TSTP Solution File: SEU407+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU407+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 13:31:37 EDT 2022
% Result : Theorem 1.65s 1.98s
% Output : Refutation 1.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU407+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 08:20:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/1.07 ============================== Prover9 ===============================
% 0.46/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.07 Process 8274 was started by sandbox2 on n015.cluster.edu,
% 0.46/1.07 Sun Jun 19 08:21:00 2022
% 0.46/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8013_n015.cluster.edu".
% 0.46/1.07 ============================== end of head ===========================
% 0.46/1.07
% 0.46/1.07 ============================== INPUT =================================
% 0.46/1.07
% 0.46/1.07 % Reading from file /tmp/Prover9_8013_n015.cluster.edu
% 0.46/1.07
% 0.46/1.07 set(prolog_style_variables).
% 0.46/1.07 set(auto2).
% 0.46/1.07 % set(auto2) -> set(auto).
% 0.46/1.07 % set(auto) -> set(auto_inference).
% 0.46/1.07 % set(auto) -> set(auto_setup).
% 0.46/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.07 % set(auto) -> set(auto_limits).
% 0.46/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.07 % set(auto) -> set(auto_denials).
% 0.46/1.07 % set(auto) -> set(auto_process).
% 0.46/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.07 % set(auto2) -> assign(stats, some).
% 0.46/1.07 % set(auto2) -> clear(echo_input).
% 0.46/1.07 % set(auto2) -> set(quiet).
% 0.46/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.07 % set(auto2) -> clear(print_given).
% 0.46/1.07 assign(lrs_ticks,-1).
% 0.46/1.07 assign(sos_limit,10000).
% 0.46/1.07 assign(order,kbo).
% 0.46/1.07 set(lex_order_vars).
% 0.46/1.07 clear(print_given).
% 0.46/1.07
% 0.46/1.07 % formulas(sos). % not echoed (55 formulas)
% 0.46/1.07
% 0.46/1.07 ============================== end of input ==========================
% 0.46/1.07
% 0.46/1.07 % From the command line: assign(max_seconds, 300).
% 0.46/1.07
% 0.46/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.07
% 0.46/1.07 % Formulas that are not ordinary clauses:
% 0.46/1.07 1 (all A (l1_orders_2(A) -> (v1_orders_2(A) -> A = g1_orders_2(u1_struct_0(A),u1_orders_2(A))))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 2 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 3 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> v1_relat_1(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 4 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 5 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C (v1_orders_2(C) & l1_orders_2(C) -> (C = k1_latsum_1(A,B) <-> u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) & u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B)))))))))) # label(d2_latsum_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 6 (all A all B all C (C = k2_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,A) | r2_hidden(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 7 (all A all B (m1_relset_1(B,A,A) -> v1_orders_2(g1_orders_2(A,B)) & l1_orders_2(g1_orders_2(A,B)))) # label(dt_g1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 8 (all A all B (l1_orders_2(A) & l1_orders_2(B) -> v1_orders_2(k1_latsum_1(A,B)) & l1_orders_2(k1_latsum_1(A,B)))) # label(dt_k1_latsum_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 9 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 10 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 11 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 12 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 13 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 14 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 15 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 16 (all A (l1_orders_2(A) -> l1_struct_0(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 17 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 18 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 19 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 20 (all A all B all C (m2_relset_1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 21 (all A (l1_orders_2(A) -> m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 22 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 23 (exists A l1_orders_2(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 24 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 25 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 26 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 27 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 28 (all A all B (l1_orders_2(A) & -v3_struct_0(B) & l1_orders_2(B) -> -v3_struct_0(k1_latsum_1(A,B)) & v1_orders_2(k1_latsum_1(A,B)))) # label(fc1_latsum_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 29 (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].
% 0.46/1.08 30 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & l1_orders_2(B) -> -v3_struct_0(k1_latsum_1(A,B)) & v1_orders_2(k1_latsum_1(A,B)))) # label(fc2_latsum_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 31 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 32 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 33 (all A all B (m1_relset_1(B,A,A) -> (all C all D (g1_orders_2(A,B) = g1_orders_2(C,D) -> A = C & B = D)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 34 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 35 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 36 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 37 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 38 (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].
% 0.46/1.08 39 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 40 (all A all B all C (m2_relset_1(C,A,B) <-> m1_relset_1(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 41 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 42 (all A k2_xboole_0(A,k1_xboole_0) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 43 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 44 (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].
% 0.46/1.08 45 (all A all B k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 46 (all A k4_xboole_0(A,k1_xboole_0) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 47 (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].
% 0.46/1.08 48 (all A k4_xboole_0(k1_xboole_0,A) = k1_xboole_0) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 49 (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].
% 0.46/1.08 50 (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].
% 0.46/1.08 51 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 52 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 53 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.08 54 -(all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) -> r2_hidden(C,u1_struct_0(A)) | r2_hidden(C,k4_xboole_0(u1_struct_0(B),u1_struct_0(A))))))))) # label(t7_latsum_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.08
% 0.46/1.08 ============================== end of process non-clausal formulas ===
% 0.46/1.08
% 0.46/1.08 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.08
% 0.46/1.08 ============================== PREDICATE ELIMINATION =================
% 0.46/1.08 55 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(29)].
% 0.46/1.08 56 l1_struct_0(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(24)].
% 0.46/1.08 57 l1_struct_0(c5) # label(rc3_struct_0) # label(axiom). [clausify(37)].
% 0.46/1.08 58 -l1_orders_2(A) | l1_struct_0(A) # label(dt_l1_orders_2) # label(axiom). [clausify(16)].
% 0.46/1.08 Derived: v3_struct_0(c2) | -v1_xboole_0(u1_struct_0(c2)). [resolve(55,b,56,a)].
% 0.46/1.08 Derived: v3_struct_0(c5) | -v1_xboole_0(u1_struct_0(c5)). [resolve(55,b,57,a)].
% 0.46/1.08 Derived: v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l1_orders_2(A). [resolve(55,b,58,b)].
% 0.46/1.08 59 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(f5(A)) # label(rc5_struct_0) # label(axiom). [clausify(38)].
% 0.46/1.08 Derived: v3_struct_0(c2) | -v1_xboole_0(f5(c2)). [resolve(59,b,56,a)].
% 0.46/1.08 Derived: v3_struct_0(c5) | -v1_xboole_0(f5(c5)). [resolve(59,b,57,a)].
% 0.46/1.08 Derived: v3_struct_0(A) | -v1_xboole_0(f5(A)) | -l1_orders_2(A). [resolve(59,b,58,b)].
% 0.46/1.08 60 v3_struct_0(A) | -l1_struct_0(A) | m1_subset_1(f5(A),k1_zfmisc_1(u1_struct_0(A))) # label(rc5_struct_0) # label(axiom). [clausify(38)].
% 0.46/1.08 Derived: v3_struct_0(c2) | m1_subset_1(f5(c2),k1_zfmisc_1(u1_struct_0(c2))). [resolve(60,b,56,a)].
% 0.46/1.08 Derived: v3_struct_0(c5) | m1_subset_1(f5(c5),k1_zfmisc_1(u1_struct_0(c5))). [resolve(60,b,57,a)].
% 0.46/1.08 Derived: v3_struct_0(A) | m1_subset_1(f5(A),k1_zfmisc_1(u1_struct_0(A))) | -l1_orders_2(A). [resolve(60,b,58,b)].
% 0.46/1.08 61 m1_subset_1(A,k1_zfmisc_1(B)) | -r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(47)].
% 0.46/1.08 62 r1_tarski(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(41)].
% 0.46/1.08 63 -m1_subset_1(A,k1_zfmisc_1(B)) | r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(47)].
% 0.46/1.08 Derived: m1_subset_1(A,k1_zfmisc_1(A)). [resolve(61,b,62,a)].
% 0.46/1.08 64 -m2_relset_1(A,B,C) | m1_relset_1(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(40)].
% 0.46/1.08 65 m2_relset_1(f4(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(27)].
% 0.46/1.08 Derived: m1_relset_1(f4(A,B),A,B). [resolve(64,a,65,a)].
% 0.46/1.08 66 m2_relset_1(A,B,C) | -m1_relset_1(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(40)].
% 0.46/1.08 67 -l1_orders_2(A) | m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) # label(dt_u1_orders_2) # label(axiom). [clausify(21)].
% 0.46/1.08 Derived: -l1_orders_2(A) | m1_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)). [resolve(67,b,64,a)].
% 0.46/1.08 68 -m2_relset_1(A,B,C) | m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(20)].
% 0.46/1.08 Derived: m1_subset_1(f4(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))). [resolve(68,a,65,a)].
% 0.46/1.08 Derived: m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) | -m1_relset_1(A,B,C). [resolve(68,a,66,a)].
% 0.46/1.08 Derived: m1_subset_1(u1_orders_2(A),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) | -l1_orders_2(A). [resolve(68,a,67,b)].
% 0.46/1.08 69 -m1_relset_1(A,B,C) | -m1_relset_1(D,E,F) | m2_relset_1(k7_relset_1(B,C,E,F,A,D),B,F) # label(dt_k7_relset_1) # label(axiom). [clausify(15)].
% 0.46/1.08 Derived: -m1_relset_1(A,B,C) | -m1_relset_1(D,E,F) | m1_relset_1(k7_relset_1(B,C,E,F,A,D),B,F). [resolve(69,c,64,a)].
% 0.46/1.08 Derived: -m1_relset_1(A,B,C) | -m1_relset_1(D,E,F) | m1_subset_1(k7_relset_1(B,C,E,F,A,D),k1_zfmisc_1(k2_zfmisc_1(B,F))). [resolve(69,c,68,a)].
% 0.46/1.08 70 -l1_orders_2(A) | -v1_orders_2(A) | g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = A # label(abstractness_v1_orders_2) # label(axiom). [clausify(1)].
% 0.46/1.08 71 -m1_relset_1(A,B,B) | v1_orders_2(g1_orders_2(B,A)) # label(dt_g1_orders_2) # label(axiom). [clausify(7)].
% 0.46/1.08 72 -l1_orders_2(A) | -l1_orders_2(B) | v1_orders_2(k1_latsum_1(A,B)) # label(dt_k1_latsum_1) # label(axiom). [clausify(8)].
% 0.46/1.08 73 -l1_orders_2(A) | v3_struct_0(B) | -l1_orders_2(B) | v1_orders_2(k1_latsum_1(A,B)) # label(fc1_latsum_1) # label(axiom). [clausify(28)].
% 0.46/1.08 74 v3_struct_0(A) | -l1_orders_2(A) | -l1_orders_2(B) | v1_orders_2(k1_latsum_1(A,B)) # label(fc2_latsum_1) # label(axiom). [clausify(30)].
% 0.46/1.08 Derived: -l1_orders_2(g1_orders_2(A,B)) | g1_orders_2(u1_struct_0(g1_orders_2(A,B)),u1_orders_2(g1_orders_2(A,B))) = g1_orders_2(A,B) | -m1_relset_1(B,A,A). [resolve(70,b,71,b)].
% 0.46/1.08 Derived: -l1_orders_2(k1_latsum_1(A,B)) | g1_orders_2(u1_struct_0(k1_latsum_1(A,B)),u1_orders_2(k1_latsum_1(A,B))) = k1_latsum_1(A,B) | -l1_orders_2(A) | -l1_orders_2(B). [resolve(70,b,72,c)].
% 0.46/1.08 75 -l1_orders_2(A) | -l1_orders_2(B) | -v1_orders_2(C) | -l1_orders_2(C) | k1_latsum_1(A,B) != C | k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) = u1_struct_0(C) # label(d2_latsum_1) # label(axiom). [clausify(5)].
% 0.46/1.08 Derived: -l1_orders_2(A) | -l1_orders_2(B) | -l1_orders_2(g1_orders_2(C,D)) | k1_latsum_1(A,B) != g1_orders_2(C,D) | k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) = u1_struct_0(g1_orders_2(C,D)) | -m1_relset_1(D,C,C). [resolve(75,c,71,b)].
% 0.46/1.08 Derived: -l1_orders_2(A) | -l1_orders_2(B) | -l1_orders_2(k1_latsum_1(C,D)) | k1_latsum_1(A,B) != k1_latsum_1(C,D) | k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) = u1_struct_0(k1_latsum_1(C,D)) | -l1_orders_2(C) | -l1_orders_2(D). [resolve(75,c,72,c)].
% 0.46/1.08 76 -l1_orders_2(A) | -l1_orders_2(B) | -v1_orders_2(C) | -l1_orders_2(C) | k1_latsum_1(A,B) != C | k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B))) = u1_orders_2(C) # label(d2_latsum_1) # label(axiom). [clausify(5)].
% 0.46/1.08 Derived: -l1_orders_2(A) | -l1_orders_2(B) | -l1_orders_2(g1_orders_2(C,D)) | k1_latsum_1(A,B) != g1_orders_2(C,D) | k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B))) = u1_orders_2(g1_orders_2(C,D)) | -m1_relset_1(D,C,C). [resolve(76,c,71,b)].
% 0.46/1.08 Derived: -l1_orders_2(A) | -l1_orders_2(B) | -l1_orders_2(k1_latsum_1(C,D)) | k1_latsum_1(A,B) != k1_latsum_1(C,D) | k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B))) = u1_orders_2(k1_latsum_1(C,D)) | -l1_orders_2(C) | -l1_orders_2(D). [resolve(76,c,72,c)].
% 0.46/1.08 77 -l1_orders_2(A) | -l1_orders_2(B) | -v1_orders_2(C) | -l1_orders_2(C) | k1_latsum_1(A,B) = C | k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) != u1_struct_0(C) | k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B))) != u1_orders_2(C) # label(d2_latsum_1) # label(axiom). [clausify(5)].
% 1.65/1.98 Derived: -l1_orders_2(A) | -l1_orders_2(B) | -l1_orders_2(g1_orders_2(C,D)) | k1_latsum_1(A,B) = g1_orders_2(C,D) | k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) != u1_struct_0(g1_orders_2(C,D)) | k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B))) != u1_orders_2(g1_orders_2(C,D)) | -m1_relset_1(D,C,C). [resolve(77,c,71,b)].
% 1.65/1.98 Derived: -l1_orders_2(A) | -l1_orders_2(B) | -l1_orders_2(k1_latsum_1(C,D)) | k1_latsum_1(A,B) = k1_latsum_1(C,D) | k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) != u1_struct_0(k1_latsum_1(C,D)) | k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B))) != u1_orders_2(k1_latsum_1(C,D)) | -l1_orders_2(C) | -l1_orders_2(D). [resolve(77,c,72,c)].
% 1.65/1.98
% 1.65/1.98 ============================== end predicate elimination =============
% 1.65/1.98
% 1.65/1.98 Auto_denials: (non-Horn, no changes).
% 1.65/1.98
% 1.65/1.98 Term ordering decisions:
% 1.65/1.98 Function symbol KB weights: k1_xboole_0=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. k2_xboole_0=1. k1_latsum_1=1. g1_orders_2=1. k2_zfmisc_1=1. k4_xboole_0=1. k5_relat_1=1. f2=1. f4=1. u1_struct_0=1. u1_orders_2=1. k1_zfmisc_1=1. f3=1. f5=1. f1=1. k7_relset_1=1.
% 1.65/1.98
% 1.65/1.98 ============================== end of process initial clauses ========
% 1.65/1.98
% 1.65/1.98 ============================== CLAUSES FOR SEARCH ====================
% 1.65/1.98
% 1.65/1.98 ============================== end of clauses for search =============
% 1.65/1.98
% 1.65/1.98 ============================== SEARCH ================================
% 1.65/1.98
% 1.65/1.98 % Starting search at 0.05 seconds.
% 1.65/1.98
% 1.65/1.98 ============================== PROOF =================================
% 1.65/1.98 % SZS status Theorem
% 1.65/1.98 % SZS output start Refutation
% 1.65/1.98
% 1.65/1.98 % Proof 1 at 0.92 (+ 0.01) seconds.
% 1.65/1.98 % Length of proof is 43.
% 1.65/1.98 % Level of proof is 8.
% 1.65/1.98 % Maximum clause weight is 29.000.
% 1.65/1.98 % Given clauses 207.
% 1.65/1.98
% 1.65/1.98 4 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.98 5 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C (v1_orders_2(C) & l1_orders_2(C) -> (C = k1_latsum_1(A,B) <-> u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) & u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B)))))))))) # label(d2_latsum_1) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.98 6 (all A all B all C (C = k2_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,A) | r2_hidden(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.98 8 (all A all B (l1_orders_2(A) & l1_orders_2(B) -> v1_orders_2(k1_latsum_1(A,B)) & l1_orders_2(k1_latsum_1(A,B)))) # label(dt_k1_latsum_1) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.98 16 (all A (l1_orders_2(A) -> l1_struct_0(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.98 28 (all A all B (l1_orders_2(A) & -v3_struct_0(B) & l1_orders_2(B) -> -v3_struct_0(k1_latsum_1(A,B)) & v1_orders_2(k1_latsum_1(A,B)))) # label(fc1_latsum_1) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.98 29 (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].
% 1.65/1.98 44 (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].
% 1.65/1.98 45 (all A all B k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 1.65/1.98 54 -(all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) -> r2_hidden(C,u1_struct_0(A)) | r2_hidden(C,k4_xboole_0(u1_struct_0(B),u1_struct_0(A))))))))) # label(t7_latsum_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.65/1.98 55 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(29)].
% 1.65/1.98 58 -l1_orders_2(A) | l1_struct_0(A) # label(dt_l1_orders_2) # label(axiom). [clausify(16)].
% 1.65/1.98 72 -l1_orders_2(A) | -l1_orders_2(B) | v1_orders_2(k1_latsum_1(A,B)) # label(dt_k1_latsum_1) # label(axiom). [clausify(8)].
% 1.65/1.98 75 -l1_orders_2(A) | -l1_orders_2(B) | -v1_orders_2(C) | -l1_orders_2(C) | k1_latsum_1(A,B) != C | k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) = u1_struct_0(C) # label(d2_latsum_1) # label(axiom). [clausify(5)].
% 1.65/1.98 81 l1_orders_2(c6) # label(t7_latsum_1) # label(negated_conjecture). [clausify(54)].
% 1.65/1.98 82 l1_orders_2(c7) # label(t7_latsum_1) # label(negated_conjecture). [clausify(54)].
% 1.65/1.98 89 m1_subset_1(c8,u1_struct_0(k1_latsum_1(c6,c7))) # label(t7_latsum_1) # label(negated_conjecture). [clausify(54)].
% 1.65/1.98 90 k2_xboole_0(A,B) = k2_xboole_0(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(4)].
% 1.65/1.98 91 k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) # label(t39_xboole_1) # label(axiom). [clausify(45)].
% 1.65/1.98 96 -v3_struct_0(c7) # label(t7_latsum_1) # label(negated_conjecture). [clausify(54)].
% 1.65/1.98 97 -r2_hidden(c8,u1_struct_0(c6)) # label(t7_latsum_1) # label(negated_conjecture). [clausify(54)].
% 1.65/1.98 100 -r2_hidden(c8,k4_xboole_0(u1_struct_0(c7),u1_struct_0(c6))) # label(t7_latsum_1) # label(negated_conjecture). [clausify(54)].
% 1.65/1.98 109 -l1_orders_2(A) | -l1_orders_2(B) | l1_orders_2(k1_latsum_1(A,B)) # label(dt_k1_latsum_1) # label(axiom). [clausify(8)].
% 1.65/1.98 111 -m1_subset_1(A,B) | v1_xboole_0(B) | r2_hidden(A,B) # label(t2_subset) # label(axiom). [clausify(44)].
% 1.65/1.98 112 -l1_orders_2(A) | v3_struct_0(B) | -l1_orders_2(B) | -v3_struct_0(k1_latsum_1(A,B)) # label(fc1_latsum_1) # label(axiom). [clausify(28)].
% 1.65/1.98 117 k2_xboole_0(A,B) != C | -r2_hidden(D,C) | r2_hidden(D,A) | r2_hidden(D,B) # label(d2_xboole_0) # label(axiom). [clausify(6)].
% 1.65/1.98 127 v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l1_orders_2(A). [resolve(55,b,58,b)].
% 1.65/1.98 147 -l1_orders_2(A) | -l1_orders_2(B) | -l1_orders_2(k1_latsum_1(C,D)) | k1_latsum_1(A,B) != k1_latsum_1(C,D) | k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) = u1_struct_0(k1_latsum_1(C,D)) | -l1_orders_2(C) | -l1_orders_2(D). [resolve(75,c,72,c)].
% 1.65/1.98 171 -l1_orders_2(A) | -l1_orders_2(B) | -l1_orders_2(k1_latsum_1(A,C)) | k1_latsum_1(A,B) != k1_latsum_1(A,C) | k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) = u1_struct_0(k1_latsum_1(A,C)) | -l1_orders_2(C). [factor(147,a,f)].
% 1.65/1.98 207 -l1_orders_2(A) | -l1_orders_2(B) | -l1_orders_2(k1_latsum_1(A,B)) | k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) = u1_struct_0(k1_latsum_1(A,B)). [factor(171,b,f),xx(d)].
% 1.65/1.98 284 -l1_orders_2(A) | l1_orders_2(k1_latsum_1(c7,A)). [resolve(109,a,82,a)].
% 1.65/1.98 285 -l1_orders_2(A) | l1_orders_2(k1_latsum_1(c6,A)). [resolve(109,a,81,a)].
% 1.65/1.98 290 v1_xboole_0(u1_struct_0(k1_latsum_1(c6,c7))) | r2_hidden(c8,u1_struct_0(k1_latsum_1(c6,c7))). [resolve(111,a,89,a)].
% 1.65/1.98 294 -v3_struct_0(k1_latsum_1(c6,c7)). [ur(112,a,81,a,b,96,a,c,82,a)].
% 1.65/1.98 334 -r2_hidden(c8,k2_xboole_0(u1_struct_0(c6),u1_struct_0(c7))). [ur(117,a,91,a,c,97,a,d,100,a)].
% 1.65/1.98 1086 l1_orders_2(k1_latsum_1(c7,c6)). [resolve(284,a,81,a)].
% 1.65/1.98 1121 k2_xboole_0(u1_struct_0(c6),u1_struct_0(c7)) = u1_struct_0(k1_latsum_1(c7,c6)). [resolve(1086,a,207,c),rewrite([90(9)]),unit_del(a,82),unit_del(b,81)].
% 1.65/1.98 1212 -r2_hidden(c8,u1_struct_0(k1_latsum_1(c7,c6))). [back_rewrite(334),rewrite([1121(6)])].
% 1.65/1.98 1359 l1_orders_2(k1_latsum_1(c6,c7)). [resolve(285,a,82,a)].
% 1.65/1.98 1405 u1_struct_0(k1_latsum_1(c7,c6)) = u1_struct_0(k1_latsum_1(c6,c7)). [resolve(1359,a,207,c),rewrite([1121(9)]),unit_del(a,81),unit_del(b,82)].
% 1.65/1.98 1479 -v1_xboole_0(u1_struct_0(k1_latsum_1(c6,c7))). [ur(127,a,294,a,c,1359,a)].
% 1.65/1.98 1511 -r2_hidden(c8,u1_struct_0(k1_latsum_1(c6,c7))). [back_rewrite(1212),rewrite([1405(5)])].
% 1.65/1.98 1614 $F. [back_unit_del(290),unit_del(a,1479),unit_del(b,1511)].
% 1.65/1.98
% 1.65/1.98 % SZS output end Refutation
% 1.65/1.98 ============================== end of proof ==========================
% 1.65/1.98
% 1.65/1.98 ============================== STATISTICS ============================
% 1.65/1.98
% 1.65/1.98 Given=207. Generated=2891. Kept=1531. proofs=1.
% 1.65/1.98 Usable=204. Sos=1018. Demods=29. Limbo=135, Disabled=267. Hints=0.
% 1.65/1.98 Megabytes=2.34.
% 1.65/1.98 User_CPU=0.92, System_CPU=0.01, Wall_clock=1.
% 1.65/1.98
% 1.65/1.98 ============================== end of statistics =====================
% 1.65/1.98
% 1.65/1.98 ============================== end of search =========================
% 1.65/1.98
% 1.65/1.98 THEOREM PROVED
% 1.65/1.98 % SZS status Theorem
% 1.65/1.98
% 1.65/1.98 Exiting with 1 proof.
% 1.65/1.98
% 1.65/1.98 Process 8274 exit (max_proofs) Sun Jun 19 08:21:01 2022
% 1.65/1.99 Prover9 interrupted
%------------------------------------------------------------------------------