%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU359+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:27:42 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU359+1 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:52:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(join_on_relstr_type, type, (
% 0.12/0.38 join_on_relstr: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_C_7_type, type, (
% 0.12/0.38 tptp_fun_C_7: $i)).
% 0.12/0.38 tff(tptp_fun_A_5_type, type, (
% 0.12/0.38 tptp_fun_A_5: $i)).
% 0.12/0.38 tff(tptp_fun_B_6_type, type, (
% 0.12/0.38 tptp_fun_B_6: $i)).
% 0.12/0.38 tff(related_type, type, (
% 0.12/0.38 related: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_D_0_type, type, (
% 0.12/0.38 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.12/0.38 tff(relstr_set_smaller_type, type, (
% 0.12/0.38 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(element_type, type, (
% 0.12/0.38 element: ( $i * $i ) > $o)).
% 0.12/0.38 tff(the_carrier_type, type, (
% 0.12/0.38 the_carrier: $i > $i)).
% 0.12/0.38 tff(ex_sup_of_relstr_set_type, type, (
% 0.12/0.38 ex_sup_of_relstr_set: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_C_4_type, type, (
% 0.12/0.38 tptp_fun_C_4: ( $i * $i ) > $i)).
% 0.12/0.38 tff(rel_str_type, type, (
% 0.12/0.38 rel_str: $i > $o)).
% 0.12/0.38 tff(tptp_fun_D_8_type, type, (
% 0.12/0.38 tptp_fun_D_8: $i)).
% 0.12/0.38 tff(antisymmetric_relstr_type, type, (
% 0.12/0.38 antisymmetric_relstr: $i > $o)).
% 0.12/0.38 tff(1,assumption,(~ex_sup_of_relstr_set(A!5, C!7)), introduced(assumption)).
% 0.12/0.38 tff(2,assumption,((~(ex_sup_of_relstr_set(A!5, C!7) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, C!7)) | (~((~element(tptp_fun_C_4(C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_C_4(C!7, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, tptp_fun_C_4(C!7, A!5), D)))))))), introduced(assumption)).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (((antisymmetric_relstr(A!5) & rel_str(A!5)) & (element(B!6, the_carrier(A!5)) & (((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | (relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7))))))) <=> (antisymmetric_relstr(A!5) & rel_str(A!5) & element(B!6, the_carrier(A!5)) & (((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | (relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 ((element(B!6, the_carrier(A!5)) & ((((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7)) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | ((relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : (related(A!5, B!6, D) | (~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7)))))) <=> (element(B!6, the_carrier(A!5)) & (((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | (relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (((antisymmetric_relstr(A!5) & rel_str(A!5)) & (element(B!6, the_carrier(A!5)) & ((((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7)) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | ((relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : (related(A!5, B!6, D) | (~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7))))))) <=> ((antisymmetric_relstr(A!5) & rel_str(A!5)) & (element(B!6, the_carrier(A!5)) & (((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | (relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7)))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[4])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (((antisymmetric_relstr(A!5) & rel_str(A!5)) & (element(B!6, the_carrier(A!5)) & ((((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7)) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | ((relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : (related(A!5, B!6, D) | (~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7))))))) <=> (antisymmetric_relstr(A!5) & rel_str(A!5) & element(B!6, the_carrier(A!5)) & (((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | (relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[5, 3])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 ((~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))) <=> (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))) <=> (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(9,axiom,(~![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t30_yellow_0')).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, C, D))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (antisymmetric_relstr(A!5) & rel_str(A!5) & element(B!6, the_carrier(A!5)) & (((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | (relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (rel_str(A!5)),
% 0.12/0.39 inference(and_elim,[status(thm)],[14])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (antisymmetric_relstr(A!5)),
% 0.12/0.39 inference(and_elim,[status(thm)],[14])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (^[A: $i] : refl(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (^[A: $i] : rewrite(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[20, 18])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((antisymmetric_relstr(A) & rel_str(A)) <=> (~((~antisymmetric_relstr(A)) | (~rel_str(A))))), ((~(antisymmetric_relstr(A) & rel_str(A))) <=> (~(~((~antisymmetric_relstr(A)) | (~rel_str(A))))))), rewrite((~(~((~antisymmetric_relstr(A)) | (~rel_str(A))))) <=> ((~antisymmetric_relstr(A)) | (~rel_str(A)))), ((~(antisymmetric_relstr(A) & rel_str(A))) <=> ((~antisymmetric_relstr(A)) | (~rel_str(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))) <=> ((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))), rewrite((ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) <=> (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))), ((((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))) <=> (((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))), rewrite((((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))) <=> (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))), ((((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))) <=> (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))), (![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))) <=> ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> (((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))), rewrite((((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (^[A: $i] : rewrite(((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : (related(A, tptp_fun_C_4(B, A), D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : (related(A, tptp_fun_C_4(B, A), D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))) <=> (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))), (![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))) <=> ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))))) <=> ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))), rewrite(((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.40 tff(29,axiom,(![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t15_yellow_0')).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.12/0.40 tff(32,plain,(
% 0.12/0.40 ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : (related(A, tptp_fun_C_4(B, A), D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[31])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_4(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_4(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D)))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[34, 21])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~antisymmetric_relstr(A!5)) | (~rel_str(A!5)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | (~antisymmetric_relstr(A!5)) | (~rel_str(A!5)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (((~rel_str(A!5)) | (~antisymmetric_relstr(A!5)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D)))))))))) <=> ((~antisymmetric_relstr(A!5)) | (~rel_str(A!5)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (^[B: $i] : rewrite((~((~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))) | (~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))))) <=> (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (![B: $i] : (~((~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))) | (~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))))) <=> ![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (((~rel_str(A!5)) | (~antisymmetric_relstr(A!5)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))) | (~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))))))))) <=> ((~rel_str(A!5)) | (~antisymmetric_relstr(A!5)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (((~rel_str(A!5)) | (~antisymmetric_relstr(A!5)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))) | (~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))))))))) <=> ((~antisymmetric_relstr(A!5)) | (~rel_str(A!5)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[40, 37])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!5)) | (~antisymmetric_relstr(A!5)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))) | (~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~antisymmetric_relstr(A!5)) | (~rel_str(A!5)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D)))))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!5)) | (~antisymmetric_relstr(A!5)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))) | (~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | (~antisymmetric_relstr(A!5)) | (~rel_str(A!5)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[42, 36])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!5)) | (~antisymmetric_relstr(A!5)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D))))))) | (~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_4(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_4(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)) | related(A, tptp_fun_C_4(B, A), D))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | (~antisymmetric_relstr(A!5)) | (~rel_str(A!5)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D)))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D)))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 35, 16, 15])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 ((~![B: $i] : (~((~(ex_sup_of_relstr_set(A!5, B) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, B)) | (~((~element(tptp_fun_C_4(B, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, tptp_fun_C_4(B, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, B, D)) | related(A!5, tptp_fun_C_4(B, A!5), D)))))))))) | (~((~(ex_sup_of_relstr_set(A!5, C!7) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, C!7)) | (~((~element(tptp_fun_C_4(C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_C_4(C!7, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, tptp_fun_C_4(C!7, A!5), D)))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[47, 46, 2])).
% 0.20/0.41 tff(49,plain,(~((~(ex_sup_of_relstr_set(A!5, C!7) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, C!7)) | (~((~element(tptp_fun_C_4(C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_C_4(C!7, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, tptp_fun_C_4(C!7, A!5), D))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (((~(ex_sup_of_relstr_set(A!5, C!7) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5)))))))) | (~((~ex_sup_of_relstr_set(A!5, C!7)) | (~((~element(tptp_fun_C_4(C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_C_4(C!7, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, tptp_fun_C_4(C!7, A!5), D)))))))) | (ex_sup_of_relstr_set(A!5, C!7) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5)))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (ex_sup_of_relstr_set(A!5, C!7) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~(ex_sup_of_relstr_set(A!5, C!7) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5)))))))) | ex_sup_of_relstr_set(A!5, C!7) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (ex_sup_of_relstr_set(A!5, C!7) | ![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[53, 1])).
% 0.20/0.41 tff(55,assumption,(~relstr_set_smaller(A!5, C!7, B!6)), introduced(assumption)).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))) | relstr_set_smaller(A!5, C!7, B!6)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 ((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (((~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))) <=> ((~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (((~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))) <=> ((~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 ((relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & ((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) <=> (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((~(~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7))))) <=> ((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7)) <=> (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 ((~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7))) <=> (~(~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 ((~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7))) <=> ((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 ((relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7)))) <=> (relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & ((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 ((relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7)))) <=> (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[65, 60])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) <=> (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 ((~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))) <=> (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))) <=> ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) <=> ((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) <=> (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[70, 67])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 ((((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | (relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7))))) <=> ((~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[71, 66])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | (relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7))))) <=> ((~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[72, 59])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7) & ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | (relstr_set_smaller(A!5, C!7, B!6) & ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))) & (~((B!6 = join_on_relstr(A!5, C!7)) & ex_sup_of_relstr_set(A!5, C!7))))),
% 0.20/0.42 inference(and_elim,[status(thm)],[14])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 ((~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 ((~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[75, 58])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[76, 57])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))))) | (B!6 = join_on_relstr(A!5, C!7))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (B!6 = join_on_relstr(A!5, C!7)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (join_on_relstr(A!5, C!7) = B!6),
% 0.20/0.43 inference(symmetry,[status(thm)],[79])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7)) <=> relstr_set_smaller(A!5, C!7, B!6)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (relstr_set_smaller(A!5, C!7, B!6) <=> relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))),
% 0.20/0.43 inference(symmetry,[status(thm)],[81])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 ((~relstr_set_smaller(A!5, C!7, B!6)) <=> (~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[82])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[55, 83])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (element(join_on_relstr(A!5, C!7), the_carrier(A!5)) <=> element(B!6, the_carrier(A!5))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (element(B!6, the_carrier(A!5)) <=> element(join_on_relstr(A!5, C!7), the_carrier(A!5))),
% 0.20/0.43 inference(symmetry,[status(thm)],[85])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (element(B!6, the_carrier(A!5))),
% 0.20/0.43 inference(and_elim,[status(thm)],[14])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (element(join_on_relstr(A!5, C!7), the_carrier(A!5))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) | (~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) | (~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[94, 92])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (((~(C = join_on_relstr(A, B))) | (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) & ((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (((~(C = join_on_relstr(A, B))) | (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) & ((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((((~(C = join_on_relstr(A, B))) | (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) & ((C = join_on_relstr(A, B)) | ((~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (((~(C = join_on_relstr(A, B))) | (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) & ((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((((~(C = join_on_relstr(A, B))) | (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) & ((C = join_on_relstr(A, B)) | ((~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (((~(C = join_on_relstr(A, B))) | (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) & ((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))) <=> ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))), ((ex_sup_of_relstr_set(A, B) => ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))))) <=> (ex_sup_of_relstr_set(A, B) => ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))), rewrite((ex_sup_of_relstr_set(A, B) => ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))) <=> ((~ex_sup_of_relstr_set(A, B)) | ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))), ((ex_sup_of_relstr_set(A, B) => ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))))) <=> ((~ex_sup_of_relstr_set(A, B)) | ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))), ((element(C, the_carrier(A)) => (ex_sup_of_relstr_set(A, B) => ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))))) <=> (element(C, the_carrier(A)) => ((~ex_sup_of_relstr_set(A, B)) | ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))), rewrite((element(C, the_carrier(A)) => ((~ex_sup_of_relstr_set(A, B)) | ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))) <=> (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))))), ((element(C, the_carrier(A)) => (ex_sup_of_relstr_set(A, B) => ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))))) <=> (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))))))), (![B: $i, C: $i] : (element(C, the_carrier(A)) => (ex_sup_of_relstr_set(A, B) => ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))))) <=> ![B: $i, C: $i] : (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A)))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (ex_sup_of_relstr_set(A, B) => ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))))))) <=> (rel_str(A) => ![B: $i, C: $i] : (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))))))), rewrite((rel_str(A) => ![B: $i, C: $i] : (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A)))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (ex_sup_of_relstr_set(A, B) => ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (ex_sup_of_relstr_set(A, B) => ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.43 tff(103,axiom,(![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (ex_sup_of_relstr_set(A, B) => ((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_yellow_0')).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : (((C = join_on_relstr(A, B)) <=> (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.20/0.43 tff(106,plain,(
% 0.20/0.43 ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((((~(C = join_on_relstr(A, B))) | (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) & ((C = join_on_relstr(A, B)) | ((~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))) | (~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A)))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[105])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (((~(C = join_on_relstr(A, B))) | (relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))) & ((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[107, 97])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))) | (~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[108, 95])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.44 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) | (~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[109, 90])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) | (~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!5)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D))))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) | (~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))))))) | (~rel_str(A!5)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D))))))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (((~rel_str(A!5)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((C = join_on_relstr(A!5, B)) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : (related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)) | (~element(D, the_carrier(A!5))))))))))))) <=> ((~rel_str(A!5)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D))))))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) | (~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!5)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((C = join_on_relstr(A!5, B)) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : (related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)) | (~element(D, the_carrier(A!5)))))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) | (~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!5)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) | (~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!5)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((C = join_on_relstr(A!5, B)) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : (related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)) | (~element(D, the_carrier(A!5)))))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) | (~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))))))) | (~rel_str(A!5)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D))))))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[113, 111])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) | (~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!5)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((C = join_on_relstr(A!5, B)) | (~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : (related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)) | (~element(D, the_carrier(A!5)))))))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A, B)) | (~element(C, the_carrier(A))) | (~((~((C = join_on_relstr(A, B)) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_0(C, B, A))) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))) | (~((~(C = join_on_relstr(A, B))) | (~((~relstr_set_smaller(A, B, C)) | (~![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))))))))) | (~rel_str(A!5)) | ![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[116, 110, 15])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))))) | ex_sup_of_relstr_set(A!5, C!7)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (ex_sup_of_relstr_set(A!5, C!7)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[118, 77])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 (((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(join_on_relstr(A!5, C!7), the_carrier(A!5))) | (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, join_on_relstr(A!5, C!7), D))))))) <=> ((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~element(join_on_relstr(A!5, C!7), the_carrier(A!5))) | (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, join_on_relstr(A!5, C!7), D))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(join_on_relstr(A!5, C!7), the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~(related(A!5, join_on_relstr(A!5, C!7), tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5))) | (~element(tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5), the_carrier(A!5))))) | (join_on_relstr(A!5, C!7) = join_on_relstr(A!5, C!7)))) | (~((~(join_on_relstr(A!5, C!7) = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, join_on_relstr(A!5, C!7), D) | (~relstr_set_smaller(A!5, C!7, D))))))))))) <=> ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(join_on_relstr(A!5, C!7), the_carrier(A!5))) | (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, join_on_relstr(A!5, C!7), D))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(join_on_relstr(A!5, C!7), the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~(related(A!5, join_on_relstr(A!5, C!7), tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5))) | (~element(tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5), the_carrier(A!5))))) | (join_on_relstr(A!5, C!7) = join_on_relstr(A!5, C!7)))) | (~((~(join_on_relstr(A!5, C!7) = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, join_on_relstr(A!5, C!7), D) | (~relstr_set_smaller(A!5, C!7, D)))))))))))) <=> ((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(join_on_relstr(A!5, C!7), the_carrier(A!5))) | (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, join_on_relstr(A!5, C!7), D)))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[121])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 (((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(join_on_relstr(A!5, C!7), the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~(related(A!5, join_on_relstr(A!5, C!7), tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5))) | (~element(tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5), the_carrier(A!5))))) | (join_on_relstr(A!5, C!7) = join_on_relstr(A!5, C!7)))) | (~((~(join_on_relstr(A!5, C!7) = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, join_on_relstr(A!5, C!7), D) | (~relstr_set_smaller(A!5, C!7, D)))))))))))) <=> ((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~element(join_on_relstr(A!5, C!7), the_carrier(A!5))) | (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, join_on_relstr(A!5, C!7), D))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[122, 120])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 ((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(join_on_relstr(A!5, C!7), the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~(related(A!5, join_on_relstr(A!5, C!7), tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5))) | (~element(tptp_fun_D_0(join_on_relstr(A!5, C!7), C!7, A!5), the_carrier(A!5))))) | (join_on_relstr(A!5, C!7) = join_on_relstr(A!5, C!7)))) | (~((~(join_on_relstr(A!5, C!7) = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, join_on_relstr(A!5, C!7), D) | (~relstr_set_smaller(A!5, C!7, D)))))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 ((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~element(join_on_relstr(A!5, C!7), the_carrier(A!5))) | (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, join_on_relstr(A!5, C!7), D)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 ((~element(join_on_relstr(A!5, C!7), the_carrier(A!5))) | (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, join_on_relstr(A!5, C!7), D)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[125, 119, 117])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 (~((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, join_on_relstr(A!5, C!7), D))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[126, 88])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 (((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, join_on_relstr(A!5, C!7), D)))) | relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[128, 127, 84])).
% 0.20/0.45 tff(130,plain,(relstr_set_smaller(A!5, C!7, B!6)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(131,assumption,(![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))), introduced(assumption)).
% 0.20/0.45 tff(132,assumption,((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))), introduced(assumption)).
% 0.20/0.45 tff(133,assumption,(relstr_set_smaller(A!5, C!7, B!6)), introduced(assumption)).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (((~![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))) | ((~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))) | (~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (((~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))))) <=> ((~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 ((~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))) <=> (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (((~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5)))))) <=> ((~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 (((~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5)))))) <=> ((~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (((~![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))) | ((~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))) | ((~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[138])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 (((~![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))) | ((~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))) | (~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[139, 134])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 ((~![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))) | ((~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 ((~![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))) | (~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[142, 87, 133, 132, 131])).
% 0.20/0.46 tff(144,plain,((~![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(145,plain,
% 0.20/0.46 ((~![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[144, 130])).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[145, 54])).
% 0.20/0.46 tff(147,plain,
% 0.20/0.46 ((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[118, 1])).
% 0.20/0.46 tff(148,plain,
% 0.20/0.46 (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[76, 147])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 (((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))) | ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 (![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.46 tff(151,assumption,(~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))), introduced(assumption)).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 (((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))) | (~related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 (~related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 (((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))) | relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[154, 151])).
% 0.20/0.46 tff(156,plain,
% 0.20/0.46 (((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))) | element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 (element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[156, 151])).
% 0.20/0.46 tff(158,assumption,(![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))), introduced(assumption)).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 (((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | ((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 (((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5)))) <=> ((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | ((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | ((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 (((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | ((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[161, 159])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | ((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[164, 158, 157, 155, 153])).
% 0.20/0.46 tff(166,plain,(((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[166, 150, 146])).
% 0.20/0.46 tff(168,plain,(ex_sup_of_relstr_set(A!5, C!7)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(B!6, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))))))) <=> ((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~element(B!6, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(B!6, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))))))) <=> ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(B!6, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 (((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(B!6, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))))))) <=> ((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(B!6, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[170])).
% 0.20/0.47 tff(172,plain,
% 0.20/0.47 (((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(B!6, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))))))) <=> ((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~element(B!6, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[171, 169])).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 ((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | ((~ex_sup_of_relstr_set(A!5, C!7)) | (~element(B!6, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 ((~![B: $i, C: $i] : ((~ex_sup_of_relstr_set(A!5, B)) | (~element(C, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, B, C)) | (~(related(A!5, C, tptp_fun_D_0(C, B, A!5)) | (~relstr_set_smaller(A!5, B, tptp_fun_D_0(C, B, A!5))) | (~element(tptp_fun_D_0(C, B, A!5), the_carrier(A!5))))) | (C = join_on_relstr(A!5, B)))) | (~((~(C = join_on_relstr(A!5, B))) | (~((~relstr_set_smaller(A!5, B, C)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, C, D) | (~relstr_set_smaller(A!5, B, D)))))))))))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~element(B!6, the_carrier(A!5))) | (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 ((~ex_sup_of_relstr_set(A!5, C!7)) | (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[174, 87, 117])).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 (~((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[175, 168])).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 (((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))))) | ((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 ((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 (((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))))) | ((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 ((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[179, 176])).
% 0.20/0.47 tff(181,assumption,(~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))))), introduced(assumption)).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 (B!6 = join_on_relstr(A!5, C!7)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[78, 181])).
% 0.20/0.47 tff(183,plain,
% 0.20/0.47 ((~((~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))))) | (~(B!6 = join_on_relstr(A!5, C!7))) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[183, 182, 180])).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 (((~relstr_set_smaller(A!5, C!7, B!6)) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))) | ![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 (![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.20/0.47 tff(187,plain,
% 0.20/0.47 (((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))))) | ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(188,plain,
% 0.20/0.47 ((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[187, 181])).
% 0.20/0.47 tff(189,plain,
% 0.20/0.47 ((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(190,plain,
% 0.20/0.47 ((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))))) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[189, 130])).
% 0.20/0.47 tff(191,plain,
% 0.20/0.47 (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[190, 188])).
% 0.20/0.47 tff(192,plain,
% 0.20/0.47 ((related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))) | relstr_set_smaller(A!5, C!7, D!8)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(193,plain,
% 0.20/0.47 (relstr_set_smaller(A!5, C!7, D!8)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.20/0.47 tff(194,plain,
% 0.20/0.47 ((related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))) | element(D!8, the_carrier(A!5))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(195,plain,
% 0.20/0.47 (element(D!8, the_carrier(A!5))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[194, 191])).
% 0.20/0.47 tff(196,plain,
% 0.20/0.47 ((related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))) | (~related(A!5, B!6, D!8))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(197,plain,
% 0.20/0.47 (~related(A!5, B!6, D!8)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[196, 191])).
% 0.20/0.47 tff(198,plain,
% 0.20/0.47 (((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | (related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(199,plain,
% 0.20/0.47 (((~element(D!8, the_carrier(A!5))) | related(A!5, B!6, D!8) | (~relstr_set_smaller(A!5, C!7, D!8))) <=> (related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(200,plain,
% 0.20/0.47 (((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | ((~element(D!8, the_carrier(A!5))) | related(A!5, B!6, D!8) | (~relstr_set_smaller(A!5, C!7, D!8)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | (related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[199])).
% 0.20/0.47 tff(201,plain,
% 0.20/0.47 (((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | ((~element(D!8, the_carrier(A!5))) | related(A!5, B!6, D!8) | (~relstr_set_smaller(A!5, C!7, D!8)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[200, 198])).
% 0.20/0.47 tff(202,plain,
% 0.20/0.47 ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | ((~element(D!8, the_carrier(A!5))) | related(A!5, B!6, D!8) | (~relstr_set_smaller(A!5, C!7, D!8)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[203, 197, 195, 193, 186])).
% 0.20/0.47 tff(205,plain,((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)) | (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 (~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[76, 205])).
% 0.20/0.47 tff(207,plain,
% 0.20/0.47 (((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))) | ((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(208,plain,
% 0.20/0.47 ((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 ((~((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7)))) | (~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(210,plain,
% 0.20/0.48 (~(B!6 = join_on_relstr(A!5, C!7))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[209, 208, 168])).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 (![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[149, 206])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 ((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[166, 211])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 ((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 ((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~((~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))) | (B!6 = join_on_relstr(A!5, C!7))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[213, 130])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[214, 212, 210, 178])).
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------