TSTP Solution File: SEU275+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 13:30:34 EDT 2022
% Result : Theorem 0.72s 0.99s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 03:13:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/0.99 ============================== Prover9 ===============================
% 0.72/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.72/0.99 Process 4314 was started by sandbox2 on n020.cluster.edu,
% 0.72/0.99 Sun Jun 19 03:13:04 2022
% 0.72/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4161_n020.cluster.edu".
% 0.72/0.99 ============================== end of head ===========================
% 0.72/0.99
% 0.72/0.99 ============================== INPUT =================================
% 0.72/0.99
% 0.72/0.99 % Reading from file /tmp/Prover9_4161_n020.cluster.edu
% 0.72/0.99
% 0.72/0.99 set(prolog_style_variables).
% 0.72/0.99 set(auto2).
% 0.72/0.99 % set(auto2) -> set(auto).
% 0.72/0.99 % set(auto) -> set(auto_inference).
% 0.72/0.99 % set(auto) -> set(auto_setup).
% 0.72/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.72/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/0.99 % set(auto) -> set(auto_limits).
% 0.72/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/0.99 % set(auto) -> set(auto_denials).
% 0.72/0.99 % set(auto) -> set(auto_process).
% 0.72/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.72/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.72/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.72/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.72/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.72/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.72/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.72/0.99 % set(auto2) -> assign(stats, some).
% 0.72/0.99 % set(auto2) -> clear(echo_input).
% 0.72/0.99 % set(auto2) -> set(quiet).
% 0.72/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.72/0.99 % set(auto2) -> clear(print_given).
% 0.72/0.99 assign(lrs_ticks,-1).
% 0.72/0.99 assign(sos_limit,10000).
% 0.72/0.99 assign(order,kbo).
% 0.72/0.99 set(lex_order_vars).
% 0.72/0.99 clear(print_given).
% 0.72/0.99
% 0.72/0.99 % formulas(sos). % not echoed (11 formulas)
% 0.72/0.99
% 0.72/0.99 ============================== end of input ==========================
% 0.72/0.99
% 0.72/0.99 % From the command line: assign(max_seconds, 300).
% 0.72/0.99
% 0.72/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/0.99
% 0.72/0.99 % Formulas that are not ordinary clauses:
% 0.72/0.99 1 (all A (ordinal(A) -> epsilon_transitive(A) & epsilon_connected(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 2 (all A (epsilon_transitive(A) & epsilon_connected(A) -> ordinal(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 3 (all A (relation(A) -> (well_ordering(A) <-> reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 4 (all A relation(inclusion_relation(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 5 (exists A (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 6 (all A reflexive(inclusion_relation(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 7 (all A transitive(inclusion_relation(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 8 (all A (ordinal(A) -> connected(inclusion_relation(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 9 (all A antisymmetric(inclusion_relation(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 10 (all A (ordinal(A) -> well_founded_relation(inclusion_relation(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 11 -(all A (ordinal(A) -> well_ordering(inclusion_relation(A)))) # label(t7_wellord2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/0.99
% 0.72/0.99 ============================== end of process non-clausal formulas ===
% 0.72/0.99
% 0.72/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/0.99
% 0.72/0.99 ============================== PREDICATE ELIMINATION =================
% 0.72/0.99 12 -epsilon_transitive(A) | -epsilon_connected(A) | ordinal(A) # label(cc2_ordinal1) # label(axiom). [clausify(2)].
% 0.72/0.99 13 epsilon_transitive(c1) # label(rc1_ordinal1) # label(axiom). [clausify(5)].
% 0.72/0.99 14 -ordinal(A) | epsilon_transitive(A) # label(cc1_ordinal1) # label(axiom). [clausify(1)].
% 0.72/0.99 Derived: -epsilon_connected(c1) | ordinal(c1). [resolve(12,a,13,a)].
% 0.72/0.99 15 -epsilon_connected(c1) | ordinal(c1). [resolve(12,a,13,a)].
% 0.72/0.99 16 epsilon_connected(c1) # label(rc1_ordinal1) # label(axiom). [clausify(5)].
% 0.72/0.99 17 -ordinal(A) | epsilon_connected(A) # label(cc1_ordinal1) # label(axiom). [clausify(1)].
% 0.72/0.99 Derived: ordinal(c1). [resolve(15,a,16,a)].
% 0.72/0.99 18 -ordinal(A) | connected(inclusion_relation(A)) # label(t4_wellord2) # label(axiom). [clausify(8)].
% 0.72/0.99 19 ordinal(c1) # label(rc1_ordinal1) # label(axiom). [clausify(5)].
% 0.72/0.99 20 ordinal(c2) # label(t7_wellord2) # label(negated_conjecture). [clausify(11)].
% 0.72/0.99 Derived: connected(inclusion_relation(c1)). [resolve(18,a,19,a)].
% 0.72/0.99 Derived: connected(inclusion_relation(c2)). [resolve(18,a,20,a)].
% 0.72/0.99 21 -ordinal(A) | well_founded_relation(inclusion_relation(A)) # label(t6_wellord2) # label(axiom). [clausify(10)].
% 0.72/0.99 Derived: well_founded_relation(inclusion_relation(c1)). [resolve(21,a,19,a)].
% 0.72/0.99 Derived: well_founded_relation(inclusion_relation(c2)). [resolve(21,a,20,a)].
% 0.72/0.99 22 ordinal(c1). [resolve(15,a,16,a)].
% 0.72/0.99 23 -relation(A) | -well_ordering(A) | reflexive(A) # label(d4_wellord1) # label(axiom). [clausify(3)].
% 0.72/0.99 24 relation(inclusion_relation(A)) # label(dt_k1_wellord2) # label(axiom). [clausify(4)].
% 0.72/0.99 Derived: -well_ordering(inclusion_relation(A)) | reflexive(inclusion_relation(A)). [resolve(23,a,24,a)].
% 0.72/0.99 25 -relation(A) | -well_ordering(A) | transitive(A) # label(d4_wellord1) # label(axiom). [clausify(3)].
% 0.72/0.99 Derived: -well_ordering(inclusion_relation(A)) | transitive(inclusion_relation(A)). [resolve(25,a,24,a)].
% 0.72/0.99 26 -relation(A) | -well_ordering(A) | antisymmetric(A) # label(d4_wellord1) # label(axiom). [clausify(3)].
% 0.72/0.99 Derived: -well_ordering(inclusion_relation(A)) | antisymmetric(inclusion_relation(A)). [resolve(26,a,24,a)].
% 0.72/0.99 27 -relation(A) | -well_ordering(A) | connected(A) # label(d4_wellord1) # label(axiom). [clausify(3)].
% 0.72/0.99 Derived: -well_ordering(inclusion_relation(A)) | connected(inclusion_relation(A)). [resolve(27,a,24,a)].
% 0.72/0.99 28 -relation(A) | -well_ordering(A) | well_founded_relation(A) # label(d4_wellord1) # label(axiom). [clausify(3)].
% 0.72/0.99 Derived: -well_ordering(inclusion_relation(A)) | well_founded_relation(inclusion_relation(A)). [resolve(28,a,24,a)].
% 0.72/0.99 29 -relation(A) | well_ordering(A) | -reflexive(A) | -transitive(A) | -antisymmetric(A) | -connected(A) | -well_founded_relation(A) # label(d4_wellord1) # label(axiom). [clausify(3)].
% 0.72/0.99 Derived: well_ordering(inclusion_relation(A)) | -reflexive(inclusion_relation(A)) | -transitive(inclusion_relation(A)) | -antisymmetric(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(29,a,24,a)].
% 0.72/0.99 30 well_ordering(inclusion_relation(A)) | -reflexive(inclusion_relation(A)) | -transitive(inclusion_relation(A)) | -antisymmetric(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(29,a,24,a)].
% 0.72/0.99 31 reflexive(inclusion_relation(A)) # label(t2_wellord2) # label(axiom). [clausify(6)].
% 0.72/0.99 32 -well_ordering(inclusion_relation(A)) | reflexive(inclusion_relation(A)). [resolve(23,a,24,a)].
% 0.72/0.99 Derived: well_ordering(inclusion_relation(A)) | -transitive(inclusion_relation(A)) | -antisymmetric(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(30,b,31,a)].
% 0.72/0.99 33 well_ordering(inclusion_relation(A)) | -transitive(inclusion_relation(A)) | -antisymmetric(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(30,b,31,a)].
% 0.72/0.99 34 transitive(inclusion_relation(A)) # label(t3_wellord2) # label(axiom). [clausify(7)].
% 0.72/0.99 35 -well_ordering(inclusion_relation(A)) | transitive(inclusion_relation(A)). [resolve(25,a,24,a)].
% 0.72/0.99 Derived: well_ordering(inclusion_relation(A)) | -antisymmetric(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(33,b,34,a)].
% 0.72/0.99 36 well_ordering(inclusion_relation(A)) | -antisymmetric(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(33,b,34,a)].
% 0.72/0.99 37 antisymmetric(inclusion_relation(A)) # label(t5_wellord2) # label(axiom). [clausify(9)].
% 0.72/0.99 38 -well_ordering(inclusion_relation(A)) | antisymmetric(inclusion_relation(A)). [resolve(26,a,24,a)].
% 0.72/0.99 Derived: well_ordering(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(36,b,37,a)].
% 0.72/0.99 39 well_ordering(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(36,b,37,a)].
% 0.72/0.99 40 -well_ordering(inclusion_relation(c2)) # label(t7_wellord2) # label(negated_conjecture). [clausify(11)].
% 0.72/0.99 41 -well_ordering(inclusion_relation(A)) | connected(inclusion_relation(A)). [resolve(27,a,24,a)].
% 0.72/0.99 42 -well_ordering(inclusion_relation(A)) | well_founded_relation(inclusion_relation(A)). [resolve(28,a,24,a)].
% 0.72/0.99 Derived: -connected(inclusion_relation(c2)) | -well_founded_relation(inclusion_relation(c2)). [resolve(39,a,40,a)].
% 0.72/0.99 43 -connected(inclusion_relation(c2)) | -well_founded_relation(inclusion_relation(c2)). [resolve(39,a,40,a)].
% 0.72/0.99 44 connected(inclusion_relation(c1)). [resolve(18,a,19,a)].
% 0.72/0.99 45 connected(inclusion_relation(c2)). [resolve(18,a,20,a)].
% 0.72/0.99 Derived: -well_founded_relation(inclusion_relation(c2)). [resolve(43,a,45,a)].
% 0.72/0.99 46 -well_founded_relation(inclusion_relation(c2)). [resolve(43,a,45,a)].
% 0.72/0.99 47 well_founded_relation(inclusion_relation(c1)). [resolve(21,a,19,a)].
% 0.72/0.99 48 well_founded_relation(inclusion_relation(c2)). [resolve(21,a,20,a)].
% 0.72/0.99 Derived: $F. [resolve(46,a,48,a)].
% 0.72/0.99
% 0.72/0.99 ============================== end predicate elimination =============
% 0.72/0.99
% 0.72/0.99 Auto_denials: (no changes).
% 0.72/0.99
% 0.72/0.99 Term ordering decisions:
% 0.72/0.99 Function symbol KB weights:
% 0.72/0.99
% 0.72/0.99 ============================== PROOF =================================
% 0.72/0.99 % SZS status Theorem
% 0.72/0.99 % SZS output start Refutation
% 0.72/0.99
% 0.72/0.99 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.72/0.99 % Length of proof is 26.
% 0.72/0.99 % Level of proof is 8.
% 0.72/0.99 % Maximum clause weight is 0.000.
% 0.72/0.99 % Given clauses 0.
% 0.72/0.99
% 0.72/0.99 3 (all A (relation(A) -> (well_ordering(A) <-> reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 4 (all A relation(inclusion_relation(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 6 (all A reflexive(inclusion_relation(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 7 (all A transitive(inclusion_relation(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 8 (all A (ordinal(A) -> connected(inclusion_relation(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 9 (all A antisymmetric(inclusion_relation(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 10 (all A (ordinal(A) -> well_founded_relation(inclusion_relation(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 11 -(all A (ordinal(A) -> well_ordering(inclusion_relation(A)))) # label(t7_wellord2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/0.99 18 -ordinal(A) | connected(inclusion_relation(A)) # label(t4_wellord2) # label(axiom). [clausify(8)].
% 0.72/0.99 20 ordinal(c2) # label(t7_wellord2) # label(negated_conjecture). [clausify(11)].
% 0.72/0.99 21 -ordinal(A) | well_founded_relation(inclusion_relation(A)) # label(t6_wellord2) # label(axiom). [clausify(10)].
% 0.72/0.99 24 relation(inclusion_relation(A)) # label(dt_k1_wellord2) # label(axiom). [clausify(4)].
% 0.72/0.99 29 -relation(A) | well_ordering(A) | -reflexive(A) | -transitive(A) | -antisymmetric(A) | -connected(A) | -well_founded_relation(A) # label(d4_wellord1) # label(axiom). [clausify(3)].
% 0.72/0.99 30 well_ordering(inclusion_relation(A)) | -reflexive(inclusion_relation(A)) | -transitive(inclusion_relation(A)) | -antisymmetric(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(29,a,24,a)].
% 0.72/0.99 31 reflexive(inclusion_relation(A)) # label(t2_wellord2) # label(axiom). [clausify(6)].
% 0.72/0.99 33 well_ordering(inclusion_relation(A)) | -transitive(inclusion_relation(A)) | -antisymmetric(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(30,b,31,a)].
% 0.72/0.99 34 transitive(inclusion_relation(A)) # label(t3_wellord2) # label(axiom). [clausify(7)].
% 0.72/0.99 36 well_ordering(inclusion_relation(A)) | -antisymmetric(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(33,b,34,a)].
% 0.72/0.99 37 antisymmetric(inclusion_relation(A)) # label(t5_wellord2) # label(axiom). [clausify(9)].
% 0.72/0.99 39 well_ordering(inclusion_relation(A)) | -connected(inclusion_relation(A)) | -well_founded_relation(inclusion_relation(A)). [resolve(36,b,37,a)].
% 0.72/0.99 40 -well_ordering(inclusion_relation(c2)) # label(t7_wellord2) # label(negated_conjecture). [clausify(11)].
% 0.72/0.99 43 -connected(inclusion_relation(c2)) | -well_founded_relation(inclusion_relation(c2)). [resolve(39,a,40,a)].
% 0.72/0.99 45 connected(inclusion_relation(c2)). [resolve(18,a,20,a)].
% 0.72/0.99 46 -well_founded_relation(inclusion_relation(c2)). [resolve(43,a,45,a)].
% 0.72/0.99 48 well_founded_relation(inclusion_relation(c2)). [resolve(21,a,20,a)].
% 0.72/0.99 49 $F. [resolve(46,a,48,a)].
% 0.72/0.99
% 0.72/0.99 % SZS output end Refutation
% 0.72/0.99 ============================== end of proof ==========================
% 0.72/0.99
% 0.72/0.99 ============================== STATISTICS ============================
% 0.72/0.99
% 0.72/0.99 Given=0. Generated=1. Kept=0. proofs=1.
% 0.72/0.99 Usable=0. Sos=0. Demods=0. Limbo=0, Disabled=38. Hints=0.
% 0.72/0.99 Megabytes=0.03.
% 0.72/0.99 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.72/0.99
% 0.72/0.99 ============================== end of statistics =====================
% 0.72/0.99
% 0.72/0.99 ============================== end of search =========================
% 0.72/0.99
% 0.72/0.99 THEOREM PROVED
% 0.72/0.99 % SZS status Theorem
% 0.72/0.99
% 0.72/0.99 Exiting with 1 proof.
% 0.72/0.99
% 0.72/0.99 Process 4314 exit (max_proofs) Sun Jun 19 03:13:04 2022
% 0.72/0.99 Prover9 interrupted
%------------------------------------------------------------------------------