.46/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.04 % set(auto) -> set(auto_denials).
% 0.46/1.04 % set(auto) -> set(auto_process).
% 0.46/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.04 % set(auto2) -> assign(stats, some).
% 0.46/1.04 % set(auto2) -> clear(echo_input).
% 0.46/1.04 % set(auto2) -> set(quiet).
% 0.46/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.04 % set(auto2) -> clear(print_given).
% 0.46/1.04 assign(lrs_ticks,-1).
% 0.46/1.04 assign(sos_limit,10000).
% 0.46/1.04 assign(order,kbo).
% 0.46/1.04 set(lex_order_vars).
% 0.46/1.04 clear(print_given).
% 0.46/1.04
% 0.46/1.04 % formulas(sos). % not echoed (39 formulas)
% 0.46/1.04
% 0.46/1.04 ============================== end of input ==========================
% 0.46/1.04
% 0.46/1.04 % From the command line: assign(max_seconds, 300).
% 0.46/1.04
% 0.46/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.04
% 0.46/1.04 % Formulas that are not ordinary clauses:
% 0.46/1.04 1 (all W0 (aNaturalNumber0(W0) -> $T)) # label(mNatSort) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 2 (all W0 (aNaturalNumber0(W0) -> aNaturalNumber0(szszuzczcdt0(W0)) & szszuzczcdt0(W0) != sz00)) # label(mSuccNat) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 3 (all W0 (aNaturalNumber0(W0) & W0 != sz00 -> (exists W1 (aNaturalNumber0(W1) & W0 = szszuzczcdt0(W1))))) # label(mNatExtr) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 4 (all W0 all W1 (aNaturalNumber0(W0) & aNaturalNumber0(W1) -> (szszuzczcdt0(W0) = szszuzczcdt0(W1) -> W0 = W1))) # label(mSuccEqu) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 5 (all W0 all W1 (aNaturalNumber0(W0) & aNaturalNumber0(W1) -> (iLess0(W0,W1) -> $T))) # label(mIHOrd) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 6 (all W0 (aNaturalNumber0(W0) -> iLess0(W0,szszuzczcdt0(W0)))) # label(mIH) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 7 (all W0 (aScalar0(W0) -> $T)) # label(mScSort) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 8 (all W0 all W1 (aScalar0(W0) & aScalar0(W1) -> aScalar0(sdtpldt0(W0,W1)))) # label(mSumSc) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 9 (all W0 all W1 (aScalar0(W0) & aScalar0(W1) -> aScalar0(sdtasdt0(W0,W1)))) # label(mMulSc) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 10 (all W0 (aScalar0(W0) -> aScalar0(smndt0(W0)))) # label(mNegSc) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 11 (all W0 (aScalar0(W0) -> sdtpldt0(W0,sz0z00) = W0 & sdtpldt0(sz0z00,W0) = W0 & sdtasdt0(W0,sz0z00) = sz0z00 & sdtasdt0(sz0z00,W0) = sz0z00 & sdtpldt0(W0,smndt0(W0)) = sz0z00 & sdtpldt0(smndt0(W0),W0) = sz0z00 & smndt0(smndt0(W0)) = W0 & smndt0(sz0z00) = sz0z00)) # label(mScZero) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 12 (all W0 all W1 all W2 (aScalar0(W0) & aScalar0(W1) & aScalar0(W2) -> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) & sdtpldt0(W0,W1) = sdtpldt0(W1,W0) & sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) & sdtasdt0(W0,W1) = sdtasdt0(W1,W0))) # label(mArith) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 13 (all W0 all W1 all W2 (aScalar0(W0) & aScalar0(W1) & aScalar0(W2) -> sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) & sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)))) # label(mDistr) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 14 (all W0 all W1 all W2 all W3 (aScalar0(W0) & aScalar0(W1) & aScalar0(W2) & aScalar0(W3) -> sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))))) # label(mDistr2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 15 (all W0 all W1 (aScalar0(W0) & aScalar0(W1) -> sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) & sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)))) # label(mMNeg) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 16 (all W0 all W1 (aScalar0(W0) & aScalar0(W1) -> sdtasdt0(smndt0(W0),smndt0(W1)) = sdtasdt0(W0,W1))) # label(mMDNeg) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 17 (all W0 all W1 (aScalar0(W0) & aScalar0(W1) -> (sdtlseqdt0(W0,W1) -> $T))) # label(mLess) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 18 (all W0 (aScalar0(W0) -> sdtlseqdt0(W0,W0))) # label(mLERef) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 19 (all W0 all W1 (aScalar0(W0) & aScalar0(W1) -> (sdtlseqdt0(W0,W1) & sdtlseqdt0(W1,W0) -> W0 = W1))) # label(mLEASm) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 20 (all W0 all W1 all W2 (aScalar0(W0) & aScalar0(W1) & aScalar0(W2) -> (sdtlseqdt0(W0,W1) & sdtlseqdt0(W1,W2) -> sdtlseqdt0(W0,W2)))) # label(mLETrn) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 21 (all W0 all W1 all W2 all W3 (aScalar0(W0) & aScalar0(W1) & aScalar0(W2) & aScalar0(W3) -> (sdtlseqdt0(W0,W1) & sdtlseqdt0(W2,W3) -> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))))) # label(mLEMon) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 22 (all W0 all W1 all W2 all W3 (aScalar0(W0) & aScalar0(W1) & aScalar0(W2) & aScalar0(W3) -> (sdtlseqdt0(W0,W1) & sdtlseqdt0(sz0z00,W2) & sdtlseqdt0(W2,W3) -> sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3))))) # label(mLEMonM) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 23 (all W0 all W1 (aScalar0(W0) & aScalar0(W1) -> sdtlseqdt0(W0,W1) | sdtlseqdt0(W1,W0))) # label(mLETot) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 24 (all W0 all W1 (aScalar0(W0) & aScalar0(W1) -> (sdtlseqdt0(sz0z00,W0) & sdtlseqdt0(sz0z00,W1) -> sdtlseqdt0(sz0z00,sdtpldt0(W0,W1)) & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1))))) # label(mPosMon) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 25 (all W0 (aScalar0(W0) -> sdtlseqdt0(sz0z00,sdtasdt0(W0,W0)))) # label(mSqPos) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 26 (all W0 all W1 (aScalar0(W0) & aScalar0(W1) -> (sdtlseqdt0(sz0z00,W0) & sdtlseqdt0(sz0z00,W1) & sdtasdt0(W0,W0) = sdtasdt0(W1,W1) -> W0 = W1))) # label(mSqrt) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 27 (all W0 (aVector0(W0) -> $T)) # label(mVcSort) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 28 (all W0 (aVector0(W0) -> aNaturalNumber0(aDimensionOf0(W0)))) # label(mDimNat) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 29 (all W0 all W1 (aVector0(W0) & aNaturalNumber0(W1) -> aScalar0(sdtlbdtrb0(W0,W1)))) # label(mElmSc) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 30 (all W0 (aVector0(W0) -> (aDimensionOf0(W0) != sz00 -> (all W1 (W1 = sziznziztdt0(W0) <-> aVector0(W1) & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0) & (all W2 (aNaturalNumber0(W2) -> sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2)))))))) # label(mDefInit) # label(definition) # label(non_clause). [assumption].
% 0.46/1.05 31 (all W0 all W1 (aVector0(W0) & aVector0(W1) -> (aDimensionOf0(W0) = aDimensionOf0(W1) & aDimensionOf0(W1) != sz00 -> aDimensionOf0(sziznziztdt0(W0)) = aDimensionOf0(sziznziztdt0(W1))))) # label(mEqInit) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 32 (all W0 all W1 (aVector0(W0) & aVector0(W1) -> (aDimensionOf0(W0) = aDimensionOf0(W1) -> aScalar0(sdtasasdt0(W0,W1))))) # label(mScPr) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 33 (all W0 all W1 (aVector0(W0) & aVector0(W1) -> (aDimensionOf0(W0) = aDimensionOf0(W1) & aDimensionOf0(W1) = sz00 -> sdtasasdt0(W0,W1) = sz0z00))) # label(mDefSPZ) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 34 (all W0 all W1 (aVector0(W0) & aVector0(W1) -> (aDimensionOf0(W0) = aDimensionOf0(W1) & aDimensionOf0(W1) != sz00 -> sdtasasdt0(W0,W1) = sdtpldt0(sdtasasdt0(sziznziztdt0(W0),sziznziztdt0(W1)),sdtasdt0(sdtlbdtrb0(W0,aDimensionOf0(W0)),sdtlbdtrb0(W1,aDimensionOf0(W1))))))) # label(mDefSPN) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 35 (all W0 (aVector0(W0) -> (iLess0(aDimensionOf0(W0),aDimensionOf0(xs)) -> sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0))))) # label(m__1516) # label(hypothesis) # label(non_clause). [assumption].
% 0.46/1.07 36 -((aDimensionOf0(xs) != sz00 -> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))) -> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))) # label(m__) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.07
% 0.46/1.07 ============================== end of process non-clausal formulas ===
% 0.46/1.07
% 0.46/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.07
% 0.46/1.07 ============================== PREDICATE ELIMINATION =================
% 0.46/1.07
% 0.46/1.07 ============================== end predicate elimination =============
% 0.46/1.07
% 0.46/1.07 Auto_denials: (non-Horn, no changes).
% 0.46/1.07
% 0.46/1.07 Term ordering decisions:
% 0.46/1.07 Function symbol KB weights: sz0z00=1. sz00=1. xs=1. sdtasdt0=1. sdtpldt0=1. sdtlbdtrb0=1. sdtasasdt0=1. f2=1. aDimensionOf0=1. smndt0=1. sziznziztdt0=1. szszuzczcdt0=1. f1=1.
% 0.46/1.07
% 0.46/1.07 ============================== end of process initial clauses ========
% 0.46/1.07
% 0.46/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.46/1.07
% 0.46/1.07 ============================== end of clauses for search =============
% 0.46/1.07
% 0.46/1.07 ============================== SEARCH ================================
% 0.46/1.07
% 0.46/1.07 % Starting search at 0.03 seconds.
% 0.46/1.07
% 0.46/1.07 ============================== PROOF =================================
% 0.46/1.07 % SZS status Theorem
% 0.46/1.07 % SZS output start Refutation
% 0.46/1.07
% 0.46/1.07 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.46/1.07 % Length of proof is 14.
% 0.46/1.07 % Level of proof is 4.
% 0.46/1.07 % Maximum clause weight is 18.000.
% 0.46/1.07 % Given clauses 67.
% 0.46/1.07
% 0.46/1.07 18 (all W0 (aScalar0(W0) -> sdtlseqdt0(W0,W0))) # label(mLERef) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 33 (all W0 all W1 (aVector0(W0) & aVector0(W1) -> (aDimensionOf0(W0) = aDimensionOf0(W1) & aDimensionOf0(W1) = sz00 -> sdtasasdt0(W0,W1) = sz0z00))) # label(mDefSPZ) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 36 -((aDimensionOf0(xs) != sz00 -> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))) -> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))) # label(m__) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.07 38 aScalar0(sz0z00) # label(mSZeroSc) # label(axiom). [assumption].
% 0.46/1.07 39 aVector0(xs) # label(m__1542) # label(hypothesis). [assumption].
% 0.46/1.07 40 aDimensionOf0(xs) = sz00 | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) # label(m__) # label(negated_conjecture). [clausify(36)].
% 0.46/1.07 41 -sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) # label(m__) # label(negated_conjecture). [clausify(36)].
% 0.46/1.07 45 -aScalar0(A) | sdtlseqdt0(A,A) # label(mLERef) # label(axiom). [clausify(18)].
% 0.46/1.07 79 -aVector0(A) | -aVector0(B) | aDimensionOf0(B) != aDimensionOf0(A) | aDimensionOf0(B) != sz00 | sdtasasdt0(A,B) = sz0z00 # label(mDefSPZ) # label(axiom). [clausify(33)].
% 0.46/1.07 95 aDimensionOf0(xs) = sz00. [back_unit_del(40),unit_del(b,41)].
% 0.46/1.07 111 -aVector0(A) | aDimensionOf0(A) != sz00 | sdtasasdt0(A,A) = sz0z00. [factor(79,a,b),xx(b)].
% 0.46/1.07 180 sdtlseqdt0(sz0z00,sz0z00). [resolve(45,a,38,a)].
% 0.46/1.07 267 sdtasasdt0(xs,xs) = sz0z00. [resolve(111,a,39,a),rewrite([95(2)]),xx(a)].
% 0.46/1.07 268 $F. [back_rewrite(41),rewrite([267(4)]),unit_del(a,180)].
% 0.46/1.07
% 0.46/1.07 % SZS output end Refutation
% 0.46/1.07 ============================== end of proof ==========================
% 0.46/1.07
% 0.46/1.07 ============================== STATISTICS ============================
% 0.46/1.07
% 0.46/1.07 Given=67. Generated=410. Kept=227. proofs=1.
% 0.46/1.07 Usable=65. Sos=142. Demods=5. Limbo=1, Disabled=73. Hints=0.
% 0.46/1.07 Megabytes=0.32.
% 0.46/1.07 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.46/1.07
% 0.46/1.07 ============================== end of statistics =====================
% 0.46/1.07
% 0.46/1.07 ============================== end of search =========================
% 0.46/1.07
% 0.46/1.07 THEOREM PROVED
% 0.46/1.07 % SZS status Theorem
% 0.46/1.07
% 0.46/1.07 Exiting with 1 proof.
% 0.46/1.07
% 0.46/1.07 Process 13722 exit (max_proofs) Mon May 30 15:49:26 2022
% 0.46/1.07 Prover9 interrupted
%------------------------------------------------------------------------------