TSTP Solution File: SEU261+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU261+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 07:28:34 EDT 2022
% Result : Theorem 9.05s 6.05s
% Output : Proof 9.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU261+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 11:26:17 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 9.05/6.05 % SZS status Theorem
% 9.05/6.05 % SZS output start Proof
% 9.05/6.05 tff(antisymmetric_type, type, (
% 9.05/6.05 antisymmetric: $i > $o)).
% 9.05/6.05 tff(tptp_fun_B_116_type, type, (
% 9.05/6.05 tptp_fun_B_116: $i)).
% 9.05/6.05 tff(connected_type, type, (
% 9.05/6.05 connected: $i > $o)).
% 9.05/6.05 tff(transitive_type, type, (
% 9.05/6.05 transitive: $i > $o)).
% 9.05/6.05 tff(reflexive_type, type, (
% 9.05/6.05 reflexive: $i > $o)).
% 9.05/6.05 tff(well_founded_relation_type, type, (
% 9.05/6.05 well_founded_relation: $i > $o)).
% 9.05/6.05 tff(well_ordering_type, type, (
% 9.05/6.05 well_ordering: $i > $o)).
% 9.05/6.05 tff(relation_type, type, (
% 9.05/6.05 relation: $i > $o)).
% 9.05/6.05 tff(relation_isomorphism_type, type, (
% 9.05/6.05 relation_isomorphism: ( $i * $i * $i ) > $o)).
% 9.05/6.05 tff(tptp_fun_C_117_type, type, (
% 9.05/6.05 tptp_fun_C_117: $i)).
% 9.05/6.05 tff(tptp_fun_A_115_type, type, (
% 9.05/6.05 tptp_fun_A_115: $i)).
% 9.05/6.05 tff(function_type, type, (
% 9.05/6.05 function: $i > $o)).
% 9.05/6.05 tff(1,plain,
% 9.05/6.05 ((relation(A!115) & (relation(B!116) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117))))))) <=> (relation(A!115) & relation(B!116) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117))))))),
% 9.05/6.05 inference(rewrite,[status(thm)],[])).
% 9.05/6.05 tff(2,plain,
% 9.05/6.05 (((~(~relation(B!116))) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117)))))) <=> (relation(B!116) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117))))))),
% 9.05/6.05 inference(rewrite,[status(thm)],[])).
% 9.05/6.05 tff(3,plain,
% 9.05/6.05 ((~(~relation(A!115))) <=> relation(A!115)),
% 9.05/6.05 inference(rewrite,[status(thm)],[])).
% 9.05/6.05 tff(4,plain,
% 9.05/6.05 (((~(~relation(A!115))) & ((~(~relation(B!116))) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117))))))) <=> (relation(A!115) & (relation(B!116) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117)))))))),
% 9.05/6.05 inference(monotonicity,[status(thm)],[3, 2])).
% 9.05/6.05 tff(5,plain,
% 9.05/6.05 (((~(~relation(A!115))) & ((~(~relation(B!116))) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117))))))) <=> (relation(A!115) & relation(B!116) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117))))))),
% 9.05/6.05 inference(transitivity,[status(thm)],[4, 1])).
% 9.05/6.05 tff(6,plain,
% 9.05/6.05 ((~![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)))))))),
% 9.05/6.05 inference(rewrite,[status(thm)],[])).
% 9.05/6.05 tff(7,plain,
% 9.05/6.05 ((~![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)))))))),
% 9.05/6.05 inference(rewrite,[status(thm)],[])).
% 9.05/6.05 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/sandbox/benchmark/theBenchmark.p','t54_wellord1')).
% 9.05/6.05 tff(9,plain,
% 9.05/6.05 (~![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))))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[8, 7])).
% 9.05/6.05 tff(10,plain,
% 9.05/6.05 (~![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))))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[9, 6])).
% 9.05/6.05 tff(11,plain,
% 9.05/6.05 (~![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))))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[10, 6])).
% 9.05/6.05 tff(12,plain,
% 9.05/6.05 (~![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))))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[11, 6])).
% 9.05/6.05 tff(13,plain,
% 9.05/6.05 (~![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))))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[12, 6])).
% 9.05/6.05 tff(14,plain,
% 9.05/6.05 (~![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))))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[13, 6])).
% 9.05/6.05 tff(15,plain,
% 9.05/6.05 (~![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))))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[14, 6])).
% 9.05/6.05 tff(16,plain,
% 9.05/6.05 (relation(A!115) & relation(B!116) & (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117)))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[15, 5])).
% 9.05/6.05 tff(17,plain,
% 9.05/6.05 (relation(B!116)),
% 9.05/6.05 inference(and_elim,[status(thm)],[16])).
% 9.05/6.05 tff(18,plain,
% 9.05/6.05 (^[A: $i] : refl(((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A)))))) <=> ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A)))))))),
% 9.05/6.05 inference(bind,[status(th)],[])).
% 9.05/6.05 tff(19,plain,
% 9.05/6.05 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A)))))) <=> ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))),
% 9.05/6.05 inference(quant_intro,[status(thm)],[18])).
% 9.05/6.05 tff(20,plain,
% 9.05/6.05 (^[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)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A)))))))),
% 9.05/6.05 inference(bind,[status(th)],[])).
% 9.05/6.05 tff(21,plain,
% 9.05/6.05 (![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)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))),
% 9.05/6.05 inference(quant_intro,[status(thm)],[20])).
% 9.05/6.05 tff(22,plain,
% 9.05/6.05 (![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))))),
% 9.05/6.05 inference(rewrite,[status(thm)],[])).
% 9.05/6.05 tff(23,plain,
% 9.05/6.05 (^[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))))))),
% 9.05/6.05 inference(bind,[status(th)],[])).
% 9.05/6.05 tff(24,plain,
% 9.05/6.05 (![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))))),
% 9.05/6.05 inference(quant_intro,[status(thm)],[23])).
% 9.05/6.05 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/sandbox/benchmark/theBenchmark.p','d4_wellord1')).
% 9.05/6.05 tff(26,plain,
% 9.05/6.05 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[25, 24])).
% 9.05/6.05 tff(27,plain,
% 9.05/6.05 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[26, 22])).
% 9.05/6.05 tff(28,plain,(
% 9.05/6.05 ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 9.05/6.05 inference(skolemize,[status(sab)],[27])).
% 9.05/6.05 tff(29,plain,
% 9.05/6.05 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[28, 21])).
% 9.05/6.05 tff(30,plain,
% 9.05/6.05 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))),
% 9.05/6.05 inference(modus_ponens,[status(thm)],[29, 19])).
% 9.05/6.05 tff(31,plain,
% 9.05/6.05 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(B!116)) | (well_ordering(B!116) <=> (~((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | (~relation(B!116)) | (well_ordering(B!116) <=> (~((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))))))),
% 9.05/6.05 inference(rewrite,[status(thm)],[])).
% 9.05/6.05 tff(32,plain,
% 9.05/6.05 (((~relation(B!116)) | (well_ordering(B!116) <=> (~((~reflexive(B!116)) | (~connected(B!116)) | (~transitive(B!116)) | (~antisymmetric(B!116)) | (~well_founded_relation(B!116)))))) <=> ((~relation(B!116)) | (well_ordering(B!116) <=> (~((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))))))),
% 9.05/6.05 inference(rewrite,[status(thm)],[])).
% 9.05/6.05 tff(33,plain,
% 9.05/6.05 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(B!116)) | (well_ordering(B!116) <=> (~((~reflexive(B!116)) | (~connected(B!116)) | (~transitive(B!116)) | (~antisymmetric(B!116)) | (~well_founded_relation(B!116))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(B!116)) | (well_ordering(B!116) <=> (~((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116)))))))),
% 9.05/6.06 inference(monotonicity,[status(thm)],[32])).
% 9.05/6.06 tff(34,plain,
% 9.05/6.06 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(B!116)) | (well_ordering(B!116) <=> (~((~reflexive(B!116)) | (~connected(B!116)) | (~transitive(B!116)) | (~antisymmetric(B!116)) | (~well_founded_relation(B!116))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | (~relation(B!116)) | (well_ordering(B!116) <=> (~((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))))))),
% 9.05/6.06 inference(transitivity,[status(thm)],[33, 31])).
% 9.05/6.06 tff(35,plain,
% 9.05/6.06 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(B!116)) | (well_ordering(B!116) <=> (~((~reflexive(B!116)) | (~connected(B!116)) | (~transitive(B!116)) | (~antisymmetric(B!116)) | (~well_founded_relation(B!116))))))),
% 9.05/6.06 inference(quant_inst,[status(thm)],[])).
% 9.05/6.06 tff(36,plain,
% 9.05/6.06 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | (~relation(B!116)) | (well_ordering(B!116) <=> (~((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116)))))),
% 9.05/6.06 inference(modus_ponens,[status(thm)],[35, 34])).
% 9.05/6.06 tff(37,plain,
% 9.05/6.06 (well_ordering(B!116) <=> (~((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))))),
% 9.05/6.06 inference(unit_resolution,[status(thm)],[36, 30, 17])).
% 9.05/6.06 tff(38,plain,
% 9.05/6.06 (~(well_ordering(B!116) | (~(relation(C!117) & function(C!117))) | (~(well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117))))),
% 9.05/6.06 inference(and_elim,[status(thm)],[16])).
% 9.05/6.06 tff(39,plain,
% 9.05/6.06 (~well_ordering(B!116)),
% 9.05/6.06 inference(or_elim,[status(thm)],[38])).
% 9.05/6.06 tff(40,plain,
% 9.05/6.06 ((~(well_ordering(B!116) <=> (~((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116)))))) | well_ordering(B!116) | ((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116)))),
% 9.05/6.06 inference(tautology,[status(thm)],[])).
% 9.05/6.06 tff(41,plain,
% 9.05/6.06 ((~(well_ordering(B!116) <=> (~((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116)))))) | ((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116)))),
% 9.05/6.06 inference(unit_resolution,[status(thm)],[40, 39])).
% 9.05/6.06 tff(42,plain,
% 9.05/6.06 ((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))),
% 9.05/6.06 inference(unit_resolution,[status(thm)],[41, 37])).
% 9.05/6.06 tff(43,plain,
% 9.05/6.06 (relation(A!115)),
% 9.05/6.06 inference(and_elim,[status(thm)],[16])).
% 9.05/6.06 tff(44,plain,
% 9.05/6.06 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))))),
% 9.05/6.06 inference(bind,[status(th)],[])).
% 9.05/6.06 tff(45,plain,
% 9.05/6.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 9.05/6.06 inference(quant_intro,[status(thm)],[44])).
% 9.05/6.06 tff(46,plain,
% 9.05/6.06 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))))),
% 9.05/6.06 inference(bind,[status(th)],[])).
% 9.05/6.06 tff(47,plain,
% 9.05/6.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 9.05/6.06 inference(quant_intro,[status(thm)],[46])).
% 9.05/6.06 tff(48,plain,
% 9.05/6.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 9.05/6.06 inference(transitivity,[status(thm)],[47, 45])).
% 9.05/6.06 tff(49,plain,
% 9.05/6.06 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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))))))))))),
% 9.05/6.06 inference(bind,[status(th)],[])).
% 9.05/6.06 tff(50,plain,
% 9.05/6.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 9.05/6.06 inference(quant_intro,[status(thm)],[49])).
% 9.05/6.06 tff(51,plain,
% 9.05/6.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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)))))))),
% 9.05/6.06 inference(rewrite,[status(thm)],[])).
% 9.05/6.06 tff(52,plain,
% 9.05/6.06 (^[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)))))) <=> ((~(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)))))), (((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)))))))), (![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] : ((~(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))))))), ((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] : ((~(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(B) => ![C: $i] : ((~(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)))))) <=> ((~relation(B)) | ![C: $i] : ((~(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))))))), ((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] : ((~(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))))))))), (![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] : ((~(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)))))))), ((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] : ((~(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(A) => ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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)))))))), ((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] : ((~(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)))))))))),
% 9.05/6.06 inference(bind,[status(th)],[])).
% 9.05/6.06 tff(53,plain,
% 9.05/6.06 (![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] : ((~(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)))))))),
% 9.05/6.06 inference(quant_intro,[status(thm)],[52])).
% 9.05/6.06 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/sandbox/benchmark/theBenchmark.p','t53_wellord1')).
% 9.05/6.06 tff(55,plain,
% 9.05/6.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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)))))))),
% 9.05/6.06 inference(modus_ponens,[status(thm)],[54, 53])).
% 9.05/6.06 tff(56,plain,
% 9.05/6.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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)))))))),
% 9.05/6.06 inference(modus_ponens,[status(thm)],[55, 51])).
% 9.05/6.06 tff(57,plain,(
% 9.05/6.06 ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~(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)))))))),
% 9.05/6.06 inference(skolemize,[status(sab)],[56])).
% 9.05/6.06 tff(58,plain,
% 9.05/6.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 9.05/6.06 inference(modus_ponens,[status(thm)],[57, 50])).
% 9.05/6.06 tff(59,plain,
% 9.05/6.06 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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)))))))))),
% 9.05/6.06 inference(modus_ponens,[status(thm)],[58, 48])).
% 9.05/6.06 tff(60,plain,
% 9.05/6.06 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))),
% 9.05/6.06 inference(rewrite,[status(thm)],[])).
% 9.05/6.06 tff(61,plain,
% 9.05/6.06 (((~relation(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!115, B, C)) | (~function(C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))) <=> ((~relation(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))),
% 9.05/6.06 inference(rewrite,[status(thm)],[])).
% 9.05/6.06 tff(62,plain,
% 9.05/6.06 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!115, B, C)) | (~function(C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))))),
% 9.05/6.06 inference(monotonicity,[status(thm)],[61])).
% 9.05/6.06 tff(63,plain,
% 9.05/6.06 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!115, B, C)) | (~function(C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))),
% 9.05/6.06 inference(transitivity,[status(thm)],[62, 60])).
% 9.05/6.06 tff(64,plain,
% 9.05/6.06 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A!115, B, C)) | (~function(C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115)))))))))),
% 9.05/6.06 inference(quant_inst,[status(thm)],[])).
% 9.05/6.06 tff(65,plain,
% 9.05/6.06 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~relation_isomorphism(A, B, C)) | (~function(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(A!115)) | ![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))),
% 9.05/6.06 inference(modus_ponens,[status(thm)],[64, 63])).
% 9.05/6.06 tff(66,plain,
% 9.05/6.06 (![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))),
% 9.05/6.06 inference(unit_resolution,[status(thm)],[65, 59, 43])).
% 9.05/6.06 tff(67,plain,
% 9.05/6.06 (((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))) | ((~relation(B!116)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))))) <=> ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))) | (~relation(B!116)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))))),
% 9.05/6.06 inference(rewrite,[status(thm)],[])).
% 9.05/6.06 tff(68,plain,
% 9.05/6.06 ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))) | ((~relation(B!116)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))))),
% 9.05/6.06 inference(quant_inst,[status(thm)],[])).
% 9.05/6.06 tff(69,plain,
% 9.05/6.06 ((~![B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B, C)) | (~((~(reflexive(B) | (~reflexive(A!115)))) | (~(transitive(B) | (~transitive(A!115)))) | (~(connected(B) | (~connected(A!115)))) | (~(antisymmetric(B) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B) | (~well_founded_relation(A!115))))))))) | (~relation(B!116)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))),
% 9.05/6.06 inference(modus_ponens,[status(thm)],[68, 67])).
% 9.05/6.06 tff(70,plain,
% 9.05/6.06 (![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))),
% 9.05/6.06 inference(unit_resolution,[status(thm)],[69, 17, 66])).
% 9.05/6.06 tff(71,plain,
% 9.05/6.06 (well_ordering(A!115) & relation_isomorphism(A!115, B!116, C!117)),
% 9.05/6.06 inference(or_elim,[status(thm)],[38])).
% 9.05/6.06 tff(72,plain,
% 9.05/6.06 (relation_isomorphism(A!115, B!116, C!117)),
% 9.05/6.06 inference(and_elim,[status(thm)],[71])).
% 9.05/6.06 tff(73,plain,
% 9.05/6.06 (relation(C!117) & function(C!117)),
% 9.05/6.06 inference(or_elim,[status(thm)],[38])).
% 9.05/6.06 tff(74,plain,
% 9.05/6.06 (function(C!117)),
% 9.05/6.06 inference(and_elim,[status(thm)],[73])).
% 9.05/6.06 tff(75,plain,
% 9.05/6.06 (relation(C!117)),
% 9.05/6.06 inference(and_elim,[status(thm)],[73])).
% 9.05/6.06 tff(76,plain,
% 9.05/6.06 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | ((~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117)))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | (~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117)))),
% 9.05/6.06 inference(rewrite,[status(thm)],[])).
% 9.05/6.06 tff(77,plain,
% 9.05/6.06 (((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))) <=> ((~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117)))),
% 9.05/6.06 inference(rewrite,[status(thm)],[])).
% 9.05/6.06 tff(78,plain,
% 9.05/6.06 ((~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) <=> (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))),
% 9.05/6.06 inference(rewrite,[status(thm)],[])).
% 9.05/6.06 tff(79,plain,
% 9.05/6.06 (((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))) <=> ((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))),
% 9.05/6.06 inference(monotonicity,[status(thm)],[78])).
% 9.05/6.06 tff(80,plain,
% 9.05/6.06 (((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))))) <=> ((~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117)))),
% 9.05/6.06 inference(transitivity,[status(thm)],[79, 77])).
% 9.05/6.06 tff(81,plain,
% 9.05/6.06 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | ((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | ((~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117))))),
% 9.05/6.06 inference(monotonicity,[status(thm)],[80])).
% 9.05/6.06 tff(82,plain,
% 9.05/6.06 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | ((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | (~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117)))),
% 9.05/6.06 inference(transitivity,[status(thm)],[81, 76])).
% 9.05/6.06 tff(83,plain,
% 9.05/6.06 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | ((~relation(C!117)) | (~function(C!117)) | (~relation_isomorphism(A!115, B!116, C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))),
% 9.05/6.07 inference(quant_inst,[status(thm)],[])).
% 9.05/6.07 tff(84,plain,
% 9.05/6.07 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~relation_isomorphism(A!115, B!116, C)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))))) | (~relation(C!117)) | (~function(C!117)) | (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))) | (~relation_isomorphism(A!115, B!116, C!117))),
% 9.05/6.07 inference(modus_ponens,[status(thm)],[83, 82])).
% 9.05/6.07 tff(85,plain,
% 9.05/6.07 (~((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))))),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[84, 75, 74, 72, 70])).
% 9.05/6.07 tff(86,plain,
% 9.05/6.07 (((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))) | (reflexive(B!116) | (~reflexive(A!115)))),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(87,plain,
% 9.05/6.07 (reflexive(B!116) | (~reflexive(A!115))),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[86, 85])).
% 9.05/6.07 tff(88,plain,
% 9.05/6.07 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(A!115)) | (well_ordering(A!115) <=> (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | (~relation(A!115)) | (well_ordering(A!115) <=> (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))))))),
% 9.05/6.07 inference(rewrite,[status(thm)],[])).
% 9.05/6.07 tff(89,plain,
% 9.05/6.07 (((~relation(A!115)) | (well_ordering(A!115) <=> (~((~reflexive(A!115)) | (~connected(A!115)) | (~transitive(A!115)) | (~antisymmetric(A!115)) | (~well_founded_relation(A!115)))))) <=> ((~relation(A!115)) | (well_ordering(A!115) <=> (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))))))),
% 9.05/6.07 inference(rewrite,[status(thm)],[])).
% 9.05/6.07 tff(90,plain,
% 9.05/6.07 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(A!115)) | (well_ordering(A!115) <=> (~((~reflexive(A!115)) | (~connected(A!115)) | (~transitive(A!115)) | (~antisymmetric(A!115)) | (~well_founded_relation(A!115))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(A!115)) | (well_ordering(A!115) <=> (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115)))))))),
% 9.05/6.07 inference(monotonicity,[status(thm)],[89])).
% 9.05/6.07 tff(91,plain,
% 9.05/6.07 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(A!115)) | (well_ordering(A!115) <=> (~((~reflexive(A!115)) | (~connected(A!115)) | (~transitive(A!115)) | (~antisymmetric(A!115)) | (~well_founded_relation(A!115))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | (~relation(A!115)) | (well_ordering(A!115) <=> (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))))))),
% 9.05/6.07 inference(transitivity,[status(thm)],[90, 88])).
% 9.05/6.07 tff(92,plain,
% 9.05/6.07 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(A!115)) | (well_ordering(A!115) <=> (~((~reflexive(A!115)) | (~connected(A!115)) | (~transitive(A!115)) | (~antisymmetric(A!115)) | (~well_founded_relation(A!115))))))),
% 9.05/6.07 inference(quant_inst,[status(thm)],[])).
% 9.05/6.07 tff(93,plain,
% 9.05/6.07 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | (~relation(A!115)) | (well_ordering(A!115) <=> (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115)))))),
% 9.05/6.07 inference(modus_ponens,[status(thm)],[92, 91])).
% 9.05/6.07 tff(94,plain,
% 9.05/6.07 (well_ordering(A!115) <=> (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))))),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[93, 30, 43])).
% 9.05/6.07 tff(95,plain,
% 9.05/6.07 (well_ordering(A!115)),
% 9.05/6.07 inference(and_elim,[status(thm)],[71])).
% 9.05/6.07 tff(96,plain,
% 9.05/6.07 ((~(well_ordering(A!115) <=> (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115)))))) | (~well_ordering(A!115)) | (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))))),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(97,plain,
% 9.05/6.07 ((~(well_ordering(A!115) <=> (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115)))))) | (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))))),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[96, 95])).
% 9.05/6.07 tff(98,plain,
% 9.05/6.07 (~((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115)))),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[97, 94])).
% 9.05/6.07 tff(99,plain,
% 9.05/6.07 (((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) | reflexive(A!115)),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(100,plain,
% 9.05/6.07 (reflexive(A!115)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[99, 98])).
% 9.05/6.07 tff(101,plain,
% 9.05/6.07 ((~(reflexive(B!116) | (~reflexive(A!115)))) | reflexive(B!116) | (~reflexive(A!115))),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(102,plain,
% 9.05/6.07 ((~(reflexive(B!116) | (~reflexive(A!115)))) | reflexive(B!116)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[101, 100])).
% 9.05/6.07 tff(103,plain,
% 9.05/6.07 (reflexive(B!116)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[102, 87])).
% 9.05/6.07 tff(104,plain,
% 9.05/6.07 (((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))) | (transitive(B!116) | (~transitive(A!115)))),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(105,plain,
% 9.05/6.07 (transitive(B!116) | (~transitive(A!115))),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[104, 85])).
% 9.05/6.07 tff(106,plain,
% 9.05/6.07 (((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) | transitive(A!115)),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(107,plain,
% 9.05/6.07 (transitive(A!115)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[106, 98])).
% 9.05/6.07 tff(108,plain,
% 9.05/6.07 ((~(transitive(B!116) | (~transitive(A!115)))) | transitive(B!116) | (~transitive(A!115))),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(109,plain,
% 9.05/6.07 ((~(transitive(B!116) | (~transitive(A!115)))) | transitive(B!116)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[108, 107])).
% 9.05/6.07 tff(110,plain,
% 9.05/6.07 (transitive(B!116)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[109, 105])).
% 9.05/6.07 tff(111,plain,
% 9.05/6.07 (((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))) | (antisymmetric(B!116) | (~antisymmetric(A!115)))),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(112,plain,
% 9.05/6.07 (antisymmetric(B!116) | (~antisymmetric(A!115))),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[111, 85])).
% 9.05/6.07 tff(113,plain,
% 9.05/6.07 (((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) | antisymmetric(A!115)),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(114,plain,
% 9.05/6.07 (antisymmetric(A!115)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[113, 98])).
% 9.05/6.07 tff(115,plain,
% 9.05/6.07 ((~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | antisymmetric(B!116) | (~antisymmetric(A!115))),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(116,plain,
% 9.05/6.07 ((~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | antisymmetric(B!116)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[115, 114])).
% 9.05/6.07 tff(117,plain,
% 9.05/6.07 (antisymmetric(B!116)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[116, 112])).
% 9.05/6.07 tff(118,plain,
% 9.05/6.07 (((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))) | (connected(B!116) | (~connected(A!115)))),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(119,plain,
% 9.05/6.07 (connected(B!116) | (~connected(A!115))),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[118, 85])).
% 9.05/6.07 tff(120,plain,
% 9.05/6.07 (((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) | connected(A!115)),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(121,plain,
% 9.05/6.07 (connected(A!115)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[120, 98])).
% 9.05/6.07 tff(122,plain,
% 9.05/6.07 ((~(connected(B!116) | (~connected(A!115)))) | connected(B!116) | (~connected(A!115))),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(123,plain,
% 9.05/6.07 ((~(connected(B!116) | (~connected(A!115)))) | connected(B!116)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[122, 121])).
% 9.05/6.07 tff(124,plain,
% 9.05/6.07 (connected(B!116)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[123, 119])).
% 9.05/6.07 tff(125,plain,
% 9.05/6.07 (((~(reflexive(B!116) | (~reflexive(A!115)))) | (~(transitive(B!116) | (~transitive(A!115)))) | (~(connected(B!116) | (~connected(A!115)))) | (~(antisymmetric(B!116) | (~antisymmetric(A!115)))) | (~(well_founded_relation(B!116) | (~well_founded_relation(A!115))))) | (well_founded_relation(B!116) | (~well_founded_relation(A!115)))),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(126,plain,
% 9.05/6.07 (well_founded_relation(B!116) | (~well_founded_relation(A!115))),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[125, 85])).
% 9.05/6.07 tff(127,plain,
% 9.05/6.07 (((~well_founded_relation(A!115)) | (~reflexive(A!115)) | (~transitive(A!115)) | (~connected(A!115)) | (~antisymmetric(A!115))) | well_founded_relation(A!115)),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(128,plain,
% 9.05/6.07 (well_founded_relation(A!115)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[127, 98])).
% 9.05/6.07 tff(129,plain,
% 9.05/6.07 ((~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))) | well_founded_relation(B!116) | (~well_founded_relation(A!115))),
% 9.05/6.07 inference(tautology,[status(thm)],[])).
% 9.05/6.07 tff(130,plain,
% 9.05/6.07 ((~(well_founded_relation(B!116) | (~well_founded_relation(A!115)))) | well_founded_relation(B!116)),
% 9.05/6.07 inference(unit_resolution,[status(thm)],[129, 128])).
% 9.05/6.07 tff(131,plain,
% 9.05/6.07 (well_founded_relation(B!116)),
% 9.15/6.09 inference(unit_resolution,[status(thm)],[130, 126])).
% 9.15/6.09 tff(132,plain,
% 9.15/6.09 ((~((~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116)))) | (~well_founded_relation(B!116)) | (~reflexive(B!116)) | (~transitive(B!116)) | (~connected(B!116)) | (~antisymmetric(B!116))),
% 9.15/6.09 inference(tautology,[status(thm)],[])).
% 9.15/6.09 tff(133,plain,
% 9.15/6.09 ($false),
% 9.15/6.09 inference(unit_resolution,[status(thm)],[132, 131, 124, 117, 110, 103, 42])).
% 9.15/6.09 % SZS output end Proof
%------------------------------------------------------------------------------