TSTP Solution File: NUM422+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM422+1 : TPTP v8.1.0. Released v4.0.0.
% 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 13:27:24 EDT 2022
% Result : Theorem 1.21s 1.48s
% Output : Refutation 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM422+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jul 7 08:09:28 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.43/0.98 ============================== Prover9 ===============================
% 0.43/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.98 Process 19179 was started by sandbox on n029.cluster.edu,
% 0.43/0.98 Thu Jul 7 08:09:29 2022
% 0.43/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19026_n029.cluster.edu".
% 0.43/0.98 ============================== end of head ===========================
% 0.43/0.98
% 0.43/0.98 ============================== INPUT =================================
% 0.43/0.98
% 0.43/0.98 % Reading from file /tmp/Prover9_19026_n029.cluster.edu
% 0.43/0.98
% 0.43/0.98 set(prolog_style_variables).
% 0.43/0.98 set(auto2).
% 0.43/0.98 % set(auto2) -> set(auto).
% 0.43/0.98 % set(auto) -> set(auto_inference).
% 0.43/0.98 % set(auto) -> set(auto_setup).
% 0.43/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.98 % set(auto) -> set(auto_limits).
% 0.43/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.98 % set(auto) -> set(auto_denials).
% 0.43/0.98 % set(auto) -> set(auto_process).
% 0.43/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.98 % set(auto2) -> assign(stats, some).
% 0.43/0.98 % set(auto2) -> clear(echo_input).
% 0.43/0.98 % set(auto2) -> set(quiet).
% 0.43/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.98 % set(auto2) -> clear(print_given).
% 0.43/0.98 assign(lrs_ticks,-1).
% 0.43/0.98 assign(sos_limit,10000).
% 0.43/0.98 assign(order,kbo).
% 0.43/0.98 set(lex_order_vars).
% 0.43/0.98 clear(print_given).
% 0.43/0.98
% 0.43/0.98 % formulas(sos). % not echoed (17 formulas)
% 0.43/0.98
% 0.43/0.98 ============================== end of input ==========================
% 0.43/0.98
% 0.43/0.98 % From the command line: assign(max_seconds, 300).
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.98
% 0.43/0.98 % Formulas that are not ordinary clauses:
% 0.43/0.98 1 (all W0 (aInteger0(W0) -> $T)) # label(mIntegers) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 2 (all W0 (aInteger0(W0) -> aInteger0(smndt0(W0)))) # label(mIntNeg) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 3 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> aInteger0(sdtpldt0(W0,W1)))) # label(mIntPlus) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 4 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> aInteger0(sdtasdt0(W0,W1)))) # label(mIntMult) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 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].
% 0.43/0.98 6 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> sdtpldt0(W0,W1) = sdtpldt0(W1,W0))) # label(mAddComm) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 7 (all W0 (aInteger0(W0) -> sdtpldt0(W0,sz00) = W0 & W0 = sdtpldt0(sz00,W0))) # label(mAddZero) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 8 (all W0 (aInteger0(W0) -> sdtpldt0(W0,smndt0(W0)) = sz00 & sz00 = sdtpldt0(smndt0(W0),W0))) # label(mAddNeg) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 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].
% 0.43/0.98 10 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> sdtasdt0(W0,W1) = sdtasdt0(W1,W0))) # label(mMulComm) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 11 (all W0 (aInteger0(W0) -> sdtasdt0(W0,sz10) = W0 & W0 = sdtasdt0(sz10,W0))) # label(mMulOne) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 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].
% 1.21/1.48 13 (all W0 (aInteger0(W0) -> sdtasdt0(W0,sz00) = sz00 & sz00 = sdtasdt0(sz00,W0))) # label(mMulZero) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.48
% 1.21/1.48 ============================== end of process non-clausal formulas ===
% 1.21/1.48
% 1.21/1.48 ============================== PROCESS INITIAL CLAUSES ===============
% 1.21/1.48
% 1.21/1.48 ============================== PREDICATE ELIMINATION =================
% 1.21/1.48
% 1.21/1.48 ============================== end predicate elimination =============
% 1.21/1.48
% 1.21/1.48 Auto_denials:
% 1.21/1.48 % copying label m__ to answer in negative clause
% 1.21/1.48
% 1.21/1.48 Term ordering decisions:
% 1.21/1.48
% 1.21/1.48 % Assigning unary symbol smndt0 kb_weight 0 and highest precedence (8).
% 1.21/1.48 Function symbol KB weights: sz00=1. sz10=1. xa=1. sdtasdt0=1. sdtpldt0=1. smndt0=0.
% 1.21/1.48
% 1.21/1.48 ============================== end of process initial clauses ========
% 1.21/1.48
% 1.21/1.48 ============================== CLAUSES FOR SEARCH ====================
% 1.21/1.48
% 1.21/1.48 ============================== end of clauses for search =============
% 1.21/1.48
% 1.21/1.48 ============================== SEARCH ================================
% 1.21/1.48
% 1.21/1.48 % Starting search at 0.01 seconds.
% 1.21/1.48
% 1.21/1.48 ============================== PROOF =================================
% 1.21/1.48 % SZS status Theorem
% 1.21/1.48 % SZS output start Refutation
% 1.21/1.48
% 1.21/1.48 % Proof 1 at 0.50 (+ 0.01) seconds: m__.
% 1.21/1.48 % Length of proof is 53.
% 1.21/1.48 % Level of proof is 7.
% 1.21/1.48 % Maximum clause weight is 19.000.
% 1.21/1.48 % Given clauses 49.
% 1.21/1.48
% 1.21/1.48 2 (all W0 (aInteger0(W0) -> aInteger0(smndt0(W0)))) # label(mIntNeg) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.48 3 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> aInteger0(sdtpldt0(W0,W1)))) # label(mIntPlus) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.48 4 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> aInteger0(sdtasdt0(W0,W1)))) # label(mIntMult) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.48 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].
% 1.21/1.48 7 (all W0 (aInteger0(W0) -> sdtpldt0(W0,sz00) = W0 & W0 = sdtpldt0(sz00,W0))) # label(mAddZero) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 8 (all W0 (aInteger0(W0) -> sdtpldt0(W0,smndt0(W0)) = sz00 & sz00 = sdtpldt0(smndt0(W0),W0))) # label(mAddNeg) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 10 (all W0 all W1 (aInteger0(W0) & aInteger0(W1) -> sdtasdt0(W0,W1) = sdtasdt0(W1,W0))) # label(mMulComm) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 11 (all W0 (aInteger0(W0) -> sdtasdt0(W0,sz10) = W0 & W0 = sdtasdt0(sz10,W0))) # label(mMulOne) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 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].
% 1.21/1.49 13 (all W0 (aInteger0(W0) -> sdtasdt0(W0,sz00) = sz00 & sz00 = sdtasdt0(sz00,W0))) # label(mMulZero) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 14 aInteger0(sz00) # label(mIntZero) # label(axiom). [assumption].
% 1.21/1.49 15 aInteger0(sz10) # label(mIntOne) # label(axiom). [assumption].
% 1.21/1.49 16 aInteger0(xa) # label(m__446) # label(hypothesis). [assumption].
% 1.21/1.49 17 sdtasdt0(smndt0(sz10),xa) != smndt0(xa) # label(m__) # label(negated_conjecture) # answer(m__). [assumption].
% 1.21/1.49 18 -aInteger0(A) | aInteger0(smndt0(A)) # label(mIntNeg) # label(axiom). [clausify(2)].
% 1.21/1.49 19 -aInteger0(A) | sdtpldt0(A,sz00) = A # label(mAddZero) # label(axiom). [clausify(7)].
% 1.21/1.49 20 -aInteger0(A) | sdtpldt0(sz00,A) = A # label(mAddZero) # label(axiom). [clausify(7)].
% 1.21/1.49 21 -aInteger0(A) | sdtasdt0(A,sz10) = A # label(mMulOne) # label(axiom). [clausify(11)].
% 1.21/1.49 23 -aInteger0(A) | sdtasdt0(A,sz00) = sz00 # label(mMulZero) # label(axiom). [clausify(13)].
% 1.21/1.49 25 -aInteger0(A) | -aInteger0(B) | aInteger0(sdtpldt0(A,B)) # label(mIntPlus) # label(axiom). [clausify(3)].
% 1.21/1.49 26 -aInteger0(A) | -aInteger0(B) | aInteger0(sdtasdt0(A,B)) # label(mIntMult) # label(axiom). [clausify(4)].
% 1.21/1.49 27 -aInteger0(A) | sdtpldt0(A,smndt0(A)) = sz00 # label(mAddNeg) # label(axiom). [clausify(8)].
% 1.21/1.49 28 -aInteger0(A) | sdtpldt0(smndt0(A),A) = sz00 # label(mAddNeg) # label(axiom). [clausify(8)].
% 1.21/1.49 30 -aInteger0(A) | -aInteger0(B) | sdtasdt0(B,A) = sdtasdt0(A,B) # label(mMulComm) # label(axiom). [clausify(10)].
% 1.21/1.49 31 -aInteger0(A) | -aInteger0(B) | -aInteger0(C) | sdtpldt0(sdtpldt0(A,B),C) = sdtpldt0(A,sdtpldt0(B,C)) # label(mAddAsso) # label(axiom). [clausify(5)].
% 1.21/1.49 33 -aInteger0(A) | -aInteger0(B) | -aInteger0(C) | sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) # label(mDistrib) # label(axiom). [clausify(12)].
% 1.21/1.49 34 -aInteger0(A) | -aInteger0(B) | -aInteger0(C) | sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C)). [copy(33),flip(d)].
% 1.21/1.49 37 aInteger0(smndt0(xa)). [hyper(18,a,16,a)].
% 1.21/1.49 38 aInteger0(smndt0(sz10)). [hyper(18,a,15,a)].
% 1.21/1.49 41 sdtpldt0(sz10,sz00) = sz10. [hyper(19,a,15,a)].
% 1.21/1.49 45 sdtasdt0(xa,sz10) = xa. [hyper(21,a,16,a)].
% 1.21/1.49 50 sdtasdt0(xa,sz00) = sz00. [hyper(23,a,16,a)].
% 1.21/1.49 58 sdtpldt0(xa,smndt0(xa)) = sz00. [hyper(27,a,16,a)].
% 1.21/1.49 59 sdtpldt0(sz10,smndt0(sz10)) = sz00. [hyper(27,a,15,a)].
% 1.21/1.49 61 sdtpldt0(smndt0(xa),xa) = sz00. [hyper(28,a,16,a)].
% 1.21/1.49 62 sdtpldt0(smndt0(sz10),sz10) = sz00. [hyper(28,a,15,a)].
% 1.21/1.49 220 sdtpldt0(smndt0(xa),sz00) = sdtpldt0(sz00,smndt0(xa)). [hyper(31,a,37,a,b,16,a,c,37,a),rewrite([61(4),58(10)]),flip(a)].
% 1.21/1.49 230 sdtpldt0(sz10,sdtpldt0(sz00,smndt0(xa))) = sdtpldt0(sz10,smndt0(xa)). [hyper(31,a,15,a,b,14,a,c,37,a),rewrite([41(3)]),flip(a)].
% 1.21/1.49 238 sdtpldt0(sdtpldt0(sz10,smndt0(xa)),xa) = sz10. [hyper(31,a,15,a,b,37,a,c,16,a),rewrite([61(11),41(9)])].
% 1.21/1.49 240 sdtpldt0(sdtpldt0(sz10,smndt0(xa)),sz00) = sdtpldt0(sz10,smndt0(xa)). [hyper(31,a,15,a,b,37,a,c,14,a),rewrite([220(11),230(12)])].
% 1.21/1.49 261 aInteger0(sdtpldt0(sz10,smndt0(xa))). [hyper(25,a,15,a,b,37,a)].
% 1.21/1.49 265 sdtpldt0(sz00,smndt0(xa)) = smndt0(xa). [hyper(20,a,37,a)].
% 1.21/1.49 392 sdtpldt0(xa,sdtasdt0(xa,smndt0(sz10))) = sz00. [hyper(34,a,16,a,b,15,a,c,38,a),rewrite([45(3),59(11),50(9)])].
% 1.21/1.49 393 sdtpldt0(sz00,sdtasdt0(xa,smndt0(sz10))) = sdtasdt0(xa,sdtpldt0(sz00,smndt0(sz10))). [hyper(34,a,16,a,b,14,a,c,38,a),rewrite([50(3)])].
% 1.21/1.49 551 sdtpldt0(smndt0(sz10),sdtpldt0(sz10,smndt0(xa))) = smndt0(xa). [hyper(31,a,38,a,b,15,a,c,37,a),rewrite([62(4),265(4)]),flip(a)].
% 1.21/1.49 557 sdtasdt0(smndt0(sz10),xa) = sdtasdt0(xa,smndt0(sz10)). [hyper(30,a,16,a,b,38,a)].
% 1.21/1.49 566 aInteger0(sdtasdt0(xa,smndt0(sz10))). [hyper(26,a,16,a,b,38,a)].
% 1.21/1.49 575 sdtpldt0(sz00,smndt0(sz10)) = smndt0(sz10). [hyper(20,a,38,a)].
% 1.21/1.49 615 sdtasdt0(xa,smndt0(sz10)) != smndt0(xa) # answer(m__). [back_rewrite(17),rewrite([557(4)])].
% 1.21/1.49 658 sdtpldt0(sz00,sdtasdt0(xa,smndt0(sz10))) = sdtasdt0(xa,smndt0(sz10)). [back_rewrite(393),rewrite([575(11)])].
% 1.21/1.49 7714 sdtpldt0(sz10,sdtasdt0(xa,smndt0(sz10))) = sdtpldt0(sz10,smndt0(xa)). [hyper(31,a,261,a,b,16,a,c,566,a),rewrite([238(6),392(16),240(12)])].
% 1.21/1.49 7770 sdtasdt0(xa,smndt0(sz10)) = smndt0(xa). [hyper(31,a,38,a,b,15,a,c,566,a),rewrite([62(4),658(6),7714(12),551(11)])].
% 1.21/1.49 7771 $F # answer(m__). [resolve(7770,a,615,a)].
% 1.21/1.49
% 1.21/1.49 % SZS output end Refutation
% 1.21/1.49 ============================== end of proof ==========================
% 1.21/1.49
% 1.21/1.49 ============================== STATISTICS ============================
% 1.21/1.49
% 1.21/1.49 Given=49. Generated=15280. Kept=7755. proofs=1.
% 1.21/1.49 Usable=45. Sos=2796. Demods=3497. Limbo=754, Disabled=4180. Hints=0.
% 1.21/1.49 Megabytes=7.02.
% 1.21/1.49 User_CPU=0.50, System_CPU=0.01, Wall_clock=1.
% 1.21/1.49
% 1.21/1.49 ============================== end of statistics =====================
% 1.21/1.49
% 1.21/1.49 ============================== end of search =========================
% 1.21/1.49
% 1.21/1.49 THEOREM PROVED
% 1.21/1.49 % SZS status Theorem
% 1.21/1.49
% 1.21/1.49 Exiting with 1 proof.
% 1.21/1.49
% 1.21/1.49 Process 19179 exit (max_proofs) Thu Jul 7 08:09:30 2022
% 1.21/1.49 Prover9 interrupted
%------------------------------------------------------------------------------