TSTP Solution File: SEU257+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU257+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 07:28:32 EDT 2022
% Result : Theorem 0.45s 0.55s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU257+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.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 11:13:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.45/0.55 % SZS status Theorem
% 0.45/0.55 % SZS output start Proof
% 0.45/0.55 tff(well_founded_relation_type, type, (
% 0.45/0.55 well_founded_relation: $i > $o)).
% 0.45/0.55 tff(relation_restriction_type, type, (
% 0.45/0.55 relation_restriction: ( $i * $i ) > $i)).
% 0.45/0.55 tff(tptp_fun_A_107_type, type, (
% 0.45/0.55 tptp_fun_A_107: $i)).
% 0.45/0.55 tff(tptp_fun_B_106_type, type, (
% 0.45/0.55 tptp_fun_B_106: $i)).
% 0.45/0.55 tff(antisymmetric_type, type, (
% 0.45/0.55 antisymmetric: $i > $o)).
% 0.45/0.55 tff(transitive_type, type, (
% 0.45/0.55 transitive: $i > $o)).
% 0.45/0.55 tff(connected_type, type, (
% 0.45/0.55 connected: $i > $o)).
% 0.45/0.55 tff(reflexive_type, type, (
% 0.45/0.55 reflexive: $i > $o)).
% 0.45/0.55 tff(well_ordering_type, type, (
% 0.45/0.55 well_ordering: $i > $o)).
% 0.45/0.55 tff(relation_type, type, (
% 0.45/0.55 relation: $i > $o)).
% 0.45/0.55 tff(1,plain,
% 0.45/0.55 ((~(well_ordering(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_ordering(B!106)))) <=> (~(well_ordering(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_ordering(B!106))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(2,plain,
% 0.45/0.55 ((~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))) <=> (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(3,plain,
% 0.45/0.55 ((~![A: $i, B: $i] : (relation(B) => (well_ordering(B) => well_ordering(relation_restriction(B, A))))) <=> (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(4,axiom,(~![A: $i, B: $i] : (relation(B) => (well_ordering(B) => well_ordering(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t32_wellord1')).
% 0.45/0.55 tff(5,plain,
% 0.45/0.55 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.45/0.55 tff(6,plain,
% 0.45/0.55 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.45/0.55 tff(7,plain,
% 0.45/0.55 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.45/0.55 tff(8,plain,
% 0.45/0.55 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.45/0.55 tff(9,plain,
% 0.45/0.55 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.45/0.55 tff(10,plain,
% 0.45/0.55 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.45/0.55 tff(11,plain,
% 0.45/0.55 (~![A: $i, B: $i] : (well_ordering(relation_restriction(B, A)) | (~relation(B)) | (~well_ordering(B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.45/0.55 tff(12,plain,(
% 0.45/0.55 ~(well_ordering(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_ordering(B!106)))),
% 0.45/0.55 inference(skolemize,[status(sab)],[11])).
% 0.45/0.55 tff(13,plain,
% 0.45/0.55 (~(well_ordering(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_ordering(B!106)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.45/0.55 tff(14,plain,
% 0.45/0.55 (relation(B!106)),
% 0.45/0.55 inference(or_elim,[status(thm)],[13])).
% 0.45/0.55 tff(15,plain,
% 0.45/0.55 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(16,plain,
% 0.45/0.55 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[15])).
% 0.45/0.55 tff(17,plain,
% 0.45/0.55 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(18,plain,
% 0.45/0.55 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(19,plain,
% 0.45/0.55 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[18])).
% 0.45/0.55 tff(20,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.45/0.55 tff(21,plain,
% 0.45/0.55 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.45/0.55 tff(22,plain,
% 0.45/0.55 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.45/0.55 tff(23,plain,(
% 0.45/0.55 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.45/0.55 inference(skolemize,[status(sab)],[22])).
% 0.45/0.55 tff(24,plain,
% 0.45/0.55 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.45/0.55 tff(25,plain,
% 0.45/0.55 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!106)) | relation(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!106)) | relation(relation_restriction(B!106, A!107)))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(26,plain,
% 0.45/0.55 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!106)) | relation(relation_restriction(B!106, A!107)))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(27,plain,
% 0.45/0.55 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!106)) | relation(relation_restriction(B!106, A!107))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.45/0.55 tff(28,plain,
% 0.45/0.55 (relation(relation_restriction(B!106, A!107))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.45/0.55 tff(29,plain,
% 0.45/0.55 (^[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)))))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(30,plain,
% 0.45/0.55 (![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))))))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[29])).
% 0.45/0.55 tff(31,plain,
% 0.45/0.55 (^[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)))))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(32,plain,
% 0.45/0.55 (![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))))))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[31])).
% 0.45/0.55 tff(33,plain,
% 0.45/0.55 (![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))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(34,plain,
% 0.45/0.55 (^[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))))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(35,plain,
% 0.45/0.55 (![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))))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[34])).
% 0.45/0.55 tff(36,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')).
% 0.45/0.55 tff(37,plain,
% 0.45/0.55 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.45/0.55 tff(38,plain,
% 0.45/0.55 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.45/0.55 tff(39,plain,(
% 0.45/0.55 ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.45/0.55 inference(skolemize,[status(sab)],[38])).
% 0.45/0.55 tff(40,plain,
% 0.45/0.55 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.45/0.55 tff(41,plain,
% 0.45/0.55 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.45/0.55 tff(42,plain,
% 0.45/0.55 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(relation_restriction(B!106, A!107))) | (well_ordering(relation_restriction(B!106, A!107)) <=> (~((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | (~relation(relation_restriction(B!106, A!107))) | (well_ordering(relation_restriction(B!106, A!107)) <=> (~((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(43,plain,
% 0.45/0.55 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(relation_restriction(B!106, A!107))) | (well_ordering(relation_restriction(B!106, A!107)) <=> (~((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))))))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(44,plain,
% 0.45/0.55 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | (~relation(relation_restriction(B!106, A!107))) | (well_ordering(relation_restriction(B!106, A!107)) <=> (~((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107))))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.45/0.55 tff(45,plain,
% 0.45/0.55 ((~relation(relation_restriction(B!106, A!107))) | (well_ordering(relation_restriction(B!106, A!107)) <=> (~((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107))))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[44, 41])).
% 0.45/0.55 tff(46,plain,
% 0.45/0.55 (well_ordering(relation_restriction(B!106, A!107)) <=> (~((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[45, 28])).
% 0.45/0.55 tff(47,plain,
% 0.45/0.55 (~well_ordering(relation_restriction(B!106, A!107))),
% 0.45/0.55 inference(or_elim,[status(thm)],[13])).
% 0.45/0.55 tff(48,plain,
% 0.45/0.55 ((~(well_ordering(relation_restriction(B!106, A!107)) <=> (~((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107))))))) | well_ordering(relation_restriction(B!106, A!107)) | ((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107))))),
% 0.45/0.55 inference(tautology,[status(thm)],[])).
% 0.45/0.55 tff(49,plain,
% 0.45/0.55 ((~(well_ordering(relation_restriction(B!106, A!107)) <=> (~((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107))))))) | ((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.45/0.55 tff(50,plain,
% 0.45/0.55 ((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.45/0.55 tff(51,plain,
% 0.45/0.55 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(B!106)) | (well_ordering(B!106) <=> (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | (~relation(B!106)) | (well_ordering(B!106) <=> (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(52,plain,
% 0.45/0.55 (((~relation(B!106)) | (well_ordering(B!106) <=> (~((~reflexive(B!106)) | (~connected(B!106)) | (~transitive(B!106)) | (~antisymmetric(B!106)) | (~well_founded_relation(B!106)))))) <=> ((~relation(B!106)) | (well_ordering(B!106) <=> (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(53,plain,
% 0.45/0.55 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(B!106)) | (well_ordering(B!106) <=> (~((~reflexive(B!106)) | (~connected(B!106)) | (~transitive(B!106)) | (~antisymmetric(B!106)) | (~well_founded_relation(B!106))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(B!106)) | (well_ordering(B!106) <=> (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106)))))))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[52])).
% 0.45/0.55 tff(54,plain,
% 0.45/0.55 (((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(B!106)) | (well_ordering(B!106) <=> (~((~reflexive(B!106)) | (~connected(B!106)) | (~transitive(B!106)) | (~antisymmetric(B!106)) | (~well_founded_relation(B!106))))))) <=> ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | (~relation(B!106)) | (well_ordering(B!106) <=> (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))))))),
% 0.45/0.55 inference(transitivity,[status(thm)],[53, 51])).
% 0.45/0.55 tff(55,plain,
% 0.45/0.55 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | ((~relation(B!106)) | (well_ordering(B!106) <=> (~((~reflexive(B!106)) | (~connected(B!106)) | (~transitive(B!106)) | (~antisymmetric(B!106)) | (~well_founded_relation(B!106))))))),
% 0.45/0.55 inference(quant_inst,[status(thm)],[])).
% 0.45/0.55 tff(56,plain,
% 0.45/0.55 ((~![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (~((~reflexive(A)) | (~connected(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~well_founded_relation(A))))))) | (~relation(B!106)) | (well_ordering(B!106) <=> (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106)))))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.45/0.55 tff(57,plain,
% 0.45/0.55 (well_ordering(B!106) <=> (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[56, 41, 14])).
% 0.45/0.55 tff(58,plain,
% 0.45/0.55 (well_ordering(B!106)),
% 0.45/0.55 inference(or_elim,[status(thm)],[13])).
% 0.45/0.55 tff(59,plain,
% 0.45/0.55 ((~(well_ordering(B!106) <=> (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106)))))) | (~well_ordering(B!106)) | (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))))),
% 0.45/0.55 inference(tautology,[status(thm)],[])).
% 0.45/0.55 tff(60,plain,
% 0.45/0.55 ((~(well_ordering(B!106) <=> (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106)))))) | (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.45/0.55 tff(61,plain,
% 0.45/0.55 (~((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106)))),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.45/0.55 tff(62,plain,
% 0.45/0.55 (((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) | well_founded_relation(B!106)),
% 0.45/0.55 inference(tautology,[status(thm)],[])).
% 0.45/0.55 tff(63,plain,
% 0.45/0.55 (well_founded_relation(B!106)),
% 0.45/0.55 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.45/0.55 tff(64,plain,
% 0.45/0.55 (^[A: $i, B: $i] : refl((well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B))) <=> (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(65,plain,
% 0.45/0.55 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B))) <=> ![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[64])).
% 0.45/0.55 tff(66,plain,
% 0.45/0.55 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B))) <=> ![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(67,plain,
% 0.45/0.55 (^[A: $i, B: $i] : trans(monotonicity(rewrite((well_founded_relation(B) => well_founded_relation(relation_restriction(B, A))) <=> ((~well_founded_relation(B)) | well_founded_relation(relation_restriction(B, A)))), ((relation(B) => (well_founded_relation(B) => well_founded_relation(relation_restriction(B, A)))) <=> (relation(B) => ((~well_founded_relation(B)) | well_founded_relation(relation_restriction(B, A)))))), rewrite((relation(B) => ((~well_founded_relation(B)) | well_founded_relation(relation_restriction(B, A)))) <=> (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))), ((relation(B) => (well_founded_relation(B) => well_founded_relation(relation_restriction(B, A)))) <=> (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))))),
% 0.45/0.55 inference(bind,[status(th)],[])).
% 0.45/0.55 tff(68,plain,
% 0.45/0.55 (![A: $i, B: $i] : (relation(B) => (well_founded_relation(B) => well_founded_relation(relation_restriction(B, A)))) <=> ![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.45/0.55 inference(quant_intro,[status(thm)],[67])).
% 0.45/0.55 tff(69,axiom,(![A: $i, B: $i] : (relation(B) => (well_founded_relation(B) => well_founded_relation(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t31_wellord1')).
% 0.45/0.55 tff(70,plain,
% 0.45/0.55 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.45/0.55 tff(71,plain,
% 0.45/0.55 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.45/0.55 tff(72,plain,(
% 0.45/0.55 ![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.45/0.55 inference(skolemize,[status(sab)],[71])).
% 0.45/0.55 tff(73,plain,
% 0.45/0.55 (![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))),
% 0.45/0.55 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.45/0.55 tff(74,plain,
% 0.45/0.55 (((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | ((~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(75,plain,
% 0.45/0.56 ((well_founded_relation(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_founded_relation(B!106))) <=> ((~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(76,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (well_founded_relation(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_founded_relation(B!106)))) <=> ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | ((~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107))))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[75])).
% 0.45/0.56 tff(77,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (well_founded_relation(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_founded_relation(B!106)))) <=> ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(transitivity,[status(thm)],[76, 74])).
% 0.45/0.56 tff(78,plain,
% 0.45/0.56 ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (well_founded_relation(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~well_founded_relation(B!106)))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(79,plain,
% 0.45/0.56 ((~![A: $i, B: $i] : (well_founded_relation(relation_restriction(B, A)) | (~relation(B)) | (~well_founded_relation(B)))) | (~relation(B!106)) | (~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.45/0.56 tff(80,plain,
% 0.45/0.56 ((~well_founded_relation(B!106)) | well_founded_relation(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[79, 73, 14])).
% 0.45/0.56 tff(81,plain,
% 0.45/0.56 (well_founded_relation(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[80, 63])).
% 0.45/0.56 tff(82,plain,
% 0.45/0.56 (((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) | antisymmetric(B!106)),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(83,plain,
% 0.45/0.56 (antisymmetric(B!106)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[82, 61])).
% 0.45/0.56 tff(84,plain,
% 0.45/0.56 (^[A: $i, B: $i] : refl((antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))) <=> (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(85,plain,
% 0.45/0.56 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))) <=> ![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.45/0.56 inference(quant_intro,[status(thm)],[84])).
% 0.45/0.56 tff(86,plain,
% 0.45/0.56 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B))) <=> ![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(87,plain,
% 0.45/0.56 (^[A: $i, B: $i] : trans(monotonicity(rewrite((antisymmetric(B) => antisymmetric(relation_restriction(B, A))) <=> (antisymmetric(relation_restriction(B, A)) | (~antisymmetric(B)))), ((relation(B) => (antisymmetric(B) => antisymmetric(relation_restriction(B, A)))) <=> (relation(B) => (antisymmetric(relation_restriction(B, A)) | (~antisymmetric(B)))))), rewrite((relation(B) => (antisymmetric(relation_restriction(B, A)) | (~antisymmetric(B)))) <=> (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))), ((relation(B) => (antisymmetric(B) => antisymmetric(relation_restriction(B, A)))) <=> (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(88,plain,
% 0.45/0.56 (![A: $i, B: $i] : (relation(B) => (antisymmetric(B) => antisymmetric(relation_restriction(B, A)))) <=> ![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.45/0.56 inference(quant_intro,[status(thm)],[87])).
% 0.45/0.56 tff(89,axiom,(![A: $i, B: $i] : (relation(B) => (antisymmetric(B) => antisymmetric(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_wellord1')).
% 0.45/0.56 tff(90,plain,
% 0.45/0.56 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.45/0.56 tff(91,plain,
% 0.45/0.56 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.45/0.56 tff(92,plain,(
% 0.45/0.56 ![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.45/0.56 inference(skolemize,[status(sab)],[91])).
% 0.45/0.56 tff(93,plain,
% 0.45/0.56 (![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.45/0.56 tff(94,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | ((~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(95,plain,
% 0.45/0.56 ((antisymmetric(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~antisymmetric(B!106))) <=> ((~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(96,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (antisymmetric(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~antisymmetric(B!106)))) <=> ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | ((~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107))))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[95])).
% 0.45/0.56 tff(97,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (antisymmetric(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~antisymmetric(B!106)))) <=> ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(transitivity,[status(thm)],[96, 94])).
% 0.45/0.56 tff(98,plain,
% 0.45/0.56 ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (antisymmetric(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~antisymmetric(B!106)))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(99,plain,
% 0.45/0.56 ((~![A: $i, B: $i] : (antisymmetric(relation_restriction(B, A)) | (~relation(B)) | (~antisymmetric(B)))) | (~relation(B!106)) | (~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.45/0.56 tff(100,plain,
% 0.45/0.56 ((~antisymmetric(B!106)) | antisymmetric(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[99, 93, 14])).
% 0.45/0.56 tff(101,plain,
% 0.45/0.56 (antisymmetric(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[100, 83])).
% 0.45/0.56 tff(102,plain,
% 0.45/0.56 (((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) | transitive(B!106)),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(103,plain,
% 0.45/0.56 (transitive(B!106)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[102, 61])).
% 0.45/0.56 tff(104,plain,
% 0.45/0.56 (^[A: $i, B: $i] : refl((transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))) <=> (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(105,plain,
% 0.45/0.56 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))) <=> ![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.45/0.56 inference(quant_intro,[status(thm)],[104])).
% 0.45/0.56 tff(106,plain,
% 0.45/0.56 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))) <=> ![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(107,plain,
% 0.45/0.56 (^[A: $i, B: $i] : trans(monotonicity(rewrite((transitive(B) => transitive(relation_restriction(B, A))) <=> ((~transitive(B)) | transitive(relation_restriction(B, A)))), ((relation(B) => (transitive(B) => transitive(relation_restriction(B, A)))) <=> (relation(B) => ((~transitive(B)) | transitive(relation_restriction(B, A)))))), rewrite((relation(B) => ((~transitive(B)) | transitive(relation_restriction(B, A)))) <=> (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))), ((relation(B) => (transitive(B) => transitive(relation_restriction(B, A)))) <=> (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(108,plain,
% 0.45/0.56 (![A: $i, B: $i] : (relation(B) => (transitive(B) => transitive(relation_restriction(B, A)))) <=> ![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.45/0.56 inference(quant_intro,[status(thm)],[107])).
% 0.45/0.56 tff(109,axiom,(![A: $i, B: $i] : (relation(B) => (transitive(B) => transitive(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t24_wellord1')).
% 0.45/0.56 tff(110,plain,
% 0.45/0.56 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.45/0.56 tff(111,plain,
% 0.45/0.56 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.45/0.56 tff(112,plain,(
% 0.45/0.56 ![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.45/0.56 inference(skolemize,[status(sab)],[111])).
% 0.45/0.56 tff(113,plain,
% 0.45/0.56 (![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.45/0.56 tff(114,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | ((~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(115,plain,
% 0.45/0.56 ((transitive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~transitive(B!106))) <=> ((~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(116,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (transitive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~transitive(B!106)))) <=> ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | ((~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107))))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[115])).
% 0.45/0.56 tff(117,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (transitive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~transitive(B!106)))) <=> ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(transitivity,[status(thm)],[116, 114])).
% 0.45/0.56 tff(118,plain,
% 0.45/0.56 ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (transitive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~transitive(B!106)))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(119,plain,
% 0.45/0.56 ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) | (~relation(B!106)) | (~transitive(B!106)) | transitive(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.45/0.56 tff(120,plain,
% 0.45/0.56 ((~transitive(B!106)) | transitive(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[119, 113, 14])).
% 0.45/0.56 tff(121,plain,
% 0.45/0.56 (transitive(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[120, 103])).
% 0.45/0.56 tff(122,plain,
% 0.45/0.56 (((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) | connected(B!106)),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(123,plain,
% 0.45/0.56 (connected(B!106)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[122, 61])).
% 0.45/0.56 tff(124,plain,
% 0.45/0.56 (^[A: $i, B: $i] : refl((connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))) <=> (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(125,plain,
% 0.45/0.56 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))) <=> ![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.45/0.56 inference(quant_intro,[status(thm)],[124])).
% 0.45/0.56 tff(126,plain,
% 0.45/0.56 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))) <=> ![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(127,plain,
% 0.45/0.56 (^[A: $i, B: $i] : trans(monotonicity(rewrite((connected(B) => connected(relation_restriction(B, A))) <=> (connected(relation_restriction(B, A)) | (~connected(B)))), ((relation(B) => (connected(B) => connected(relation_restriction(B, A)))) <=> (relation(B) => (connected(relation_restriction(B, A)) | (~connected(B)))))), rewrite((relation(B) => (connected(relation_restriction(B, A)) | (~connected(B)))) <=> (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))), ((relation(B) => (connected(B) => connected(relation_restriction(B, A)))) <=> (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(128,plain,
% 0.45/0.56 (![A: $i, B: $i] : (relation(B) => (connected(B) => connected(relation_restriction(B, A)))) <=> ![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.45/0.56 inference(quant_intro,[status(thm)],[127])).
% 0.45/0.56 tff(129,axiom,(![A: $i, B: $i] : (relation(B) => (connected(B) => connected(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_wellord1')).
% 0.45/0.56 tff(130,plain,
% 0.45/0.56 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.45/0.56 tff(131,plain,
% 0.45/0.56 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.45/0.56 tff(132,plain,(
% 0.45/0.56 ![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.45/0.56 inference(skolemize,[status(sab)],[131])).
% 0.45/0.56 tff(133,plain,
% 0.45/0.56 (![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.45/0.56 tff(134,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | ((~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(135,plain,
% 0.45/0.56 ((connected(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~connected(B!106))) <=> ((~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(136,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (connected(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~connected(B!106)))) <=> ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | ((~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107))))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[135])).
% 0.45/0.56 tff(137,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (connected(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~connected(B!106)))) <=> ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(transitivity,[status(thm)],[136, 134])).
% 0.45/0.56 tff(138,plain,
% 0.45/0.56 ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (connected(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~connected(B!106)))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(139,plain,
% 0.45/0.56 ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) | (~relation(B!106)) | (~connected(B!106)) | connected(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.45/0.56 tff(140,plain,
% 0.45/0.56 ((~connected(B!106)) | connected(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[139, 133, 14])).
% 0.45/0.56 tff(141,plain,
% 0.45/0.56 (connected(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[140, 123])).
% 0.45/0.56 tff(142,plain,
% 0.45/0.56 (((~well_founded_relation(B!106)) | (~connected(B!106)) | (~antisymmetric(B!106)) | (~transitive(B!106)) | (~reflexive(B!106))) | reflexive(B!106)),
% 0.45/0.56 inference(tautology,[status(thm)],[])).
% 0.45/0.56 tff(143,plain,
% 0.45/0.56 (reflexive(B!106)),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[142, 61])).
% 0.45/0.56 tff(144,plain,
% 0.45/0.56 (^[A: $i, B: $i] : refl((reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))) <=> (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(145,plain,
% 0.45/0.56 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))) <=> ![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.45/0.56 inference(quant_intro,[status(thm)],[144])).
% 0.45/0.56 tff(146,plain,
% 0.45/0.56 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))) <=> ![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(147,plain,
% 0.45/0.56 (^[A: $i, B: $i] : trans(monotonicity(rewrite((reflexive(B) => reflexive(relation_restriction(B, A))) <=> ((~reflexive(B)) | reflexive(relation_restriction(B, A)))), ((relation(B) => (reflexive(B) => reflexive(relation_restriction(B, A)))) <=> (relation(B) => ((~reflexive(B)) | reflexive(relation_restriction(B, A)))))), rewrite((relation(B) => ((~reflexive(B)) | reflexive(relation_restriction(B, A)))) <=> (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))), ((relation(B) => (reflexive(B) => reflexive(relation_restriction(B, A)))) <=> (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))))),
% 0.45/0.56 inference(bind,[status(th)],[])).
% 0.45/0.56 tff(148,plain,
% 0.45/0.56 (![A: $i, B: $i] : (relation(B) => (reflexive(B) => reflexive(relation_restriction(B, A)))) <=> ![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.45/0.56 inference(quant_intro,[status(thm)],[147])).
% 0.45/0.56 tff(149,axiom,(![A: $i, B: $i] : (relation(B) => (reflexive(B) => reflexive(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t22_wellord1')).
% 0.45/0.56 tff(150,plain,
% 0.45/0.56 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.45/0.56 tff(151,plain,
% 0.45/0.56 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.45/0.56 tff(152,plain,(
% 0.45/0.56 ![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.45/0.56 inference(skolemize,[status(sab)],[151])).
% 0.45/0.56 tff(153,plain,
% 0.45/0.56 (![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.45/0.56 tff(154,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | ((~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107)))) <=> ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(155,plain,
% 0.45/0.56 ((reflexive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~reflexive(B!106))) <=> ((~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(rewrite,[status(thm)],[])).
% 0.45/0.56 tff(156,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (reflexive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~reflexive(B!106)))) <=> ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | ((~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107))))),
% 0.45/0.56 inference(monotonicity,[status(thm)],[155])).
% 0.45/0.56 tff(157,plain,
% 0.45/0.56 (((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (reflexive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~reflexive(B!106)))) <=> ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107)))),
% 0.45/0.56 inference(transitivity,[status(thm)],[156, 154])).
% 0.45/0.56 tff(158,plain,
% 0.45/0.56 ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (reflexive(relation_restriction(B!106, A!107)) | (~relation(B!106)) | (~reflexive(B!106)))),
% 0.45/0.56 inference(quant_inst,[status(thm)],[])).
% 0.45/0.56 tff(159,plain,
% 0.45/0.56 ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) | (~relation(B!106)) | (~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.45/0.56 tff(160,plain,
% 0.45/0.56 ((~reflexive(B!106)) | reflexive(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[159, 153, 14])).
% 0.45/0.56 tff(161,plain,
% 0.45/0.56 (reflexive(relation_restriction(B!106, A!107))),
% 0.45/0.56 inference(unit_resolution,[status(thm)],[160, 143])).
% 0.45/0.56 tff(162,plain,
% 0.45/0.56 ((~((~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107))))) | (~reflexive(relation_restriction(B!106, A!107))) | (~connected(relation_restriction(B!106, A!107))) | (~transitive(relation_restriction(B!106, A!107))) | (~antisymmetric(relation_restriction(B!106, A!107))) | (~well_founded_relation(relation_restriction(B!106, A!107)))),
% 0.45/0.57 inference(tautology,[status(thm)],[])).
% 0.45/0.57 tff(163,plain,
% 0.45/0.57 ($false),
% 0.45/0.57 inference(unit_resolution,[status(thm)],[162, 161, 141, 121, 101, 81, 50])).
% 0.45/0.57 % SZS output end Proof
%------------------------------------------------------------------------------