TSTP Solution File: SEU359+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU359+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:29:07 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU359+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 12:35:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(join_on_relstr_type, type, (
% 0.19/0.39 join_on_relstr: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_C_7_type, type, (
% 0.19/0.39 tptp_fun_C_7: $i)).
% 0.19/0.39 tff(tptp_fun_A_5_type, type, (
% 0.19/0.39 tptp_fun_A_5: $i)).
% 0.19/0.39 tff(tptp_fun_B_6_type, type, (
% 0.19/0.39 tptp_fun_B_6: $i)).
% 0.19/0.39 tff(element_type, type, (
% 0.19/0.39 element: ( $i * $i ) > $o)).
% 0.19/0.39 tff(the_carrier_type, type, (
% 0.19/0.39 the_carrier: $i > $i)).
% 0.19/0.39 tff(tptp_fun_D_0_type, type, (
% 0.19/0.39 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(relstr_set_smaller_type, type, (
% 0.19/0.39 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(related_type, type, (
% 0.19/0.39 related: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(ex_sup_of_relstr_set_type, type, (
% 0.19/0.39 ex_sup_of_relstr_set: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_C_4_type, type, (
% 0.19/0.39 tptp_fun_C_4: ( $i * $i ) > $i)).
% 0.19/0.39 tff(rel_str_type, type, (
% 0.19/0.39 rel_str: $i > $o)).
% 0.19/0.39 tff(tptp_fun_D_8_type, type, (
% 0.19/0.39 tptp_fun_D_8: $i)).
% 0.19/0.39 tff(antisymmetric_relstr_type, type, (
% 0.19/0.39 antisymmetric_relstr: $i > $o)).
% 0.19/0.39 tff(1,assumption,(~ex_sup_of_relstr_set(A!5, C!7)), introduced(assumption)).
% 0.19/0.39 tff(2,assumption,((~((~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))))))))), introduced(assumption)).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (((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))))))) <=> (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))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (((~(~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))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 ((~(~(antisymmetric_relstr(A!5) & rel_str(A!5)))) <=> (antisymmetric_relstr(A!5) & rel_str(A!5))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (((~(~(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)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[5, 4])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (((~(~(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))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[6, 3])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 ((~![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)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 ((~![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)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(10,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')).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (~![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (~![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (~![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (~![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (~![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (~![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (~![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 8])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (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)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (rel_str(A!5)),
% 0.19/0.40 inference(and_elim,[status(thm)],[18])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (antisymmetric_relstr(A!5)),
% 0.19/0.40 inference(and_elim,[status(thm)],[18])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (^[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))))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![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))))))))))) <=> ![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)))))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (^[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))))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![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))))))))))) <=> ![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)))))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![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))))))))))) <=> ![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)))))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[24, 22])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (^[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)))))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![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))))))))) <=> ![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)))))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (^[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))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (![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))))))))) <=> ![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)))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (^[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)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.41 tff(33,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')).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.41 tff(36,plain,(
% 0.19/0.41 ![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)))))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[35])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![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)))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![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)))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![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)))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 25])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (((~![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)))))))))))) | (~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)))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 ((~![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)))))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 ((~![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))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (![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))))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[42, 39, 20, 19])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((~![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))))))))))) | (~((~((~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: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[44, 43, 2])).
% 0.19/0.41 tff(46,plain,(~((~((~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)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (((~((~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))))))))) | (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)))))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (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))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.42 ((~(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))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (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))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (![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))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[50, 1])).
% 0.19/0.42 tff(52,assumption,(~relstr_set_smaller(A!5, C!7, B!6)), introduced(assumption)).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (((~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)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 ((~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))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (((~((~(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)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (((~((~(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)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 ((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))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 ((~(~((~(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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (((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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 ((~((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)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 ((~((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)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 ((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))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 ((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))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[62, 57])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (((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))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 ((~(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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (((~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)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[65])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (((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))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (((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))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[67, 64])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 ((((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) & ![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)))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[68, 63])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 ((((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) & ![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)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[69, 56])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (((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) & ![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))))),
% 0.19/0.43 inference(and_elim,[status(thm)],[18])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 ((~((~(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))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 ((~((~(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))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[72, 55])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (~((~(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)))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[73, 54])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (((~(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))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (B!6 = join_on_relstr(A!5, C!7)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (join_on_relstr(A!5, C!7) = B!6),
% 0.19/0.43 inference(symmetry,[status(thm)],[76])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 (relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7)) <=> relstr_set_smaller(A!5, C!7, B!6)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 (relstr_set_smaller(A!5, C!7, B!6) <=> relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))),
% 0.19/0.43 inference(symmetry,[status(thm)],[78])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 ((~relstr_set_smaller(A!5, C!7, B!6)) <=> (~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[52, 80])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (element(join_on_relstr(A!5, C!7), the_carrier(A!5)) <=> element(B!6, the_carrier(A!5))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (element(B!6, the_carrier(A!5)) <=> element(join_on_relstr(A!5, C!7), the_carrier(A!5))),
% 0.19/0.43 inference(symmetry,[status(thm)],[82])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 (element(B!6, the_carrier(A!5))),
% 0.19/0.43 inference(and_elim,[status(thm)],[18])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 (element(join_on_relstr(A!5, C!7), the_carrier(A!5))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 (^[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))))))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (![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)))))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 (^[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))))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 (![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)))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (^[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))))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (![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)))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 (![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)))))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[91, 89])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 (^[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))))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 (![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)))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (^[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))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 (![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)))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 (![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)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (^[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)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 (![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)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.44 tff(100,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')).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 (![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)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (![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)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.44 tff(103,plain,(
% 0.19/0.44 ![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)))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[102])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 (![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) & ![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)))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 (![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)) | (~![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)))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 (![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)) | (~![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)))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[105, 92])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 (![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)))))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[106, 87])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 (((~![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))))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 (((~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))))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 (((~![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)))))))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 (((~![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))))))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[110, 108])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 ((~![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)))))))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(113,plain,
% 0.19/0.44 ((~![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)))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.44 tff(114,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[113, 107, 19])).
% 0.19/0.45 tff(115,plain,
% 0.19/0.45 (((~(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)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(116,plain,
% 0.19/0.45 (ex_sup_of_relstr_set(A!5, C!7)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[115, 74])).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 (((~![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))))))) <=> ((~![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))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(118,plain,
% 0.19/0.45 (((~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))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(119,plain,
% 0.19/0.45 (((~![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)))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[118])).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 (((~![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))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[119, 117])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 ((~![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)))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 ((~![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)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 ((~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)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[122, 116, 114])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 (~((~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))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[123, 85])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 (((~relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D)) | related(A!5, join_on_relstr(A!5, C!7), D)))) | relstr_set_smaller(A!5, C!7, join_on_relstr(A!5, C!7))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[125, 124, 81])).
% 0.19/0.45 tff(127,plain,(relstr_set_smaller(A!5, C!7, B!6)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(128,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)).
% 0.19/0.46 tff(129,assumption,(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)))), introduced(assumption)).
% 0.19/0.46 tff(130,assumption,(relstr_set_smaller(A!5, C!7, B!6)), introduced(assumption)).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 (((~![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)) | (~(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))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 ((~![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))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 ((~![C: $i] : ((~element(C, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, C)) | (~(related(A!5, C, tptp_fun_D_0(C, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(C, C!7, A!5))) | (~element(tptp_fun_D_0(C, C!7, A!5), the_carrier(A!5))))))) | (~element(B!6, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[133, 84, 130, 129, 128])).
% 0.19/0.46 tff(135,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)) | (~(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)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 ((~![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))))))) | (~(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)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[135, 127])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 (~(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))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[136, 51])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 ((~(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))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[115, 1])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 (~((~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)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[73, 138])).
% 0.19/0.46 tff(140,plain,
% 0.19/0.46 (((~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)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 (![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.19/0.46 tff(142,assumption,(~(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))))), introduced(assumption)).
% 0.19/0.46 tff(143,plain,
% 0.19/0.46 ((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))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 (element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 ((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))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 (relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[145, 142])).
% 0.19/0.46 tff(147,plain,
% 0.19/0.46 ((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)))) | (~related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(148,plain,
% 0.19/0.46 (~related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[147, 142])).
% 0.19/0.46 tff(149,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)).
% 0.19/0.46 tff(150,plain,
% 0.19/0.46 (((~![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, 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))))) <=> ((~![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, 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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(151,plain,
% 0.19/0.46 (((~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)))) <=> (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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 (((~![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)))) | (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)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[151])).
% 0.19/0.47 tff(153,plain,
% 0.19/0.47 (((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | ((~element(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)))) | 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))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[152, 150])).
% 0.19/0.47 tff(154,plain,
% 0.19/0.47 ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | ((~element(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))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(155,plain,
% 0.19/0.47 ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.47 tff(156,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[155, 149, 148, 146, 144])).
% 0.19/0.47 tff(157,plain,((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)))) | (~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(158,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[157, 141, 137])).
% 0.19/0.47 tff(159,plain,(ex_sup_of_relstr_set(A!5, C!7)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(160,plain,
% 0.19/0.47 (((~![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)) | (~(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)))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(161,plain,
% 0.19/0.47 ((~![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)))))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(162,plain,
% 0.19/0.47 ((~![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))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.47 tff(163,plain,
% 0.19/0.47 ((~ex_sup_of_relstr_set(A!5, C!7)) | (~((~((~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))))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[162, 84, 114])).
% 0.19/0.47 tff(164,plain,
% 0.19/0.47 (~((~((~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)))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[163, 159])).
% 0.19/0.47 tff(165,plain,
% 0.19/0.47 (((~((~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))))))))) | ((~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)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(166,plain,
% 0.19/0.47 ((~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))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.47 tff(167,plain,
% 0.19/0.47 (((~((~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!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)))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(168,plain,
% 0.19/0.47 ((~(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))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[167, 164])).
% 0.19/0.47 tff(169,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)).
% 0.19/0.47 tff(170,plain,
% 0.19/0.47 (B!6 = join_on_relstr(A!5, C!7)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[75, 169])).
% 0.19/0.47 tff(171,plain,
% 0.19/0.47 ((~((~(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))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(172,plain,
% 0.19/0.47 (~((~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)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[171, 170, 168])).
% 0.19/0.47 tff(173,plain,
% 0.19/0.47 (((~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)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(174,plain,
% 0.19/0.47 (![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.19/0.47 tff(175,plain,
% 0.19/0.47 (((~(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)))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(176,plain,
% 0.19/0.47 ((~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))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[175, 169])).
% 0.19/0.48 tff(177,plain,
% 0.19/0.48 ((~((~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))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(178,plain,
% 0.19/0.48 ((~((~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))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[177, 127])).
% 0.19/0.48 tff(179,plain,
% 0.19/0.48 (~(related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[178, 176])).
% 0.19/0.48 tff(180,plain,
% 0.19/0.48 ((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)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(181,plain,
% 0.19/0.48 (relstr_set_smaller(A!5, C!7, D!8)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.19/0.48 tff(182,plain,
% 0.19/0.48 ((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))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(183,plain,
% 0.19/0.48 (element(D!8, the_carrier(A!5))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[182, 179])).
% 0.19/0.48 tff(184,plain,
% 0.19/0.48 ((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))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(185,plain,
% 0.19/0.48 (~related(A!5, B!6, D!8)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[184, 179])).
% 0.19/0.48 tff(186,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(187,plain,
% 0.19/0.48 (((~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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(188,plain,
% 0.19/0.48 (((~![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))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[187])).
% 0.19/0.48 tff(189,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[188, 186])).
% 0.19/0.48 tff(190,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(191,plain,
% 0.19/0.48 ((~![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))) | related(A!5, B!6, D!8) | (~element(D!8, the_carrier(A!5))) | (~relstr_set_smaller(A!5, C!7, D!8))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.48 tff(192,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[191, 185, 183, 181, 174])).
% 0.19/0.48 tff(193,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,[]))).
% 0.19/0.48 tff(194,plain,
% 0.19/0.48 (~((~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)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[73, 193])).
% 0.19/0.48 tff(195,plain,
% 0.19/0.48 (((~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)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(196,plain,
% 0.19/0.48 ((~(B!6 = join_on_relstr(A!5, C!7))) | (~ex_sup_of_relstr_set(A!5, C!7))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.19/0.48 tff(197,plain,
% 0.19/0.48 ((~((~(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))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(198,plain,
% 0.19/0.48 (~(B!6 = join_on_relstr(A!5, C!7))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[197, 196, 159])).
% 0.19/0.48 tff(199,plain,
% 0.19/0.48 (![D: $i] : ((~element(D, the_carrier(A!5))) | related(A!5, B!6, D) | (~relstr_set_smaller(A!5, C!7, D)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[140, 194])).
% 0.19/0.48 tff(200,plain,
% 0.19/0.48 (related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[157, 199])).
% 0.19/0.48 tff(201,plain,
% 0.19/0.48 ((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))) | (B!6 = join_on_relstr(A!5, C!7))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(202,plain,
% 0.19/0.48 ((~((~relstr_set_smaller(A!5, C!7, B!6)) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))) | (B!6 = join_on_relstr(A!5, C!7)))) | (~(related(A!5, B!6, tptp_fun_D_0(B!6, C!7, A!5)) | (~relstr_set_smaller(A!5, C!7, tptp_fun_D_0(B!6, C!7, A!5))) | (~element(tptp_fun_D_0(B!6, C!7, A!5), the_carrier(A!5))))) | (B!6 = join_on_relstr(A!5, C!7))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[201, 127])).
% 0.19/0.48 tff(203,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[202, 200, 198, 166])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------