TSTP Solution File: SEU240+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU240+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 13:30:16 EDT 2022
% Result : Theorem 0.74s 1.17s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU240+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n016.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 : Mon Jun 20 01:35:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.74/1.01 ============================== Prover9 ===============================
% 0.74/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.01 Process 3065 was started by sandbox2 on n016.cluster.edu,
% 0.74/1.01 Mon Jun 20 01:35:40 2022
% 0.74/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2695_n016.cluster.edu".
% 0.74/1.01 ============================== end of head ===========================
% 0.74/1.01
% 0.74/1.01 ============================== INPUT =================================
% 0.74/1.01
% 0.74/1.01 % Reading from file /tmp/Prover9_2695_n016.cluster.edu
% 0.74/1.01
% 0.74/1.01 set(prolog_style_variables).
% 0.74/1.01 set(auto2).
% 0.74/1.01 % set(auto2) -> set(auto).
% 0.74/1.01 % set(auto) -> set(auto_inference).
% 0.74/1.01 % set(auto) -> set(auto_setup).
% 0.74/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.01 % set(auto) -> set(auto_limits).
% 0.74/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.01 % set(auto) -> set(auto_denials).
% 0.74/1.01 % set(auto) -> set(auto_process).
% 0.74/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.01 % set(auto2) -> assign(stats, some).
% 0.74/1.01 % set(auto2) -> clear(echo_input).
% 0.74/1.01 % set(auto2) -> set(quiet).
% 0.74/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.01 % set(auto2) -> clear(print_given).
% 0.74/1.01 assign(lrs_ticks,-1).
% 0.74/1.01 assign(sos_limit,10000).
% 0.74/1.01 assign(order,kbo).
% 0.74/1.01 set(lex_order_vars).
% 0.74/1.01 clear(print_given).
% 0.74/1.01
% 0.74/1.01 % formulas(sos). % not echoed (37 formulas)
% 0.74/1.01
% 0.74/1.01 ============================== end of input ==========================
% 0.74/1.01
% 0.74/1.01 % From the command line: assign(max_seconds, 300).
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.01
% 0.74/1.01 % Formulas that are not ordinary clauses:
% 0.74/1.01 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 2 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 3 (all A (relation(A) & empty(A) & function(A) -> relation(A) & function(A) & one_to_one(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 4 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 5 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 6 (all A (relation(A) -> (transitive(A) <-> is_transitive_in(A,relation_field(A))))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 7 (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].
% 0.74/1.01 8 (all A (relation(A) -> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 9 (all A (relation(A) -> (all B (is_transitive_in(A,B) <-> (all C all D all E (in(C,B) & in(D,B) & in(E,B) & in(ordered_pair(C,D),A) & in(ordered_pair(D,E),A) -> in(ordered_pair(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 10 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 11 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 12 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 13 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 14 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 15 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 16 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 17 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 18 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 19 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 20 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 21 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 22 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 23 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 24 (exists A (relation(A) & function(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 25 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 26 (exists A (relation(A) & empty(A) & function(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 27 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 28 (exists A (relation(A) & function(A) & one_to_one(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 29 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 30 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 31 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 32 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_field(C)) & in(B,relation_field(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 33 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 34 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 35 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 36 -(all A (relation(A) -> (transitive(A) <-> (all B all C all D (in(ordered_pair(B,C),A) & in(ordered_pair(C,D),A) -> in(ordered_pair(B,D),A)))))) # label(l2_wellord1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.01
% 0.74/1.01 ============================== end of process non-clausal formulas ===
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.01
% 0.74/1.01 ============================== PREDICATE ELIMINATION =================
% 0.74/1.01 37 -relation(A) | -empty(A) | -function(A) | one_to_one(A) # label(cc2_funct_1) # label(axiom). [clausify(3)].
% 0.74/1.01 38 relation(c1) # label(rc1_funct_1) # label(axiom). [clausify(24)].
% 0.74/1.01 39 relation(c3) # label(rc2_funct_1) # label(axiom). [clausify(26)].
% 0.74/1.01 40 relation(c5) # label(rc3_funct_1) # label(axiom). [clausify(28)].
% 0.74/1.01 41 relation(c6) # label(l2_wellord1) # label(negated_conjecture). [clausify(36)].
% 0.74/1.01 Derived: -empty(c1) | -function(c1) | one_to_one(c1). [resolve(37,a,38,a)].
% 0.74/1.01 Derived: -empty(c3) | -function(c3) | one_to_one(c3). [resolve(37,a,39,a)].
% 0.74/1.01 Derived: -empty(c5) | -function(c5) | one_to_one(c5). [resolve(37,a,40,a)].
% 0.74/1.01 Derived: -empty(c6) | -function(c6) | one_to_one(c6). [resolve(37,a,41,a)].
% 0.74/1.01 42 -relation(A) | -transitive(A) | is_transitive_in(A,relation_field(A)) # label(d16_relat_2) # label(axiom). [clausify(6)].
% 0.74/1.01 Derived: -transitive(c1) | is_transitive_in(c1,relation_field(c1)). [resolve(42,a,38,a)].
% 0.74/1.01 Derived: -transitive(c3) | is_transitive_in(c3,relation_field(c3)). [resolve(42,a,39,a)].
% 0.74/1.01 Derived: -transitive(c5) | is_transitive_in(c5,relation_field(c5)). [resolve(42,a,40,a)].
% 0.74/1.01 Derived: -transitive(c6) | is_transitive_in(c6,relation_field(c6)). [resolve(42,a,41,a)].
% 0.74/1.01 43 -relation(A) | transitive(A) | -is_transitive_in(A,relation_field(A)) # label(d16_relat_2) # label(axiom). [clausify(6)].
% 0.74/1.01 Derived: transitive(c1) | -is_transitive_in(c1,relation_field(c1)). [resolve(43,a,38,a)].
% 0.74/1.01 Derived: transitive(c3) | -is_transitive_in(c3,relation_field(c3)). [resolve(43,a,39,a)].
% 0.74/1.01 Derived: transitive(c5) | -is_transitive_in(c5,relation_field(c5)). [resolve(43,a,40,a)].
% 0.74/1.01 Derived: transitive(c6) | -is_transitive_in(c6,relation_field(c6)). [resolve(43,a,41,a)].
% 0.74/1.01 44 -relation(A) | relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) # label(d6_relat_1) # label(axiom). [clausify(8)].
% 0.74/1.01 Derived: relation_field(c1) = set_union2(relation_dom(c1),relation_rng(c1)). [resolve(44,a,38,a)].
% 0.74/1.01 Derived: relation_field(c3) = set_union2(relation_dom(c3),relation_rng(c3)). [resolve(44,a,39,a)].
% 0.74/1.01 Derived: relation_field(c5) = set_union2(relation_dom(c5),relation_rng(c5)). [resolve(44,a,40,a)].
% 0.74/1.01 Derived: relation_field(c6) = set_union2(relation_dom(c6),relation_rng(c6)). [resolve(44,a,41,a)].
% 0.74/1.01 45 -relation(A) | is_transitive_in(A,B) | in(f1(A,B),B) # label(d8_relat_2) # label(axiom). [clausify(9)].
% 0.74/1.01 Derived: is_transitive_in(c1,A) | in(f1(c1,A),A). [resolve(45,a,38,a)].
% 0.74/1.01 Derived: is_transitive_in(c3,A) | in(f1(c3,A),A). [resolve(45,a,39,a)].
% 0.74/1.01 Derived: is_transitive_in(c5,A) | in(f1(c5,A),A). [resolve(45,a,40,a)].
% 0.74/1.01 Derived: is_transitive_in(c6,A) | in(f1(c6,A),A). [resolve(45,a,41,a)].
% 0.74/1.01 46 -relation(A) | is_transitive_in(A,B) | in(f2(A,B),B) # label(d8_relat_2) # label(axiom). [clausify(9)].
% 0.74/1.01 Derived: is_transitive_in(c1,A) | in(f2(c1,A),A). [resolve(46,a,38,a)].
% 0.74/1.01 Derived: is_transitive_in(c3,A) | in(f2(c3,A),A). [resolve(46,a,39,a)].
% 0.74/1.01 Derived: is_transitive_in(c5,A) | in(f2(c5,A),A). [resolve(46,a,40,a)].
% 0.74/1.01 Derived: is_transitive_in(c6,A) | in(f2(c6,A),A). [resolve(46,a,41,a)].
% 0.74/1.01 47 -relation(A) | is_transitive_in(A,B) | in(f3(A,B),B) # label(d8_relat_2) # label(axiom). [clausify(9)].
% 0.74/1.01 Derived: is_transitive_in(c1,A) | in(f3(c1,A),A). [resolve(47,a,38,a)].
% 0.74/1.01 Derived: is_transitive_in(c3,A) | in(f3(c3,A),A). [resolve(47,a,39,a)].
% 0.74/1.01 Derived: is_transitive_in(c5,A) | in(f3(c5,A),A). [resolve(47,a,40,a)].
% 0.74/1.01 Derived: is_transitive_in(c6,A) | in(f3(c6,A),A). [resolve(47,a,41,a)].
% 0.74/1.01 48 -relation(A) | -in(ordered_pair(B,C),A) | in(B,relation_field(A)) # label(t30_relat_1) # label(axiom). [clausify(32)].
% 0.74/1.01 Derived: -in(ordered_pair(A,B),c1) | in(A,relation_field(c1)). [resolve(48,a,38,a)].
% 0.74/1.01 Derived: -in(ordered_pair(A,B),c3) | in(A,relation_field(c3)). [resolve(48,a,39,a)].
% 0.74/1.01 Derived: -in(ordered_pair(A,B),c5) | in(A,relation_field(c5)). [resolve(48,a,40,a)].
% 0.74/1.01 Derived: -in(ordered_pair(A,B),c6) | in(A,relation_field(c6)). [resolve(48,a,41,a)].
% 0.74/1.01 49 -relation(A) | -in(ordered_pair(B,C),A) | in(C,relation_field(A)) # label(t30_relat_1) # label(axiom). [clausify(32)].
% 0.74/1.01 Derived: -in(ordered_pair(A,B),c1) | in(B,relation_field(c1)). [resolve(49,a,38,a)].
% 0.74/1.01 Derived: -in(ordered_pair(A,B),c3) | in(B,relation_field(c3)). [resolve(49,a,39,a)].
% 0.74/1.01 Derived: -in(ordered_pair(A,B),c5) | in(B,relation_field(c5)). [resolve(49,a,40,a)].
% 0.74/1.01 Derived: -in(ordered_pair(A,B),c6) | in(B,relation_field(c6)). [resolve(49,a,41,a)].
% 0.74/1.01 50 -relation(A) | is_transitive_in(A,B) | in(ordered_pair(f1(A,B),f2(A,B)),A) # label(d8_relat_2) # label(axiom). [clausify(9)].
% 0.74/1.01 Derived: is_transitive_in(c1,A) | in(ordered_pair(f1(c1,A),f2(c1,A)),c1). [resolve(50,a,38,a)].
% 0.74/1.01 Derived: is_transitive_in(c3,A) | in(ordered_pair(f1(c3,A),f2(c3,A)),c3). [resolve(50,a,39,a)].
% 0.74/1.01 Derived: is_transitive_in(c5,A) | in(ordered_pair(f1(c5,A),f2(c5,A)),c5). [resolve(50,a,40,a)].
% 0.74/1.01 Derived: is_transitive_in(c6,A) | in(ordered_pair(f1(c6,A),f2(c6,A)),c6). [resolve(50,a,41,a)].
% 0.74/1.01 51 -relation(A) | is_transitive_in(A,B) | in(ordered_pair(f2(A,B),f3(A,B)),A) # label(d8_relat_2) # label(axiom). [clausify(9)].
% 0.74/1.01 Derived: is_transitive_in(c1,A) | in(ordered_pair(f2(c1,A),f3(c1,A)),c1). [resolve(51,a,38,a)].
% 0.74/1.01 Derived: is_transitive_in(c3,A) | in(ordered_pair(f2(c3,A),f3(c3,A)),c3). [resolve(51,a,39,a)].
% 0.74/1.01 Derived: is_transitive_in(c5,A) | in(ordered_pair(f2(c5,A),f3(c5,A)),c5). [resolve(51,a,40,a)].
% 0.74/1.01 Derived: is_transitive_in(c6,A) | in(ordered_pair(f2(c6,A),f3(c6,A)),c6). [resolve(51,a,41,a)].
% 0.74/1.01 52 -relation(A) | is_transitive_in(A,B) | -in(ordered_pair(f1(A,B),f3(A,B)),A) # label(d8_relat_2) # label(axiom). [clausify(9)].
% 0.74/1.01 Derived: is_transitive_in(c1,A) | -in(ordered_pair(f1(c1,A),f3(c1,A)),c1). [resolve(52,a,38,a)].
% 0.74/1.17 Derived: is_transitive_in(c3,A) | -in(ordered_pair(f1(c3,A),f3(c3,A)),c3). [resolve(52,a,39,a)].
% 0.74/1.17 Derived: is_transitive_in(c5,A) | -in(ordered_pair(f1(c5,A),f3(c5,A)),c5). [resolve(52,a,40,a)].
% 0.74/1.17 Derived: is_transitive_in(c6,A) | -in(ordered_pair(f1(c6,A),f3(c6,A)),c6). [resolve(52,a,41,a)].
% 0.74/1.17 53 -relation(A) | -is_transitive_in(A,B) | -in(C,B) | -in(D,B) | -in(E,B) | -in(ordered_pair(C,D),A) | -in(ordered_pair(D,E),A) | in(ordered_pair(C,E),A) # label(d8_relat_2) # label(axiom). [clausify(9)].
% 0.74/1.17 Derived: -is_transitive_in(c1,A) | -in(B,A) | -in(C,A) | -in(D,A) | -in(ordered_pair(B,C),c1) | -in(ordered_pair(C,D),c1) | in(ordered_pair(B,D),c1). [resolve(53,a,38,a)].
% 0.74/1.17 Derived: -is_transitive_in(c3,A) | -in(B,A) | -in(C,A) | -in(D,A) | -in(ordered_pair(B,C),c3) | -in(ordered_pair(C,D),c3) | in(ordered_pair(B,D),c3). [resolve(53,a,39,a)].
% 0.74/1.17 Derived: -is_transitive_in(c5,A) | -in(B,A) | -in(C,A) | -in(D,A) | -in(ordered_pair(B,C),c5) | -in(ordered_pair(C,D),c5) | in(ordered_pair(B,D),c5). [resolve(53,a,40,a)].
% 0.74/1.17 Derived: -is_transitive_in(c6,A) | -in(B,A) | -in(C,A) | -in(D,A) | -in(ordered_pair(B,C),c6) | -in(ordered_pair(C,D),c6) | in(ordered_pair(B,D),c6). [resolve(53,a,41,a)].
% 0.74/1.17 54 -element(A,B) | empty(B) | in(A,B) # label(t2_subset) # label(axiom). [clausify(31)].
% 0.74/1.17 55 element(f4(A),A) # label(existence_m1_subset_1) # label(axiom). [clausify(19)].
% 0.74/1.17 56 -in(A,B) | element(A,B) # label(t1_subset) # label(axiom). [clausify(30)].
% 0.74/1.17 Derived: empty(A) | in(f4(A),A). [resolve(54,a,55,a)].
% 0.74/1.17
% 0.74/1.17 ============================== end predicate elimination =============
% 0.74/1.17
% 0.74/1.17 Auto_denials: (non-Horn, no changes).
% 0.74/1.17
% 0.74/1.17 Term ordering decisions:
% 0.74/1.17 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. ordered_pair=1. set_union2=1. unordered_pair=1. f1=1. f2=1. f3=1. relation_field=1. relation_dom=1. relation_rng=1. singleton=1. f4=1.
% 0.74/1.17
% 0.74/1.17 ============================== end of process initial clauses ========
% 0.74/1.17
% 0.74/1.17 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.17
% 0.74/1.17 ============================== end of clauses for search =============
% 0.74/1.17
% 0.74/1.17 ============================== SEARCH ================================
% 0.74/1.17
% 0.74/1.17 % Starting search at 0.02 seconds.
% 0.74/1.17
% 0.74/1.17 ============================== PROOF =================================
% 0.74/1.17 % SZS status Theorem
% 0.74/1.17 % SZS output start Refutation
% 0.74/1.17
% 0.74/1.17 % Proof 1 at 0.17 (+ 0.01) seconds.
% 0.74/1.17 % Length of proof is 54.
% 0.74/1.17 % Level of proof is 11.
% 0.74/1.17 % Maximum clause weight is 36.000.
% 0.74/1.17 % Given clauses 174.
% 0.74/1.17
% 0.74/1.17 4 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.17 6 (all A (relation(A) -> (transitive(A) <-> is_transitive_in(A,relation_field(A))))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.17 7 (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].
% 0.74/1.17 9 (all A (relation(A) -> (all B (is_transitive_in(A,B) <-> (all C all D all E (in(C,B) & in(D,B) & in(E,B) & in(ordered_pair(C,D),A) & in(ordered_pair(D,E),A) -> in(ordered_pair(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.17 32 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_field(C)) & in(B,relation_field(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.17 36 -(all A (relation(A) -> (transitive(A) <-> (all B all C all D (in(ordered_pair(B,C),A) & in(ordered_pair(C,D),A) -> in(ordered_pair(B,D),A)))))) # label(l2_wellord1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.17 41 relation(c6) # label(l2_wellord1) # label(negated_conjecture). [clausify(36)].
% 0.74/1.17 42 -relation(A) | -transitive(A) | is_transitive_in(A,relation_field(A)) # label(d16_relat_2) # label(axiom). [clausify(6)].
% 0.74/1.17 43 -relation(A) | transitive(A) | -is_transitive_in(A,relation_field(A)) # label(d16_relat_2) # label(axiom). [clausify(6)].
% 0.74/1.17 48 -relation(A) | -in(ordered_pair(B,C),A) | in(B,relation_field(A)) # label(t30_relat_1) # label(axiom). [clausify(32)].
% 0.74/1.17 49 -relation(A) | -in(ordered_pair(B,C),A) | in(C,relation_field(A)) # label(t30_relat_1) # label(axiom). [clausify(32)].
% 0.74/1.17 50 -relation(A) | is_transitive_in(A,B) | in(ordered_pair(f1(A,B),f2(A,B)),A) # label(d8_relat_2) # label(axiom). [clausify(9)].
% 0.74/1.17 51 -relation(A) | is_transitive_in(A,B) | in(ordered_pair(f2(A,B),f3(A,B)),A) # label(d8_relat_2) # label(axiom). [clausify(9)].
% 0.74/1.17 52 -relation(A) | is_transitive_in(A,B) | -in(ordered_pair(f1(A,B),f3(A,B)),A) # label(d8_relat_2) # label(axiom). [clausify(9)].
% 0.74/1.17 53 -relation(A) | -is_transitive_in(A,B) | -in(C,B) | -in(D,B) | -in(E,B) | -in(ordered_pair(C,D),A) | -in(ordered_pair(D,E),A) | in(ordered_pair(C,E),A) # label(d8_relat_2) # label(axiom). [clausify(9)].
% 0.74/1.17 62 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(4)].
% 0.74/1.17 64 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(7)].
% 0.74/1.17 65 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(64),rewrite([62(4)])].
% 0.74/1.17 71 -transitive(c6) | -in(ordered_pair(c7,c9),c6) # label(l2_wellord1) # label(negated_conjecture). [clausify(36)].
% 0.74/1.17 72 -transitive(c6) | -in(unordered_pair(singleton(c7),unordered_pair(c7,c9)),c6). [copy(71),rewrite([65(5)])].
% 0.74/1.17 77 -transitive(c6) | in(ordered_pair(c7,c8),c6) # label(l2_wellord1) # label(negated_conjecture). [clausify(36)].
% 0.74/1.17 78 -transitive(c6) | in(unordered_pair(singleton(c7),unordered_pair(c7,c8)),c6). [copy(77),rewrite([65(5)])].
% 0.74/1.17 79 -transitive(c6) | in(ordered_pair(c8,c9),c6) # label(l2_wellord1) # label(negated_conjecture). [clausify(36)].
% 0.74/1.17 80 -transitive(c6) | in(unordered_pair(singleton(c8),unordered_pair(c8,c9)),c6). [copy(79),rewrite([65(5)])].
% 0.74/1.17 81 transitive(c6) | -in(ordered_pair(A,B),c6) | -in(ordered_pair(B,C),c6) | in(ordered_pair(A,C),c6) # label(l2_wellord1) # label(negated_conjecture). [clausify(36)].
% 0.74/1.17 82 transitive(c6) | -in(unordered_pair(singleton(A),unordered_pair(A,B)),c6) | -in(unordered_pair(singleton(B),unordered_pair(B,C)),c6) | in(unordered_pair(singleton(A),unordered_pair(A,C)),c6). [copy(81),rewrite([65(3),65(8),65(13)])].
% 0.74/1.17 86 -transitive(c6) | is_transitive_in(c6,relation_field(c6)). [resolve(42,a,41,a)].
% 0.74/1.17 90 transitive(c6) | -is_transitive_in(c6,relation_field(c6)). [resolve(43,a,41,a)].
% 0.74/1.17 117 -in(ordered_pair(A,B),c6) | in(A,relation_field(c6)). [resolve(48,a,41,a)].
% 0.74/1.17 118 -in(unordered_pair(singleton(A),unordered_pair(A,B)),c6) | in(A,relation_field(c6)). [copy(117),rewrite([65(1)])].
% 0.74/1.17 125 -in(ordered_pair(A,B),c6) | in(B,relation_field(c6)). [resolve(49,a,41,a)].
% 0.74/1.17 126 -in(unordered_pair(singleton(A),unordered_pair(A,B)),c6) | in(B,relation_field(c6)). [copy(125),rewrite([65(1)])].
% 0.74/1.17 133 is_transitive_in(c6,A) | in(ordered_pair(f1(c6,A),f2(c6,A)),c6). [resolve(50,a,41,a)].
% 0.74/1.17 134 is_transitive_in(c6,A) | in(unordered_pair(singleton(f1(c6,A)),unordered_pair(f1(c6,A),f2(c6,A))),c6). [copy(133),rewrite([65(7)])].
% 0.74/1.17 141 is_transitive_in(c6,A) | in(ordered_pair(f2(c6,A),f3(c6,A)),c6). [resolve(51,a,41,a)].
% 0.74/1.17 142 is_transitive_in(c6,A) | in(unordered_pair(singleton(f2(c6,A)),unordered_pair(f2(c6,A),f3(c6,A))),c6). [copy(141),rewrite([65(7)])].
% 0.74/1.17 149 is_transitive_in(c6,A) | -in(ordered_pair(f1(c6,A),f3(c6,A)),c6). [resolve(52,a,41,a)].
% 0.74/1.17 150 is_transitive_in(c6,A) | -in(unordered_pair(singleton(f1(c6,A)),unordered_pair(f1(c6,A),f3(c6,A))),c6). [copy(149),rewrite([65(7)])].
% 0.74/1.17 157 -is_transitive_in(c6,A) | -in(B,A) | -in(C,A) | -in(D,A) | -in(ordered_pair(B,C),c6) | -in(ordered_pair(C,D),c6) | in(ordered_pair(B,D),c6). [resolve(53,a,41,a)].
% 0.74/1.17 158 -is_transitive_in(c6,A) | -in(B,A) | -in(C,A) | -in(D,A) | -in(unordered_pair(singleton(B),unordered_pair(B,C)),c6) | -in(unordered_pair(singleton(C),unordered_pair(C,D)),c6) | in(unordered_pair(singleton(B),unordered_pair(B,D)),c6). [copy(157),rewrite([65(6),65(11),65(16)])].
% 0.74/1.17 199 in(unordered_pair(singleton(f1(c6,relation_field(c6))),unordered_pair(f1(c6,relation_field(c6)),f2(c6,relation_field(c6)))),c6) | transitive(c6). [resolve(134,a,90,b)].
% 0.74/1.17 202 in(unordered_pair(singleton(f2(c6,relation_field(c6))),unordered_pair(f2(c6,relation_field(c6)),f3(c6,relation_field(c6)))),c6) | transitive(c6). [resolve(142,a,90,b)].
% 0.74/1.17 337 transitive(c6) | -in(unordered_pair(singleton(A),unordered_pair(A,f2(c6,relation_field(c6)))),c6) | in(unordered_pair(singleton(A),unordered_pair(A,f3(c6,relation_field(c6)))),c6). [resolve(202,a,82,c),merge(b)].
% 0.74/1.17 433 transitive(c6) | in(unordered_pair(singleton(f1(c6,relation_field(c6))),unordered_pair(f1(c6,relation_field(c6)),f3(c6,relation_field(c6)))),c6). [resolve(337,b,199,a),merge(c)].
% 0.74/1.17 529 transitive(c6) | is_transitive_in(c6,relation_field(c6)). [resolve(433,b,150,b)].
% 0.74/1.17 538 transitive(c6). [resolve(529,b,90,b),merge(b)].
% 0.74/1.17 539 is_transitive_in(c6,relation_field(c6)). [back_unit_del(86),unit_del(a,538)].
% 0.74/1.17 540 in(unordered_pair(singleton(c8),unordered_pair(c8,c9)),c6). [back_unit_del(80),unit_del(a,538)].
% 0.74/1.17 541 in(unordered_pair(singleton(c7),unordered_pair(c7,c8)),c6). [back_unit_del(78),unit_del(a,538)].
% 0.74/1.17 542 -in(unordered_pair(singleton(c7),unordered_pair(c7,c9)),c6). [back_unit_del(72),unit_del(a,538)].
% 0.74/1.17 608 in(c9,relation_field(c6)). [resolve(540,a,126,a)].
% 0.74/1.17 609 in(c8,relation_field(c6)). [resolve(540,a,118,a)].
% 0.74/1.17 657 in(c7,relation_field(c6)). [resolve(541,a,118,a)].
% 0.74/1.17 659 $F. [ur(158,a,539,a,c,609,a,d,608,a,e,541,a,f,540,a,g,542,a),unit_del(a,657)].
% 0.74/1.17
% 0.74/1.17 % SZS output end Refutation
% 0.74/1.17 ============================== end of proof ==========================
% 0.74/1.17
% 0.74/1.17 ============================== STATISTICS ============================
% 0.74/1.17
% 0.74/1.17 Given=174. Generated=1891. Kept=567. proofs=1.
% 0.74/1.17 Usable=149. Sos=297. Demods=11. Limbo=11, Disabled=208. Hints=0.
% 0.74/1.17 Megabytes=1.32.
% 0.74/1.17 User_CPU=0.17, System_CPU=0.01, Wall_clock=0.
% 0.74/1.17
% 0.74/1.17 ============================== end of statistics =====================
% 0.74/1.17
% 0.74/1.17 ============================== end of search =========================
% 0.74/1.17
% 0.74/1.17 THEOREM PROVED
% 0.74/1.17 % SZS status Theorem
% 0.74/1.17
% 0.74/1.17 Exiting with 1 proof.
% 0.74/1.17
% 0.74/1.17 Process 3065 exit (max_proofs) Mon Jun 20 01:35:40 2022
% 0.74/1.17 Prover9 interrupted
%------------------------------------------------------------------------------