TSTP Solution File: SEU261+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU261+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 07:28:33 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU261+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 11:12:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(well_founded_relation_type, type, (
% 0.19/0.40 well_founded_relation: $i > $o)).
% 0.19/0.40 tff(tptp_fun_B_2_type, type, (
% 0.19/0.40 tptp_fun_B_2: $i)).
% 0.19/0.40 tff(connected_type, type, (
% 0.19/0.40 connected: $i > $o)).
% 0.19/0.40 tff(transitive_type, type, (
% 0.19/0.40 transitive: $i > $o)).
% 0.19/0.40 tff(antisymmetric_type, type, (
% 0.19/0.40 antisymmetric: $i > $o)).
% 0.19/0.40 tff(reflexive_type, type, (
% 0.19/0.40 reflexive: $i > $o)).
% 0.19/0.40 tff(well_ordering_type, type, (
% 0.19/0.40 well_ordering: $i > $o)).
% 0.19/0.40 tff(relation_type, type, (
% 0.19/0.40 relation: $i > $o)).
% 0.19/0.40 tff(relation_isomorphism_type, type, (
% 0.19/0.40 relation_isomorphism: ( $i * $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_C_3_type, type, (
% 0.19/0.40 tptp_fun_C_3: $i)).
% 0.19/0.40 tff(tptp_fun_A_1_type, type, (
% 0.19/0.40 tptp_fun_A_1: $i)).
% 0.19/0.40 tff(function_type, type, (
% 0.19/0.40 function: $i > $o)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 ((relation(A!1) & (relation(B!2) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3))))))) <=> (relation(A!1) & relation(B!2) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (((~(~relation(B!2))) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3)))))) <=> (relation(B!2) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 ((~(~relation(A!1))) <=> relation(A!1)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (((~(~relation(A!1))) & ((~(~relation(B!2))) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3))))))) <=> (relation(A!1) & (relation(B!2) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[3, 2])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (((~(~relation(A!1))) & ((~(~relation(B!2))) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3))))))) <=> (relation(A!1) & relation(B!2) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[4, 1])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))) <=> (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 ((~![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => ((well_ordering(A) & relation_isomorphism(A, B, C)) => well_ordering(B)))))) <=> (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(8,axiom,(~![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => ((well_ordering(A) & relation_isomorphism(A, B, C)) => well_ordering(B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t54_wellord1')).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (well_ordering(B) | (~(relation(C) & function(C))) | (~(well_ordering(A) & relation_isomorphism(A, B, C))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (relation(A!1) & relation(B!2) & (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (relation(B!2)),
% 0.19/0.40 inference(and_elim,[status(thm)],[16])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (^[A: $i] : refl(((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A)))))) <=> ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A)))))) <=> ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (^[A: $i] : rewrite(((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (^[A: $i] : trans(monotonicity(rewrite((well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A))) <=> (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))), ((relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A)))) <=> (relation(A) => (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))))), rewrite((relation(A) => (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))), ((relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A)))) <=> ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![A: $i] : (relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A)))) <=> ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.40 tff(25,axiom,(![A: $i] : (relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_wellord1')).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.40 tff(28,plain,(
% 0.19/0.40 ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[27])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | ((~relation(B!2)) | (well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | (~relation(B!2)) | (well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (((~relation(B!2)) | (well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~transitive(B!2)) | (~antisymmetric(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2)))))) <=> ((~relation(B!2)) | (well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | ((~relation(B!2)) | (well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~transitive(B!2)) | (~antisymmetric(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | ((~relation(B!2)) | (well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | ((~relation(B!2)) | (well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~transitive(B!2)) | (~antisymmetric(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | (~relation(B!2)) | (well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[33, 31])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | ((~relation(B!2)) | (well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~transitive(B!2)) | (~antisymmetric(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | (~relation(B!2)) | (well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[36, 30, 17])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (~(well_ordering(B!2) | (~(relation(C!3) & function(C!3))) | (~(well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3))))),
% 0.19/0.40 inference(and_elim,[status(thm)],[16])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (~well_ordering(B!2)),
% 0.19/0.40 inference(or_elim,[status(thm)],[38])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 ((~(well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2)))))) | well_ordering(B!2) | ((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((~(well_ordering(B!2) <=> (~((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2)))))) | ((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 ((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[41, 37])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (relation(A!1)),
% 0.19/0.40 inference(and_elim,[status(thm)],[16])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))))), rewrite((connected(A) => connected(B)) <=> (connected(B) | (~connected(A)))), ((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) <=> (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A)))) & (connected(B) | (~connected(A)))))), rewrite((((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A)))) & (connected(B) | (~connected(A)))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))))), ((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A)))))), rewrite((antisymmetric(A) => antisymmetric(B)) <=> (antisymmetric(B) | (~antisymmetric(A)))), (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) <=> (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A)))) & (antisymmetric(B) | (~antisymmetric(A)))))), rewrite((((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A)))) & (antisymmetric(B) | (~antisymmetric(A)))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))))), (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A)))))), rewrite((well_founded_relation(A) => well_founded_relation(B)) <=> (well_founded_relation(B) | (~well_founded_relation(A)))), ((((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))) <=> (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A)))) & (well_founded_relation(B) | (~well_founded_relation(A)))))), rewrite((((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A)))) & (well_founded_relation(B) | (~well_founded_relation(A)))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A))))), ((((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))) <=> ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))))), ((relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))) <=> (relation_isomorphism(A, B, C) => ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A))))))), rewrite((relation_isomorphism(A, B, C) => ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A))))) <=> ((~relation_isomorphism(A, B, C)) | ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))))), ((relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))) <=> ((~relation_isomorphism(A, B, C)) | ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A))))))), (((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))) <=> ((relation(C) & function(C)) => ((~relation_isomorphism(A, B, C)) | ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))))))), rewrite(((relation(C) & function(C)) => ((~relation_isomorphism(A, B, C)) | ((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))))) <=> (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))), (((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))) <=> (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))), (![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))) <=> ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))), ((relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))))) <=> (relation(B) => ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))), rewrite((relation(B) => ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))) <=> ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))), ((relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))))) <=> ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))))), (![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))))) <=> ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))), ((relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))))) <=> (relation(A) => ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))))), rewrite((relation(A) => ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C)))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))), ((relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.41 tff(54,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => ![C: $i] : ((relation(C) & function(C)) => (relation_isomorphism(A, B, C) => (((((reflexive(A) => reflexive(B)) & (transitive(A) => transitive(B))) & (connected(A) => connected(B))) & (antisymmetric(A) => antisymmetric(B))) & (well_founded_relation(A) => well_founded_relation(B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t53_wellord1')).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.41 tff(57,plain,(
% 0.19/0.41 ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : (((reflexive(B) | (~reflexive(A))) & (transitive(B) | (~transitive(A))) & (connected(B) | (~connected(A))) & (antisymmetric(B) | (~antisymmetric(A))) & (well_founded_relation(B) | (~well_founded_relation(A)))) | (~relation_isomorphism(A, B, C)) | (~(relation(C) & function(C))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[56])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))) | ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))) | (~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))))) | (~function(C))))) <=> ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))) | ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))))) | (~function(C)))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))) | ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1))))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))) | ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))))) | (~function(C)))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))) | (~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[62, 60])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))) | ((~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1)))))) | (~function(C)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~((~(reflexive(B) | (~reflexive(A)))) | (~(transitive(B) | (~transitive(A)))) | (~(connected(B) | (~connected(A)))) | (~(antisymmetric(B) | (~antisymmetric(A)))) | (~(well_founded_relation(B) | (~well_founded_relation(A)))))) | (~function(C)))))) | (~relation(A!1)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[65, 59, 43])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1))))))))) | ((~relation(B!2)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))))))) <=> ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1))))))))) | (~relation(B!2)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1))))))))) | ((~relation(B!2)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B, C)) | (~((~(reflexive(B) | (~reflexive(A!1)))) | (~(transitive(B) | (~transitive(A!1)))) | (~(connected(B) | (~connected(A!1)))) | (~(antisymmetric(B) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!1))))))))) | (~relation(B!2)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[69, 17, 66])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (well_ordering(A!1) & relation_isomorphism(A!1, B!2, C!3)),
% 0.19/0.41 inference(or_elim,[status(thm)],[38])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (relation_isomorphism(A!1, B!2, C!3)),
% 0.19/0.41 inference(and_elim,[status(thm)],[71])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (relation(C!3) & function(C!3)),
% 0.19/0.41 inference(or_elim,[status(thm)],[38])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (function(C!3)),
% 0.19/0.41 inference(and_elim,[status(thm)],[73])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (relation(C!3)),
% 0.19/0.41 inference(and_elim,[status(thm)],[73])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))) | ((~relation(C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))) | (~relation(C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))))) <=> ((~relation(C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))) <=> (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))))) <=> ((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))))) <=> ((~relation(C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[79, 77])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))) | ((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))) | ((~relation(C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[80])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))) | ((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))) | (~relation(C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[81, 76])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))) | ((~relation(C!3)) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!1, B!2, C)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))))) | (~relation(C!3)) | (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))) | (~function(C!3)) | (~relation_isomorphism(A!1, B!2, C!3))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (~((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[84, 75, 74, 72, 70])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))) | (well_founded_relation(B!2) | (~well_founded_relation(A!1)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (well_founded_relation(B!2) | (~well_founded_relation(A!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | ((~relation(A!1)) | (well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | (~relation(A!1)) | (well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~relation(A!1)) | (well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~transitive(A!1)) | (~antisymmetric(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1)))))) <=> ((~relation(A!1)) | (well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | ((~relation(A!1)) | (well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~transitive(A!1)) | (~antisymmetric(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | ((~relation(A!1)) | (well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1)))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | ((~relation(A!1)) | (well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~transitive(A!1)) | (~antisymmetric(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | (~relation(A!1)) | (well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[90, 88])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | ((~relation(A!1)) | (well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~transitive(A!1)) | (~antisymmetric(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))))))) | (~relation(A!1)) | (well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[93, 30, 43])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (well_ordering(A!1)),
% 0.19/0.42 inference(and_elim,[status(thm)],[71])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 ((~(well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1)))))) | (~well_ordering(A!1)) | (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 ((~(well_ordering(A!1) <=> (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1)))))) | (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (~((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) | well_founded_relation(A!1)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (well_founded_relation(A!1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 ((~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | well_founded_relation(B!2) | (~well_founded_relation(A!1))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 ((~(well_founded_relation(B!2) | (~well_founded_relation(A!1)))) | well_founded_relation(B!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (well_founded_relation(B!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[102, 87])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))) | (connected(B!2) | (~connected(A!1)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (connected(B!2) | (~connected(A!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[104, 85])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) | connected(A!1)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (connected(A!1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[106, 98])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 ((~(connected(B!2) | (~connected(A!1)))) | connected(B!2) | (~connected(A!1))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 ((~(connected(B!2) | (~connected(A!1)))) | connected(B!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (connected(B!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[109, 105])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))) | (transitive(B!2) | (~transitive(A!1)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (transitive(B!2) | (~transitive(A!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[111, 85])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 (((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) | transitive(A!1)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (transitive(A!1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[113, 98])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 ((~(transitive(B!2) | (~transitive(A!1)))) | transitive(B!2) | (~transitive(A!1))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 ((~(transitive(B!2) | (~transitive(A!1)))) | transitive(B!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 (transitive(B!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[116, 112])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))) | (reflexive(B!2) | (~reflexive(A!1)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (reflexive(B!2) | (~reflexive(A!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[118, 85])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) | reflexive(A!1)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (reflexive(A!1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[120, 98])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 ((~(reflexive(B!2) | (~reflexive(A!1)))) | reflexive(B!2) | (~reflexive(A!1))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 ((~(reflexive(B!2) | (~reflexive(A!1)))) | reflexive(B!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (reflexive(B!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[123, 119])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 (((~(reflexive(B!2) | (~reflexive(A!1)))) | (~(transitive(B!2) | (~transitive(A!1)))) | (~(connected(B!2) | (~connected(A!1)))) | (~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | (~(well_founded_relation(B!2) | (~well_founded_relation(A!1))))) | (antisymmetric(B!2) | (~antisymmetric(A!1)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 (antisymmetric(B!2) | (~antisymmetric(A!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[125, 85])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 (((~reflexive(A!1)) | (~antisymmetric(A!1)) | (~transitive(A!1)) | (~connected(A!1)) | (~well_founded_relation(A!1))) | antisymmetric(A!1)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 (antisymmetric(A!1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[127, 98])).
% 0.19/0.43 tff(129,plain,
% 0.19/0.43 ((~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | antisymmetric(B!2) | (~antisymmetric(A!1))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 ((~(antisymmetric(B!2) | (~antisymmetric(A!1)))) | antisymmetric(B!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (antisymmetric(B!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[130, 126])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 ((~((~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2)))) | (~reflexive(B!2)) | (~antisymmetric(B!2)) | (~transitive(B!2)) | (~connected(B!2)) | (~well_founded_relation(B!2))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[132, 131, 124, 117, 110, 103, 42])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------