TSTP Solution File: SEU310+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU310+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 13:30:51 EDT 2022
% Result : Theorem 1.28s 1.63s
% Output : Refutation 1.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU310+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % 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 : Sat Jun 18 23:06:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.74/1.02 ============================== Prover9 ===============================
% 0.74/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.02 Process 22450 was started by sandbox2 on n016.cluster.edu,
% 0.74/1.02 Sat Jun 18 23:06:53 2022
% 0.74/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22296_n016.cluster.edu".
% 0.74/1.02 ============================== end of head ===========================
% 0.74/1.02
% 0.74/1.02 ============================== INPUT =================================
% 0.74/1.02
% 0.74/1.02 % Reading from file /tmp/Prover9_22296_n016.cluster.edu
% 0.74/1.02
% 0.74/1.02 set(prolog_style_variables).
% 0.74/1.02 set(auto2).
% 0.74/1.02 % set(auto2) -> set(auto).
% 0.74/1.02 % set(auto) -> set(auto_inference).
% 0.74/1.02 % set(auto) -> set(auto_setup).
% 0.74/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.02 % set(auto) -> set(auto_limits).
% 0.74/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.02 % set(auto) -> set(auto_denials).
% 0.74/1.02 % set(auto) -> set(auto_process).
% 0.74/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.02 % set(auto2) -> assign(stats, some).
% 0.74/1.02 % set(auto2) -> clear(echo_input).
% 0.74/1.02 % set(auto2) -> set(quiet).
% 0.74/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.02 % set(auto2) -> clear(print_given).
% 0.74/1.02 assign(lrs_ticks,-1).
% 0.74/1.02 assign(sos_limit,10000).
% 0.74/1.02 assign(order,kbo).
% 0.74/1.02 set(lex_order_vars).
% 0.74/1.02 clear(print_given).
% 0.74/1.02
% 0.74/1.02 % formulas(sos). % not echoed (36 formulas)
% 0.74/1.02
% 0.74/1.02 ============================== end of input ==========================
% 0.74/1.02
% 0.74/1.02 % From the command line: assign(max_seconds, 300).
% 0.74/1.02
% 0.74/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.02
% 0.74/1.02 % Formulas that are not ordinary clauses:
% 0.74/1.02 1 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 2 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 3 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 4 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 5 (exists A (-empty(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 6 (all A (v1_membered(A) -> (all B (element(B,A) -> v1_xcmplx_0(B))))) # label(cc10_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 7 (all A (v2_membered(A) -> (all B (element(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B))))) # label(cc11_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 8 (all A (v3_membered(A) -> (all B (element(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 9 (all A (v4_membered(A) -> (all B (element(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 10 (all A (v5_membered(A) -> (all B (element(B,A) -> v1_xcmplx_0(B) & natural(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 11 (all A (v1_membered(A) -> (all B (element(B,powerset(A)) -> v1_membered(B))))) # label(cc16_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 12 (all A (v2_membered(A) -> (all B (element(B,powerset(A)) -> v1_membered(B) & v2_membered(B))))) # label(cc17_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 13 (all A (v3_membered(A) -> (all B (element(B,powerset(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 14 (all A (v4_membered(A) -> (all B (element(B,powerset(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 15 (all A (v5_membered(A) -> (all B (element(B,powerset(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 16 (all A all B (v1_membered(A) -> v1_membered(set_difference(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 17 (all A all B (v2_membered(A) -> v1_membered(set_difference(A,B)) & v2_membered(set_difference(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 18 (all A all B (v3_membered(A) -> v1_membered(set_difference(A,B)) & v2_membered(set_difference(A,B)) & v3_membered(set_difference(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 19 (all A all B (v4_membered(A) -> v1_membered(set_difference(A,B)) & v2_membered(set_difference(A,B)) & v3_membered(set_difference(A,B)) & v4_membered(set_difference(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 20 (all A all B (v5_membered(A) -> v1_membered(set_difference(A,B)) & v2_membered(set_difference(A,B)) & v3_membered(set_difference(A,B)) & v4_membered(set_difference(A,B)) & v5_membered(set_difference(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 21 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 22 (all A (topological_space(A) & top_str(A) -> (exists B (element(B,powerset(the_carrier(A))) & closed_subset(B,A))))) # label(rc6_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 23 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 24 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 25 (all A (empty(A) -> v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 26 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 27 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 28 (all A (one_sorted_str(A) -> element(cast_as_carrier_subset(A),powerset(the_carrier(A))))) # label(dt_k2_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 29 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 30 (all A (top_str(A) -> one_sorted_str(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 31 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 32 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 33 (all A (topological_space(A) & top_str(A) -> closed_subset(cast_as_carrier_subset(A),A))) # label(fc5_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 34 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 35 (all A all B (topological_space(A) & top_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> ((all C all D all E (C = D & in(set_difference(cast_as_carrier_subset(A),D),B) & C = E & in(set_difference(cast_as_carrier_subset(A),E),B) -> D = E)) -> (exists C all D (in(D,C) <-> (exists E (in(E,powerset(the_carrier(A))) & E = D & in(set_difference(cast_as_carrier_subset(A),D),B)))))))) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 36 -(all A all B (topological_space(A) & top_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> (exists C all D (in(D,C) <-> in(D,powerset(the_carrier(A))) & in(set_difference(cast_as_carrier_subset(A),D),B))))) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.03
% 0.74/1.03 ============================== end of process non-clausal formulas ===
% 0.74/1.03
% 0.74/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.03
% 0.74/1.03 ============================== PREDICATE ELIMINATION =================
% 0.74/1.03 37 -topological_space(A) | -top_str(A) | closed_subset(f1(A),A) # label(rc6_pre_topc) # label(axiom). [clausify(22)].
% 0.74/1.03 38 topological_space(c2) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(negated_conjecture). [clausify(36)].
% 0.74/1.03 Derived: -top_str(c2) | closed_subset(f1(c2),c2). [resolve(37,a,38,a)].
% 0.74/1.03 39 -topological_space(A) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) # label(fc5_pre_topc) # label(axiom). [clausify(33)].
% 0.74/1.03 Derived: -top_str(c2) | closed_subset(cast_as_carrier_subset(c2),c2). [resolve(39,a,38,a)].
% 0.74/1.03 40 -topological_space(A) | -top_str(A) | element(f1(A),powerset(the_carrier(A))) # label(rc6_pre_topc) # label(axiom). [clausify(22)].
% 0.74/1.03 Derived: -top_str(c2) | element(f1(c2),powerset(the_carrier(c2))). [resolve(40,a,38,a)].
% 0.74/1.03 41 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f5(A,B) = f4(A,B) | -in(C,f7(A,B)) | f8(A,B,C) = C # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | f8(c2,A,B) = B. [resolve(41,a,38,a)].
% 0.74/1.03 42 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f5(A,B) = f4(A,B) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(42,a,38,a)].
% 0.74/1.03 43 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) = f4(A,B) | -in(C,f7(A,B)) | f8(A,B,C) = C # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | f8(c2,A,B) = B. [resolve(43,a,38,a)].
% 0.74/1.03 44 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) = f4(A,B) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(44,a,38,a)].
% 0.74/1.03 45 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) != f5(A,B) | -in(C,f7(A,B)) | f8(A,B,C) = C # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | -in(B,f7(c2,A)) | f8(c2,A,B) = B. [resolve(45,a,38,a)].
% 0.74/1.03 46 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) != f5(A,B) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | -in(B,f7(c2,A)) | in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(46,a,38,a)].
% 0.74/1.03 47 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f5(A,B)),B) | -in(C,f7(A,B)) | f8(A,B,C) = C # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | in(set_difference(cast_as_carrier_subset(c2),f5(c2,A)),A) | -in(B,f7(c2,A)) | f8(c2,A,B) = B. [resolve(47,a,38,a)].
% 0.74/1.03 48 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f5(A,B)),B) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | in(set_difference(cast_as_carrier_subset(c2),f5(c2,A)),A) | -in(B,f7(c2,A)) | in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(48,a,38,a)].
% 0.74/1.03 49 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f6(A,B)),B) | -in(C,f7(A,B)) | f8(A,B,C) = C # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | in(set_difference(cast_as_carrier_subset(c2),f6(c2,A)),A) | -in(B,f7(c2,A)) | f8(c2,A,B) = B. [resolve(49,a,38,a)].
% 0.74/1.03 50 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f6(A,B)),B) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | in(set_difference(cast_as_carrier_subset(c2),f6(c2,A)),A) | -in(B,f7(c2,A)) | in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(50,a,38,a)].
% 0.74/1.03 51 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f5(A,B) = f4(A,B) | -in(C,f7(A,B)) | in(f8(A,B,C),powerset(the_carrier(A))) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(f8(c2,A,B),powerset(the_carrier(c2))). [resolve(51,a,38,a)].
% 0.74/1.03 52 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) = f4(A,B) | -in(C,f7(A,B)) | in(f8(A,B,C),powerset(the_carrier(A))) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(f8(c2,A,B),powerset(the_carrier(c2))). [resolve(52,a,38,a)].
% 0.74/1.03 53 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) != f5(A,B) | -in(C,f7(A,B)) | in(f8(A,B,C),powerset(the_carrier(A))) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | -in(B,f7(c2,A)) | in(f8(c2,A,B),powerset(the_carrier(c2))). [resolve(53,a,38,a)].
% 0.74/1.03 54 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f5(A,B)),B) | -in(C,f7(A,B)) | in(f8(A,B,C),powerset(the_carrier(A))) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | in(set_difference(cast_as_carrier_subset(c2),f5(c2,A)),A) | -in(B,f7(c2,A)) | in(f8(c2,A,B),powerset(the_carrier(c2))). [resolve(54,a,38,a)].
% 0.74/1.03 55 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f6(A,B)),B) | -in(C,f7(A,B)) | in(f8(A,B,C),powerset(the_carrier(A))) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | in(set_difference(cast_as_carrier_subset(c2),f6(c2,A)),A) | -in(B,f7(c2,A)) | in(f8(c2,A,B),powerset(the_carrier(c2))). [resolve(55,a,38,a)].
% 0.74/1.03 56 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f5(A,B) = f4(A,B) | in(C,f7(A,B)) | -in(D,powerset(the_carrier(A))) | D != C | -in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 0.74/1.03 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | in(B,f7(c2,A)) | -in(C,powerset(the_carrier(c2))) | C != B | -in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(56,a,38,a)].
% 0.74/1.03 57 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) = f4(A,B) | in(C,f7(A,B)) | -in(D,powerset(the_carrier(A))) | D != C | -in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | in(B,f7(c2,A)) | -in(C,powerset(the_carrier(c2))) | C != B | -in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(57,a,38,a)].
% 1.28/1.63 58 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) != f5(A,B) | in(C,f7(A,B)) | -in(D,powerset(the_carrier(A))) | D != C | -in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | in(B,f7(c2,A)) | -in(C,powerset(the_carrier(c2))) | C != B | -in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(58,a,38,a)].
% 1.28/1.63 59 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f5(A,B)),B) | in(C,f7(A,B)) | -in(D,powerset(the_carrier(A))) | D != C | -in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | in(set_difference(cast_as_carrier_subset(c2),f5(c2,A)),A) | in(B,f7(c2,A)) | -in(C,powerset(the_carrier(c2))) | C != B | -in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(59,a,38,a)].
% 1.28/1.63 60 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f6(A,B)),B) | in(C,f7(A,B)) | -in(D,powerset(the_carrier(A))) | D != C | -in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 Derived: -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | in(set_difference(cast_as_carrier_subset(c2),f6(c2,A)),A) | in(B,f7(c2,A)) | -in(C,powerset(the_carrier(c2))) | C != B | -in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(60,a,38,a)].
% 1.28/1.63 61 -one_sorted_str(A) | element(cast_as_carrier_subset(A),powerset(the_carrier(A))) # label(dt_k2_pre_topc) # label(axiom). [clausify(28)].
% 1.28/1.63 62 -top_str(A) | one_sorted_str(A) # label(dt_l1_pre_topc) # label(axiom). [clausify(30)].
% 1.28/1.63 Derived: element(cast_as_carrier_subset(A),powerset(the_carrier(A))) | -top_str(A). [resolve(61,a,62,b)].
% 1.28/1.63
% 1.28/1.63 ============================== end predicate elimination =============
% 1.28/1.63
% 1.28/1.63 Auto_denials: (non-Horn, no changes).
% 1.28/1.63
% 1.28/1.63 Term ordering decisions:
% 1.28/1.63 Function symbol KB weights: c1=1. c2=1. c3=1. set_difference=1. f4=1. f5=1. f6=1. f7=1. powerset=1. the_carrier=1. cast_as_carrier_subset=1. f1=1. f2=1. f3=1. f9=1. f8=1.
% 1.28/1.63
% 1.28/1.63 ============================== end of process initial clauses ========
% 1.28/1.63
% 1.28/1.63 ============================== CLAUSES FOR SEARCH ====================
% 1.28/1.63
% 1.28/1.63 ============================== end of clauses for search =============
% 1.28/1.63
% 1.28/1.63 ============================== SEARCH ================================
% 1.28/1.63
% 1.28/1.63 % Starting search at 0.03 seconds.
% 1.28/1.63
% 1.28/1.63 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 180 (0.00 of 0.14 sec).
% 1.28/1.63
% 1.28/1.63 ============================== PROOF =================================
% 1.28/1.63 % SZS status Theorem
% 1.28/1.63 % SZS output start Refutation
% 1.28/1.63
% 1.28/1.63 % Proof 1 at 0.61 (+ 0.01) seconds.
% 1.28/1.63 % Length of proof is 93.
% 1.28/1.63 % Level of proof is 17.
% 1.28/1.63 % Maximum clause weight is 32.000.
% 1.28/1.63 % Given clauses 1564.
% 1.28/1.63
% 1.28/1.63 35 (all A all B (topological_space(A) & top_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> ((all C all D all E (C = D & in(set_difference(cast_as_carrier_subset(A),D),B) & C = E & in(set_difference(cast_as_carrier_subset(A),E),B) -> D = E)) -> (exists C all D (in(D,C) <-> (exists E (in(E,powerset(the_carrier(A))) & E = D & in(set_difference(cast_as_carrier_subset(A),D),B)))))))) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.63 36 -(all A all B (topological_space(A) & top_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> (exists C all D (in(D,C) <-> in(D,powerset(the_carrier(A))) & in(set_difference(cast_as_carrier_subset(A),D),B))))) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.28/1.63 38 topological_space(c2) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(negated_conjecture). [clausify(36)].
% 1.28/1.63 41 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f5(A,B) = f4(A,B) | -in(C,f7(A,B)) | f8(A,B,C) = C # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 42 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f5(A,B) = f4(A,B) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 43 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) = f4(A,B) | -in(C,f7(A,B)) | f8(A,B,C) = C # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 44 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) = f4(A,B) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 45 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) != f5(A,B) | -in(C,f7(A,B)) | f8(A,B,C) = C # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 46 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) != f5(A,B) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 51 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f5(A,B) = f4(A,B) | -in(C,f7(A,B)) | in(f8(A,B,C),powerset(the_carrier(A))) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 52 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) = f4(A,B) | -in(C,f7(A,B)) | in(f8(A,B,C),powerset(the_carrier(A))) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 53 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) != f5(A,B) | -in(C,f7(A,B)) | in(f8(A,B,C),powerset(the_carrier(A))) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 56 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f5(A,B) = f4(A,B) | in(C,f7(A,B)) | -in(D,powerset(the_carrier(A))) | D != C | -in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 57 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) = f4(A,B) | in(C,f7(A,B)) | -in(D,powerset(the_carrier(A))) | D != C | -in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 58 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f6(A,B) != f5(A,B) | in(C,f7(A,B)) | -in(D,powerset(the_carrier(A))) | D != C | -in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(35)].
% 1.28/1.63 68 top_str(c2) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(negated_conjecture). [clausify(36)].
% 1.28/1.63 71 element(c3,powerset(powerset(the_carrier(c2)))) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(negated_conjecture). [clausify(36)].
% 1.28/1.63 73 in(f9(A),A) | in(f9(A),powerset(the_carrier(c2))) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(negated_conjecture). [clausify(36)].
% 1.28/1.63 74 in(f9(A),A) | in(set_difference(cast_as_carrier_subset(c2),f9(A)),c3) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(negated_conjecture). [clausify(36)].
% 1.28/1.63 78 -in(f9(A),A) | -in(f9(A),powerset(the_carrier(c2))) | -in(set_difference(cast_as_carrier_subset(c2),f9(A)),c3) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(negated_conjecture). [clausify(36)].
% 1.28/1.63 121 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | f8(c2,A,B) = B. [resolve(41,a,38,a)].
% 1.28/1.63 122 -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | f8(c2,A,B) = B. [copy(121),unit_del(a,68)].
% 1.28/1.63 123 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(42,a,38,a)].
% 1.28/1.63 124 -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(set_difference(cast_as_carrier_subset(c2),B),A). [copy(123),unit_del(a,68)].
% 1.28/1.63 125 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | f8(c2,A,B) = B. [resolve(43,a,38,a)].
% 1.28/1.63 126 -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | f8(c2,A,B) = B. [copy(125),unit_del(a,68)].
% 1.28/1.63 127 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(44,a,38,a)].
% 1.28/1.63 128 -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(set_difference(cast_as_carrier_subset(c2),B),A). [copy(127),unit_del(a,68)].
% 1.28/1.63 129 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | -in(B,f7(c2,A)) | f8(c2,A,B) = B. [resolve(45,a,38,a)].
% 1.28/1.63 130 -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | -in(B,f7(c2,A)) | f8(c2,A,B) = B. [copy(129),unit_del(a,68)].
% 1.28/1.63 131 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | -in(B,f7(c2,A)) | in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(46,a,38,a)].
% 1.28/1.63 132 -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | -in(B,f7(c2,A)) | in(set_difference(cast_as_carrier_subset(c2),B),A). [copy(131),unit_del(a,68)].
% 1.28/1.63 141 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(f8(c2,A,B),powerset(the_carrier(c2))). [resolve(51,a,38,a)].
% 1.28/1.63 142 -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(f8(c2,A,B),powerset(the_carrier(c2))). [copy(141),unit_del(a,68)].
% 1.28/1.63 143 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(f8(c2,A,B),powerset(the_carrier(c2))). [resolve(52,a,38,a)].
% 1.28/1.63 144 -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | -in(B,f7(c2,A)) | in(f8(c2,A,B),powerset(the_carrier(c2))). [copy(143),unit_del(a,68)].
% 1.28/1.63 145 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | -in(B,f7(c2,A)) | in(f8(c2,A,B),powerset(the_carrier(c2))). [resolve(53,a,38,a)].
% 1.28/1.63 146 -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | -in(B,f7(c2,A)) | in(f8(c2,A,B),powerset(the_carrier(c2))). [copy(145),unit_del(a,68)].
% 1.28/1.63 151 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | in(B,f7(c2,A)) | -in(C,powerset(the_carrier(c2))) | C != B | -in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(56,a,38,a)].
% 1.28/1.63 152 -element(A,powerset(powerset(the_carrier(c2)))) | f5(c2,A) = f4(c2,A) | in(B,f7(c2,A)) | -in(C,powerset(the_carrier(c2))) | C != B | -in(set_difference(cast_as_carrier_subset(c2),B),A). [copy(151),unit_del(a,68)].
% 1.28/1.63 153 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | in(B,f7(c2,A)) | -in(C,powerset(the_carrier(c2))) | C != B | -in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(57,a,38,a)].
% 1.28/1.63 154 -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) = f4(c2,A) | in(B,f7(c2,A)) | -in(C,powerset(the_carrier(c2))) | C != B | -in(set_difference(cast_as_carrier_subset(c2),B),A). [copy(153),unit_del(a,68)].
% 1.28/1.63 155 -top_str(c2) | -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | in(B,f7(c2,A)) | -in(C,powerset(the_carrier(c2))) | C != B | -in(set_difference(cast_as_carrier_subset(c2),B),A). [resolve(58,a,38,a)].
% 1.28/1.63 156 -element(A,powerset(powerset(the_carrier(c2)))) | f6(c2,A) != f5(c2,A) | in(B,f7(c2,A)) | -in(C,powerset(the_carrier(c2))) | C != B | -in(set_difference(cast_as_carrier_subset(c2),B),A). [copy(155),unit_del(a,68)].
% 1.28/1.63 235 f5(c2,c3) = f4(c2,c3) | -in(A,f7(c2,c3)) | f8(c2,c3,A) = A. [resolve(122,a,71,a)].
% 1.28/1.63 238 f5(c2,c3) = f4(c2,c3) | -in(A,f7(c2,c3)) | in(set_difference(cast_as_carrier_subset(c2),A),c3). [resolve(124,a,71,a)].
% 1.28/1.63 241 f6(c2,c3) = f4(c2,c3) | -in(A,f7(c2,c3)) | f8(c2,c3,A) = A. [resolve(126,a,71,a)].
% 1.28/1.63 244 f6(c2,c3) = f4(c2,c3) | -in(A,f7(c2,c3)) | in(set_difference(cast_as_carrier_subset(c2),A),c3). [resolve(128,a,71,a)].
% 1.28/1.63 247 f6(c2,c3) != f5(c2,c3) | -in(A,f7(c2,c3)) | f8(c2,c3,A) = A. [resolve(130,a,71,a)].
% 1.28/1.63 250 f6(c2,c3) != f5(c2,c3) | -in(A,f7(c2,c3)) | in(set_difference(cast_as_carrier_subset(c2),A),c3). [resolve(132,a,71,a)].
% 1.28/1.63 271 f5(c2,c3) = f4(c2,c3) | -in(A,f7(c2,c3)) | in(f8(c2,c3,A),powerset(the_carrier(c2))). [resolve(142,a,71,a)].
% 1.28/1.63 274 f6(c2,c3) = f4(c2,c3) | -in(A,f7(c2,c3)) | in(f8(c2,c3,A),powerset(the_carrier(c2))). [resolve(144,a,71,a)].
% 1.28/1.63 277 f6(c2,c3) != f5(c2,c3) | -in(A,f7(c2,c3)) | in(f8(c2,c3,A),powerset(the_carrier(c2))). [resolve(146,a,71,a)].
% 1.28/1.63 286 f5(c2,c3) = f4(c2,c3) | in(A,f7(c2,c3)) | -in(B,powerset(the_carrier(c2))) | B != A | -in(set_difference(cast_as_carrier_subset(c2),A),c3). [resolve(152,a,71,a)].
% 1.28/1.63 289 f6(c2,c3) = f4(c2,c3) | in(A,f7(c2,c3)) | -in(B,powerset(the_carrier(c2))) | B != A | -in(set_difference(cast_as_carrier_subset(c2),A),c3). [resolve(154,a,71,a)].
% 1.28/1.63 292 f6(c2,c3) != f5(c2,c3) | in(A,f7(c2,c3)) | -in(B,powerset(the_carrier(c2))) | B != A | -in(set_difference(cast_as_carrier_subset(c2),A),c3). [resolve(156,a,71,a)].
% 1.28/1.63 515 f5(c2,c3) = f4(c2,c3) | in(set_difference(cast_as_carrier_subset(c2),f9(f7(c2,c3))),c3). [resolve(238,b,74,a),merge(c)].
% 1.28/1.63 594 f6(c2,c3) = f4(c2,c3) | in(set_difference(cast_as_carrier_subset(c2),f9(f7(c2,c3))),c3). [resolve(244,b,74,a),merge(c)].
% 1.28/1.63 636 f6(c2,c3) != f5(c2,c3) | f8(c2,c3,f9(f7(c2,c3))) = f9(f7(c2,c3)) | in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [resolve(247,b,73,a)].
% 1.28/1.63 669 f6(c2,c3) != f5(c2,c3) | in(set_difference(cast_as_carrier_subset(c2),f9(f7(c2,c3))),c3). [resolve(250,b,74,a),merge(c)].
% 1.28/1.63 926 f5(c2,c3) = f4(c2,c3) | in(f8(c2,c3,f9(f7(c2,c3))),powerset(the_carrier(c2))) | in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [resolve(271,b,73,a)].
% 1.28/1.63 967 f6(c2,c3) = f4(c2,c3) | in(f8(c2,c3,f9(f7(c2,c3))),powerset(the_carrier(c2))) | in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [resolve(274,b,73,a)].
% 1.28/1.63 1008 f6(c2,c3) != f5(c2,c3) | in(f8(c2,c3,f9(f7(c2,c3))),powerset(the_carrier(c2))) | in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [resolve(277,b,73,a)].
% 1.28/1.63 1113 f5(c2,c3) = f4(c2,c3) | in(A,f7(c2,c3)) | f9(B) != A | -in(set_difference(cast_as_carrier_subset(c2),A),c3) | in(f9(B),B). [resolve(286,c,73,b)].
% 1.28/1.63 1115 f5(c2,c3) = f4(c2,c3) | in(f9(f7(c2,c3)),f7(c2,c3)) | -in(set_difference(cast_as_carrier_subset(c2),f9(f7(c2,c3))),c3). [factor(1113,b,e),xx(c)].
% 1.28/1.63 1160 f6(c2,c3) = f4(c2,c3) | in(A,f7(c2,c3)) | f9(B) != A | -in(set_difference(cast_as_carrier_subset(c2),A),c3) | in(f9(B),B). [resolve(289,c,73,b)].
% 1.28/1.63 1162 f6(c2,c3) = f4(c2,c3) | in(f9(f7(c2,c3)),f7(c2,c3)) | -in(set_difference(cast_as_carrier_subset(c2),f9(f7(c2,c3))),c3). [factor(1160,b,e),xx(c)].
% 1.28/1.63 1207 f6(c2,c3) != f5(c2,c3) | in(A,f7(c2,c3)) | f9(B) != A | -in(set_difference(cast_as_carrier_subset(c2),A),c3) | in(f9(B),B). [resolve(292,c,73,b)].
% 1.28/1.63 1209 f6(c2,c3) != f5(c2,c3) | in(f9(f7(c2,c3)),f7(c2,c3)) | -in(set_difference(cast_as_carrier_subset(c2),f9(f7(c2,c3))),c3). [factor(1207,b,e),xx(c)].
% 1.28/1.63 1484 f5(c2,c3) = f4(c2,c3) | -in(f9(f7(c2,c3)),f7(c2,c3)) | -in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [resolve(515,b,78,c)].
% 1.28/1.63 1555 f6(c2,c3) = f4(c2,c3) | -in(f9(f7(c2,c3)),f7(c2,c3)) | -in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [resolve(594,b,78,c)].
% 1.28/1.63 2556 f5(c2,c3) = f4(c2,c3) | in(f9(f7(c2,c3)),f7(c2,c3)). [resolve(1115,c,515,b),merge(c)].
% 1.28/1.63 2581 f5(c2,c3) = f4(c2,c3) | f8(c2,c3,f9(f7(c2,c3))) = f9(f7(c2,c3)). [resolve(2556,b,235,b),merge(b)].
% 1.28/1.63 2615 f5(c2,c3) = f4(c2,c3) | in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [para(2581(b,1),926(b,1)),merge(b),merge(d)].
% 1.28/1.63 2618 f5(c2,c3) = f4(c2,c3) | -in(f9(f7(c2,c3)),f7(c2,c3)). [resolve(2615,b,1484,c),merge(b)].
% 1.28/1.63 2634 f5(c2,c3) = f4(c2,c3). [resolve(2618,b,2556,b),merge(b)].
% 1.28/1.63 2676 f6(c2,c3) != f4(c2,c3) | in(f9(f7(c2,c3)),f7(c2,c3)) | -in(set_difference(cast_as_carrier_subset(c2),f9(f7(c2,c3))),c3). [back_rewrite(1209),rewrite([2634(6)])].
% 1.28/1.63 2681 f6(c2,c3) != f4(c2,c3) | in(f8(c2,c3,f9(f7(c2,c3))),powerset(the_carrier(c2))) | in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [back_rewrite(1008),rewrite([2634(6)])].
% 1.28/1.63 2684 f6(c2,c3) != f4(c2,c3) | in(set_difference(cast_as_carrier_subset(c2),f9(f7(c2,c3))),c3). [back_rewrite(669),rewrite([2634(6)])].
% 1.28/1.63 2685 f6(c2,c3) != f4(c2,c3) | f8(c2,c3,f9(f7(c2,c3))) = f9(f7(c2,c3)) | in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [back_rewrite(636),rewrite([2634(6)])].
% 1.28/1.63 2706 f6(c2,c3) = f4(c2,c3) | in(f9(f7(c2,c3)),f7(c2,c3)). [resolve(1162,c,594,b),merge(c)].
% 1.28/1.63 2712 f6(c2,c3) = f4(c2,c3) | f8(c2,c3,f9(f7(c2,c3))) = f9(f7(c2,c3)). [resolve(2706,b,241,b),merge(b)].
% 1.28/1.63 2728 f6(c2,c3) = f4(c2,c3) | in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [para(2712(b,1),967(b,1)),merge(b),merge(d)].
% 1.28/1.63 2730 f6(c2,c3) = f4(c2,c3) | -in(f9(f7(c2,c3)),f7(c2,c3)). [resolve(2728,b,1555,c),merge(b)].
% 1.28/1.63 2743 f6(c2,c3) = f4(c2,c3). [resolve(2730,b,2706,b),merge(b)].
% 1.28/1.63 2749 f8(c2,c3,f9(f7(c2,c3))) = f9(f7(c2,c3)) | in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [back_rewrite(2685),rewrite([2743(3)]),xx(a)].
% 1.28/1.63 2750 in(set_difference(cast_as_carrier_subset(c2),f9(f7(c2,c3))),c3). [back_rewrite(2684),rewrite([2743(3)]),xx(a)].
% 1.28/1.63 2751 in(f8(c2,c3,f9(f7(c2,c3))),powerset(the_carrier(c2))) | in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [back_rewrite(2681),rewrite([2743(3)]),xx(a)].
% 1.28/1.63 2755 in(f9(f7(c2,c3)),f7(c2,c3)). [back_rewrite(2676),rewrite([2743(3)]),xx(a),unit_del(b,2750)].
% 1.28/1.63 2775 -in(f9(f7(c2,c3)),powerset(the_carrier(c2))). [resolve(2755,a,78,a),unit_del(b,2750)].
% 1.28/1.63 2777 in(f8(c2,c3,f9(f7(c2,c3))),powerset(the_carrier(c2))). [back_unit_del(2751),unit_del(b,2775)].
% 1.28/1.63 2778 f8(c2,c3,f9(f7(c2,c3))) = f9(f7(c2,c3)). [back_unit_del(2749),unit_del(b,2775)].
% 1.28/1.63 2780 $F. [back_rewrite(2777),rewrite([2778(7)]),unit_del(a,2775)].
% 1.28/1.63
% 1.28/1.63 % SZS output end Refutation
% 1.28/1.63 ============================== end of proof ==========================
% 1.28/1.63
% 1.28/1.63 ============================== STATISTICS ============================
% 1.28/1.63
% 1.28/1.63 Given=1564. Generated=7448. Kept=2696. proofs=1.
% 1.28/1.63 Usable=1498. Sos=832. Demods=3. Limbo=2, Disabled=485. Hints=0.
% 1.28/1.63 Megabytes=4.63.
% 1.28/1.63 User_CPU=0.61, System_CPU=0.01, Wall_clock=1.
% 1.28/1.63
% 1.28/1.63 ============================== end of statistics =====================
% 1.28/1.63
% 1.28/1.63 ============================== end of search =========================
% 1.28/1.63
% 1.28/1.63 THEOREM PROVED
% 1.28/1.63 % SZS status Theorem
% 1.28/1.63
% 1.28/1.63 Exiting with 1 proof.
% 1.28/1.63
% 1.28/1.63 Process 22450 exit (max_proofs) Sat Jun 18 23:06:54 2022
% 1.28/1.63 Prover9 interrupted
%------------------------------------------------------------------------------