%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU350+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 : Sat Jun 21 05:27:40 AM UTC 2025
% Result : Theorem 4.78s 4.99s
% Output : Proof 4.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU350+1 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.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 : Fri Jun 20 06:50:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.78/4.99 % SZS status Theorem
% 4.78/4.99 % SZS output start Proof
% 4.78/4.99 tff(relstr_set_smaller_type, type, (
% 4.78/4.99 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 4.78/4.99 tff(cast_to_el_of_LattPOSet_type, type, (
% 4.78/4.99 cast_to_el_of_LattPOSet: ( $i * $i ) > $i)).
% 4.78/4.99 tff(cast_to_el_of_lattice_type, type, (
% 4.78/4.99 cast_to_el_of_lattice: ( $i * $i ) > $i)).
% 4.78/4.99 tff(tptp_fun_C_18_type, type, (
% 4.78/4.99 tptp_fun_C_18: $i)).
% 4.78/4.99 tff(tptp_fun_B_16_type, type, (
% 4.78/4.99 tptp_fun_B_16: $i)).
% 4.78/4.99 tff(tptp_fun_A_17_type, type, (
% 4.78/4.99 tptp_fun_A_17: $i)).
% 4.78/4.99 tff(poset_of_lattice_type, type, (
% 4.78/4.99 poset_of_lattice: $i > $i)).
% 4.78/4.99 tff(element_type, type, (
% 4.78/4.99 element: ( $i * $i ) > $o)).
% 4.78/4.99 tff(the_carrier_type, type, (
% 4.78/4.99 the_carrier: $i > $i)).
% 4.78/4.99 tff(latt_element_smaller_type, type, (
% 4.78/4.99 latt_element_smaller: ( $i * $i * $i ) > $o)).
% 4.78/4.99 tff(latt_str_type, type, (
% 4.78/4.99 latt_str: $i > $o)).
% 4.78/4.99 tff(lattice_type, type, (
% 4.78/4.99 lattice: $i > $o)).
% 4.78/4.99 tff(empty_carrier_type, type, (
% 4.78/4.99 empty_carrier: $i > $o)).
% 4.78/4.99 tff(1,plain,
% 4.78/4.99 ((((~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)))))),
% 4.78/4.99 inference(rewrite,[status(thm)],[])).
% 4.78/4.99 tff(2,plain,
% 4.78/4.99 ((~![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)))))),
% 4.78/4.99 inference(rewrite,[status(thm)],[])).
% 4.78/4.99 tff(3,plain,
% 4.78/4.99 ((~![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)))))),
% 4.78/4.99 inference(rewrite,[status(thm)],[])).
% 4.78/4.99 tff(4,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/sandbox2/benchmark/theBenchmark.p','t31_lattice3')).
% 4.78/4.99 tff(5,plain,
% 4.78/4.99 (~![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))))),
% 4.78/4.99 inference(modus_ponens,[status(thm)],[4, 3])).
% 4.78/4.99 tff(6,plain,
% 4.78/4.99 (~![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))))),
% 4.78/4.99 inference(modus_ponens,[status(thm)],[5, 2])).
% 4.78/4.99 tff(7,plain,
% 4.78/4.99 (~![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))))),
% 4.78/4.99 inference(modus_ponens,[status(thm)],[6, 2])).
% 4.78/4.99 tff(8,plain,
% 4.78/4.99 (~![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))))),
% 4.78/4.99 inference(modus_ponens,[status(thm)],[7, 2])).
% 4.78/4.99 tff(9,plain,
% 4.78/4.99 ((~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))))),
% 4.78/4.99 inference(modus_ponens,[status(thm)],[8, 1])).
% 4.78/4.99 tff(10,plain,
% 4.78/4.99 (~((~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)))),
% 4.78/4.99 inference(and_elim,[status(thm)],[9])).
% 4.78/4.99 tff(11,plain,
% 4.78/4.99 (element(C!18, the_carrier(poset_of_lattice(B!16)))),
% 4.78/4.99 inference(or_elim,[status(thm)],[10])).
% 4.78/4.99 tff(12,plain,
% 4.78/4.99 (latt_str(B!16)),
% 4.78/4.99 inference(and_elim,[status(thm)],[9])).
% 4.78/4.99 tff(13,plain,
% 4.78/4.99 (lattice(B!16)),
% 4.78/4.99 inference(and_elim,[status(thm)],[9])).
% 4.78/4.99 tff(14,plain,
% 4.78/4.99 (~empty_carrier(B!16)),
% 4.78/4.99 inference(and_elim,[status(thm)],[9])).
% 4.78/4.99 tff(15,plain,
% 4.78/4.99 (^[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))))),
% 4.78/4.99 inference(bind,[status(th)],[])).
% 4.78/4.99 tff(16,plain,
% 4.78/4.99 (![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)))),
% 4.78/4.99 inference(quant_intro,[status(thm)],[15])).
% 4.78/4.99 tff(17,plain,
% 4.78/4.99 (^[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)))))),
% 4.78/4.99 inference(bind,[status(th)],[])).
% 4.78/4.99 tff(18,plain,
% 4.78/4.99 (![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)))),
% 4.78/4.99 inference(quant_intro,[status(thm)],[17])).
% 4.78/4.99 tff(19,plain,
% 4.78/4.99 (![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)))),
% 4.78/4.99 inference(rewrite,[status(thm)],[])).
% 4.78/4.99 tff(20,plain,
% 4.78/4.99 (^[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)))))),
% 4.78/4.99 inference(bind,[status(th)],[])).
% 4.78/4.99 tff(21,plain,
% 4.78/4.99 (![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)))),
% 4.78/4.99 inference(quant_intro,[status(thm)],[20])).
% 4.78/4.99 tff(22,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/sandbox2/benchmark/theBenchmark.p','dt_k5_lattice3')).
% 4.78/4.99 tff(23,plain,
% 4.78/4.99 (![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)))),
% 4.78/4.99 inference(modus_ponens,[status(thm)],[22, 21])).
% 4.78/4.99 tff(24,plain,
% 4.78/4.99 (![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)))),
% 4.78/4.99 inference(modus_ponens,[status(thm)],[23, 19])).
% 4.78/4.99 tff(25,plain,(
% 4.78/4.99 ![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)))),
% 4.78/4.99 inference(skolemize,[status(sab)],[24])).
% 4.78/4.99 tff(26,plain,
% 4.78/4.99 (![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)))),
% 4.78/4.99 inference(modus_ponens,[status(thm)],[25, 18])).
% 4.78/4.99 tff(27,plain,
% 4.78/4.99 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[26, 16])).
% 4.78/5.00 tff(28,plain,
% 4.78/5.00 (((~![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)))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(29,plain,
% 4.78/5.00 ((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)))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(30,plain,
% 4.78/5.00 (((~![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))))),
% 4.78/5.00 inference(monotonicity,[status(thm)],[29])).
% 4.78/5.00 tff(31,plain,
% 4.78/5.00 (((~![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)))),
% 4.78/5.00 inference(transitivity,[status(thm)],[30, 28])).
% 4.78/5.00 tff(32,plain,
% 4.78/5.00 ((~![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)))),
% 4.78/5.00 inference(quant_inst,[status(thm)],[])).
% 4.78/5.00 tff(33,plain,
% 4.78/5.00 ((~![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))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[32, 31])).
% 4.78/5.00 tff(34,plain,
% 4.78/5.00 (element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16))),
% 4.78/5.00 inference(unit_resolution,[status(thm)],[33, 27, 14, 13, 12, 11])).
% 4.78/5.00 tff(35,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(36,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[35])).
% 4.78/5.00 tff(37,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(38,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[37])).
% 4.78/5.00 tff(39,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(40,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[39])).
% 4.78/5.00 tff(41,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(transitivity,[status(thm)],[40, 38])).
% 4.78/5.00 tff(42,plain,
% 4.78/5.00 (^[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)))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(43,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[42])).
% 4.78/5.00 tff(44,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(45,plain,
% 4.78/5.00 (^[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)))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(46,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[45])).
% 4.78/5.00 tff(47,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/sandbox2/benchmark/theBenchmark.p','d3_lattice3')).
% 4.78/5.00 tff(48,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[47, 46])).
% 4.78/5.00 tff(49,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[48, 44])).
% 4.78/5.00 tff(50,plain,(
% 4.78/5.00 ![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)))),
% 4.78/5.00 inference(skolemize,[status(sab)],[49])).
% 4.78/5.00 tff(51,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[50, 43])).
% 4.78/5.00 tff(52,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[51, 41])).
% 4.78/5.00 tff(53,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[52, 36])).
% 4.78/5.00 tff(54,plain,
% 4.78/5.00 (((~![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)))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(55,plain,
% 4.78/5.00 ((~![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)))),
% 4.78/5.00 inference(quant_inst,[status(thm)],[])).
% 4.78/5.00 tff(56,plain,
% 4.78/5.00 ((~![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))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[55, 54])).
% 4.78/5.00 tff(57,plain,
% 4.78/5.00 (![B: $i] : ((~element(B, the_carrier(B!16))) | (cast_to_el_of_LattPOSet(B!16, B) = B))),
% 4.78/5.00 inference(unit_resolution,[status(thm)],[56, 53, 14, 13, 12])).
% 4.78/5.00 tff(58,plain,
% 4.78/5.00 (((~![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)))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(59,plain,
% 4.78/5.00 ((~![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)))),
% 4.78/5.00 inference(quant_inst,[status(thm)],[])).
% 4.78/5.00 tff(60,plain,
% 4.78/5.00 ((~![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))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[59, 58])).
% 4.78/5.00 tff(61,plain,
% 4.78/5.00 (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)),
% 4.78/5.00 inference(unit_resolution,[status(thm)],[60, 57, 34])).
% 4.78/5.00 tff(62,plain,
% 4.78/5.00 (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))),
% 4.78/5.00 inference(symmetry,[status(thm)],[61])).
% 4.78/5.00 tff(63,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(64,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[63])).
% 4.78/5.00 tff(65,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(66,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[65])).
% 4.78/5.00 tff(67,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(68,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[67])).
% 4.78/5.00 tff(69,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(transitivity,[status(thm)],[68, 66])).
% 4.78/5.00 tff(70,plain,
% 4.78/5.00 (^[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)))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(71,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[70])).
% 4.78/5.00 tff(72,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(73,plain,
% 4.78/5.00 (^[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)))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(74,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[73])).
% 4.78/5.00 tff(75,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/sandbox2/benchmark/theBenchmark.p','d4_lattice3')).
% 4.78/5.00 tff(76,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[75, 74])).
% 4.78/5.00 tff(77,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[76, 72])).
% 4.78/5.00 tff(78,plain,(
% 4.78/5.00 ![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)))),
% 4.78/5.00 inference(skolemize,[status(sab)],[77])).
% 4.78/5.00 tff(79,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[78, 71])).
% 4.78/5.00 tff(80,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[79, 69])).
% 4.78/5.00 tff(81,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[80, 64])).
% 4.78/5.00 tff(82,plain,
% 4.78/5.00 (((~![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)))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(83,plain,
% 4.78/5.00 ((~![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)))),
% 4.78/5.00 inference(quant_inst,[status(thm)],[])).
% 4.78/5.00 tff(84,plain,
% 4.78/5.00 ((~![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))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[83, 82])).
% 4.78/5.00 tff(85,plain,
% 4.78/5.00 (![B: $i] : ((~element(B, the_carrier(poset_of_lattice(B!16)))) | (cast_to_el_of_lattice(B!16, B) = B))),
% 4.78/5.00 inference(unit_resolution,[status(thm)],[84, 81, 14, 13, 12])).
% 4.78/5.00 tff(86,plain,
% 4.78/5.00 (((~![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))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(87,plain,
% 4.78/5.00 ((~![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))),
% 4.78/5.00 inference(quant_inst,[status(thm)],[])).
% 4.78/5.00 tff(88,plain,
% 4.78/5.00 ((~![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)),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[87, 86])).
% 4.78/5.00 tff(89,plain,
% 4.78/5.00 (cast_to_el_of_lattice(B!16, C!18) = C!18),
% 4.78/5.00 inference(unit_resolution,[status(thm)],[88, 11, 85])).
% 4.78/5.00 tff(90,plain,
% 4.78/5.00 (C!18 = cast_to_el_of_lattice(B!16, C!18)),
% 4.78/5.00 inference(symmetry,[status(thm)],[89])).
% 4.78/5.00 tff(91,plain,
% 4.78/5.00 (C!18 = cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18))),
% 4.78/5.00 inference(transitivity,[status(thm)],[90, 62])).
% 4.78/5.00 tff(92,plain,
% 4.78/5.00 (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)))),
% 4.78/5.00 inference(monotonicity,[status(thm)],[91])).
% 4.78/5.00 tff(93,plain,
% 4.78/5.00 ((~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))))),
% 4.78/5.00 inference(monotonicity,[status(thm)],[92])).
% 4.78/5.00 tff(94,assumption,(~latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)), introduced(assumption)).
% 4.78/5.00 tff(95,plain,
% 4.78/5.00 (~(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))),
% 4.78/5.00 inference(or_elim,[status(thm)],[10])).
% 4.78/5.00 tff(96,plain,
% 4.78/5.00 ((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)),
% 4.78/5.00 inference(tautology,[status(thm)],[])).
% 4.78/5.00 tff(97,plain,
% 4.78/5.00 (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)),
% 4.78/5.00 inference(unit_resolution,[status(thm)],[96, 95])).
% 4.78/5.00 tff(98,plain,
% 4.78/5.00 (relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18)),
% 4.78/5.00 inference(unit_resolution,[status(thm)],[97, 94])).
% 4.78/5.00 tff(99,plain,
% 4.78/5.00 (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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[98, 92])).
% 4.78/5.00 tff(100,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(101,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[100])).
% 4.78/5.00 tff(102,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(103,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[102])).
% 4.78/5.00 tff(104,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(pull_quant,[status(thm)],[])).
% 4.78/5.00 tff(105,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(106,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[105])).
% 4.78/5.00 tff(107,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(transitivity,[status(thm)],[106, 104])).
% 4.78/5.00 tff(108,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(transitivity,[status(thm)],[107, 103])).
% 4.78/5.00 tff(109,plain,
% 4.78/5.00 (^[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))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(110,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[109])).
% 4.78/5.00 tff(111,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(transitivity,[status(thm)],[110, 108])).
% 4.78/5.00 tff(112,plain,
% 4.78/5.00 (^[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)))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(113,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[112])).
% 4.78/5.00 tff(114,plain,
% 4.78/5.00 (![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)))))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(115,plain,
% 4.78/5.00 (^[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)))))))),
% 4.78/5.00 inference(bind,[status(th)],[])).
% 4.78/5.00 tff(116,plain,
% 4.78/5.00 (![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)))))),
% 4.78/5.00 inference(quant_intro,[status(thm)],[115])).
% 4.78/5.00 tff(117,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/sandbox2/benchmark/theBenchmark.p','t30_lattice3')).
% 4.78/5.00 tff(118,plain,
% 4.78/5.00 (![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)))))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[117, 116])).
% 4.78/5.00 tff(119,plain,
% 4.78/5.00 (![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)))))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[118, 114])).
% 4.78/5.00 tff(120,plain,(
% 4.78/5.00 ![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)))))),
% 4.78/5.00 inference(skolemize,[status(sab)],[119])).
% 4.78/5.00 tff(121,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[120, 113])).
% 4.78/5.00 tff(122,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[121, 111])).
% 4.78/5.00 tff(123,plain,
% 4.78/5.00 (![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)))),
% 4.78/5.00 inference(modus_ponens,[status(thm)],[122, 101])).
% 4.78/5.00 tff(124,plain,
% 4.78/5.00 (((~![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))))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(125,plain,
% 4.78/5.00 ((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))))),
% 4.78/5.00 inference(rewrite,[status(thm)],[])).
% 4.78/5.00 tff(126,plain,
% 4.78/5.00 (((~![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)))))),
% 4.78/5.01 inference(monotonicity,[status(thm)],[125])).
% 4.78/5.01 tff(127,plain,
% 4.78/5.01 (((~![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))))),
% 4.78/5.01 inference(transitivity,[status(thm)],[126, 124])).
% 4.78/5.01 tff(128,plain,
% 4.78/5.01 ((~![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)))),
% 4.78/5.01 inference(quant_inst,[status(thm)],[])).
% 4.78/5.01 tff(129,plain,
% 4.78/5.01 ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (latt_element_smaller(B, C, A) <=> relstr_set_smaller(poset_of_lattice(B), A, cast_to_el_of_LattPOSet(B, C))) | (~element(C, the_carrier(B))) | (~lattice(B)) | (~latt_str(B)))) | empty_carrier(B!16) | (~latt_str(B!16)) | (~lattice(B!16)) | (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))) | (~element(cast_to_el_of_lattice(B!16, C!18), the_carrier(B!16)))),
% 4.78/5.01 inference(modus_ponens,[status(thm)],[128, 127])).
% 4.78/5.01 tff(130,plain,
% 4.78/5.01 (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))),
% 4.78/5.01 inference(unit_resolution,[status(thm)],[129, 123, 14, 13, 12, 34])).
% 4.78/5.01 tff(131,plain,
% 4.78/5.01 ((~(latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) <=> relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18))))) | latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) | (~relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18))))),
% 4.78/5.01 inference(tautology,[status(thm)],[])).
% 4.78/5.01 tff(132,plain,
% 4.78/5.01 (latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17) | (~relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18))))),
% 4.78/5.01 inference(unit_resolution,[status(thm)],[131, 130])).
% 4.78/5.01 tff(133,plain,
% 4.78/5.01 (~relstr_set_smaller(poset_of_lattice(B!16), A!17, cast_to_el_of_LattPOSet(B!16, cast_to_el_of_lattice(B!16, C!18)))),
% 4.86/5.03 inference(unit_resolution,[status(thm)],[132, 94])).
% 4.86/5.03 tff(134,plain,
% 4.86/5.03 ($false),
% 4.86/5.03 inference(unit_resolution,[status(thm)],[133, 99])).
% 4.86/5.03 tff(135,plain,(latt_element_smaller(B!16, cast_to_el_of_lattice(B!16, C!18), A!17)), inference(lemma,lemma(discharge,[]))).
% 4.86/5.03 tff(136,plain,
% 4.86/5.03 ((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))),
% 4.86/5.03 inference(tautology,[status(thm)],[])).
% 4.86/5.03 tff(137,plain,
% 4.86/5.03 ((~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))),
% 4.86/5.03 inference(unit_resolution,[status(thm)],[136, 95])).
% 4.86/5.03 tff(138,plain,
% 4.86/5.03 (~relstr_set_smaller(poset_of_lattice(B!16), A!17, C!18)),
% 4.86/5.03 inference(unit_resolution,[status(thm)],[137, 135])).
% 4.86/5.03 tff(139,plain,
% 4.86/5.03 (~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)))),
% 4.86/5.03 inference(modus_ponens,[status(thm)],[138, 93])).
% 4.86/5.03 tff(140,plain,
% 4.86/5.03 ((~(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)))),
% 4.86/5.03 inference(tautology,[status(thm)],[])).
% 4.86/5.03 tff(141,plain,
% 4.86/5.03 ((~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)))),
% 4.86/5.03 inference(unit_resolution,[status(thm)],[140, 130])).
% 4.86/5.03 tff(142,plain,
% 4.86/5.03 (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)))),
% 4.86/5.03 inference(unit_resolution,[status(thm)],[141, 135])).
% 4.86/5.03 tff(143,plain,
% 4.86/5.03 ($false),
% 4.86/5.03 inference(unit_resolution,[status(thm)],[142, 139])).
% 4.86/5.03 % SZS output end Proof
% 4.86/5.04 % E exiting
%------------------------------------------------------------------------------