TSTP Solution File: SEU280+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU280+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 : Tue Jul 19 13:30:37 EDT 2022
% Result : Theorem 0.74s 1.06s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU280+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n011.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 : Mon Jun 20 01:22:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.43/1.02 ============================== Prover9 ===============================
% 0.43/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.02 Process 25773 was started by sandbox2 on n011.cluster.edu,
% 0.43/1.02 Mon Jun 20 01:22:25 2022
% 0.43/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25601_n011.cluster.edu".
% 0.43/1.02 ============================== end of head ===========================
% 0.43/1.02
% 0.43/1.02 ============================== INPUT =================================
% 0.43/1.02
% 0.43/1.02 % Reading from file /tmp/Prover9_25601_n011.cluster.edu
% 0.43/1.02
% 0.43/1.02 set(prolog_style_variables).
% 0.43/1.02 set(auto2).
% 0.43/1.02 % set(auto2) -> set(auto).
% 0.43/1.02 % set(auto) -> set(auto_inference).
% 0.43/1.02 % set(auto) -> set(auto_setup).
% 0.43/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.02 % set(auto) -> set(auto_limits).
% 0.43/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.02 % set(auto) -> set(auto_denials).
% 0.43/1.02 % set(auto) -> set(auto_process).
% 0.43/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.02 % set(auto2) -> assign(stats, some).
% 0.43/1.02 % set(auto2) -> clear(echo_input).
% 0.43/1.02 % set(auto2) -> set(quiet).
% 0.43/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.02 % set(auto2) -> clear(print_given).
% 0.43/1.02 assign(lrs_ticks,-1).
% 0.43/1.02 assign(sos_limit,10000).
% 0.43/1.02 assign(order,kbo).
% 0.43/1.02 set(lex_order_vars).
% 0.43/1.02 clear(print_given).
% 0.43/1.02
% 0.43/1.02 % formulas(sos). % not echoed (6 formulas)
% 0.43/1.02
% 0.43/1.02 ============================== end of input ==========================
% 0.43/1.02
% 0.43/1.02 % From the command line: assign(max_seconds, 300).
% 0.43/1.02
% 0.43/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.02
% 0.43/1.02 % Formulas that are not ordinary clauses:
% 0.43/1.02 1 (all A (epsilon_transitive(A) & epsilon_connected(A) -> ordinal(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 2 (exists A (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 3 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 4 (all A (ordinal(A) -> epsilon_transitive(A) & epsilon_connected(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 5 (all A ((all B all C all D (B = C & ordinal(C) & B = D & ordinal(D) -> C = D)) -> (exists B all C (in(C,B) <-> (exists D (in(D,A) & D = C & ordinal(C))))))) # label(s1_tarski__e6_22__wellord2__1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 6 -(all A exists B all C (in(C,B) <-> in(C,A) & ordinal(C))) # label(s1_xboole_0__e6_22__wellord2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.02
% 0.43/1.02 ============================== end of process non-clausal formulas ===
% 0.43/1.02
% 0.43/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.02
% 0.43/1.02 ============================== PREDICATE ELIMINATION =================
% 0.43/1.02 7 -epsilon_transitive(A) | -epsilon_connected(A) | ordinal(A) # label(cc2_ordinal1) # label(axiom). [clausify(1)].
% 0.43/1.02 8 epsilon_transitive(c1) # label(rc1_ordinal1) # label(axiom). [clausify(2)].
% 0.43/1.02 9 -ordinal(A) | epsilon_transitive(A) # label(cc1_ordinal1) # label(axiom). [clausify(4)].
% 0.43/1.02 Derived: -epsilon_connected(c1) | ordinal(c1). [resolve(7,a,8,a)].
% 0.43/1.02
% 0.43/1.02 ============================== end predicate elimination =============
% 0.43/1.02
% 0.43/1.02 Auto_denials: (non-Horn, no changes).
% 0.43/1.02
% 0.43/1.02 Term ordering decisions:
% 0.43/1.02 Function symbol KB weights: c1=1. c2=1. f5=1. f1=1. f2=1. f3=1. f4=1. f6=1.
% 0.43/1.02
% 0.43/1.02 ============================== end of process initial clauses ========
% 0.43/1.02
% 0.43/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.43/1.02
% 0.43/1.02 ============================== end of clauses for search =============
% 0.74/1.06
% 0.74/1.06 ============================== SEARCH ================================
% 0.74/1.06
% 0.74/1.06 % Starting search at 0.01 seconds.
% 0.74/1.06
% 0.74/1.06 ============================== PROOF =================================
% 0.74/1.06 % SZS status Theorem
% 0.74/1.06 % SZS output start Refutation
% 0.74/1.06
% 0.74/1.06 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.74/1.06 % Length of proof is 47.
% 0.74/1.06 % Level of proof is 14.
% 0.74/1.06 % Maximum clause weight is 19.000.
% 0.74/1.06 % Given clauses 136.
% 0.74/1.06
% 0.74/1.06 5 (all A ((all B all C all D (B = C & ordinal(C) & B = D & ordinal(D) -> C = D)) -> (exists B all C (in(C,B) <-> (exists D (in(D,A) & D = C & ordinal(C))))))) # label(s1_tarski__e6_22__wellord2__1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 6 -(all A exists B all C (in(C,B) <-> in(C,A) & ordinal(C))) # label(s1_xboole_0__e6_22__wellord2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.06 12 in(f6(A),A) | ordinal(f6(A)) # label(s1_xboole_0__e6_22__wellord2) # label(negated_conjecture). [clausify(6)].
% 0.74/1.06 13 in(f6(A),A) | in(f6(A),c2) # label(s1_xboole_0__e6_22__wellord2) # label(negated_conjecture). [clausify(6)].
% 0.74/1.06 15 -in(f6(A),A) | -in(f6(A),c2) | -ordinal(f6(A)) # label(s1_xboole_0__e6_22__wellord2) # label(negated_conjecture). [clausify(6)].
% 0.74/1.06 19 f2(A) = f1(A) | -in(B,f4(A)) | ordinal(B) # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 20 f3(A) = f1(A) | -in(B,f4(A)) | ordinal(B) # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 21 f3(A) != f2(A) | -in(B,f4(A)) | ordinal(B) # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 26 f2(A) = f1(A) | -in(B,f4(A)) | in(f5(A,B),A) # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 27 f2(A) = f1(A) | -in(B,f4(A)) | f5(A,B) = B # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 28 f3(A) = f1(A) | -in(B,f4(A)) | in(f5(A,B),A) # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 29 f3(A) = f1(A) | -in(B,f4(A)) | f5(A,B) = B # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 30 f3(A) != f2(A) | -in(B,f4(A)) | in(f5(A,B),A) # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 31 f3(A) != f2(A) | -in(B,f4(A)) | f5(A,B) = B # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 34 f2(A) = f1(A) | in(B,f4(A)) | -in(C,A) | C != B | -ordinal(B) # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 35 f3(A) = f1(A) | in(B,f4(A)) | -in(C,A) | C != B | -ordinal(B) # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 36 f3(A) != f2(A) | in(B,f4(A)) | -in(C,A) | C != B | -ordinal(B) # label(s1_tarski__e6_22__wellord2__1) # label(axiom). [clausify(5)].
% 0.74/1.06 52 f2(A) = f1(A) | ordinal(f6(f4(A))). [resolve(19,b,12,a),merge(c)].
% 0.74/1.06 54 f3(A) = f1(A) | ordinal(f6(f4(A))). [resolve(20,b,12,a),merge(c)].
% 0.74/1.06 56 f3(A) != f2(A) | ordinal(f6(f4(A))). [resolve(21,b,12,a),merge(c)].
% 0.74/1.06 61 f2(A) = f1(A) | in(f5(A,f6(f4(A))),A) | in(f6(f4(A)),c2). [resolve(26,b,13,a)].
% 0.74/1.06 63 f3(A) = f1(A) | in(f5(A,f6(f4(A))),A) | in(f6(f4(A)),c2). [resolve(28,b,13,a)].
% 0.74/1.06 75 f2(c2) = f1(c2) | in(A,f4(c2)) | f6(B) != A | -ordinal(A) | in(f6(B),B). [resolve(34,c,13,b)].
% 0.74/1.06 78 f2(c2) = f1(c2) | in(f6(f4(c2)),f4(c2)) | -ordinal(f6(f4(c2))). [factor(75,b,e),xx(c)].
% 0.74/1.06 79 f3(c2) = f1(c2) | in(A,f4(c2)) | f6(B) != A | -ordinal(A) | in(f6(B),B). [resolve(35,c,13,b)].
% 0.74/1.06 82 f3(c2) = f1(c2) | in(f6(f4(c2)),f4(c2)) | -ordinal(f6(f4(c2))). [factor(79,b,e),xx(c)].
% 0.74/1.06 83 f3(c2) != f2(c2) | in(A,f4(c2)) | f6(B) != A | -ordinal(A) | in(f6(B),B). [resolve(36,c,13,b)].
% 0.74/1.06 86 f3(c2) != f2(c2) | in(f6(f4(c2)),f4(c2)) | -ordinal(f6(f4(c2))). [factor(83,b,e),xx(c)].
% 0.74/1.06 239 f2(c2) = f1(c2) | in(f6(f4(c2)),f4(c2)). [resolve(78,c,52,b),merge(c)].
% 0.74/1.06 249 f2(c2) = f1(c2) | f5(c2,f6(f4(c2))) = f6(f4(c2)). [resolve(239,b,27,b),merge(b)].
% 0.74/1.06 251 f2(c2) = f1(c2) | -in(f6(f4(c2)),c2) | -ordinal(f6(f4(c2))). [resolve(239,b,15,a)].
% 0.74/1.06 279 f2(c2) = f1(c2) | in(f6(f4(c2)),c2). [para(249(b,1),61(b,1)),merge(b),merge(d)].
% 0.74/1.06 301 f2(c2) = f1(c2) | -ordinal(f6(f4(c2))). [resolve(251,b,279,b),merge(c)].
% 0.74/1.06 303 f2(c2) = f1(c2). [resolve(301,b,52,b),merge(b)].
% 0.74/1.06 332 f3(c2) != f1(c2) | in(f6(f4(c2)),f4(c2)) | -ordinal(f6(f4(c2))). [back_rewrite(86),rewrite([303(4)])].
% 0.74/1.06 336 f3(c2) != f1(c2) | ordinal(f6(f4(c2))). [para(303(a,1),56(a,2))].
% 0.74/1.06 373 f3(c2) = f1(c2) | in(f6(f4(c2)),f4(c2)). [resolve(82,c,54,b),merge(c)].
% 0.74/1.06 379 f3(c2) = f1(c2) | f5(c2,f6(f4(c2))) = f6(f4(c2)). [resolve(373,b,29,b),merge(b)].
% 0.74/1.06 381 f3(c2) = f1(c2) | -in(f6(f4(c2)),c2) | -ordinal(f6(f4(c2))). [resolve(373,b,15,a)].
% 0.74/1.06 397 f3(c2) = f1(c2) | in(f6(f4(c2)),c2). [para(379(b,1),63(b,1)),merge(b),merge(d)].
% 0.74/1.06 440 f3(c2) = f1(c2) | -ordinal(f6(f4(c2))). [resolve(381,b,397,b),merge(c)].
% 0.74/1.06 448 f3(c2) = f1(c2). [resolve(440,b,54,b),merge(b)].
% 0.74/1.06 456 ordinal(f6(f4(c2))). [back_rewrite(336),rewrite([448(2)]),xx(a)].
% 0.74/1.06 458 in(f6(f4(c2)),f4(c2)). [back_rewrite(332),rewrite([448(2)]),xx(a),unit_del(b,456)].
% 0.74/1.06 486 f5(c2,f6(f4(c2))) = f6(f4(c2)). [resolve(458,a,31,b),rewrite([448(2),303(4)]),xx(a)].
% 0.74/1.06 487 in(f6(f4(c2)),c2). [resolve(458,a,30,b),rewrite([448(2),303(4),486(10)]),xx(a)].
% 0.74/1.06 488 $F. [resolve(458,a,15,a),unit_del(a,487),unit_del(b,456)].
% 0.74/1.06
% 0.74/1.06 % SZS output end Refutation
% 0.74/1.06 ============================== end of proof ==========================
% 0.74/1.06
% 0.74/1.06 ============================== STATISTICS ============================
% 0.74/1.06
% 0.74/1.06 Given=136. Generated=771. Kept=477. proofs=1.
% 0.74/1.06 Usable=76. Sos=155. Demods=3. Limbo=7, Disabled=270. Hints=0.
% 0.74/1.06 Megabytes=0.43.
% 0.74/1.06 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.74/1.06
% 0.74/1.06 ============================== end of statistics =====================
% 0.74/1.06
% 0.74/1.06 ============================== end of search =========================
% 0.74/1.06
% 0.74/1.06 THEOREM PROVED
% 0.74/1.06 % SZS status Theorem
% 0.74/1.06
% 0.74/1.06 Exiting with 1 proof.
% 0.74/1.06
% 0.74/1.06 Process 25773 exit (max_proofs) Mon Jun 20 01:22:25 2022
% 0.74/1.06 Prover9 interrupted
%------------------------------------------------------------------------------