TSTP Solution File: SEU411+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU411+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 13:31:40 EDT 2022
% Result : Theorem 7.12s 7.41s
% Output : Refutation 7.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU411+1 : TPTP v8.1.0. Released v3.4.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 00:52:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.67/0.97 ============================== Prover9 ===============================
% 0.67/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.97 Process 5808 was started by sandbox on n012.cluster.edu,
% 0.67/0.97 Mon Jun 20 00:52:38 2022
% 0.67/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5655_n012.cluster.edu".
% 0.67/0.97 ============================== end of head ===========================
% 0.67/0.97
% 0.67/0.97 ============================== INPUT =================================
% 0.67/0.97
% 0.67/0.97 % Reading from file /tmp/Prover9_5655_n012.cluster.edu
% 0.67/0.97
% 0.67/0.97 set(prolog_style_variables).
% 0.67/0.97 set(auto2).
% 0.67/0.97 % set(auto2) -> set(auto).
% 0.67/0.97 % set(auto) -> set(auto_inference).
% 0.67/0.97 % set(auto) -> set(auto_setup).
% 0.67/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.97 % set(auto) -> set(auto_limits).
% 0.67/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.97 % set(auto) -> set(auto_denials).
% 0.67/0.97 % set(auto) -> set(auto_process).
% 0.67/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.97 % set(auto2) -> assign(stats, some).
% 0.67/0.97 % set(auto2) -> clear(echo_input).
% 0.67/0.97 % set(auto2) -> set(quiet).
% 0.67/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.97 % set(auto2) -> clear(print_given).
% 0.67/0.97 assign(lrs_ticks,-1).
% 0.67/0.97 assign(sos_limit,10000).
% 0.67/0.97 assign(order,kbo).
% 0.67/0.97 set(lex_order_vars).
% 0.67/0.97 clear(print_given).
% 0.67/0.97
% 0.67/0.97 % formulas(sos). % not echoed (39 formulas)
% 0.67/0.97
% 0.67/0.97 ============================== end of input ==========================
% 0.67/0.97
% 0.67/0.97 % From the command line: assign(max_seconds, 300).
% 0.67/0.97
% 0.67/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.97
% 0.67/0.97 % Formulas that are not ordinary clauses:
% 0.67/0.97 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 2 (all A all B k3_xboole_0(A,B) = k3_xboole_0(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 3 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v12_waybel_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r1_orders_2(A,D,C) -> r2_hidden(D,B))))))))))) # label(d19_waybel_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 4 (all A (A = k1_xboole_0 <-> (all B -r2_hidden(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 5 (all A all B all C (C = k3_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,A) & r2_hidden(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 6 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 7 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 8 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 9 (all A (l1_orders_2(A) -> m1_subset_1(k3_yellow_0(A),u1_struct_0(A)))) # label(dt_k3_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 10 (all A (l1_orders_2(A) -> l1_struct_0(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 11 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 12 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 13 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 14 (exists A l1_orders_2(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 15 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 16 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 17 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 18 (all A all B k3_xboole_0(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 19 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 20 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 21 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 22 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 23 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v1_waybel_0(B,A) & v12_waybel_0(B,A))))) # label(rc9_waybel_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 24 (all A all B all C (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> (r3_orders_2(A,B,C) <-> r1_orders_2(A,B,C)))) # label(redefinition_r3_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 25 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 26 (all A all B all C (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> r3_orders_2(A,B,B))) # label(reflexivity_r3_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 27 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (r2_hidden(C,k3_xboole_0(u1_struct_0(A),u1_struct_0(B))) -> m1_subset_1(C,u1_struct_0(B)))))))) # label(t13_latsum_1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 28 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 29 (all A k3_xboole_0(A,k1_xboole_0) = k1_xboole_0) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 30 (all A all B (m1_subset_1(A,B) -> v1_xboole_0(B) | r2_hidden(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 31 (all A all B (m1_subset_1(A,k1_zfmisc_1(B)) <-> r1_tarski(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 32 (all A (-v3_struct_0(A) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_orders_2(A,k3_yellow_0(A),B))))) # label(t44_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 33 (all A all B all C (r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 34 (all A all B all C -(r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 35 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 36 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 37 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 38 -(all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B) -> (-v1_xboole_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) & m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B))) -> r2_hidden(k3_yellow_0(B),u1_struct_0(A))))))) # label(t20_latsum_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.67/0.98
% 0.67/0.98 ============================== end of process non-clausal formulas ===
% 0.67/0.98
% 0.67/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.67/0.98
% 0.67/0.98 ============================== PREDICATE ELIMINATION =================
% 0.67/0.98 39 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(17)].
% 0.67/0.98 40 l1_struct_0(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(15)].
% 0.67/0.98 41 l1_struct_0(c5) # label(rc3_struct_0) # label(axiom). [clausify(21)].
% 0.67/0.98 42 -l1_orders_2(A) | l1_struct_0(A) # label(dt_l1_orders_2) # label(axiom). [clausify(10)].
% 0.67/0.98 Derived: v3_struct_0(c2) | -v1_xboole_0(u1_struct_0(c2)). [resolve(39,b,40,a)].
% 0.67/0.98 Derived: v3_struct_0(c5) | -v1_xboole_0(u1_struct_0(c5)). [resolve(39,b,41,a)].
% 0.67/0.98 Derived: v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l1_orders_2(A). [resolve(39,b,42,b)].
% 0.67/0.98 43 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(f6(A)) # label(rc5_struct_0) # label(axiom). [clausify(22)].
% 0.67/0.98 Derived: v3_struct_0(c2) | -v1_xboole_0(f6(c2)). [resolve(43,b,40,a)].
% 0.67/0.98 Derived: v3_struct_0(c5) | -v1_xboole_0(f6(c5)). [resolve(43,b,41,a)].
% 0.67/0.98 Derived: v3_struct_0(A) | -v1_xboole_0(f6(A)) | -l1_orders_2(A). [resolve(43,b,42,b)].
% 0.67/0.98 44 v3_struct_0(A) | -l1_struct_0(A) | m1_subset_1(f6(A),k1_zfmisc_1(u1_struct_0(A))) # label(rc5_struct_0) # label(axiom). [clausify(22)].
% 0.67/0.98 Derived: v3_struct_0(c2) | m1_subset_1(f6(c2),k1_zfmisc_1(u1_struct_0(c2))). [resolve(44,b,40,a)].
% 0.67/0.98 Derived: v3_struct_0(c5) | m1_subset_1(f6(c5),k1_zfmisc_1(u1_struct_0(c5))). [resolve(44,b,41,a)].
% 0.67/0.98 Derived: v3_struct_0(A) | m1_subset_1(f6(A),k1_zfmisc_1(u1_struct_0(A))) | -l1_orders_2(A). [resolve(44,b,42,b)].
% 0.67/0.98 45 v3_struct_0(A) | -v2_orders_2(A) | -v3_orders_2(A) | -l1_orders_2(A) | -v1_xboole_0(f7(A)) # label(rc9_waybel_0) # label(axiom). [clausify(23)].
% 0.67/0.98 46 v2_orders_2(c6) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 0.67/0.98 47 v2_orders_2(c7) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 0.67/0.98 Derived: v3_struct_0(c6) | -v3_orders_2(c6) | -l1_orders_2(c6) | -v1_xboole_0(f7(c6)). [resolve(45,b,46,a)].
% 0.67/0.98 Derived: v3_struct_0(c7) | -v3_orders_2(c7) | -l1_orders_2(c7) | -v1_xboole_0(f7(c7)). [resolve(45,b,47,a)].
% 0.67/0.98 48 v3_struct_0(A) | -v2_orders_2(A) | -v3_orders_2(A) | -l1_orders_2(A) | v1_waybel_0(f7(A),A) # label(rc9_waybel_0) # label(axiom). [clausify(23)].
% 0.67/0.98 Derived: v3_struct_0(c6) | -v3_orders_2(c6) | -l1_orders_2(c6) | v1_waybel_0(f7(c6),c6). [resolve(48,b,46,a)].
% 0.67/0.98 Derived: v3_struct_0(c7) | -v3_orders_2(c7) | -l1_orders_2(c7) | v1_waybel_0(f7(c7),c7). [resolve(48,b,47,a)].
% 0.67/0.98 49 v3_struct_0(A) | -v2_orders_2(A) | -v3_orders_2(A) | -l1_orders_2(A) | v12_waybel_0(f7(A),A) # label(rc9_waybel_0) # label(axiom). [clausify(23)].
% 0.67/0.98 Derived: v3_struct_0(c6) | -v3_orders_2(c6) | -l1_orders_2(c6) | v12_waybel_0(f7(c6),c6). [resolve(49,b,46,a)].
% 0.67/0.98 Derived: v3_struct_0(c7) | -v3_orders_2(c7) | -l1_orders_2(c7) | v12_waybel_0(f7(c7),c7). [resolve(49,b,47,a)].
% 0.67/0.98 50 v3_struct_0(A) | -v2_orders_2(A) | -v3_orders_2(A) | -l1_orders_2(A) | m1_subset_1(f7(A),k1_zfmisc_1(u1_struct_0(A))) # label(rc9_waybel_0) # label(axiom). [clausify(23)].
% 0.67/0.98 Derived: v3_struct_0(c6) | -v3_orders_2(c6) | -l1_orders_2(c6) | m1_subset_1(f7(c6),k1_zfmisc_1(u1_struct_0(c6))). [resolve(50,b,46,a)].
% 0.67/0.98 Derived: v3_struct_0(c7) | -v3_orders_2(c7) | -l1_orders_2(c7) | m1_subset_1(f7(c7),k1_zfmisc_1(u1_struct_0(c7))). [resolve(50,b,47,a)].
% 0.67/0.98 51 v3_struct_0(A) | -v2_orders_2(A) | -l1_orders_2(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | r3_orders_2(A,B,B) # label(reflexivity_r3_orders_2) # label(axiom). [clausify(26)].
% 0.67/0.98 Derived: v3_struct_0(c6) | -l1_orders_2(c6) | -m1_subset_1(A,u1_struct_0(c6)) | -m1_subset_1(B,u1_struct_0(c6)) | r3_orders_2(c6,A,A). [resolve(51,b,46,a)].
% 0.67/0.98 Derived: v3_struct_0(c7) | -l1_orders_2(c7) | -m1_subset_1(A,u1_struct_0(c7)) | -m1_subset_1(B,u1_struct_0(c7)) | r3_orders_2(c7,A,A). [resolve(51,b,47,a)].
% 0.67/0.98 52 v3_struct_0(A) | -v2_orders_2(A) | -l1_orders_2(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | -r3_orders_2(A,B,C) | r1_orders_2(A,B,C) # label(redefinition_r3_orders_2) # label(axiom). [clausify(24)].
% 0.67/0.98 Derived: v3_struct_0(c6) | -l1_orders_2(c6) | -m1_subset_1(A,u1_struct_0(c6)) | -m1_subset_1(B,u1_struct_0(c6)) | -r3_orders_2(c6,A,B) | r1_orders_2(c6,A,B). [resolve(52,b,46,a)].
% 0.67/0.98 Derived: v3_struct_0(c7) | -l1_orders_2(c7) | -m1_subset_1(A,u1_struct_0(c7)) | -m1_subset_1(B,u1_struct_0(c7)) | -r3_orders_2(c7,A,B) | r1_orders_2(c7,A,B). [resolve(52,b,47,a)].
% 0.67/0.98 53 v3_struct_0(A) | -v2_orders_2(A) | -l1_orders_2(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | r3_orders_2(A,B,C) | -r1_orders_2(A,B,C) # label(redefinition_r3_orders_2) # label(axiom). [clausify(24)].
% 0.67/0.98 Derived: v3_struct_0(c6) | -l1_orders_2(c6) | -m1_subset_1(A,u1_struct_0(c6)) | -m1_subset_1(B,u1_struct_0(c6)) | r3_orders_2(c6,A,B) | -r1_orders_2(c6,A,B). [resolve(53,b,46,a)].
% 0.67/0.98 Derived: v3_struct_0(c7) | -l1_orders_2(c7) | -m1_subset_1(A,u1_struct_0(c7)) | -m1_subset_1(B,u1_struct_0(c7)) | r3_orders_2(c7,A,B) | -r1_orders_2(c7,A,B). [resolve(53,b,47,a)].
% 0.67/0.98 54 v3_struct_0(A) | -v4_orders_2(A) | -v1_yellow_0(A) | -l1_orders_2(A) | -m1_subset_1(B,u1_struct_0(A)) | r1_orders_2(A,k3_yellow_0(A),B) # label(t44_yellow_0) # label(axiom). [clausify(32)].
% 0.67/0.98 55 v4_orders_2(c6) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 0.67/0.98 56 v4_orders_2(c7) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 0.67/0.98 Derived: v3_struct_0(c6) | -v1_yellow_0(c6) | -l1_orders_2(c6) | -m1_subset_1(A,u1_struct_0(c6)) | r1_orders_2(c6,k3_yellow_0(c6),A). [resolve(54,b,55,a)].
% 0.67/0.98 Derived: v3_struct_0(c7) | -v1_yellow_0(c7) | -l1_orders_2(c7) | -m1_subset_1(A,u1_struct_0(c7)) | r1_orders_2(c7,k3_yellow_0(c7),A). [resolve(54,b,56,a)].
% 0.67/0.98 57 m1_subset_1(A,k1_zfmisc_1(B)) | -r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(31)].
% 0.67/0.98 58 r1_tarski(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(25)].
% 0.67/0.98 59 -m1_subset_1(A,k1_zfmisc_1(B)) | r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(31)].
% 0.67/0.98 Derived: m1_subset_1(A,k1_zfmisc_1(A)). [resolve(57,b,58,a)].
% 0.67/0.98 60 -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v12_waybel_0(B,A) | -m1_subset_1(C,u1_struct_0(A)) | -m1_subset_1(D,u1_struct_0(A)) | -r2_hidden(C,B) | -r1_orders_2(A,D,C) | r2_hidden(D,B) # label(d19_waybel_0) # label(axiom). [clausify(3)].
% 0.67/0.98 61 v12_waybel_0(k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)),c7) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 0.67/0.98 62 -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | v12_waybel_0(B,A) | r2_hidden(f1(A,B),B) # label(d19_waybel_0) # label(axiom). [clausify(3)].
% 0.67/0.98 63 -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | v12_waybel_0(B,A) | -r2_hidden(f2(A,B),B) # label(d19_waybel_0) # label(axiom). [clausify(3)].
% 0.67/0.98 64 -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | v12_waybel_0(B,A) | m1_subset_1(f1(A,B),u1_struct_0(A)) # label(d19_waybel_0) # label(axiom). [clausify(3)].
% 0.67/0.98 65 -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | v12_waybel_0(B,A) | m1_subset_1(f2(A,B),u1_struct_0(A)) # label(d19_waybel_0) # label(axiom). [clausify(3)].
% 0.67/0.98 66 -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | v12_waybel_0(B,A) | r1_orders_2(A,f2(A,B),f1(A,B)) # label(d19_waybel_0) # label(axiom). [clausify(3)].
% 0.67/0.98 Derived: -l1_orders_2(c7) | -m1_subset_1(k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)),k1_zfmisc_1(u1_struct_0(c7))) | -m1_subset_1(A,u1_struct_0(c7)) | -m1_subset_1(B,u1_struct_0(c7)) | -r2_hidden(A,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))) | -r1_orders_2(c7,B,A) | r2_hidden(B,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))). [resolve(60,c,61,a)].
% 0.67/0.98 Derived: -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -m1_subset_1(C,u1_struct_0(A)) | -m1_subset_1(D,u1_struct_0(A)) | -r2_hidden(C,B) | -r1_orders_2(A,D,C) | r2_hidden(D,B) | -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | r2_hidden(f1(A,B),B). [resolve(60,c,62,c)].
% 0.67/0.98 Derived: -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -m1_subset_1(C,u1_struct_0(A)) | -m1_subset_1(D,u1_struct_0(A)) | -r2_hidden(C,B) | -r1_orders_2(A,D,C) | r2_hidden(D,B) | -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -r2_hidden(f2(A,B),B). [resolve(60,c,63,c)].
% 7.12/7.41 Derived: -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -m1_subset_1(C,u1_struct_0(A)) | -m1_subset_1(D,u1_struct_0(A)) | -r2_hidden(C,B) | -r1_orders_2(A,D,C) | r2_hidden(D,B) | -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m1_subset_1(f1(A,B),u1_struct_0(A)). [resolve(60,c,64,c)].
% 7.12/7.41 Derived: -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -m1_subset_1(C,u1_struct_0(A)) | -m1_subset_1(D,u1_struct_0(A)) | -r2_hidden(C,B) | -r1_orders_2(A,D,C) | r2_hidden(D,B) | -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m1_subset_1(f2(A,B),u1_struct_0(A)). [resolve(60,c,65,c)].
% 7.12/7.41 Derived: -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -m1_subset_1(C,u1_struct_0(A)) | -m1_subset_1(D,u1_struct_0(A)) | -r2_hidden(C,B) | -r1_orders_2(A,D,C) | r2_hidden(D,B) | -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | r1_orders_2(A,f2(A,B),f1(A,B)). [resolve(60,c,66,c)].
% 7.12/7.41 67 v3_struct_0(c6) | -v3_orders_2(c6) | -l1_orders_2(c6) | v12_waybel_0(f7(c6),c6). [resolve(49,b,46,a)].
% 7.12/7.41 Derived: v3_struct_0(c6) | -v3_orders_2(c6) | -l1_orders_2(c6) | -l1_orders_2(c6) | -m1_subset_1(f7(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m1_subset_1(A,u1_struct_0(c6)) | -m1_subset_1(B,u1_struct_0(c6)) | -r2_hidden(A,f7(c6)) | -r1_orders_2(c6,B,A) | r2_hidden(B,f7(c6)). [resolve(67,d,60,c)].
% 7.12/7.41 68 v3_struct_0(c7) | -v3_orders_2(c7) | -l1_orders_2(c7) | v12_waybel_0(f7(c7),c7). [resolve(49,b,47,a)].
% 7.12/7.41 Derived: v3_struct_0(c7) | -v3_orders_2(c7) | -l1_orders_2(c7) | -l1_orders_2(c7) | -m1_subset_1(f7(c7),k1_zfmisc_1(u1_struct_0(c7))) | -m1_subset_1(A,u1_struct_0(c7)) | -m1_subset_1(B,u1_struct_0(c7)) | -r2_hidden(A,f7(c7)) | -r1_orders_2(c7,B,A) | r2_hidden(B,f7(c7)). [resolve(68,d,60,c)].
% 7.12/7.41
% 7.12/7.41 ============================== end predicate elimination =============
% 7.12/7.41
% 7.12/7.41 Auto_denials: (non-Horn, no changes).
% 7.12/7.41
% 7.12/7.41 Term ordering decisions:
% 7.12/7.41 Function symbol KB weights: k1_xboole_0=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. k3_xboole_0=1. f1=1. f2=1. u1_struct_0=1. k1_zfmisc_1=1. k3_yellow_0=1. f3=1. f5=1. f6=1. f7=1. f4=1.
% 7.12/7.41
% 7.12/7.41 ============================== end of process initial clauses ========
% 7.12/7.41
% 7.12/7.41 ============================== CLAUSES FOR SEARCH ====================
% 7.12/7.41
% 7.12/7.41 ============================== end of clauses for search =============
% 7.12/7.41
% 7.12/7.41 ============================== SEARCH ================================
% 7.12/7.41
% 7.12/7.41 % Starting search at 0.03 seconds.
% 7.12/7.41
% 7.12/7.41 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 195 (0.00 of 0.37 sec).
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=47.000, iters=3369
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=41.000, iters=3409
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=39.000, iters=3339
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=37.000, iters=3398
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=35.000, iters=3407
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=32.000, iters=3348
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=31.000, iters=3357
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=30.000, iters=3381
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=29.000, iters=3366
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=23.000, iters=3371
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=21.000, iters=3343
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=20.000, iters=3342
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=19.000, iters=3367
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=18.000, iters=3333
% 7.12/7.41
% 7.12/7.41 Low Water (keep): wt=17.000, iters=3344
% 7.12/7.41
% 7.12/7.41 ============================== PROOF =================================
% 7.12/7.41 % SZS status Theorem
% 7.12/7.41 % SZS output start Refutation
% 7.12/7.41
% 7.12/7.41 % Proof 1 at 6.41 (+ 0.04) seconds.
% 7.12/7.41 % Length of proof is 90.
% 7.12/7.41 % Level of proof is 12.
% 7.12/7.41 % Maximum clause weight is 30.000.
% 7.12/7.41 % Given clauses 2301.
% 7.12/7.41
% 7.12/7.41 2 (all A all B k3_xboole_0(A,B) = k3_xboole_0(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 3 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v12_waybel_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r1_orders_2(A,D,C) -> r2_hidden(D,B))))))))))) # label(d19_waybel_0) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 4 (all A (A = k1_xboole_0 <-> (all B -r2_hidden(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 5 (all A all B all C (C = k3_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,A) & r2_hidden(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 9 (all A (l1_orders_2(A) -> m1_subset_1(k3_yellow_0(A),u1_struct_0(A)))) # label(dt_k3_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 10 (all A (l1_orders_2(A) -> l1_struct_0(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 16 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 17 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 18 (all A all B k3_xboole_0(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 27 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (r2_hidden(C,k3_xboole_0(u1_struct_0(A),u1_struct_0(B))) -> m1_subset_1(C,u1_struct_0(B)))))))) # label(t13_latsum_1) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 28 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 29 (all A k3_xboole_0(A,k1_xboole_0) = k1_xboole_0) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 30 (all A all B (m1_subset_1(A,B) -> v1_xboole_0(B) | r2_hidden(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 32 (all A (-v3_struct_0(A) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_orders_2(A,k3_yellow_0(A),B))))) # label(t44_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 33 (all A all B all C (r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 36 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.41 38 -(all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B) -> (-v1_xboole_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B))) & v1_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) & v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) & m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B))) -> r2_hidden(k3_yellow_0(B),u1_struct_0(A))))))) # label(t20_latsum_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 7.12/7.41 39 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(17)].
% 7.12/7.41 42 -l1_orders_2(A) | l1_struct_0(A) # label(dt_l1_orders_2) # label(axiom). [clausify(10)].
% 7.12/7.41 54 v3_struct_0(A) | -v4_orders_2(A) | -v1_yellow_0(A) | -l1_orders_2(A) | -m1_subset_1(B,u1_struct_0(A)) | r1_orders_2(A,k3_yellow_0(A),B) # label(t44_yellow_0) # label(axiom). [clausify(32)].
% 7.12/7.41 56 v4_orders_2(c7) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 7.12/7.41 60 -l1_orders_2(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v12_waybel_0(B,A) | -m1_subset_1(C,u1_struct_0(A)) | -m1_subset_1(D,u1_struct_0(A)) | -r2_hidden(C,B) | -r1_orders_2(A,D,C) | r2_hidden(D,B) # label(d19_waybel_0) # label(axiom). [clausify(3)].
% 7.12/7.41 61 v12_waybel_0(k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)),c7) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 7.12/7.41 70 v1_xboole_0(k1_xboole_0) # label(fc1_xboole_0) # label(axiom). [assumption].
% 7.12/7.41 74 l1_orders_2(c6) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 7.12/7.41 76 v1_yellow_0(c7) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 7.12/7.41 77 l1_orders_2(c7) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 7.12/7.41 78 m1_subset_1(f5(A),A) # label(existence_m1_subset_1) # label(axiom). [clausify(16)].
% 7.12/7.41 79 k3_xboole_0(A,A) = A # label(idempotence_k3_xboole_0) # label(axiom). [clausify(18)].
% 7.12/7.41 80 k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 # label(t2_boole) # label(axiom). [clausify(29)].
% 7.12/7.41 81 k3_xboole_0(A,B) = k3_xboole_0(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(2)].
% 7.12/7.41 83 m1_subset_1(k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)),k1_zfmisc_1(u1_struct_0(c7))) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 7.12/7.41 84 k3_xboole_0(A,B) = C | r2_hidden(f4(A,B,C),C) | r2_hidden(f4(A,B,C),A) # label(d3_xboole_0) # label(axiom). [clausify(5)].
% 7.12/7.41 85 k3_xboole_0(A,B) = C | r2_hidden(f4(A,B,C),C) | r2_hidden(f4(A,B,C),B) # label(d3_xboole_0) # label(axiom). [clausify(5)].
% 7.12/7.41 88 -v3_struct_0(c6) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 7.12/7.41 89 -v3_struct_0(c7) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 7.12/7.41 90 -r2_hidden(A,B) | -v1_xboole_0(B) # label(t7_boole) # label(axiom). [clausify(36)].
% 7.12/7.41 91 -r2_hidden(k3_yellow_0(c7),u1_struct_0(c6)) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 7.12/7.41 93 k1_xboole_0 != A | -r2_hidden(B,A) # label(d1_xboole_0) # label(axiom). [clausify(4)].
% 7.12/7.41 94 -v1_xboole_0(k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))) # label(t20_latsum_1) # label(negated_conjecture). [clausify(38)].
% 7.12/7.41 97 -r2_hidden(A,B) | m1_subset_1(A,B) # label(t1_subset) # label(axiom). [clausify(28)].
% 7.12/7.41 98 -l1_orders_2(A) | m1_subset_1(k3_yellow_0(A),u1_struct_0(A)) # label(dt_k3_yellow_0) # label(axiom). [clausify(9)].
% 7.12/7.41 100 -m1_subset_1(A,B) | v1_xboole_0(B) | r2_hidden(A,B) # label(t2_subset) # label(axiom). [clausify(30)].
% 7.12/7.41 101 -r2_hidden(A,B) | -m1_subset_1(B,k1_zfmisc_1(C)) | m1_subset_1(A,C) # label(t4_subset) # label(axiom). [clausify(33)].
% 7.12/7.41 103 k3_xboole_0(A,B) != C | -r2_hidden(D,C) | r2_hidden(D,B) # label(d3_xboole_0) # label(axiom). [clausify(5)].
% 7.12/7.41 104 k3_xboole_0(A,B) != C | r2_hidden(D,C) | -r2_hidden(D,A) | -r2_hidden(D,B) # label(d3_xboole_0) # label(axiom). [clausify(5)].
% 7.12/7.41 105 v3_struct_0(A) | -l1_orders_2(A) | v3_struct_0(B) | -l1_orders_2(B) | -r2_hidden(C,k3_xboole_0(u1_struct_0(A),u1_struct_0(B))) | m1_subset_1(C,u1_struct_0(B)) # label(t13_latsum_1) # label(axiom). [clausify(27)].
% 7.12/7.41 106 k3_xboole_0(A,B) = C | -r2_hidden(f4(A,B,C),C) | -r2_hidden(f4(A,B,C),A) | -r2_hidden(f4(A,B,C),B) # label(d3_xboole_0) # label(axiom). [clausify(5)].
% 7.12/7.41 110 v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l1_orders_2(A). [resolve(39,b,42,b)].
% 7.12/7.41 141 v3_struct_0(c7) | -v1_yellow_0(c7) | -l1_orders_2(c7) | -m1_subset_1(A,u1_struct_0(c7)) | r1_orders_2(c7,k3_yellow_0(c7),A). [resolve(54,b,56,a)].
% 7.12/7.41 142 -m1_subset_1(A,u1_struct_0(c7)) | r1_orders_2(c7,k3_yellow_0(c7),A). [copy(141),unit_del(a,89),unit_del(b,76),unit_del(c,77)].
% 7.12/7.41 144 -l1_orders_2(c7) | -m1_subset_1(k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)),k1_zfmisc_1(u1_struct_0(c7))) | -m1_subset_1(A,u1_struct_0(c7)) | -m1_subset_1(B,u1_struct_0(c7)) | -r2_hidden(A,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))) | -r1_orders_2(c7,B,A) | r2_hidden(B,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))). [resolve(60,c,61,a)].
% 7.12/7.41 145 -m1_subset_1(A,u1_struct_0(c7)) | -m1_subset_1(B,u1_struct_0(c7)) | -r2_hidden(A,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))) | -r1_orders_2(c7,B,A) | r2_hidden(B,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))). [copy(144),unit_del(a,77),unit_del(b,83)].
% 7.12/7.41 160 k3_xboole_0(A,B) = A | r2_hidden(f4(A,B,A),A). [factor(84,b,c)].
% 7.12/7.41 164 k3_xboole_0(A,B) = A | -r2_hidden(f4(A,B,A),A) | -r2_hidden(f4(A,B,A),B). [factor(106,b,c)].
% 7.12/7.41 173 -v1_xboole_0(A) | k3_xboole_0(A,B) = C | r2_hidden(f4(B,A,C),C). [resolve(90,a,85,c),rewrite([81(2)])].
% 7.12/7.41 178 -r2_hidden(A,k1_xboole_0). [ur(90,b,70,a)].
% 7.12/7.41 196 m1_subset_1(f4(A,B,C),B) | k3_xboole_0(A,B) = C | r2_hidden(f4(A,B,C),C). [resolve(97,a,85,c)].
% 7.12/7.41 201 m1_subset_1(k3_yellow_0(c7),u1_struct_0(c7)). [resolve(98,a,77,a)].
% 7.12/7.41 205 v1_xboole_0(A) | r2_hidden(f5(A),A). [resolve(100,a,78,a)].
% 7.12/7.41 237 k3_xboole_0(A,B) != C | r2_hidden(f4(B,D,E),C) | -r2_hidden(f4(B,D,E),A) | k3_xboole_0(B,D) = E | r2_hidden(f4(B,D,E),E). [resolve(104,d,84,c)].
% 7.12/7.41 246 k3_xboole_0(A,B) != C | r2_hidden(f4(B,D,C),C) | -r2_hidden(f4(B,D,C),A) | k3_xboole_0(B,D) = C. [factor(237,b,e)].
% 7.12/7.41 257 -v1_xboole_0(u1_struct_0(c7)). [ur(110,a,89,a,c,77,a)].
% 7.12/7.41 258 -v1_xboole_0(u1_struct_0(c6)). [ur(110,a,88,a,c,74,a)].
% 7.12/7.41 310 k3_xboole_0(A,B) = A | -r2_hidden(f4(A,B,A),B). [resolve(164,b,160,b),merge(c)].
% 7.12/7.41 314 k1_xboole_0 = A | r2_hidden(f4(B,k1_xboole_0,A),A). [resolve(173,a,70,a),rewrite([81(2),80(2)])].
% 7.12/7.41 316 k1_xboole_0 = A | r2_hidden(f4(k1_xboole_0,B,A),A). [resolve(178,a,84,c),rewrite([81(2),80(2)])].
% 7.12/7.41 320 -m1_subset_1(k3_yellow_0(c7),u1_struct_0(c6)). [ur(100,b,258,a,c,91,a)].
% 7.12/7.41 372 v1_xboole_0(A) | k1_xboole_0 != A. [resolve(205,b,93,b)].
% 7.12/7.41 382 k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)) != k1_xboole_0. [ur(372,a,94,a),flip(a)].
% 7.12/7.41 451 -r2_hidden(k3_yellow_0(c7),k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))). [ur(105,a,89,a,b,77,a,c,88,a,d,74,a,f,320,a),rewrite([81(7)])].
% 7.12/7.41 537 k1_xboole_0 = A | -m1_subset_1(A,k1_zfmisc_1(B)) | m1_subset_1(f4(C,k1_xboole_0,A),B). [resolve(314,b,101,a)].
% 7.12/7.41 544 k1_xboole_0 = A | k3_xboole_0(B,C) != A | r2_hidden(f4(k1_xboole_0,D,A),C). [resolve(316,b,103,b)].
% 7.12/7.41 546 k1_xboole_0 = A | -m1_subset_1(A,k1_zfmisc_1(B)) | m1_subset_1(f4(k1_xboole_0,C,A),B). [resolve(316,b,101,a)].
% 7.12/7.41 681 m1_subset_1(f4(A,B,C),B) | k3_xboole_0(A,B) = C | -m1_subset_1(C,k1_zfmisc_1(D)) | m1_subset_1(f4(A,B,C),D). [resolve(196,c,101,a)].
% 7.12/7.41 3189 m1_subset_1(f4(A,k1_xboole_0,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))),u1_struct_0(c7)). [resolve(537,b,83,a),flip(a),unit_del(a,382)].
% 7.12/7.41 3347 r1_orders_2(c7,k3_yellow_0(c7),f4(A,k1_xboole_0,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)))). [resolve(3189,a,142,a)].
% 7.12/7.41 3348 r2_hidden(f4(A,k1_xboole_0,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))),u1_struct_0(c7)). [resolve(3189,a,100,a),unit_del(a,257)].
% 7.12/7.41 3418 k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)) != k3_xboole_0(A,u1_struct_0(c7)) | r2_hidden(f4(A,k1_xboole_0,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))),k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))). [resolve(3348,a,246,c),rewrite([81(3),80(24)]),flip(a),flip(c),unit_del(c,382)].
% 7.12/7.41 3552 -r2_hidden(f4(A,k1_xboole_0,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))),k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))). [resolve(3347,a,145,d),unit_del(a,3189),unit_del(b,201),unit_del(d,451)].
% 7.12/7.41 3557 k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)) != k3_xboole_0(A,u1_struct_0(c7)). [back_unit_del(3418),unit_del(b,3552)].
% 7.12/7.41 3738 m1_subset_1(f4(k1_xboole_0,A,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))),u1_struct_0(c7)). [resolve(546,b,83,a),flip(a),unit_del(a,382)].
% 7.12/7.41 4033 r1_orders_2(c7,k3_yellow_0(c7),f4(k1_xboole_0,A,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)))). [resolve(3738,a,142,a)].
% 7.12/7.41 4100 -r2_hidden(f4(k1_xboole_0,A,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))),k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))). [resolve(4033,a,145,d),unit_del(a,3738),unit_del(b,201),unit_del(d,451)].
% 7.12/7.41 4390 k1_xboole_0 = A | B != A | r2_hidden(f4(k1_xboole_0,C,A),B). [para(79(a,1),544(b,1))].
% 7.12/7.41 6280 m1_subset_1(f4(A,B,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))),B) | k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)) = k3_xboole_0(A,B) | m1_subset_1(f4(A,B,k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))),u1_struct_0(c7)). [resolve(681,c,83,a),flip(b)].
% 7.12/7.41 6305 m1_subset_1(f4(A,u1_struct_0(c7),k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))),u1_struct_0(c7)). [factor(6280,a,c),unit_del(b,3557)].
% 7.12/7.41 6313 r2_hidden(f4(A,u1_struct_0(c7),k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))),u1_struct_0(c7)). [resolve(6305,a,100,a),unit_del(a,257)].
% 7.12/7.41 6315 k3_xboole_0(u1_struct_0(c7),k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7))) = k3_xboole_0(u1_struct_0(c6),u1_struct_0(c7)). [resolve(6313,a,310,b),rewrite([81(8)])].
% 7.12/7.41 10872 $F. [resolve(6315,a,4390,b),rewrite([6315(22)]),flip(a),unit_del(a,382),unit_del(b,4100)].
% 7.12/7.41
% 7.12/7.41 % SZS output end Refutation
% 7.12/7.41 ============================== end of proof ==========================
% 7.12/7.41
% 7.12/7.41 ============================== STATISTICS ============================
% 7.12/7.41
% 7.12/7.41 Given=2301. Generated=57228. Kept=10780. proofs=1.
% 7.12/7.41 Usable=2293. Sos=8372. Demods=7. Limbo=0, Disabled=218. Hints=0.
% 7.12/7.41 Megabytes=11.36.
% 7.12/7.41 User_CPU=6.41, System_CPU=0.04, Wall_clock=6.
% 7.12/7.41
% 7.12/7.41 ============================== end of statistics =====================
% 7.12/7.41
% 7.12/7.41 ============================== end of search =========================
% 7.12/7.41
% 7.12/7.41 THEOREM PROVED
% 7.12/7.41 % SZS status Theorem
% 7.12/7.41
% 7.12/7.41 Exiting with 1 proof.
% 7.12/7.41
% 7.12/7.41 Process 5808 exit (max_proofs) Mon Jun 20 00:52:44 2022
% 7.12/7.41 Prover9 interrupted
%------------------------------------------------------------------------------