TSTP Solution File: SEU177+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU177+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 13:29:40 EDT 2022
% Result : Theorem 0.72s 0.98s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU177+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 : n017.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 : Sun Jun 19 06:29:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.72/0.98 ============================== Prover9 ===============================
% 0.72/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.72/0.98 Process 30581 was started by sandbox on n017.cluster.edu,
% 0.72/0.98 Sun Jun 19 06:29:58 2022
% 0.72/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30428_n017.cluster.edu".
% 0.72/0.98 ============================== end of head ===========================
% 0.72/0.98
% 0.72/0.98 ============================== INPUT =================================
% 0.72/0.98
% 0.72/0.98 % Reading from file /tmp/Prover9_30428_n017.cluster.edu
% 0.72/0.98
% 0.72/0.98 set(prolog_style_variables).
% 0.72/0.98 set(auto2).
% 0.72/0.98 % set(auto2) -> set(auto).
% 0.72/0.98 % set(auto) -> set(auto_inference).
% 0.72/0.98 % set(auto) -> set(auto_setup).
% 0.72/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.72/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/0.98 % set(auto) -> set(auto_limits).
% 0.72/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/0.98 % set(auto) -> set(auto_denials).
% 0.72/0.98 % set(auto) -> set(auto_process).
% 0.72/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.72/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.72/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.72/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.72/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.72/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.72/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.72/0.98 % set(auto2) -> assign(stats, some).
% 0.72/0.98 % set(auto2) -> clear(echo_input).
% 0.72/0.98 % set(auto2) -> set(quiet).
% 0.72/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.72/0.98 % set(auto2) -> clear(print_given).
% 0.72/0.98 assign(lrs_ticks,-1).
% 0.72/0.98 assign(sos_limit,10000).
% 0.72/0.98 assign(order,kbo).
% 0.72/0.98 set(lex_order_vars).
% 0.72/0.98 clear(print_given).
% 0.72/0.98
% 0.72/0.98 % formulas(sos). % not echoed (26 formulas)
% 0.72/0.98
% 0.72/0.98 ============================== end of input ==========================
% 0.72/0.98
% 0.72/0.98 % From the command line: assign(max_seconds, 300).
% 0.72/0.98
% 0.72/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/0.98
% 0.72/0.98 % Formulas that are not ordinary clauses:
% 0.72/0.98 1 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 3 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 4 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 5 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 6 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 7 (exists A (empty(A) & relation(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 8 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 9 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 10 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 11 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 12 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 13 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 14 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 15 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 16 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 17 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 18 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 19 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 20 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 21 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 22 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 23 (all A (relation(A) -> (all B (B = relation_dom(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 24 (all A (relation(A) -> (all B (B = relation_rng(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(D,C),A)))))))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 25 -(all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_dom(C)) & in(B,relation_rng(C))))) # label(t20_relat_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/0.98
% 0.72/0.98 ============================== end of process non-clausal formulas ===
% 0.72/0.98
% 0.72/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/0.98
% 0.72/0.98 ============================== PREDICATE ELIMINATION =================
% 0.72/0.98 26 -relation(A) | relation_dom(A) != B | in(C,B) | -in(ordered_pair(C,D),A) # label(d4_relat_1) # label(axiom). [clausify(23)].
% 0.72/0.98 27 relation(c1) # label(rc1_relat_1) # label(axiom). [clausify(7)].
% 0.72/0.98 28 relation(c6) # label(t20_relat_1) # label(negated_conjecture). [clausify(25)].
% 0.72/0.98 Derived: relation_dom(c1) != A | in(B,A) | -in(ordered_pair(B,C),c1). [resolve(26,a,27,a)].
% 0.72/0.98 Derived: relation_dom(c6) != A | in(B,A) | -in(ordered_pair(B,C),c6). [resolve(26,a,28,a)].
% 0.72/0.98 29 -relation(A) | relation_rng(A) != B | in(C,B) | -in(ordered_pair(D,C),A) # label(d5_relat_1) # label(axiom). [clausify(24)].
% 0.72/0.98 Derived: relation_rng(c1) != A | in(B,A) | -in(ordered_pair(C,B),c1). [resolve(29,a,27,a)].
% 0.72/0.98 Derived: relation_rng(c6) != A | in(B,A) | -in(ordered_pair(C,B),c6). [resolve(29,a,28,a)].
% 0.72/0.98 30 -relation(A) | relation_dom(A) != B | -in(C,B) | in(ordered_pair(C,f2(A,B,C)),A) # label(d4_relat_1) # label(axiom). [clausify(23)].
% 0.72/0.98 Derived: relation_dom(c1) != A | -in(B,A) | in(ordered_pair(B,f2(c1,A,B)),c1). [resolve(30,a,27,a)].
% 0.72/0.98 Derived: relation_dom(c6) != A | -in(B,A) | in(ordered_pair(B,f2(c6,A,B)),c6). [resolve(30,a,28,a)].
% 0.72/0.98 31 -relation(A) | relation_rng(A) != B | -in(C,B) | in(ordered_pair(f5(A,B,C),C),A) # label(d5_relat_1) # label(axiom). [clausify(24)].
% 0.72/0.98 Derived: relation_rng(c1) != A | -in(B,A) | in(ordered_pair(f5(c1,A,B),B),c1). [resolve(31,a,27,a)].
% 0.72/0.98 Derived: relation_rng(c6) != A | -in(B,A) | in(ordered_pair(f5(c6,A,B),B),c6). [resolve(31,a,28,a)].
% 0.72/0.98 32 -relation(A) | relation_dom(A) = B | -in(f3(A,B),B) | -in(ordered_pair(f3(A,B),C),A) # label(d4_relat_1) # label(axiom). [clausify(23)].
% 0.72/0.98 Derived: relation_dom(c1) = A | -in(f3(c1,A),A) | -in(ordered_pair(f3(c1,A),B),c1). [resolve(32,a,27,a)].
% 0.72/0.98 Derived: relation_dom(c6) = A | -in(f3(c6,A),A) | -in(ordered_pair(f3(c6,A),B),c6). [resolve(32,a,28,a)].
% 0.72/0.98 33 -relation(A) | relation_rng(A) = B | -in(f6(A,B),B) | -in(ordered_pair(C,f6(A,B)),A) # label(d5_relat_1) # label(axiom). [clausify(24)].
% 0.72/0.98 Derived: relation_rng(c1) = A | -in(f6(c1,A),A) | -in(ordered_pair(B,f6(c1,A)),c1). [resolve(33,a,27,a)].
% 0.72/0.98 Derived: relation_rng(c6) = A | -in(f6(c6,A),A) | -in(ordered_pair(B,f6(c6,A)),c6). [resolve(33,a,28,a)].
% 0.72/0.98 34 -relation(A) | relation_dom(A) = B | in(f3(A,B),B) | in(ordered_pair(f3(A,B),f4(A,B)),A) # label(d4_relat_1) # label(axiom). [clausify(23)].
% 0.72/0.98 Derived: relation_dom(c1) = A | in(f3(c1,A),A) | in(ordered_pair(f3(c1,A),f4(c1,A)),c1). [resolve(34,a,27,a)].
% 0.72/0.98 Derived: relation_dom(c6) = A | in(f3(c6,A),A) | in(ordered_pair(f3(c6,A),f4(c6,A)),c6). [resolve(34,a,28,a)].
% 0.72/0.98 35 -relation(A) | relation_rng(A) = B | in(f6(A,B),B) | in(ordered_pair(f7(A,B),f6(A,B)),A) # label(d5_relat_1) # label(axiom). [clausify(24)].
% 0.72/0.98 Derived: relation_rng(c1) = A | in(f6(c1,A),A) | in(ordered_pair(f7(c1,A),f6(c1,A)),c1). [resolve(35,a,27,a)].
% 0.72/0.98 Derived: relation_rng(c6) = A | in(f6(c6,A),A) | in(ordered_pair(f7(c6,A),f6(c6,A)),c6). [resolve(35,a,28,a)].
% 0.72/0.98 36 -element(A,B) | empty(B) | in(A,B) # label(t2_subset) # label(axiom). [clausify(12)].
% 0.72/0.98 37 element(f1(A),A) # label(existence_m1_subset_1) # label(axiom). [clausify(3)].
% 0.72/0.98 38 -in(A,B) | element(A,B) # label(t1_subset) # label(axiom). [clausify(20)].
% 0.72/0.98 Derived: empty(A) | in(f1(A),A). [resolve(36,a,37,a)].
% 0.72/0.98
% 0.72/0.98 ============================== end predicate elimination =============
% 0.72/0.98
% 0.72/0.98 Auto_denials: (non-Horn, no changes).
% 0.72/0.98
% 0.72/0.98 Term ordering decisions:
% 0.72/0.98 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. ordered_pair=1. unordered_pair=1. f3=1. f4=1. f6=1. f7=1. relation_dom=1. relation_rng=1. singleton=1. f1=1. f2=1. f5=1.
% 0.72/0.98
% 0.72/0.98 ============================== end of process initial clauses ========
% 0.72/0.98
% 0.72/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.72/0.98
% 0.72/0.98 ============================== end of clauses for search =============
% 0.72/0.98
% 0.72/0.98 ============================== SEARCH ================================
% 0.72/0.98
% 0.72/0.98 % Starting search at 0.02 seconds.
% 0.72/0.98
% 0.72/0.98 ============================== PROOF =================================
% 0.72/0.98 % SZS status Theorem
% 0.72/0.98 % SZS output start Refutation
% 0.72/0.98
% 0.72/0.98 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.72/0.98 % Length of proof is 23.
% 0.72/0.98 % Level of proof is 8.
% 0.72/0.98 % Maximum clause weight is 15.000.
% 0.72/0.98 % Given clauses 37.
% 0.72/0.98
% 0.72/0.98 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 22 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 23 (all A (relation(A) -> (all B (B = relation_dom(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 24 (all A (relation(A) -> (all B (B = relation_rng(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(D,C),A)))))))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.98 25 -(all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_dom(C)) & in(B,relation_rng(C))))) # label(t20_relat_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/0.98 26 -relation(A) | relation_dom(A) != B | in(C,B) | -in(ordered_pair(C,D),A) # label(d4_relat_1) # label(axiom). [clausify(23)].
% 0.72/0.98 28 relation(c6) # label(t20_relat_1) # label(negated_conjecture). [clausify(25)].
% 0.72/0.98 29 -relation(A) | relation_rng(A) != B | in(C,B) | -in(ordered_pair(D,C),A) # label(d5_relat_1) # label(axiom). [clausify(24)].
% 0.72/0.98 42 in(ordered_pair(c4,c5),c6) # label(t20_relat_1) # label(negated_conjecture). [clausify(25)].
% 0.72/0.98 43 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.72/0.98 44 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(22)].
% 0.72/0.98 45 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(44),rewrite([43(4)])].
% 0.72/0.98 52 -in(c4,relation_dom(c6)) | -in(c5,relation_rng(c6)) # label(t20_relat_1) # label(negated_conjecture). [clausify(25)].
% 0.72/0.98 58 relation_dom(c6) != A | in(B,A) | -in(ordered_pair(B,C),c6). [resolve(26,a,28,a)].
% 0.72/0.98 59 relation_dom(c6) != A | in(B,A) | -in(unordered_pair(singleton(B),unordered_pair(B,C)),c6). [copy(58),rewrite([45(5)])].
% 0.72/0.98 62 relation_rng(c6) != A | in(B,A) | -in(ordered_pair(C,B),c6). [resolve(29,a,28,a)].
% 0.72/0.98 63 relation_rng(c6) != A | in(B,A) | -in(unordered_pair(singleton(C),unordered_pair(B,C)),c6). [copy(62),rewrite([45(5),43(6)])].
% 0.72/0.98 89 in(unordered_pair(singleton(c4),unordered_pair(c4,c5)),c6). [back_rewrite(42),rewrite([45(3)])].
% 0.72/0.98 119 relation_dom(c6) != A | in(c4,A). [resolve(89,a,59,c)].
% 0.72/0.98 132 in(c4,relation_dom(c6)). [xx_res(119,a)].
% 0.72/0.98 133 -in(c5,relation_rng(c6)). [back_unit_del(52),unit_del(a,132)].
% 0.72/0.98 137 -in(unordered_pair(singleton(A),unordered_pair(A,c5)),c6). [ur(63,a,xx,b,133,a),rewrite([43(3)])].
% 0.72/0.98 138 $F. [resolve(137,a,89,a)].
% 0.72/0.98
% 0.72/0.98 % SZS output end Refutation
% 0.72/0.98 ============================== end of proof ==========================
% 0.72/0.98
% 0.72/0.98 ============================== STATISTICS ============================
% 0.72/0.98
% 0.72/0.98 Given=37. Generated=130. Kept=80. proofs=1.
% 0.72/0.98 Usable=34. Sos=25. Demods=4. Limbo=0, Disabled=65. Hints=0.
% 0.72/0.98 Megabytes=0.18.
% 0.72/0.98 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.72/0.98
% 0.72/0.98 ============================== end of statistics =====================
% 0.72/0.98
% 0.72/0.98 ============================== end of search =========================
% 0.72/0.98
% 0.72/0.98 THEOREM PROVED
% 0.72/0.98 % SZS status Theorem
% 0.72/0.98
% 0.72/0.98 Exiting with 1 proof.
% 0.72/0.98
% 0.72/0.98 Process 30581 exit (max_proofs) Sun Jun 19 06:29:58 2022
% 0.72/0.98 Prover9 interrupted
%------------------------------------------------------------------------------