TSTP Solution File: SEU350+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU350+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:29:04 EDT 2022
% Result : Theorem 6.74s 4.57s
% Output : Proof 6.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU350+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 12:39:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 6.74/4.57 % SZS status Theorem
% 6.74/4.57 % SZS output start Proof
% 6.74/4.57 tff(relstr_set_smaller_type, type, (
% 6.74/4.57 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 6.74/4.57 tff(cast_to_el_of_LattPOSet_type, type, (
% 6.74/4.57 cast_to_el_of_LattPOSet: ( $i * $i ) > $i)).
% 6.74/4.57 tff(cast_to_el_of_lattice_type, type, (
% 6.74/4.57 cast_to_el_of_lattice: ( $i * $i ) > $i)).
% 6.74/4.57 tff(tptp_fun_C_18_type, type, (
% 6.74/4.57 tptp_fun_C_18: $i)).
% 6.74/4.57 tff(tptp_fun_B_16_type, type, (
% 6.74/4.57 tptp_fun_B_16: $i)).
% 6.74/4.57 tff(tptp_fun_A_17_type, type, (
% 6.74/4.57 tptp_fun_A_17: $i)).
% 6.74/4.57 tff(poset_of_lattice_type, type, (
% 6.74/4.57 poset_of_lattice: $i > $i)).
% 6.74/4.57 tff(element_type, type, (
% 6.74/4.57 element: ( $i * $i ) > $o)).
% 6.74/4.57 tff(the_carrier_type, type, (
% 6.74/4.57 the_carrier: $i > $i)).
% 6.74/4.57 tff(latt_element_smaller_type, type, (
% 6.74/4.57 latt_element_smaller: ( $i * $i * $i ) > $o)).
% 6.74/4.57 tff(latt_str_type, type, (
% 6.74/4.57 latt_str: $i > $o)).
% 6.74/4.57 tff(lattice_type, type, (
% 6.74/4.57 lattice: $i > $o)).
% 6.74/4.57 tff(empty_carrier_type, type, (
% 6.74/4.57 empty_carrier: $i > $o)).
% 6.74/4.57 tff(1,plain,
% 6.74/4.57 ((((~empty_carrier(B!16)) & lattice(B!16) & latt_str(B!16)) & (~((~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17))))) <=> ((~empty_carrier(B!16)) & lattice(B!16) & latt_str(B!16) & (~((~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)))))),
% 6.74/4.57 inference(rewrite,[status(thm)],[])).
% 6.74/4.57 tff(2,plain,
% 6.74/4.57 ((~(~((~empty_carrier(B!16)) & lattice(B!16) & latt_str(B!16)))) <=> ((~empty_carrier(B!16)) & lattice(B!16) & latt_str(B!16))),
% 6.74/4.57 inference(rewrite,[status(thm)],[])).
% 6.74/4.57 tff(3,plain,
% 6.74/4.57 (((~(~((~empty_carrier(B!16)) & lattice(B!16) & latt_str(B!16)))) & (~((~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17))))) <=> (((~empty_carrier(B!16)) & lattice(B!16) & latt_str(B!16)) & (~((~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)))))),
% 6.74/4.57 inference(monotonicity,[status(thm)],[2])).
% 6.74/4.57 tff(4,plain,
% 6.74/4.57 (((~(~((~empty_carrier(B!16)) & lattice(B!16) & latt_str(B!16)))) & (~((~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17))))) <=> ((~empty_carrier(B!16)) & lattice(B!16) & latt_str(B!16) & (~((~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)))))),
% 6.74/4.57 inference(transitivity,[status(thm)],[3, 1])).
% 6.74/4.57 tff(5,plain,
% 6.74/4.57 ((~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(poset_of_lattice(B)))) | (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A))))) <=> (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(poset_of_lattice(B)))) | (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A)))))),
% 6.74/4.57 inference(rewrite,[status(thm)],[])).
% 6.74/4.57 tff(6,plain,
% 6.74/4.57 ((~![A: $i, B: $i] : ((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => ![C: $i] : (element(C, the_carrier(poset_of_lattice(B))) => (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A))))) <=> (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(poset_of_lattice(B)))) | (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A)))))),
% 6.74/4.57 inference(rewrite,[status(thm)],[])).
% 6.74/4.57 tff(7,axiom,(~![A: $i, B: $i] : ((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => ![C: $i] : (element(C, the_carrier(poset_of_lattice(B))) => (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t31_lattice3')).
% 6.74/4.57 tff(8,plain,
% 6.74/4.57 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(poset_of_lattice(B)))) | (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A))))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[7, 6])).
% 6.74/4.57 tff(9,plain,
% 6.74/4.57 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(poset_of_lattice(B)))) | (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A))))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[8, 5])).
% 6.74/4.57 tff(10,plain,
% 6.74/4.57 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(poset_of_lattice(B)))) | (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A))))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[9, 5])).
% 6.74/4.57 tff(11,plain,
% 6.74/4.57 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(poset_of_lattice(B)))) | (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A))))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[10, 5])).
% 6.74/4.57 tff(12,plain,
% 6.74/4.57 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(poset_of_lattice(B)))) | (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A))))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[11, 5])).
% 6.74/4.57 tff(13,plain,
% 6.74/4.57 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(poset_of_lattice(B)))) | (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A))))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[12, 5])).
% 6.74/4.57 tff(14,plain,
% 6.74/4.57 (~![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(poset_of_lattice(B)))) | (relstr_set_smaller(poset_of_lattice(B), A, C) <=> latt_element_smaller(B, cast_to_el_of_lattice(B, C), A))))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[13, 5])).
% 6.74/4.57 tff(15,plain,
% 6.74/4.57 ((~empty_carrier(B!16)) & lattice(B!16) & latt_str(B!16) & (~((~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17))))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[14, 4])).
% 6.74/4.57 tff(16,plain,
% 6.74/4.57 (~((~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)))),
% 6.74/4.57 inference(and_elim,[status(thm)],[15])).
% 6.74/4.57 tff(17,plain,
% 6.74/4.57 (element(C!18, the_carrier(poset_of_lattice(B!16)))),
% 6.74/4.57 inference(or_elim,[status(thm)],[16])).
% 6.74/4.57 tff(18,plain,
% 6.74/4.57 (latt_str(B!16)),
% 6.74/4.57 inference(and_elim,[status(thm)],[15])).
% 6.74/4.57 tff(19,plain,
% 6.74/4.57 (lattice(B!16)),
% 6.74/4.57 inference(and_elim,[status(thm)],[15])).
% 6.74/4.57 tff(20,plain,
% 6.74/4.57 (~empty_carrier(B!16)),
% 6.74/4.57 inference(and_elim,[status(thm)],[15])).
% 6.74/4.57 tff(21,plain,
% 6.74/4.57 (^[A: $i, B: $i] : refl((empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))) <=> (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))))),
% 6.74/4.57 inference(bind,[status(th)],[])).
% 6.74/4.57 tff(22,plain,
% 6.74/4.57 (![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))),
% 6.74/4.57 inference(quant_intro,[status(thm)],[21])).
% 6.74/4.57 tff(23,plain,
% 6.74/4.57 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A)))) <=> (~(empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) <=> (~(~(empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))))) <=> (empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) <=> (empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ((empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))))), rewrite(((empty_carrier(A) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))))),
% 6.74/4.57 inference(bind,[status(th)],[])).
% 6.74/4.57 tff(24,plain,
% 6.74/4.57 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))),
% 6.74/4.57 inference(quant_intro,[status(thm)],[23])).
% 6.74/4.57 tff(25,plain,
% 6.74/4.57 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))),
% 6.74/4.57 inference(rewrite,[status(thm)],[])).
% 6.74/4.57 tff(26,plain,
% 6.74/4.57 (^[A: $i, B: $i] : trans(monotonicity(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)) & element(B, the_carrier(poset_of_lattice(A)))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A)))))), ((((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))), ((((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))))),
% 6.74/4.57 inference(bind,[status(th)],[])).
% 6.74/4.57 tff(27,plain,
% 6.74/4.57 (![A: $i, B: $i] : (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))),
% 6.74/4.57 inference(quant_intro,[status(thm)],[26])).
% 6.74/4.57 tff(28,axiom,(![A: $i, B: $i] : (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) & element(B, the_carrier(poset_of_lattice(A)))) => element(cast_to_el_of_lattice(A, B), the_carrier(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_lattice3')).
% 6.74/4.57 tff(29,plain,
% 6.74/4.57 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[28, 27])).
% 6.74/4.57 tff(30,plain,
% 6.74/4.57 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[29, 25])).
% 6.74/4.57 tff(31,plain,(
% 6.74/4.57 ![A: $i, B: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A) & element(B, the_carrier(poset_of_lattice(A))))) | element(cast_to_el_of_lattice(A, B), the_carrier(A)))),
% 6.74/4.57 inference(skolemize,[status(sab)],[30])).
% 6.74/4.57 tff(32,plain,
% 6.74/4.57 (![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[31, 24])).
% 6.74/4.57 tff(33,plain,
% 6.74/4.57 (![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[32, 22])).
% 6.74/4.57 tff(34,plain,
% 6.74/4.57 (((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!16) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (~latt_str(B!16)) | (~lattice(B!16)) | element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16)))) <=> ((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | empty_carrier(B!16) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (~latt_str(B!16)) | (~lattice(B!16)) | element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16)))),
% 6.74/4.57 inference(rewrite,[status(thm)],[])).
% 6.74/4.57 tff(35,plain,
% 6.74/4.57 ((empty_carrier(B!16) | element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16)) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (~lattice(B!16)) | (~latt_str(B!16))) <=> (empty_carrier(B!16) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (~latt_str(B!16)) | (~lattice(B!16)) | element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16)))),
% 6.74/4.57 inference(rewrite,[status(thm)],[])).
% 6.74/4.57 tff(36,plain,
% 6.74/4.57 (((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!16) | element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16)) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (~lattice(B!16)) | (~latt_str(B!16)))) <=> ((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!16) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (~latt_str(B!16)) | (~lattice(B!16)) | element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))))),
% 6.74/4.57 inference(monotonicity,[status(thm)],[35])).
% 6.74/4.57 tff(37,plain,
% 6.74/4.57 (((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!16) | element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16)) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (~lattice(B!16)) | (~latt_str(B!16)))) <=> ((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | empty_carrier(B!16) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (~latt_str(B!16)) | (~lattice(B!16)) | element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16)))),
% 6.74/4.57 inference(transitivity,[status(thm)],[36, 34])).
% 6.74/4.57 tff(38,plain,
% 6.74/4.57 ((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | (empty_carrier(B!16) | element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16)) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (~lattice(B!16)) | (~latt_str(B!16)))),
% 6.74/4.57 inference(quant_inst,[status(thm)],[])).
% 6.74/4.57 tff(39,plain,
% 6.74/4.57 ((~![A: $i, B: $i] : (empty_carrier(A) | element(cast_to_el_of_lattice(A, B), the_carrier(A)) | (~element(B, the_carrier(poset_of_lattice(A)))) | (~lattice(A)) | (~latt_str(A)))) | empty_carrier(B!16) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (~latt_str(B!16)) | (~lattice(B!16)) | element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))),
% 6.74/4.57 inference(modus_ponens,[status(thm)],[38, 37])).
% 6.74/4.57 tff(40,plain,
% 6.74/4.57 (element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))),
% 6.74/4.57 inference(unit_resolution,[status(thm)],[39, 33, 20, 19, 18, 17])).
% 6.74/4.57 tff(41,plain,
% 6.74/4.57 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))))),
% 6.74/4.57 inference(bind,[status(th)],[])).
% 6.74/4.57 tff(42,plain,
% 6.74/4.57 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.74/4.57 inference(quant_intro,[status(thm)],[41])).
% 6.74/4.57 tff(43,plain,
% 6.74/4.57 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))))),
% 6.74/4.57 inference(bind,[status(th)],[])).
% 6.74/4.57 tff(44,plain,
% 6.74/4.57 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.74/4.57 inference(quant_intro,[status(thm)],[43])).
% 6.74/4.57 tff(45,plain,
% 6.74/4.57 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))))),
% 6.74/4.57 inference(bind,[status(th)],[])).
% 6.74/4.57 tff(46,plain,
% 6.74/4.57 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.74/4.58 inference(quant_intro,[status(thm)],[45])).
% 6.74/4.58 tff(47,plain,
% 6.74/4.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.74/4.58 inference(transitivity,[status(thm)],[46, 44])).
% 6.74/4.58 tff(48,plain,
% 6.74/4.58 (^[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))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))))),
% 6.74/4.58 inference(bind,[status(th)],[])).
% 6.74/4.58 tff(49,plain,
% 6.74/4.58 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.74/4.58 inference(quant_intro,[status(thm)],[48])).
% 6.74/4.58 tff(50,plain,
% 6.74/4.58 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.74/4.58 inference(rewrite,[status(thm)],[])).
% 6.74/4.58 tff(51,plain,
% 6.74/4.58 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), quant_intro(proof_bind(^[B: $i] : rewrite((element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B)) <=> ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))), (![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B)) <=> ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))))),
% 6.74/4.58 inference(bind,[status(th)],[])).
% 6.74/4.58 tff(52,plain,
% 6.74/4.58 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.74/4.58 inference(quant_intro,[status(thm)],[51])).
% 6.74/4.58 tff(53,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_lattice3')).
% 6.74/4.58 tff(54,plain,
% 6.74/4.58 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.74/4.58 inference(modus_ponens,[status(thm)],[53, 52])).
% 6.74/4.58 tff(55,plain,
% 6.74/4.58 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.74/4.58 inference(modus_ponens,[status(thm)],[54, 50])).
% 6.74/4.58 tff(56,plain,(
% 6.74/4.58 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.74/4.58 inference(skolemize,[status(sab)],[55])).
% 6.74/4.58 tff(57,plain,
% 6.74/4.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.74/4.58 inference(modus_ponens,[status(thm)],[56, 49])).
% 6.74/4.58 tff(58,plain,
% 6.74/4.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 6.74/4.58 inference(modus_ponens,[status(thm)],[57, 47])).
% 6.74/4.58 tff(59,plain,
% 6.74/4.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 6.74/4.58 inference(modus_ponens,[status(thm)],[58, 42])).
% 6.74/4.58 tff(60,plain,
% 6.74/4.58 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | (empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | ![B: $i] : ((~element(B, the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, B) = B)))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | ![B: $i] : ((~element(B, the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, B) = B)))),
% 6.74/4.58 inference(rewrite,[status(thm)],[])).
% 6.74/4.58 tff(61,plain,
% 6.74/4.58 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | (empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | ![B: $i] : ((~element(B, the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, B) = B)))),
% 6.74/4.58 inference(quant_inst,[status(thm)],[])).
% 6.74/4.58 tff(62,plain,
% 6.74/4.58 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | ![B: $i] : ((~element(B, the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, B) = B))),
% 6.74/4.58 inference(modus_ponens,[status(thm)],[61, 60])).
% 6.74/4.58 tff(63,plain,
% 6.74/4.58 (![B: $i] : ((~element(B, the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, B) = B))),
% 6.74/4.58 inference(unit_resolution,[status(thm)],[62, 59, 20, 19, 18])).
% 6.74/4.58 tff(64,plain,
% 6.74/4.58 (((~![B: $i] : ((~element(B, the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, B) = B))) | ((~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)) = cast_to_el_of_lattice(B!16, C!18)))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, B) = B))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)) = cast_to_el_of_lattice(B!16, C!18)))),
% 6.74/4.58 inference(rewrite,[status(thm)],[])).
% 6.74/4.58 tff(65,plain,
% 6.74/4.58 ((~![B: $i] : ((~element(B, the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, B) = B))) | ((~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)) = cast_to_el_of_lattice(B!16, C!18)))),
% 6.74/4.58 inference(quant_inst,[status(thm)],[])).
% 6.74/4.58 tff(66,plain,
% 6.74/4.58 ((~![B: $i] : ((~element(B, the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, B) = B))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)) = cast_to_el_of_lattice(B!16, C!18))),
% 6.74/4.58 inference(modus_ponens,[status(thm)],[65, 64])).
% 6.74/4.58 tff(67,plain,
% 6.74/4.58 (cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)) = cast_to_el_of_lattice(B!16, C!18)),
% 6.74/4.58 inference(unit_resolution,[status(thm)],[66, 63, 40])).
% 6.74/4.58 tff(68,plain,
% 6.74/4.58 (cast_to_el_of_lattice(B!16, C!18) = cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18))),
% 6.74/4.58 inference(symmetry,[status(thm)],[67])).
% 6.74/4.58 tff(69,plain,
% 6.74/4.58 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))))),
% 6.74/4.58 inference(bind,[status(th)],[])).
% 6.74/4.58 tff(70,plain,
% 6.74/4.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.74/4.58 inference(quant_intro,[status(thm)],[69])).
% 6.74/4.58 tff(71,plain,
% 6.74/4.58 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))))),
% 6.74/4.58 inference(bind,[status(th)],[])).
% 6.74/4.58 tff(72,plain,
% 6.74/4.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.74/4.58 inference(quant_intro,[status(thm)],[71])).
% 6.74/4.58 tff(73,plain,
% 6.74/4.58 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))))),
% 6.74/4.58 inference(bind,[status(th)],[])).
% 6.74/4.58 tff(74,plain,
% 6.74/4.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.74/4.58 inference(quant_intro,[status(thm)],[73])).
% 6.74/4.58 tff(75,plain,
% 6.74/4.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.74/4.58 inference(transitivity,[status(thm)],[74, 72])).
% 6.74/4.58 tff(76,plain,
% 6.74/4.58 (^[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))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))))),
% 6.86/4.58 inference(bind,[status(th)],[])).
% 6.86/4.58 tff(77,plain,
% 6.86/4.58 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.86/4.58 inference(quant_intro,[status(thm)],[76])).
% 6.86/4.58 tff(78,plain,
% 6.86/4.58 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.86/4.58 inference(rewrite,[status(thm)],[])).
% 6.86/4.58 tff(79,plain,
% 6.86/4.58 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), quant_intro(proof_bind(^[B: $i] : rewrite((element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B)) <=> ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))), (![B: $i] : (element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B)) <=> ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))))),
% 6.86/4.58 inference(bind,[status(th)],[])).
% 6.86/4.58 tff(80,plain,
% 6.86/4.58 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.86/4.58 inference(quant_intro,[status(thm)],[79])).
% 6.86/4.58 tff(81,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(poset_of_lattice(A))) => (cast_to_el_of_lattice(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_lattice3')).
% 6.86/4.58 tff(82,plain,
% 6.86/4.58 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[81, 80])).
% 6.86/4.58 tff(83,plain,
% 6.86/4.58 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[82, 78])).
% 6.86/4.58 tff(84,plain,(
% 6.86/4.58 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.86/4.58 inference(skolemize,[status(sab)],[83])).
% 6.86/4.58 tff(85,plain,
% 6.86/4.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[84, 77])).
% 6.86/4.58 tff(86,plain,
% 6.86/4.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)) | (~lattice(A)))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[85, 75])).
% 6.86/4.58 tff(87,plain,
% 6.86/4.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[86, 70])).
% 6.86/4.58 tff(88,plain,
% 6.86/4.58 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))) | (empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, B) = B)))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))) | empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, B) = B)))),
% 6.86/4.58 inference(rewrite,[status(thm)],[])).
% 6.86/4.58 tff(89,plain,
% 6.86/4.58 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))) | (empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, B) = B)))),
% 6.86/4.58 inference(quant_inst,[status(thm)],[])).
% 6.86/4.58 tff(90,plain,
% 6.86/4.58 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(A)))) | (cast_to_el_of_lattice(A, B) = B)))) | empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | ![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, B) = B))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[89, 88])).
% 6.86/4.58 tff(91,plain,
% 6.86/4.58 (![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, B) = B))),
% 6.86/4.58 inference(unit_resolution,[status(thm)],[90, 87, 20, 19, 18])).
% 6.86/4.58 tff(92,plain,
% 6.86/4.58 (((~![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, B) = B))) | ((~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, C!18) = C!18))) <=> ((~![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, B) = B))) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, C!18) = C!18))),
% 6.86/4.58 inference(rewrite,[status(thm)],[])).
% 6.86/4.58 tff(93,plain,
% 6.86/4.58 ((~![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, B) = B))) | ((~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, C!18) = C!18))),
% 6.86/4.58 inference(quant_inst,[status(thm)],[])).
% 6.86/4.58 tff(94,plain,
% 6.86/4.58 ((~![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, B) = B))) | (~element(C!18, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, C!18) = C!18)),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[93, 92])).
% 6.86/4.58 tff(95,plain,
% 6.86/4.58 (cast_to_el_of_lattice(B!16, C!18) = C!18),
% 6.86/4.58 inference(unit_resolution,[status(thm)],[94, 17, 91])).
% 6.86/4.58 tff(96,plain,
% 6.86/4.58 (C!18 = cast_to_el_of_lattice(B!16, C!18)),
% 6.86/4.58 inference(symmetry,[status(thm)],[95])).
% 6.86/4.58 tff(97,plain,
% 6.86/4.58 (C!18 = cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18))),
% 6.86/4.58 inference(transitivity,[status(thm)],[96, 68])).
% 6.86/4.58 tff(98,plain,
% 6.86/4.58 (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))),
% 6.86/4.58 inference(monotonicity,[status(thm)],[97])).
% 6.86/4.58 tff(99,plain,
% 6.86/4.58 ((~relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18)) <=> (~relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18))))),
% 6.86/4.58 inference(monotonicity,[status(thm)],[98])).
% 6.86/4.58 tff(100,assumption,(~latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)), introduced(assumption)).
% 6.86/4.58 tff(101,plain,
% 6.86/4.58 ((~(relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17))) <=> ((~relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18)) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17))),
% 6.86/4.58 inference(rewrite,[status(thm)],[])).
% 6.86/4.58 tff(102,plain,
% 6.86/4.58 (~(relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17))),
% 6.86/4.58 inference(or_elim,[status(thm)],[16])).
% 6.86/4.58 tff(103,plain,
% 6.86/4.58 ((~relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18)) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[102, 101])).
% 6.86/4.58 tff(104,plain,
% 6.86/4.58 (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) | latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) | (~((~relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18)) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)))),
% 6.86/4.58 inference(tautology,[status(thm)],[])).
% 6.86/4.58 tff(105,plain,
% 6.86/4.58 (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18) | latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)),
% 6.86/4.58 inference(unit_resolution,[status(thm)],[104, 103])).
% 6.86/4.58 tff(106,plain,
% 6.86/4.58 (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18)),
% 6.86/4.58 inference(unit_resolution,[status(thm)],[105, 100])).
% 6.86/4.58 tff(107,plain,
% 6.86/4.58 (relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[106, 98])).
% 6.86/4.58 tff(108,plain,
% 6.86/4.58 (^[A: $i, B: $i, C: $i] : rewrite((empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B))))),
% 6.86/4.58 inference(bind,[status(th)],[])).
% 6.86/4.58 tff(109,plain,
% 6.86/4.58 (![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B)))),
% 6.86/4.58 inference(quant_intro,[status(thm)],[108])).
% 6.86/4.58 tff(110,plain,
% 6.86/4.58 (^[A: $i, B: $i, C: $i] : refl((empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))))),
% 6.86/4.58 inference(bind,[status(th)],[])).
% 6.86/4.58 tff(111,plain,
% 6.86/4.58 (![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))),
% 6.86/4.58 inference(quant_intro,[status(thm)],[110])).
% 6.86/4.58 tff(112,plain,
% 6.86/4.58 (![A: $i, B: $i] : ![C: $i] : (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))),
% 6.86/4.58 inference(pull_quant,[status(thm)],[])).
% 6.86/4.58 tff(113,plain,
% 6.86/4.58 (^[A: $i, B: $i] : pull_quant((empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> ![C: $i] : (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))))),
% 6.86/4.58 inference(bind,[status(th)],[])).
% 6.86/4.58 tff(114,plain,
% 6.86/4.58 (![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> ![A: $i, B: $i] : ![C: $i] : (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))),
% 6.86/4.58 inference(quant_intro,[status(thm)],[113])).
% 6.86/4.58 tff(115,plain,
% 6.86/4.58 (![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))),
% 6.86/4.58 inference(transitivity,[status(thm)],[114, 112])).
% 6.86/4.58 tff(116,plain,
% 6.86/4.58 (![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))),
% 6.86/4.58 inference(transitivity,[status(thm)],[115, 111])).
% 6.86/4.58 tff(117,plain,
% 6.86/4.58 (^[A: $i, B: $i] : rewrite((empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> (empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))))),
% 6.86/4.58 inference(bind,[status(th)],[])).
% 6.86/4.58 tff(118,plain,
% 6.86/4.58 (![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> ![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))),
% 6.86/4.58 inference(quant_intro,[status(thm)],[117])).
% 6.86/4.58 tff(119,plain,
% 6.86/4.58 (![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))),
% 6.86/4.58 inference(transitivity,[status(thm)],[118, 116])).
% 6.86/4.58 tff(120,plain,
% 6.86/4.58 (^[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))))), (((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))) <=> ((empty_carrier(B) | (~latt_str(B)) | (~lattice(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))))), rewrite(((empty_carrier(B) | (~latt_str(B)) | (~lattice(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))) <=> (empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))), (((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))) <=> (empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))))),
% 6.86/4.58 inference(bind,[status(th)],[])).
% 6.86/4.58 tff(121,plain,
% 6.86/4.58 (![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))) <=> ![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))),
% 6.86/4.58 inference(quant_intro,[status(thm)],[120])).
% 6.86/4.58 tff(122,plain,
% 6.86/4.58 (![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.86/4.58 inference(rewrite,[status(thm)],[])).
% 6.86/4.58 tff(123,plain,
% 6.86/4.58 (^[A: $i, B: $i] : trans(monotonicity(rewrite((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) <=> ((~empty_carrier(B)) & lattice(B) & latt_str(B))), quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(B)) => (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) <=> ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))), (![C: $i] : (element(C, the_carrier(B)) => (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) <=> ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))), (((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => ![C: $i] : (element(C, the_carrier(B)) => (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))) <=> (((~empty_carrier(B)) & lattice(B) & latt_str(B)) => ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))))), rewrite((((~empty_carrier(B)) & lattice(B) & latt_str(B)) => ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))) <=> ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))), (((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => ![C: $i] : (element(C, the_carrier(B)) => (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))) <=> ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))))),
% 6.86/4.58 inference(bind,[status(th)],[])).
% 6.86/4.58 tff(124,plain,
% 6.86/4.58 (![A: $i, B: $i] : ((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => ![C: $i] : (element(C, the_carrier(B)) => (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.86/4.58 inference(quant_intro,[status(thm)],[123])).
% 6.86/4.58 tff(125,axiom,(![A: $i, B: $i] : ((((~empty_carrier(B)) & lattice(B)) & latt_str(B)) => ![C: $i] : (element(C, the_carrier(B)) => (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t30_lattice3')).
% 6.86/4.58 tff(126,plain,
% 6.86/4.58 (![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[125, 124])).
% 6.86/4.58 tff(127,plain,
% 6.86/4.58 (![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[126, 122])).
% 6.86/4.58 tff(128,plain,(
% 6.86/4.58 ![A: $i, B: $i] : ((~((~empty_carrier(B)) & lattice(B) & latt_str(B))) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))))),
% 6.86/4.58 inference(skolemize,[status(sab)],[127])).
% 6.86/4.58 tff(129,plain,
% 6.86/4.58 (![A: $i, B: $i] : (empty_carrier(B) | (~latt_str(B)) | ![C: $i] : ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[128, 121])).
% 6.86/4.58 tff(130,plain,
% 6.86/4.58 (![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | ((~element(C, the_carrier(B))) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C)))) | (~lattice(B)))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[129, 119])).
% 6.86/4.58 tff(131,plain,
% 6.86/4.58 (![A: $i, B: $i, C: $i] : (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B)))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[130, 109])).
% 6.86/4.58 tff(132,plain,
% 6.86/4.58 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B)))) | (empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B)))) | empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))))),
% 6.86/4.58 inference(rewrite,[status(thm)],[])).
% 6.86/4.58 tff(133,plain,
% 6.86/4.58 ((empty_carrier(B!16) | (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))) | (~lattice(B!16)) | (~latt_str(B!16))) <=> (empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))))),
% 6.86/4.58 inference(rewrite,[status(thm)],[])).
% 6.86/4.58 tff(134,plain,
% 6.86/4.58 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B)))) | (empty_carrier(B!16) | (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))) | (~lattice(B!16)) | (~latt_str(B!16)))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B)))) | (empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16)))))),
% 6.86/4.58 inference(monotonicity,[status(thm)],[133])).
% 6.86/4.58 tff(135,plain,
% 6.86/4.58 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B)))) | (empty_carrier(B!16) | (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))) | (~lattice(B!16)) | (~latt_str(B!16)))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B)))) | empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))))),
% 6.86/4.58 inference(transitivity,[status(thm)],[134, 132])).
% 6.86/4.58 tff(136,plain,
% 6.86/4.58 ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B)))) | (empty_carrier(B!16) | (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))) | (~lattice(B!16)) | (~latt_str(B!16)))),
% 6.86/4.58 inference(quant_inst,[status(thm)],[])).
% 6.86/4.58 tff(137,plain,
% 6.86/4.58 ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B)))) | empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16)))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[136, 135])).
% 6.86/4.58 tff(138,plain,
% 6.86/4.58 (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))),
% 6.86/4.58 inference(unit_resolution,[status(thm)],[137, 131, 20, 19, 18, 40])).
% 6.86/4.58 tff(139,plain,
% 6.86/4.58 ((~(latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18))))) | latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) | (~relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18))))),
% 6.86/4.58 inference(tautology,[status(thm)],[])).
% 6.86/4.58 tff(140,plain,
% 6.86/4.58 (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) | (~relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18))))),
% 6.86/4.58 inference(unit_resolution,[status(thm)],[139, 138])).
% 6.86/4.58 tff(141,plain,
% 6.86/4.58 (~relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))),
% 6.86/4.58 inference(unit_resolution,[status(thm)],[140, 100])).
% 6.86/4.58 tff(142,plain,
% 6.86/4.58 ($false),
% 6.86/4.58 inference(unit_resolution,[status(thm)],[141, 107])).
% 6.86/4.58 tff(143,plain,(latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)), inference(lemma,lemma(discharge,[]))).
% 6.86/4.58 tff(144,plain,
% 6.86/4.58 ((~relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18)) | (~latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)) | (~((~relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18)) <=> latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)))),
% 6.86/4.58 inference(tautology,[status(thm)],[])).
% 6.86/4.58 tff(145,plain,
% 6.86/4.58 ((~relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18)) | (~latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17))),
% 6.86/4.58 inference(unit_resolution,[status(thm)],[144, 103])).
% 6.86/4.58 tff(146,plain,
% 6.86/4.58 (~relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18)),
% 6.86/4.58 inference(unit_resolution,[status(thm)],[145, 143])).
% 6.86/4.58 tff(147,plain,
% 6.86/4.58 (~relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))),
% 6.86/4.58 inference(modus_ponens,[status(thm)],[146, 99])).
% 6.86/4.60 tff(148,plain,
% 6.86/4.60 ((~(latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18))))) | (~latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)) | relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))),
% 6.86/4.60 inference(tautology,[status(thm)],[])).
% 6.86/4.60 tff(149,plain,
% 6.86/4.60 ((~latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)) | relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))),
% 6.86/4.60 inference(unit_resolution,[status(thm)],[148, 138])).
% 6.86/4.60 tff(150,plain,
% 6.86/4.60 (relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))),
% 6.86/4.60 inference(unit_resolution,[status(thm)],[149, 143])).
% 6.86/4.60 tff(151,plain,
% 6.86/4.60 ($false),
% 6.86/4.60 inference(unit_resolution,[status(thm)],[150, 147])).
% 6.86/4.60 % SZS output end Proof
%------------------------------------------------------------------------------