%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU355+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 05:27:41 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU355+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % 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 06:51:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(in_type, type, (
% 0.21/0.39 in: ( $i * $i ) > $o)).
% 0.21/0.39 tff(empty_set_type, type, (
% 0.21/0.39 empty_set: $i)).
% 0.21/0.39 tff(tptp_fun_D_1_type, type, (
% 0.21/0.39 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_A_8_type, type, (
% 0.21/0.39 tptp_fun_A_8: $i)).
% 0.21/0.39 tff(tptp_fun_B_9_type, type, (
% 0.21/0.39 tptp_fun_B_9: $i)).
% 0.21/0.39 tff(related_type, type, (
% 0.21/0.39 related: ( $i * $i * $i ) > $o)).
% 0.21/0.39 tff(element_type, type, (
% 0.21/0.39 element: ( $i * $i ) > $o)).
% 0.21/0.39 tff(the_carrier_type, type, (
% 0.21/0.39 the_carrier: $i > $i)).
% 0.21/0.39 tff(relstr_set_smaller_type, type, (
% 0.21/0.39 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 0.21/0.39 tff(rel_str_type, type, (
% 0.21/0.39 rel_str: $i > $o)).
% 0.21/0.39 tff(relstr_element_smaller_type, type, (
% 0.21/0.39 relstr_element_smaller: ( $i * $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_D_0_type, type, (
% 0.21/0.39 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(empty_type, type, (
% 0.21/0.39 empty: $i > $o)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))) <=> (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 ((~![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))) <=> (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(3,axiom,(~![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t6_yellow_0')).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (rel_str(A!8)),
% 0.21/0.39 inference(and_elim,[status(thm)],[7])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[12, 10])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(rewrite((relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))) <=> (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))), ((element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))) <=> (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), rewrite((element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) <=> ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))))), ((element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))) <=> ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))))))), (![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))))) <=> (rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))))))), rewrite((rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.39 tff(19,axiom,(![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_lattice3')).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.21/0.39 tff(22,plain,(
% 0.21/0.39 ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[21])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~((~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(C, B, A!8), B)) | related(A!8, tptp_fun_D_1(C, B, A!8), C)))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~((~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(C, B, A!8), B)) | related(A!8, tptp_fun_D_1(C, B, A!8), C)))))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, D, C) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))))))))))) <=> ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~((~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(C, B, A!8), B)) | related(A!8, tptp_fun_D_1(C, B, A!8), C)))))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, D, C) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~((~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(C, B, A!8), B)) | related(A!8, tptp_fun_D_1(C, B, A!8), C))))))))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[26])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, D, C) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~((~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(C, B, A!8), B)) | related(A!8, tptp_fun_D_1(C, B, A!8), C)))))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[27, 25])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, D, C) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8)))))))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~((~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(C, B, A!8), B)) | related(A!8, tptp_fun_D_1(C, B, A!8), C))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~((~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(C, B, A!8), B)) | related(A!8, tptp_fun_D_1(C, B, A!8), C))))))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[30, 24, 8])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (~((~element(B!9, the_carrier(A!8))) | (relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9)))),
% 0.21/0.40 inference(and_elim,[status(thm)],[7])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (element(B!9, the_carrier(A!8))),
% 0.21/0.40 inference(or_elim,[status(thm)],[32])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~((~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(C, B, A!8), B)) | related(A!8, tptp_fun_D_1(C, B, A!8), C))))))))) | ((~element(B!9, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~((~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(C, B, A!8), B)) | related(A!8, tptp_fun_D_1(C, B, A!8), C))))))))) | (~element(B!9, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9))))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~((~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(C, B, A!8), B)) | related(A!8, tptp_fun_D_1(C, B, A!8), C))))))))) | ((~element(B!9, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9))))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~((~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(C, B, A!8), B)) | related(A!8, tptp_fun_D_1(C, B, A!8), C))))))))) | (~element(B!9, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (~((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9))))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[36, 33, 31])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 (((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9)))))) | (relstr_set_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 (relstr_set_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.40 tff(40,assumption,((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8))))))), introduced(assumption)).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[44, 42])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(rewrite((relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))) <=> (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))), ((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), rewrite((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) <=> ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))), ((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))))), (![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> (rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))))), rewrite((rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.41 tff(51,axiom,(![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_lattice3')).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.21/0.41 tff(54,plain,(
% 0.21/0.41 ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[53])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~((~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(C, B, A!8), B)) | related(A!8, C, tptp_fun_D_0(C, B, A!8))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~((~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(C, B, A!8), B)) | related(A!8, C, tptp_fun_D_0(C, B, A!8))))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))))))))))) <=> ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~((~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(C, B, A!8), B)) | related(A!8, C, tptp_fun_D_0(C, B, A!8))))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~((~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(C, B, A!8), B)) | related(A!8, C, tptp_fun_D_0(C, B, A!8)))))))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~((~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(C, B, A!8), B)) | related(A!8, C, tptp_fun_D_0(C, B, A!8))))))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[59, 57])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8)))))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~((~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(C, B, A!8), B)) | related(A!8, C, tptp_fun_D_0(C, B, A!8)))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~((~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(C, B, A!8), B)) | related(A!8, C, tptp_fun_D_0(C, B, A!8)))))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[62, 56, 8])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~((~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(C, B, A!8), B)) | related(A!8, C, tptp_fun_D_0(C, B, A!8)))))))))) | ((~element(B!9, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~((~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(C, B, A!8), B)) | related(A!8, C, tptp_fun_D_0(C, B, A!8)))))))))) | (~element(B!9, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~((~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(C, B, A!8), B)) | related(A!8, C, tptp_fun_D_0(C, B, A!8)))))))))) | ((~element(B!9, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~((~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(C, B, A!8), B)) | related(A!8, C, tptp_fun_D_0(C, B, A!8)))))))))) | (~element(B!9, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[66, 33, 63, 40])).
% 0.21/0.42 tff(68,plain,(~((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8))))))) | (relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 (relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.42 tff(71,assumption,(in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)), introduced(assumption)).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(77,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.42 tff(79,plain,(
% 0.21/0.42 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[78])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (empty(empty_set) <=> empty(empty_set)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(83,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (empty(empty_set)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[87, 84, 81, 71])).
% 0.21/0.42 tff(89,plain,(~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8))) | in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 ((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 ((~(relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)))))) | relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 ((~(relstr_element_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)))))) | relstr_element_smaller(A!8, empty_set, B!9)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (relstr_element_smaller(A!8, empty_set, B!9)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[93, 70])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 ((~(~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9))))) <=> ((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 ((relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9)) <=> (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 ((~(relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9))) <=> (~(~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[96])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 ((~(relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9))) <=> ((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[97, 95])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (~(relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9))),
% 0.21/0.42 inference(or_elim,[status(thm)],[32])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 ((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (~relstr_set_smaller(A!8, empty_set, B!9)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[100, 94])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 ((~(relstr_set_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9))))) | relstr_set_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 ((~(relstr_set_smaller(A!8, empty_set, B!9) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9))))) | (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 (~((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[103, 39])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (((~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9)) | in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[109, 84, 81, 106])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------