TSTP Solution File: ALG210+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG210+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 : Thu Jul 14 17:54:01 EDT 2022
% Result : Theorem 0.44s 1.00s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG210+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n024.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 : Wed Jun 8 17:13:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.00 ============================== Prover9 ===============================
% 0.44/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.00 Process 2145 was started by sandbox on n024.cluster.edu,
% 0.44/1.00 Wed Jun 8 17:13:35 2022
% 0.44/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1983_n024.cluster.edu".
% 0.44/1.00 ============================== end of head ===========================
% 0.44/1.00
% 0.44/1.00 ============================== INPUT =================================
% 0.44/1.00
% 0.44/1.00 % Reading from file /tmp/Prover9_1983_n024.cluster.edu
% 0.44/1.00
% 0.44/1.00 set(prolog_style_variables).
% 0.44/1.00 set(auto2).
% 0.44/1.00 % set(auto2) -> set(auto).
% 0.44/1.00 % set(auto) -> set(auto_inference).
% 0.44/1.00 % set(auto) -> set(auto_setup).
% 0.44/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.00 % set(auto) -> set(auto_limits).
% 0.44/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.00 % set(auto) -> set(auto_denials).
% 0.44/1.00 % set(auto) -> set(auto_process).
% 0.44/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.00 % set(auto2) -> assign(stats, some).
% 0.44/1.00 % set(auto2) -> clear(echo_input).
% 0.44/1.00 % set(auto2) -> set(quiet).
% 0.44/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.00 % set(auto2) -> clear(print_given).
% 0.44/1.00 assign(lrs_ticks,-1).
% 0.44/1.00 assign(sos_limit,10000).
% 0.44/1.00 assign(order,kbo).
% 0.44/1.00 set(lex_order_vars).
% 0.44/1.00 clear(print_given).
% 0.44/1.00
% 0.44/1.00 % formulas(sos). % not echoed (3 formulas)
% 0.44/1.00
% 0.44/1.00 ============================== end of input ==========================
% 0.44/1.00
% 0.44/1.00 % From the command line: assign(max_seconds, 300).
% 0.44/1.00
% 0.44/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.00
% 0.44/1.00 % Formulas that are not ordinary clauses:
% 0.44/1.00 1 (all A all B all C times(times(A,B),C) = times(B,times(C,A))) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 2 (all B (element(B) <-> (exists C (times(B,C) = B & times(B,B) = C)))) # label(axiom_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 3 -(all A all B (element(A) & element(B) -> element(times(A,B)))) # label(conjecture_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.00
% 0.44/1.00 ============================== end of process non-clausal formulas ===
% 0.44/1.00
% 0.44/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.00
% 0.44/1.00 ============================== PREDICATE ELIMINATION =================
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% 0.44/1.00 ============================== end predicate elimination =============
% 0.44/1.00
% 0.44/1.00 Auto_denials:
% 0.44/1.00 % copying label conjecture_1 to answer in negative clause
% 0.44/1.00
% 0.44/1.00 Term ordering decisions:
% 0.44/1.00
% 0.44/1.00 % Assigning unary symbol f1 kb_weight 0 and highest precedence (6).
% 0.44/1.00 Function symbol KB weights: c1=1. c2=1. times=1. f1=0.
% 0.44/1.00
% 0.44/1.00 ============================== end of process initial clauses ========
% 0.44/1.00
% 0.44/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.00
% 0.44/1.00 ============================== end of clauses for search =============
% 0.44/1.00
% 0.44/1.00 ============================== SEARCH ================================
% 0.44/1.00
% 0.44/1.00 % Starting search at 0.01 seconds.
% 0.44/1.00
% 0.44/1.00 ============================== PROOF =================================
% 0.44/1.00 % SZS status Theorem
% 0.44/1.00 % SZS output start Refutation
% 0.44/1.00
% 0.44/1.00 % Proof 1 at 0.04 (+ 0.00) seconds: conjecture_1.
% 0.44/1.00 % Length of proof is 32.
% 0.44/1.00 % Level of proof is 7.
% 0.44/1.00 % Maximum clause weight is 15.000.
% 0.44/1.00 % Given clauses 37.
% 0.44/1.00
% 0.44/1.00 1 (all A all B all C times(times(A,B),C) = times(B,times(C,A))) # label(axiom_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 2 (all B (element(B) <-> (exists C (times(B,C) = B & times(B,B) = C)))) # label(axiom_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 3 -(all A all B (element(A) & element(B) -> element(times(A,B)))) # label(conjecture_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.00 4 element(c1) # label(conjecture_1) # label(negated_conjecture). [clausify(3)].
% 0.44/1.00 5 element(c2) # label(conjecture_1) # label(negated_conjecture). [clausify(3)].
% 0.44/1.00 6 times(times(A,B),C) = times(B,times(C,A)) # label(axiom_1) # label(axiom). [clausify(1)].
% 0.44/1.00 7 -element(times(c1,c2)) # label(conjecture_1) # label(negated_conjecture) # answer(conjecture_1). [clausify(3)].
% 0.44/1.00 8 -element(A) | times(A,f1(A)) = A # label(axiom_2) # label(axiom). [clausify(2)].
% 0.44/1.00 9 -element(A) | times(A,A) = f1(A) # label(axiom_2) # label(axiom). [clausify(2)].
% 0.44/1.00 10 element(A) | times(A,B) != A | times(A,A) != B # label(axiom_2) # label(axiom). [clausify(2)].
% 0.44/1.00 11 times(A,times(B,times(C,D))) = times(C,times(D,times(A,B))). [para(6(a,1),6(a,1,1)),rewrite([6(3),6(3),6(2)])].
% 0.44/1.00 12 times(c2,f1(c2)) = c2. [hyper(8,a,5,a)].
% 0.44/1.00 13 times(c1,f1(c1)) = c1. [hyper(8,a,4,a)].
% 0.44/1.00 14 times(c2,c2) = f1(c2). [hyper(9,a,5,a)].
% 0.44/1.00 15 times(c1,c1) = f1(c1). [hyper(9,a,4,a)].
% 0.44/1.00 16 times(c2,times(f1(c1),times(c2,times(c2,c1)))) != times(c1,c2) # answer(conjecture_1). [ur(10,a,7,a,c,6,a),rewrite([6(9),15(8),6(10),6(9),6(9),6(8)])].
% 0.44/1.00 26 times(c2,times(c2,times(c1,times(f1(c1),c2)))) != times(c1,c2) # answer(conjecture_1). [para(11(a,1),16(a,1,2))].
% 0.44/1.00 29 times(c1,times(c2,times(f1(c2),f1(c1)))) != times(c1,c2) # answer(conjecture_1). [para(11(a,1),26(a,1)),rewrite([14(8),6(8)])].
% 0.44/1.00 30 times(f1(c2),times(A,c2)) = times(c2,A). [para(12(a,1),6(a,1,1)),flip(a)].
% 0.44/1.00 32 times(f1(c1),times(A,c1)) = times(c1,A). [para(13(a,1),6(a,1,1)),flip(a)].
% 0.44/1.00 34 times(c2,times(A,c2)) = times(f1(c2),A). [para(14(a,1),6(a,1,1)),flip(a)].
% 0.44/1.00 36 times(c1,times(A,c1)) = times(f1(c1),A). [para(15(a,1),6(a,1,1)),flip(a)].
% 0.44/1.00 56 times(f1(c2),times(f1(c1),times(c1,c2))) != times(c1,c2) # answer(conjecture_1). [para(11(a,1),29(a,1))].
% 0.44/1.00 58 times(A,times(c2,times(B,f1(c2)))) = times(B,times(c2,A)). [para(30(a,1),6(a,2,2)),rewrite([6(3),6(6),6(6),6(5)])].
% 0.44/1.00 109 times(A,times(c1,times(B,f1(c1)))) = times(B,times(c1,A)). [para(32(a,1),6(a,2,2)),rewrite([6(3),6(6),6(6),6(5)])].
% 0.44/1.00 212 times(f1(c2),c2) = c2. [para(14(a,1),34(a,1,2)),rewrite([12(4)]),flip(a)].
% 0.44/1.00 224 times(c2,times(A,f1(c2))) = times(c2,A). [para(212(a,1),6(a,1,1)),flip(a)].
% 0.44/1.00 228 times(A,times(c2,B)) = times(B,times(c2,A)). [back_rewrite(58),rewrite([224(5)])].
% 0.44/1.00 234 times(f1(c1),c1) = c1. [para(15(a,1),36(a,1,2)),rewrite([13(4)]),flip(a)].
% 0.44/1.00 247 times(c1,times(A,f1(c1))) = times(c1,A). [para(234(a,1),6(a,1,1)),flip(a)].
% 0.44/1.00 251 times(A,times(c1,B)) = times(B,times(c1,A)). [back_rewrite(109),rewrite([247(5)])].
% 0.44/1.00 253 $F # answer(conjecture_1). [back_rewrite(56),rewrite([251(8),13(7),228(6),12(5)]),xx(a)].
% 0.44/1.00
% 0.44/1.00 % SZS output end Refutation
% 0.44/1.00 ============================== end of proof ==========================
% 0.44/1.00
% 0.44/1.00 ============================== STATISTICS ============================
% 0.44/1.00
% 0.44/1.00 Given=37. Generated=480. Kept=249. proofs=1.
% 0.44/1.00 Usable=31. Sos=190. Demods=53. Limbo=2, Disabled=33. Hints=0.
% 0.44/1.00 Megabytes=0.31.
% 0.44/1.00 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.44/1.00
% 0.44/1.00 ============================== end of statistics =====================
% 0.44/1.00
% 0.44/1.00 ============================== end of search =========================
% 0.44/1.00
% 0.44/1.00 THEOREM PROVED
% 0.44/1.00 % SZS status Theorem
% 0.44/1.00
% 0.44/1.00 Exiting with 1 proof.
% 0.44/1.00
% 0.44/1.00 Process 2145 exit (max_proofs) Wed Jun 8 17:13:35 2022
% 0.44/1.00 Prover9 interrupted
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