TSTP Solution File: SEU342+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU342+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : 300s
% DateTime : Tue Sep 20 07:29:01 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU342+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n026.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 : 300
% 0.12/0.33 % DateTime : Sat Sep 3 12:35:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(below_refl_type, type, (
% 0.12/0.39 below_refl: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_A_11_type, type, (
% 0.12/0.39 tptp_fun_A_11: $i)).
% 0.12/0.39 tff(ordered_pair_as_product_element_type, type, (
% 0.12/0.39 ordered_pair_as_product_element: ( $i * $i * $i * $i ) > $i)).
% 0.12/0.39 tff(the_carrier_type, type, (
% 0.12/0.39 the_carrier: $i > $i)).
% 0.12/0.39 tff(tptp_fun_C_13_type, type, (
% 0.12/0.39 tptp_fun_C_13: $i)).
% 0.12/0.39 tff(tptp_fun_B_12_type, type, (
% 0.12/0.39 tptp_fun_B_12: $i)).
% 0.12/0.39 tff(element_type, type, (
% 0.12/0.39 element: ( $i * $i ) > $o)).
% 0.12/0.39 tff(in_type, type, (
% 0.12/0.39 in: ( $i * $i ) > $o)).
% 0.12/0.39 tff(a_1_0_filter_1_type, type, (
% 0.12/0.39 a_1_0_filter_1: $i > $i)).
% 0.12/0.39 tff(relation_of_lattice_type, type, (
% 0.12/0.39 relation_of_lattice: $i > $i)).
% 0.12/0.39 tff(latt_str_type, type, (
% 0.12/0.39 latt_str: $i > $o)).
% 0.12/0.39 tff(lattice_type, type, (
% 0.12/0.39 lattice: $i > $o)).
% 0.12/0.39 tff(empty_carrier_type, type, (
% 0.12/0.39 empty_carrier: $i > $o)).
% 0.12/0.39 tff(tptp_fun_D_5_type, type, (
% 0.12/0.39 tptp_fun_D_5: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_C_6_type, type, (
% 0.12/0.39 tptp_fun_C_6: ( $i * $i ) > $i)).
% 0.12/0.39 tff(ordered_pair_type, type, (
% 0.12/0.39 ordered_pair: ( $i * $i ) > $i)).
% 0.12/0.39 tff(empty_type, type, (
% 0.12/0.39 empty: $i > $o)).
% 0.12/0.39 tff(one_sorted_str_type, type, (
% 0.12/0.39 one_sorted_str: $i > $o)).
% 0.12/0.39 tff(join_semilatt_str_type, type, (
% 0.12/0.39 join_semilatt_str: $i > $o)).
% 0.12/0.39 tff(meet_semilatt_str_type, type, (
% 0.12/0.39 meet_semilatt_str: $i > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 ((((~empty_carrier(A!11)) & lattice(A!11) & latt_str(A!11)) & (element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13)))))) <=> ((~empty_carrier(A!11)) & lattice(A!11) & latt_str(A!11) & element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (((~(~element(B!12, the_carrier(A!11)))) & (~((~element(C!13, the_carrier(A!11))) | (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13))))) <=> (element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 ((~(~((~empty_carrier(A!11)) & lattice(A!11) & latt_str(A!11)))) <=> ((~empty_carrier(A!11)) & lattice(A!11) & latt_str(A!11))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (((~(~((~empty_carrier(A!11)) & lattice(A!11) & latt_str(A!11)))) & ((~(~element(B!12, the_carrier(A!11)))) & (~((~element(C!13, the_carrier(A!11))) | (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13)))))) <=> (((~empty_carrier(A!11)) & lattice(A!11) & latt_str(A!11)) & (element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[3, 2])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (((~(~((~empty_carrier(A!11)) & lattice(A!11) & latt_str(A!11)))) & ((~(~element(B!12, the_carrier(A!11)))) & (~((~element(C!13, the_carrier(A!11))) | (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13)))))) <=> ((~empty_carrier(A!11)) & lattice(A!11) & latt_str(A!11) & element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13)))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[4, 1])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 ((~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 ((~![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(8,axiom,(~![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t32_filter_1')).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(ordered_pair_as_product_element(the_carrier(A), the_carrier(A), B, C), relation_of_lattice(A)) <=> below_refl(A, B, C)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 ((~empty_carrier(A!11)) & lattice(A!11) & latt_str(A!11) & element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (latt_str(A!11)),
% 0.12/0.40 inference(and_elim,[status(thm)],[16])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (lattice(A!11)),
% 0.12/0.40 inference(and_elim,[status(thm)],[16])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (~empty_carrier(A!11)),
% 0.12/0.40 inference(and_elim,[status(thm)],[16])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (^[A: $i] : refl((empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A))) <=> (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A))) <=> (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A))) <=> (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A))) <=> ![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (relation_of_lattice(A) = a_1_0_filter_1(A))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (relation_of_lattice(A) = a_1_0_filter_1(A))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (relation_of_lattice(A) = a_1_0_filter_1(A))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (relation_of_lattice(A) = a_1_0_filter_1(A))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (relation_of_lattice(A) = a_1_0_filter_1(A))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.40 tff(27,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (relation_of_lattice(A) = a_1_0_filter_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d8_filter_1')).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.40 tff(30,plain,(
% 0.12/0.40 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (relation_of_lattice(A) = a_1_0_filter_1(A)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[29])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (((~![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!11) | (~latt_str(A!11)) | (~lattice(A!11)) | (relation_of_lattice(A!11) = a_1_0_filter_1(A!11)))) <=> ((~![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(A!11) | (~latt_str(A!11)) | (~lattice(A!11)) | (relation_of_lattice(A!11) = a_1_0_filter_1(A!11)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 ((empty_carrier(A!11) | (relation_of_lattice(A!11) = a_1_0_filter_1(A!11)) | (~latt_str(A!11)) | (~lattice(A!11))) <=> (empty_carrier(A!11) | (~latt_str(A!11)) | (~lattice(A!11)) | (relation_of_lattice(A!11) = a_1_0_filter_1(A!11)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (((~![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!11) | (relation_of_lattice(A!11) = a_1_0_filter_1(A!11)) | (~latt_str(A!11)) | (~lattice(A!11)))) <=> ((~![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!11) | (~latt_str(A!11)) | (~lattice(A!11)) | (relation_of_lattice(A!11) = a_1_0_filter_1(A!11))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (((~![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!11) | (relation_of_lattice(A!11) = a_1_0_filter_1(A!11)) | (~latt_str(A!11)) | (~lattice(A!11)))) <=> ((~![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(A!11) | (~latt_str(A!11)) | (~lattice(A!11)) | (relation_of_lattice(A!11) = a_1_0_filter_1(A!11)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[35, 33])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 ((~![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(A!11) | (relation_of_lattice(A!11) = a_1_0_filter_1(A!11)) | (~latt_str(A!11)) | (~lattice(A!11)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((~![A: $i] : (empty_carrier(A) | (relation_of_lattice(A) = a_1_0_filter_1(A)) | (~latt_str(A)) | (~lattice(A)))) | empty_carrier(A!11) | (~latt_str(A!11)) | (~lattice(A!11)) | (relation_of_lattice(A!11) = a_1_0_filter_1(A!11))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (relation_of_lattice(A!11) = a_1_0_filter_1(A!11)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[38, 32, 19, 18, 17])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (a_1_0_filter_1(A!11) = relation_of_lattice(A!11)),
% 0.12/0.40 inference(symmetry,[status(thm)],[39])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) <=> in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[40])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))),
% 0.12/0.40 inference(symmetry,[status(thm)],[41])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 ((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11))) <=> (~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[42])).
% 0.12/0.40 tff(44,assumption,(~below_refl(A!11, B!12, C!13)), introduced(assumption)).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 ((~(in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13))) <=> ((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11))) <=> below_refl(A!11, B!12, C!13))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (~((~element(C!13, the_carrier(A!11))) | (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13)))),
% 0.12/0.40 inference(and_elim,[status(thm)],[16])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (~(in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) <=> below_refl(A!11, B!12, C!13))),
% 0.12/0.40 inference(or_elim,[status(thm)],[46])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 ((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11))) <=> below_refl(A!11, B!12, C!13)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[47, 45])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) | below_refl(A!11, B!12, C!13) | (~((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11))) <=> below_refl(A!11, B!12, C!13)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11)) | below_refl(A!11, B!12, C!13)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[50, 44])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[51, 42])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (^[A: $i, B: $i] : refl((empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D)))))))) <=> (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D)))))))) <=> ![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (^[A: $i, B: $i] : rewrite((empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D)))))))) <=> (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D)))))))) <=> ![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D)))))))) <=> ![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[56, 54])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(B)) & lattice(B) & latt_str(B)) <=> (~(empty_carrier(B) | (~latt_str(B)) | (~lattice(B))))), ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) <=> (~(~(empty_carrier(B) | (~latt_str(B)) | (~lattice(B))))))), rewrite((~(~(empty_carrier(B) | (~latt_str(B)) | (~lattice(B))))) <=> (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)))), ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) <=> (empty_carrier(B) | (~latt_str(B)) | (~lattice(B))))), trans(monotonicity(rewrite(((~in(A, a_1_0_filter_1(B))) | (element(tptp_fun_C_6(B, A), the_carrier(B)) & element(tptp_fun_D_5(B, A), the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))) & below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) <=> ((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))), rewrite((in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : (~(element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D)))) <=> (in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))), ((((~in(A, a_1_0_filter_1(B))) | (element(tptp_fun_C_6(B, A), the_carrier(B)) & element(tptp_fun_D_5(B, A), the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))) & below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) & (in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : (~(element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D))))) <=> (((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))))) & (in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))), rewrite((((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))))) & (in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))) <=> (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D)))))))), ((((~in(A, a_1_0_filter_1(B))) | (element(tptp_fun_C_6(B, A), the_carrier(B)) & element(tptp_fun_D_5(B, A), the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))) & below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) & (in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : (~(element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D))))) <=> (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))), (((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | (((~in(A, a_1_0_filter_1(B))) | (element(tptp_fun_C_6(B, A), the_carrier(B)) & element(tptp_fun_D_5(B, A), the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))) & below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) & (in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : (~(element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D)))))) <=> ((empty_carrier(B) | (~latt_str(B)) | (~lattice(B))) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D)))))))))), rewrite(((empty_carrier(B) | (~latt_str(B)) | (~lattice(B))) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D)))))))) <=> (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))), (((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | (((~in(A, a_1_0_filter_1(B))) | (element(tptp_fun_C_6(B, A), the_carrier(B)) & element(tptp_fun_D_5(B, A), the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))) & below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) & (in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : (~(element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D)))))) <=> (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 (![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | (((~in(A, a_1_0_filter_1(B))) | (element(tptp_fun_C_6(B, A), the_carrier(B)) & element(tptp_fun_D_5(B, A), the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))) & below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) & (in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : (~(element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D)))))) <=> ![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.18/0.41 tff(60,plain,
% 0.18/0.41 (![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D)))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(61,plain,
% 0.18/0.41 (^[A: $i, B: $i] : trans(monotonicity(rewrite((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) <=> ((~empty_carrier(B)) & lattice(B) & latt_str(B))), rewrite((in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (((element(C, the_carrier(B)) & element(D, the_carrier(B))) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) & below_refl(B, C, D))) <=> (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D)))), (((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (((element(C, the_carrier(B)) & element(D, the_carrier(B))) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) & below_refl(B, C, D)))) <=> (((~empty_carrier(B)) & lattice(B) & latt_str(B)) => (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D)))))), rewrite((((~empty_carrier(B)) & lattice(B) & latt_str(B)) => (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D)))) <=> ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D))))), (((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (((element(C, the_carrier(B)) & element(D, the_carrier(B))) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) & below_refl(B, C, D)))) <=> ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(62,plain,
% 0.18/0.41 (![A: $i, B: $i] : ((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (((element(C, the_carrier(B)) & element(D, the_carrier(B))) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) & below_refl(B, C, D)))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.41 tff(63,axiom,(![A: $i, B: $i] : ((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (((element(C, the_carrier(B)) & element(D, the_carrier(B))) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) & below_refl(B, C, D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fraenkel_a_1_0_filter_1')).
% 0.18/0.41 tff(64,plain,
% 0.18/0.41 (![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.41 tff(65,plain,
% 0.18/0.41 (![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | (in(A, a_1_0_filter_1(B)) <=> ?[C: $i, D: $i] : (element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.18/0.41 tff(66,plain,(
% 0.18/0.41 ![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | (((~in(A, a_1_0_filter_1(B))) | (element(tptp_fun_C_6(B, A), the_carrier(B)) & element(tptp_fun_D_5(B, A), the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))) & below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) & (in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : (~(element(C, the_carrier(B)) & element(D, the_carrier(B)) & (A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D)) & below_refl(B, C, D))))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[65])).
% 0.18/0.41 tff(67,plain,
% 0.18/0.41 (![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.18/0.41 tff(68,plain,
% 0.18/0.41 (![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.18/0.41 tff(69,plain,
% 0.18/0.41 (((~![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))) | (empty_carrier(A!11) | (~latt_str(A!11)) | (~lattice(A!11)) | (~((~((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))) | (~(in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D))))))))) <=> ((~![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))) | empty_carrier(A!11) | (~latt_str(A!11)) | (~lattice(A!11)) | (~((~((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))) | (~(in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D))))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(70,plain,
% 0.18/0.41 ((~![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))) | (empty_carrier(A!11) | (~latt_str(A!11)) | (~lattice(A!11)) | (~((~((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))) | (~(in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D))))))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(71,plain,
% 0.18/0.41 ((~![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | (~lattice(B)) | (~((~((~in(A, a_1_0_filter_1(B))) | (~((~element(tptp_fun_C_6(B, A), the_carrier(B))) | (~element(tptp_fun_D_5(B, A), the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), tptp_fun_C_6(B, A), tptp_fun_D_5(B, A)))) | (~below_refl(B, tptp_fun_C_6(B, A), tptp_fun_D_5(B, A))))))) | (~(in(A, a_1_0_filter_1(B)) | ![C: $i, D: $i] : ((~element(D, the_carrier(B))) | (~element(C, the_carrier(B))) | (~(A = ordered_pair_as_product_element(the_carrier(B), the_carrier(B), C, D))) | (~below_refl(B, C, D))))))))) | empty_carrier(A!11) | (~latt_str(A!11)) | (~lattice(A!11)) | (~((~((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))) | (~(in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.42 tff(72,plain,
% 0.18/0.42 (~((~((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))) | (~(in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[71, 68, 19, 18, 17])).
% 0.18/0.42 tff(73,plain,
% 0.18/0.42 (((~((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))) | (~(in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))))) | ((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(74,plain,
% 0.18/0.42 ((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.18/0.42 tff(75,plain,
% 0.18/0.42 ((~((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))) | (~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(76,plain,
% 0.18/0.42 ((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.18/0.42 tff(77,plain,
% 0.18/0.42 (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[76, 52])).
% 0.18/0.42 tff(78,plain,
% 0.18/0.42 (((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(79,plain,
% 0.18/0.42 (element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.18/0.42 tff(80,plain,
% 0.18/0.42 (((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(81,plain,
% 0.18/0.42 (element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[80, 77])).
% 0.18/0.42 tff(82,plain,
% 0.18/0.42 (^[A: $i] : refl(((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))) <=> ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(83,plain,
% 0.18/0.42 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))) <=> ![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[82])).
% 0.18/0.42 tff(84,plain,
% 0.18/0.42 (^[A: $i] : rewrite(((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(85,plain,
% 0.18/0.42 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.18/0.42 tff(86,plain,
% 0.18/0.42 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(87,plain,
% 0.18/0.42 (^[A: $i] : rewrite((latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(88,plain,
% 0.18/0.42 (![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[87])).
% 0.18/0.42 tff(89,axiom,(![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.18/0.42 tff(90,plain,
% 0.18/0.42 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.18/0.42 tff(91,plain,
% 0.18/0.42 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.18/0.42 tff(92,plain,(
% 0.18/0.42 ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[91])).
% 0.18/0.42 tff(93,plain,
% 0.18/0.42 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.18/0.42 tff(94,plain,
% 0.18/0.42 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.18/0.42 tff(95,plain,
% 0.18/0.42 (((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(A!11)) | (~((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11)))))) <=> ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(A!11)) | (~((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(96,plain,
% 0.18/0.42 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(A!11)) | (~((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(97,plain,
% 0.18/0.42 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(A!11)) | (~((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.18/0.42 tff(98,plain,
% 0.18/0.42 (~((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[97, 94, 17])).
% 0.18/0.42 tff(99,plain,
% 0.18/0.42 (((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11))) | join_semilatt_str(A!11)),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(100,plain,
% 0.18/0.42 (join_semilatt_str(A!11)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.18/0.42 tff(101,plain,
% 0.18/0.42 (^[A: $i] : refl((one_sorted_str(A) | (~join_semilatt_str(A))) <=> (one_sorted_str(A) | (~join_semilatt_str(A))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(102,plain,
% 0.18/0.42 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[101])).
% 0.18/0.42 tff(103,plain,
% 0.18/0.42 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(104,plain,
% 0.18/0.42 (^[A: $i] : rewrite((join_semilatt_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~join_semilatt_str(A))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(105,plain,
% 0.18/0.42 (![A: $i] : (join_semilatt_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[104])).
% 0.18/0.42 tff(106,axiom,(![A: $i] : (join_semilatt_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 0.18/0.42 tff(107,plain,
% 0.18/0.42 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.18/0.42 tff(108,plain,
% 0.18/0.42 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.18/0.42 tff(109,plain,(
% 0.18/0.42 ![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[108])).
% 0.18/0.42 tff(110,plain,
% 0.18/0.42 (![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.18/0.42 tff(111,plain,
% 0.18/0.42 (((~![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))) | (one_sorted_str(A!11) | (~join_semilatt_str(A!11)))) <=> ((~![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))) | one_sorted_str(A!11) | (~join_semilatt_str(A!11)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(112,plain,
% 0.18/0.42 ((~![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))) | (one_sorted_str(A!11) | (~join_semilatt_str(A!11)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(113,plain,
% 0.18/0.42 ((~![A: $i] : (one_sorted_str(A) | (~join_semilatt_str(A)))) | one_sorted_str(A!11) | (~join_semilatt_str(A!11))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.18/0.42 tff(114,plain,
% 0.18/0.42 (one_sorted_str(A!11)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[113, 110, 100])).
% 0.18/0.42 tff(115,plain,
% 0.18/0.42 (^[A: $i] : refl((empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(116,plain,
% 0.18/0.42 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[115])).
% 0.18/0.42 tff(117,plain,
% 0.18/0.42 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & one_sorted_str(A)) <=> (~(empty_carrier(A) | (~one_sorted_str(A))))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (~(~(empty_carrier(A) | (~one_sorted_str(A))))))), rewrite((~(~(empty_carrier(A) | (~one_sorted_str(A))))) <=> (empty_carrier(A) | (~one_sorted_str(A)))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (empty_carrier(A) | (~one_sorted_str(A))))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))))), rewrite(((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(118,plain,
% 0.18/0.42 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[117])).
% 0.18/0.42 tff(119,plain,
% 0.18/0.42 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(120,plain,
% 0.18/0.43 (^[A: $i] : rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(121,plain,
% 0.18/0.43 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[120])).
% 0.18/0.43 tff(122,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.18/0.43 tff(123,plain,
% 0.18/0.43 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.18/0.43 tff(124,plain,
% 0.18/0.43 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.18/0.43 tff(125,plain,(
% 0.18/0.43 ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[124])).
% 0.18/0.43 tff(126,plain,
% 0.18/0.43 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.18/0.43 tff(127,plain,
% 0.18/0.43 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.18/0.43 tff(128,plain,
% 0.18/0.43 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!11) | (~empty(the_carrier(A!11))) | (~one_sorted_str(A!11)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!11) | (~empty(the_carrier(A!11))) | (~one_sorted_str(A!11)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(129,plain,
% 0.18/0.43 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!11) | (~empty(the_carrier(A!11))) | (~one_sorted_str(A!11)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(130,plain,
% 0.18/0.43 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!11) | (~empty(the_carrier(A!11))) | (~one_sorted_str(A!11))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.18/0.43 tff(131,plain,
% 0.18/0.43 ((~empty(the_carrier(A!11))) | (~one_sorted_str(A!11))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[130, 127, 19])).
% 0.18/0.43 tff(132,plain,
% 0.18/0.43 (~empty(the_carrier(A!11))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[131, 114])).
% 0.18/0.43 tff(133,plain,
% 0.18/0.43 (^[A: $i, B: $i, C: $i, D: $i] : refl((empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B))) <=> (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(134,plain,
% 0.18/0.43 (![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B))) <=> ![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[133])).
% 0.18/0.43 tff(135,plain,
% 0.18/0.43 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B)) <=> (~(empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))))), ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) <=> (~(~(empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))))))), rewrite((~(~(empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))))) <=> (empty(B) | empty(A) | (~element(C, A)) | (~element(D, B)))), ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) <=> (empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))))), (((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ((empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))))), rewrite(((empty(B) | empty(A) | (~element(C, A)) | (~element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))), (((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(136,plain,
% 0.18/0.43 (![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[135])).
% 0.18/0.43 tff(137,plain,
% 0.18/0.43 (![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(138,plain,
% 0.18/0.43 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty(A)) & (~empty(B))) & element(C, A)) <=> ((~empty(A)) & (~empty(B)) & element(C, A))), (((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) <=> (((~empty(A)) & (~empty(B)) & element(C, A)) & element(D, B)))), rewrite((((~empty(A)) & (~empty(B)) & element(C, A)) & element(D, B)) <=> ((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))), (((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) <=> ((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B)))), ((((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> (((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))))), rewrite((((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))), ((((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(139,plain,
% 0.18/0.43 (![A: $i, B: $i, C: $i, D: $i] : (((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[138])).
% 0.18/0.43 tff(140,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((((~empty(A)) & (~empty(B))) & element(C, A)) & element(D, B)) => (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k1_domain_1')).
% 0.18/0.43 tff(141,plain,
% 0.18/0.43 (![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.18/0.43 tff(142,plain,
% 0.18/0.43 (![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.18/0.43 tff(143,plain,(
% 0.18/0.43 ![A: $i, B: $i, C: $i, D: $i] : ((~((~empty(A)) & (~empty(B)) & element(C, A) & element(D, B))) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[142])).
% 0.18/0.43 tff(144,plain,
% 0.18/0.43 (![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.18/0.43 tff(145,plain,
% 0.18/0.43 (![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[144, 134])).
% 0.18/0.43 tff(146,plain,
% 0.18/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (empty(the_carrier(A!11)) | (~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | empty(the_carrier(A!11)) | (~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(147,plain,
% 0.18/0.43 ((empty(the_carrier(A!11)) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))) | (~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11)))) <=> (empty(the_carrier(A!11)) | (~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(148,plain,
% 0.18/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (empty(the_carrier(A!11)) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))) | (~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (empty(the_carrier(A!11)) | (~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[147])).
% 0.18/0.43 tff(149,plain,
% 0.18/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (empty(the_carrier(A!11)) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))) | (~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | empty(the_carrier(A!11)) | (~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[148, 146])).
% 0.18/0.44 tff(150,plain,
% 0.18/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (empty(the_carrier(A!11)) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))) | (~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(151,plain,
% 0.18/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | empty(the_carrier(A!11)) | (~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.18/0.44 tff(152,plain,
% 0.18/0.44 (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[151, 145, 132, 81, 79])).
% 0.18/0.44 tff(153,plain,
% 0.18/0.44 (((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(154,plain,
% 0.18/0.44 (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[153, 77])).
% 0.18/0.44 tff(155,plain,
% 0.18/0.44 (element(C!13, the_carrier(A!11))),
% 0.18/0.44 inference(or_elim,[status(thm)],[46])).
% 0.18/0.44 tff(156,plain,
% 0.18/0.44 (element(B!12, the_carrier(A!11))),
% 0.18/0.44 inference(and_elim,[status(thm)],[16])).
% 0.18/0.44 tff(157,plain,
% 0.18/0.44 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | ((~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(158,plain,
% 0.18/0.44 ((empty(the_carrier(A!11)) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13)) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11)))) <=> ((~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(159,plain,
% 0.18/0.44 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (empty(the_carrier(A!11)) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13)) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | ((~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[158])).
% 0.18/0.44 tff(160,plain,
% 0.18/0.44 (((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (empty(the_carrier(A!11)) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13)) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[159, 157])).
% 0.18/0.44 tff(161,plain,
% 0.18/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (empty(the_carrier(A!11)) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13)) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(162,plain,
% 0.18/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (empty(B) | empty(A) | (ordered_pair_as_product_element(A, B, C, D) = ordered_pair(C, D)) | (~element(C, A)) | (~element(D, B)))) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.18/0.44 tff(163,plain,
% 0.18/0.44 (empty(the_carrier(A!11)) | (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[162, 145, 156, 155])).
% 0.18/0.44 tff(164,plain,
% 0.18/0.44 (ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair(B!12, C!13)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[163, 132])).
% 0.18/0.44 tff(165,plain,
% 0.18/0.44 (ordered_pair(B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)),
% 0.18/0.44 inference(symmetry,[status(thm)],[164])).
% 0.18/0.44 tff(166,plain,
% 0.18/0.44 (ordered_pair(B!12, C!13) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[165, 154, 152])).
% 0.18/0.44 tff(167,plain,
% 0.18/0.44 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))) <=> ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(168,plain,
% 0.18/0.44 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[167])).
% 0.18/0.44 tff(169,plain,
% 0.18/0.44 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D))) <=> ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(170,plain,
% 0.18/0.44 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[169])).
% 0.18/0.44 tff(171,plain,
% 0.18/0.44 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(172,plain,
% 0.18/0.44 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((ordered_pair(A, B) = ordered_pair(C, D)) => ((A = C) & (B = D))) <=> ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(173,plain,
% 0.18/0.44 (![A: $i, B: $i, C: $i, D: $i] : ((ordered_pair(A, B) = ordered_pair(C, D)) => ((A = C) & (B = D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[172])).
% 0.18/0.44 tff(174,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((ordered_pair(A, B) = ordered_pair(C, D)) => ((A = C) & (B = D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t33_zfmisc_1')).
% 0.18/0.44 tff(175,plain,
% 0.18/0.44 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.18/0.45 tff(176,plain,
% 0.18/0.45 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.18/0.45 tff(177,plain,(
% 0.18/0.45 ![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 0.18/0.45 inference(skolemize,[status(sab)],[176])).
% 0.18/0.45 tff(178,plain,
% 0.18/0.45 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.18/0.45 tff(179,plain,
% 0.18/0.45 (![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[178, 168])).
% 0.18/0.45 tff(180,plain,
% 0.18/0.45 (((~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | ((~(ordered_pair(B!12, C!13) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~((~(B!12 = tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))) | (~(C!13 = tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | (~(ordered_pair(B!12, C!13) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~((~(B!12 = tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))) | (~(C!13 = tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(181,plain,
% 0.18/0.45 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | ((~(ordered_pair(B!12, C!13) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~((~(B!12 = tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))) | (~(C!13 = tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(182,plain,
% 0.18/0.45 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | (~(ordered_pair(B!12, C!13) = ordered_pair(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~((~(B!12 = tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))) | (~(C!13 = tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.18/0.45 tff(183,plain,
% 0.18/0.45 (~((~(B!12 = tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))) | (~(C!13 = tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[182, 179, 166])).
% 0.18/0.45 tff(184,plain,
% 0.18/0.45 (((~(B!12 = tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))) | (~(C!13 = tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (C!13 = tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(185,plain,
% 0.18/0.45 (C!13 = tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.18/0.45 tff(186,plain,
% 0.18/0.45 (((~(B!12 = tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))) | (~(C!13 = tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (B!12 = tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(187,plain,
% 0.18/0.45 (B!12 = tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[186, 183])).
% 0.18/0.45 tff(188,plain,
% 0.18/0.45 (below_refl(A!11, B!12, C!13) <=> below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[187, 185])).
% 0.18/0.45 tff(189,plain,
% 0.18/0.45 (below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) <=> below_refl(A!11, B!12, C!13)),
% 0.18/0.45 inference(symmetry,[status(thm)],[188])).
% 0.18/0.45 tff(190,plain,
% 0.18/0.45 (((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(191,plain,
% 0.18/0.45 (below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[190, 77])).
% 0.18/0.45 tff(192,plain,
% 0.18/0.45 (below_refl(A!11, B!12, C!13)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[191, 189])).
% 0.18/0.45 tff(193,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[44, 192])).
% 0.18/0.45 tff(194,plain,(below_refl(A!11, B!12, C!13)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(195,plain,
% 0.18/0.45 ((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11))) | (~below_refl(A!11, B!12, C!13)) | (~((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11))) <=> below_refl(A!11, B!12, C!13)))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(196,plain,
% 0.18/0.45 ((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11))) | (~below_refl(A!11, B!12, C!13))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[195, 48])).
% 0.18/0.45 tff(197,plain,
% 0.18/0.45 (~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), relation_of_lattice(A!11))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[196, 194])).
% 0.18/0.45 tff(198,plain,
% 0.18/0.45 (~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[197, 43])).
% 0.18/0.45 tff(199,plain,
% 0.18/0.45 (((~((~in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11))) | (~((~element(tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~element(tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))))) | (~below_refl(A!11, tptp_fun_C_6(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)), tptp_fun_D_5(A!11, ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)))))))) | (~(in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))))) | (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(200,plain,
% 0.18/0.45 (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[199, 72])).
% 0.18/0.45 tff(201,plain,
% 0.18/0.45 ((~(in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D))))) | in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(202,plain,
% 0.18/0.45 (in(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13), a_1_0_filter_1(A!11)) | ![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.18/0.45 tff(203,plain,
% 0.18/0.45 (![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[202, 198])).
% 0.18/0.46 tff(204,plain,
% 0.18/0.46 (((~![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))) | ((~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~below_refl(A!11, B!12, C!13)))) <=> ((~![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~below_refl(A!11, B!12, C!13)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(205,plain,
% 0.18/0.46 (((~element(C!13, the_carrier(A!11))) | (~element(B!12, the_carrier(A!11))) | $false | (~below_refl(A!11, B!12, C!13))) <=> ((~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~below_refl(A!11, B!12, C!13)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(206,plain,
% 0.18/0.46 ((~$true) <=> $false),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(207,plain,
% 0.18/0.46 ((ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13)) <=> $true),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(208,plain,
% 0.18/0.46 ((~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) <=> (~$true)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[207])).
% 0.18/0.46 tff(209,plain,
% 0.18/0.46 ((~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) <=> $false),
% 0.18/0.46 inference(transitivity,[status(thm)],[208, 206])).
% 0.18/0.46 tff(210,plain,
% 0.18/0.46 (((~element(C!13, the_carrier(A!11))) | (~element(B!12, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) | (~below_refl(A!11, B!12, C!13))) <=> ((~element(C!13, the_carrier(A!11))) | (~element(B!12, the_carrier(A!11))) | $false | (~below_refl(A!11, B!12, C!13)))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[209])).
% 0.18/0.46 tff(211,plain,
% 0.18/0.46 (((~element(C!13, the_carrier(A!11))) | (~element(B!12, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) | (~below_refl(A!11, B!12, C!13))) <=> ((~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~below_refl(A!11, B!12, C!13)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[210, 205])).
% 0.18/0.46 tff(212,plain,
% 0.18/0.46 (((~![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))) | ((~element(C!13, the_carrier(A!11))) | (~element(B!12, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) | (~below_refl(A!11, B!12, C!13)))) <=> ((~![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))) | ((~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~below_refl(A!11, B!12, C!13))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[211])).
% 0.18/0.46 tff(213,plain,
% 0.18/0.46 (((~![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))) | ((~element(C!13, the_carrier(A!11))) | (~element(B!12, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) | (~below_refl(A!11, B!12, C!13)))) <=> ((~![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~below_refl(A!11, B!12, C!13)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[212, 204])).
% 0.18/0.46 tff(214,plain,
% 0.18/0.46 ((~![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))) | ((~element(C!13, the_carrier(A!11))) | (~element(B!12, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13))) | (~below_refl(A!11, B!12, C!13)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(215,plain,
% 0.18/0.46 ((~![C: $i, D: $i] : ((~element(D, the_carrier(A!11))) | (~element(C, the_carrier(A!11))) | (~(ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), B!12, C!13) = ordered_pair_as_product_element(the_carrier(A!11), the_carrier(A!11), C, D))) | (~below_refl(A!11, C, D)))) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~below_refl(A!11, B!12, C!13))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.18/0.46 tff(216,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[215, 156, 155, 194, 203])).
% 0.18/0.46 % SZS output end Proof
%------------------------------------------------------------------------------