TSTP Solution File: NUM421+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM421+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 13:27:24 EDT 2022
% Result : Theorem 0.70s 1.06s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM421+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 22:44:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.40/0.98 ============================== Prover9 ===============================
% 0.40/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.40/0.98 Process 17495 was started by sandbox on n009.cluster.edu,
% 0.40/0.98 Thu Jul 7 22:44:37 2022
% 0.40/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17342_n009.cluster.edu".
% 0.40/0.98 ============================== end of head ===========================
% 0.40/0.98
% 0.40/0.98 ============================== INPUT =================================
% 0.40/0.98
% 0.40/0.98 % Reading from file /tmp/Prover9_17342_n009.cluster.edu
% 0.40/0.98
% 0.40/0.98 set(prolog_style_variables).
% 0.40/0.98 set(auto2).
% 0.40/0.98 % set(auto2) -> set(auto).
% 0.40/0.98 % set(auto) -> set(auto_inference).
% 0.40/0.98 % set(auto) -> set(auto_setup).
% 0.40/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.40/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.40/0.98 % set(auto) -> set(auto_limits).
% 0.40/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.40/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.40/0.98 % set(auto) -> set(auto_denials).
% 0.40/0.98 % set(auto) -> set(auto_process).
% 0.40/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.40/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.40/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.40/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.40/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.40/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.40/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.40/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.40/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.40/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.40/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.40/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.40/0.98 % set(auto2) -> assign(stats, some).
% 0.40/0.98 % set(auto2) -> clear(echo_input).
% 0.40/0.98 % set(auto2) -> set(quiet).
% 0.40/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.40/0.98 % set(auto2) -> clear(print_given).
% 0.40/0.98 assign(lrs_ticks,-1).
% 0.40/0.98 assign(sos_limit,10000).
% 0.40/0.98 assign(order,kbo).
% 0.40/0.98 set(lex_order_vars).
% 0.40/0.98 clear(print_given).
% 0.40/0.98
% 0.40/0.98 % formulas(sos). % not echoed (16 formulas)
% 0.40/0.98
% 0.40/0.98 ============================== end of input ==========================
% 0.40/0.98
% 0.40/0.98 % From the command line: assign(max_seconds, 300).
% 0.40/0.98
% 0.40/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.40/0.98
% 0.40/0.98 % Formulas that are not ordinary clauses:
% 0.40/0.98 1 (all W0 (aInteger0(W0) -> $T)) # label(mIntegers) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 2 (all W0 (aInteger0(W0) -> aInteger0(smndt0(W0)))) # label(mIntNeg) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 3 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> aInteger0(sdtpldt0(W0,W1)))) # label(mIntPlus) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 4 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> aInteger0(sdtasdt0(W0,W1)))) # label(mIntMult) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 5 (all W0 all W1 all W2 (aInteger0(W0) & aInteger0(W1) & aInteger0(W2) -> sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2))) # label(mAddAsso) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 6 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> sdtpldt0(W0,W1) = sdtpldt0(W1,W0))) # label(mAddComm) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 7 (all W0 (aInteger0(W0) -> sdtpldt0(W0,sz00) = W0 & W0 = sdtpldt0(sz00,W0))) # label(mAddZero) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 8 (all W0 (aInteger0(W0) -> sdtpldt0(W0,smndt0(W0)) = sz00 & sz00 = sdtpldt0(smndt0(W0),W0))) # label(mAddNeg) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 9 (all W0 all W1 all W2 (aInteger0(W0) & aInteger0(W1) & aInteger0(W2) -> sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2))) # label(mMulAsso) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 10 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> sdtasdt0(W0,W1) = sdtasdt0(W1,W0))) # label(mMulComm) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 11 (all W0 (aInteger0(W0) -> sdtasdt0(W0,sz10) = W0 & W0 = sdtasdt0(sz10,W0))) # label(mMulOne) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 12 (all W0 all W1 all W2 (aInteger0(W0) & aInteger0(W1) & aInteger0(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(mDistrib) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.06 13 -(sdtasdt0(xa,sz00) = sz00 & sz00 = sdtasdt0(sz00,xa)) # label(m__) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.70/1.06
% 0.70/1.06 ============================== end of process non-clausal formulas ===
% 0.70/1.06
% 0.70/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/1.06
% 0.70/1.06 ============================== PREDICATE ELIMINATION =================
% 0.70/1.06
% 0.70/1.06 ============================== end predicate elimination =============
% 0.70/1.06
% 0.70/1.06 Auto_denials:
% 0.70/1.06 % copying label m__ to answer in negative clause
% 0.70/1.06
% 0.70/1.06 Term ordering decisions:
% 0.70/1.06
% 0.70/1.06 % Assigning unary symbol smndt0 kb_weight 0 and highest precedence (8).
% 0.70/1.06 Function symbol KB weights: sz00=1. sz10=1. xa=1. sdtasdt0=1. sdtpldt0=1. smndt0=0.
% 0.70/1.06
% 0.70/1.06 ============================== end of process initial clauses ========
% 0.70/1.06
% 0.70/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.70/1.06
% 0.70/1.06 ============================== end of clauses for search =============
% 0.70/1.06
% 0.70/1.06 ============================== SEARCH ================================
% 0.70/1.06
% 0.70/1.06 % Starting search at 0.01 seconds.
% 0.70/1.06
% 0.70/1.06 ============================== PROOF =================================
% 0.70/1.06 % SZS status Theorem
% 0.70/1.06 % SZS output start Refutation
% 0.70/1.06
% 0.70/1.06 % Proof 1 at 0.09 (+ 0.00) seconds: m__.
% 0.70/1.06 % Length of proof is 51.
% 0.70/1.06 % Level of proof is 7.
% 0.70/1.06 % Maximum clause weight is 19.000.
% 0.70/1.06 % Given clauses 28.
% 0.70/1.06
% 0.70/1.06 2 (all W0 (aInteger0(W0) -> aInteger0(smndt0(W0)))) # label(mIntNeg) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.06 3 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> aInteger0(sdtpldt0(W0,W1)))) # label(mIntPlus) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.06 5 (all W0 all W1 all W2 (aInteger0(W0) & aInteger0(W1) & aInteger0(W2) -> sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2))) # label(mAddAsso) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.06 7 (all W0 (aInteger0(W0) -> sdtpldt0(W0,sz00) = W0 & W0 = sdtpldt0(sz00,W0))) # label(mAddZero) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.06 8 (all W0 (aInteger0(W0) -> sdtpldt0(W0,smndt0(W0)) = sz00 & sz00 = sdtpldt0(smndt0(W0),W0))) # label(mAddNeg) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.06 10 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> sdtasdt0(W0,W1) = sdtasdt0(W1,W0))) # label(mMulComm) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.06 11 (all W0 (aInteger0(W0) -> sdtasdt0(W0,sz10) = W0 & W0 = sdtasdt0(sz10,W0))) # label(mMulOne) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.06 12 (all W0 all W1 all W2 (aInteger0(W0) & aInteger0(W1) & aInteger0(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(mDistrib) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.06 13 -(sdtasdt0(xa,sz00) = sz00 & sz00 = sdtasdt0(sz00,xa)) # label(m__) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.70/1.06 14 aInteger0(sz00) # label(mIntZero) # label(axiom). [assumption].
% 0.70/1.06 15 aInteger0(sz10) # label(mIntOne) # label(axiom). [assumption].
% 0.70/1.06 16 aInteger0(xa) # label(m__419) # label(hypothesis). [assumption].
% 0.70/1.06 17 sdtasdt0(xa,sz00) != sz00 | sdtasdt0(sz00,xa) != sz00 # label(m__) # label(negated_conjecture) # answer(m__). [clausify(13)].
% 0.70/1.06 18 -aInteger0(A) | aInteger0(smndt0(A)) # label(mIntNeg) # label(axiom). [clausify(2)].
% 0.70/1.06 19 -aInteger0(A) | sdtpldt0(A,sz00) = A # label(mAddZero) # label(axiom). [clausify(7)].
% 0.70/1.06 20 -aInteger0(A) | sdtpldt0(sz00,A) = A # label(mAddZero) # label(axiom). [clausify(7)].
% 0.70/1.06 21 -aInteger0(A) | sdtasdt0(A,sz10) = A # label(mMulOne) # label(axiom). [clausify(11)].
% 0.70/1.06 22 -aInteger0(A) | sdtasdt0(sz10,A) = A # label(mMulOne) # label(axiom). [clausify(11)].
% 0.70/1.06 23 -aInteger0(A) | -aInteger0(B) | aInteger0(sdtpldt0(A,B)) # label(mIntPlus) # label(axiom). [clausify(3)].
% 0.70/1.06 26 -aInteger0(A) | sdtpldt0(smndt0(A),A) = sz00 # label(mAddNeg) # label(axiom). [clausify(8)].
% 0.70/1.06 28 -aInteger0(A) | -aInteger0(B) | sdtasdt0(B,A) = sdtasdt0(A,B) # label(mMulComm) # label(axiom). [clausify(10)].
% 0.70/1.06 29 -aInteger0(A) | -aInteger0(B) | -aInteger0(C) | sdtpldt0(sdtpldt0(A,B),C) = sdtpldt0(A,sdtpldt0(B,C)) # label(mAddAsso) # label(axiom). [clausify(5)].
% 0.70/1.06 31 -aInteger0(A) | -aInteger0(B) | -aInteger0(C) | sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) # label(mDistrib) # label(axiom). [clausify(12)].
% 0.70/1.06 32 -aInteger0(A) | -aInteger0(B) | -aInteger0(C) | sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C)). [copy(31),flip(d)].
% 0.70/1.06 33 -aInteger0(A) | -aInteger0(B) | -aInteger0(C) | sdtasdt0(sdtpldt0(A,B),C) = sdtpldt0(sdtasdt0(A,C),sdtasdt0(B,C)) # label(mDistrib) # label(axiom). [clausify(12)].
% 0.70/1.06 34 -aInteger0(A) | -aInteger0(B) | -aInteger0(C) | sdtpldt0(sdtasdt0(A,C),sdtasdt0(B,C)) = sdtasdt0(sdtpldt0(A,B),C). [copy(33),flip(d)].
% 0.70/1.06 35 aInteger0(smndt0(xa)). [hyper(18,a,16,a)].
% 0.70/1.06 36 aInteger0(smndt0(sz10)). [hyper(18,a,15,a)].
% 0.70/1.06 40 sdtpldt0(sz00,sz00) = sz00. [hyper(19,a,14,a)].
% 0.70/1.06 41 sdtpldt0(sz00,xa) = xa. [hyper(20,a,16,a)].
% 0.70/1.06 42 sdtpldt0(sz00,sz10) = sz10. [hyper(20,a,15,a)].
% 0.70/1.06 45 sdtasdt0(sz00,sz10) = sz00. [hyper(21,a,14,a)].
% 0.70/1.06 47 sdtasdt0(sz10,sz00) = sz00. [hyper(22,a,14,a)].
% 0.70/1.06 48 aInteger0(sdtpldt0(xa,xa)). [hyper(23,a,16,a,b,16,a)].
% 0.70/1.06 51 aInteger0(sdtpldt0(sz10,sz10)). [hyper(23,a,15,a,b,15,a)].
% 0.70/1.06 59 sdtpldt0(smndt0(xa),xa) = sz00. [hyper(26,a,16,a)].
% 0.70/1.06 60 sdtpldt0(smndt0(sz10),sz10) = sz00. [hyper(26,a,15,a)].
% 0.70/1.06 63 sdtasdt0(xa,sz00) = sdtasdt0(sz00,xa). [hyper(28,a,16,a,b,14,a),flip(a)].
% 0.70/1.06 64 sdtasdt0(sz00,xa) != sz00 # answer(m__). [back_rewrite(17),rewrite([63(3)]),merge(b)].
% 0.70/1.06 107 sdtpldt0(sdtasdt0(sz00,xa),sdtasdt0(sz00,xa)) = sdtasdt0(sz00,xa). [hyper(32,a,16,a,b,14,a,c,14,a),rewrite([63(3),63(6),40(11),63(10)])].
% 0.70/1.06 122 sdtasdt0(sdtpldt0(xa,xa),sz00) = sdtasdt0(sz00,xa). [hyper(34,a,16,a,b,16,a,c,14,a),rewrite([63(3),63(6),107(7)]),flip(a)].
% 0.70/1.06 128 sdtasdt0(sdtpldt0(sz10,sz10),sz00) = sz00. [hyper(34,a,15,a,b,15,a,c,14,a),rewrite([47(3),47(4),40(3)]),flip(a)].
% 0.70/1.06 191 sdtpldt0(sdtasdt0(sz00,smndt0(xa)),sdtasdt0(sz00,xa)) = sdtasdt0(sz00,sz00). [hyper(32,a,14,a,b,35,a,c,16,a),rewrite([59(13)])].
% 0.70/1.06 265 sdtpldt0(smndt0(xa),sdtpldt0(xa,xa)) = xa. [hyper(29,a,35,a,b,16,a,c,16,a),rewrite([59(4),41(3)]),flip(a)].
% 0.70/1.06 273 sdtasdt0(smndt0(xa),sz00) = sdtasdt0(sz00,smndt0(xa)). [hyper(28,a,14,a,b,35,a)].
% 0.70/1.06 450 sdtpldt0(sdtasdt0(sz00,smndt0(sz10)),sz00) = sdtasdt0(sz00,sz00). [hyper(32,a,14,a,b,36,a,c,15,a),rewrite([45(7),60(11)])].
% 0.70/1.06 581 sdtpldt0(smndt0(sz10),sdtpldt0(sz10,sz10)) = sz10. [hyper(29,a,36,a,b,15,a,c,15,a),rewrite([60(4),42(3)]),flip(a)].
% 0.70/1.06 587 sdtasdt0(smndt0(sz10),sz00) = sdtasdt0(sz00,smndt0(sz10)). [hyper(28,a,14,a,b,36,a)].
% 0.70/1.06 1132 sdtasdt0(sz00,xa) = sdtasdt0(sz00,sz00). [hyper(34,a,35,a,b,48,a,c,14,a),rewrite([273(4),122(9),191(8),265(9),63(6)]),flip(a)].
% 0.70/1.06 1346 sdtasdt0(sz00,sz00) != sz00 # answer(m__). [back_rewrite(64),rewrite([1132(3)])].
% 0.70/1.06 1839 $F # answer(m__). [hyper(34,a,36,a,b,51,a,c,14,a),rewrite([587(4),128(9),450(6),581(9),47(6)]),unit_del(a,1346)].
% 0.70/1.06
% 0.70/1.06 % SZS output end Refutation
% 0.70/1.06 ============================== end of proof ==========================
% 0.70/1.06
% 0.70/1.06 ============================== STATISTICS ============================
% 0.70/1.06
% 0.70/1.06 Given=28. Generated=3390. Kept=1823. proofs=1.
% 0.70/1.06 Usable=25. Sos=826. Demods=860. Limbo=66, Disabled=925. Hints=0.
% 0.70/1.06 Megabytes=1.46.
% 0.70/1.06 User_CPU=0.09, System_CPU=0.00, Wall_clock=1.
% 0.70/1.06
% 0.70/1.06 ============================== end of statistics =====================
% 0.70/1.06
% 0.70/1.06 ============================== end of search =========================
% 0.70/1.06
% 0.70/1.06 THEOREM PROVED
% 0.70/1.06 % SZS status Theorem
% 0.70/1.06
% 0.70/1.06 Exiting with 1 proof.
% 0.70/1.06
% 0.70/1.06 Process 17495 exit (max_proofs) Thu Jul 7 22:44:38 2022
% 0.70/1.06 Prover9 interrupted
%------------------------------------------------------------------------------