TSTP Solution File: DAT033_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT033_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 : Fri Sep 16 14:36:27 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : DAT033_1 : TPTP v8.1.0. Released v5.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n011.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 : Wed Aug 31 01:41:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(count_type, type, (
% 0.20/0.46 count: collection > $int)).
% 0.20/0.46 tff(tptp_fun_U_0_type, type, (
% 0.20/0.46 tptp_fun_U_0: collection)).
% 0.20/0.46 tff(remove_type, type, (
% 0.20/0.46 remove: ( $int * collection ) > collection)).
% 0.20/0.46 tff(in_type, type, (
% 0.20/0.46 in: ( $int * collection ) > $o)).
% 0.20/0.46 tff(add_type, type, (
% 0.20/0.46 add: ( $int * collection ) > collection)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 ((~![U: collection] : ((~($sum(count(add(3, U)), $product(-1, count(add(5, U)))) = 0)) | ($sum(count(remove(3, U)), $product(-1, count(remove(5, U)))) = 0))) <=> (~![U: collection] : ((~($sum(count(add(3, U)), $product(-1, count(add(5, U)))) = 0)) | ($sum(count(remove(3, U)), $product(-1, count(remove(5, U)))) = 0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 ((~![U: collection] : ((~($sum(count(add(5, U)), $product(-1, count(add(3, U)))) = 0)) | ($sum(count(remove(5, U)), $product(-1, count(remove(3, U)))) = 0))) <=> (~![U: collection] : ((~($sum(count(add(3, U)), $product(-1, count(add(5, U)))) = 0)) | ($sum(count(remove(3, U)), $product(-1, count(remove(5, U)))) = 0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 ((~![U: collection] : ((~(count(add(5, U)) = count(add(3, U)))) | (count(remove(5, U)) = count(remove(3, U))))) <=> (~![U: collection] : ((~($sum(count(add(5, U)), $product(-1, count(add(3, U)))) = 0)) | ($sum(count(remove(5, U)), $product(-1, count(remove(3, U)))) = 0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 ((~![U: collection] : ((~(count(add(5, U)) = count(add(3, U)))) | (count(remove(5, U)) = count(remove(3, U))))) <=> (~![U: collection] : ((~(count(add(5, U)) = count(add(3, U)))) | (count(remove(5, U)) = count(remove(3, U)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 ((~![U: collection] : ((count(add(5, U)) = count(add(3, U))) => (count(remove(5, U)) = count(remove(3, U))))) <=> (~![U: collection] : ((~(count(add(5, U)) = count(add(3, U)))) | (count(remove(5, U)) = count(remove(3, U)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(6,axiom,(~![U: collection] : ((count(add(5, U)) = count(add(3, U))) => (count(remove(5, U)) = count(remove(3, U))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (~![U: collection] : ((~(count(add(5, U)) = count(add(3, U)))) | (count(remove(5, U)) = count(remove(3, U))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 (~![U: collection] : ((~(count(add(5, U)) = count(add(3, U)))) | (count(remove(5, U)) = count(remove(3, U))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (~![U: collection] : ((~(count(add(5, U)) = count(add(3, U)))) | (count(remove(5, U)) = count(remove(3, U))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (~![U: collection] : ((~(count(add(5, U)) = count(add(3, U)))) | (count(remove(5, U)) = count(remove(3, U))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (~![U: collection] : ((~($sum(count(add(5, U)), $product(-1, count(add(3, U)))) = 0)) | ($sum(count(remove(5, U)), $product(-1, count(remove(3, U)))) = 0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (~![U: collection] : ((~($sum(count(add(3, U)), $product(-1, count(add(5, U)))) = 0)) | ($sum(count(remove(3, U)), $product(-1, count(remove(5, U)))) = 0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (~![U: collection] : ((~($sum(count(add(3, U)), $product(-1, count(add(5, U)))) = 0)) | ($sum(count(remove(3, U)), $product(-1, count(remove(5, U)))) = 0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (~![U: collection] : ((~($sum(count(add(3, U)), $product(-1, count(add(5, U)))) = 0)) | ($sum(count(remove(3, U)), $product(-1, count(remove(5, U)))) = 0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[13, 1])).
% 0.20/0.46 tff(15,plain,(
% 0.20/0.46 ~((~($sum(count(add(3, U!0)), $product(-1, count(add(5, U!0)))) = 0)) | ($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))) = 0))),
% 0.20/0.46 inference(skolemize,[status(sab)],[14])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 ($sum(count(add(3, U!0)), $product(-1, count(add(5, U!0)))) = 0),
% 0.20/0.47 inference(or_elim,[status(thm)],[15])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 ((~($sum(count(add(3, U!0)), $product(-1, count(add(5, U!0)))) = 0)) | $lesseq($sum(count(add(3, U!0)), $product(-1, count(add(5, U!0)))), 0)),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 ($lesseq($sum(count(add(3, U!0)), $product(-1, count(add(5, U!0)))), 0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.47 tff(19,assumption,(~in(3, U!0)), introduced(assumption)).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 (^[X8: $int, X9: collection] : refl(((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1)) <=> ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1)) <=> ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 (^[X8: $int, X9: collection] : rewrite(((~in(X8, X9)) <=> ($sum(count(add(X8, X9)), $product(-1, count(X9))) = 1)) <=> ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(add(X8, X9)), $product(-1, count(X9))) = 1)) <=> ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (^[X8: $int, X9: collection] : rewrite(((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9)))) <=> ((~in(X8, X9)) <=> ($sum(count(add(X8, X9)), $product(-1, count(X9))) = 1)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9)))) <=> ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(add(X8, X9)), $product(-1, count(X9))) = 1))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9)))) <=> ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (^[X8: $int, X9: collection] : rewrite(((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(count(X9), 1))) <=> ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(count(X9), 1))) <=> ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.47 tff(29,axiom,(![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(count(X9), 1)))), file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax','ax3')).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(add(X8, X9)), $product(-1, count(X9))) = 1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[32, 23])).
% 0.20/0.47 tff(34,plain,(
% 0.20/0.47 ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.20/0.47 inference(skolemize,[status(sab)],[33])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[34, 21])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (((~![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))) | ((~in(3, U!0)) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1))) <=> ((~![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))) | ((~in(3, U!0)) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 (((~in(3, U!0)) <=> ($sum(count(U!0), $product(-1, count(add(3, U!0)))) = -1)) <=> ((~in(3, U!0)) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (((~![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))) | ((~in(3, U!0)) <=> ($sum(count(U!0), $product(-1, count(add(3, U!0)))) = -1))) <=> ((~![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))) | ((~in(3, U!0)) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (((~![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))) | ((~in(3, U!0)) <=> ($sum(count(U!0), $product(-1, count(add(3, U!0)))) = -1))) <=> ((~![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))) | ((~in(3, U!0)) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 ((~![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))) | ((~in(3, U!0)) <=> ($sum(count(U!0), $product(-1, count(add(3, U!0)))) = -1))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 ((~![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))) | ((~in(3, U!0)) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 ((~in(3, U!0)) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[41, 35])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 ((~((~in(3, U!0)) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1))) | in(3, U!0) | ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 (in(3, U!0) | ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[44, 19])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 ((~($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 1)) | $greatereq($sum(count(add(3, U!0)), $product(-1, count(U!0))), 1)),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 ($greatereq($sum(count(add(3, U!0)), $product(-1, count(U!0))), 1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 ((~$lesseq($sum(count(add(5, U!0)), $product(-1, count(U!0))), 0)) | (~$greatereq($sum(count(add(3, U!0)), $product(-1, count(U!0))), 1)) | (~$lesseq($sum(count(add(3, U!0)), $product(-1, count(add(5, U!0)))), 0))),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (~$lesseq($sum(count(add(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[48, 47, 18])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 ((~($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0)) | $lesseq($sum(count(add(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (~($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (^[X10: $int, X11: collection] : refl((in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0)) <=> (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0)) <=> ![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (^[X10: $int, X11: collection] : rewrite((in(X10, X11) <=> ($sum(count(add(X10, X11)), $product(-1, count(X11))) = 0)) <=> (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(add(X10, X11)), $product(-1, count(X11))) = 0)) <=> ![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (^[X10: $int, X11: collection] : rewrite((in(X10, X11) <=> (count(add(X10, X11)) = count(X11))) <=> (in(X10, X11) <=> ($sum(count(add(X10, X11)), $product(-1, count(X11))) = 0)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (![X10: $int, X11: collection] : (in(X10, X11) <=> (count(add(X10, X11)) = count(X11))) <=> ![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(add(X10, X11)), $product(-1, count(X11))) = 0))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (![X10: $int, X11: collection] : (in(X10, X11) <=> (count(add(X10, X11)) = count(X11))) <=> ![X10: $int, X11: collection] : (in(X10, X11) <=> (count(add(X10, X11)) = count(X11)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(59,axiom,(![X10: $int, X11: collection] : (in(X10, X11) <=> (count(add(X10, X11)) = count(X11)))), file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax','ax4')).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (![X10: $int, X11: collection] : (in(X10, X11) <=> (count(add(X10, X11)) = count(X11)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(add(X10, X11)), $product(-1, count(X11))) = 0))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[60, 57])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[61, 55])).
% 0.20/0.48 tff(63,plain,(
% 0.20/0.48 ![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))),
% 0.20/0.48 inference(skolemize,[status(sab)],[62])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 (![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 (((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(5, U!0) <=> ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0))) <=> ((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(5, U!0) <=> ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 ((in(5, U!0) <=> ($sum(count(U!0), $product(-1, count(add(5, U!0)))) = 0)) <=> (in(5, U!0) <=> ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(5, U!0) <=> ($sum(count(U!0), $product(-1, count(add(5, U!0)))) = 0))) <=> ((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(5, U!0) <=> ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 (((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(5, U!0) <=> ($sum(count(U!0), $product(-1, count(add(5, U!0)))) = 0))) <=> ((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(5, U!0) <=> ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[67, 65])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 ((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(5, U!0) <=> ($sum(count(U!0), $product(-1, count(add(5, U!0)))) = 0))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 ((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(5, U!0) <=> ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (in(5, U!0) <=> ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[70, 64])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 ((~(in(5, U!0) <=> ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0))) | (~in(5, U!0)) | ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 ((~in(5, U!0)) | ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (~in(5, U!0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[73, 51])).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (^[X14: $int, X15: collection] : refl(((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0)) <=> ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0)) <=> ![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.48 tff(77,plain,
% 0.20/0.48 (^[X14: $int, X15: collection] : rewrite(((~in(X14, X15)) <=> ($sum(count(remove(X14, X15)), $product(-1, count(X15))) = 0)) <=> ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(remove(X14, X15)), $product(-1, count(X15))) = 0)) <=> ![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.48 tff(79,plain,
% 0.20/0.48 (^[X14: $int, X15: collection] : rewrite(((~in(X14, X15)) <=> (count(remove(X14, X15)) = count(X15))) <=> ((~in(X14, X15)) <=> ($sum(count(remove(X14, X15)), $product(-1, count(X15))) = 0)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(80,plain,
% 0.20/0.48 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> (count(remove(X14, X15)) = count(X15))) <=> ![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(remove(X14, X15)), $product(-1, count(X15))) = 0))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> (count(remove(X14, X15)) = count(X15))) <=> ![X14: $int, X15: collection] : ((~in(X14, X15)) <=> (count(remove(X14, X15)) = count(X15)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(82,axiom,(![X14: $int, X15: collection] : ((~in(X14, X15)) <=> (count(remove(X14, X15)) = count(X15)))), file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax','ax6')).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> (count(remove(X14, X15)) = count(X15)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(remove(X14, X15)), $product(-1, count(X15))) = 0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[84, 78])).
% 0.20/0.48 tff(86,plain,(
% 0.20/0.48 ![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))),
% 0.20/0.48 inference(skolemize,[status(sab)],[85])).
% 0.20/0.48 tff(87,plain,
% 0.20/0.48 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(5, U!0)) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(5, U!0)) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (((~in(5, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(5, U!0)))) = 0)) <=> ((~in(5, U!0)) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(5, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(5, U!0)))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(5, U!0)) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(5, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(5, U!0)))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(5, U!0)) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[90, 88])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(5, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(5, U!0)))) = 0))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(5, U!0)) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 ((~in(5, U!0)) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[93, 87])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 ((~((~in(5, U!0)) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0))) | in(5, U!0) | ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 (in(5, U!0) | ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[96, 74])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 ((~($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)) | $greatereq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.48 tff(99,plain,
% 0.20/0.48 ($greatereq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(3, U!0)) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(3, U!0)) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (((~in(3, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(3, U!0)))) = 0)) <=> ((~in(3, U!0)) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(3, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(3, U!0)))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(3, U!0)) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[101])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(3, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(3, U!0)))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(3, U!0)) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[102, 100])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(3, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(3, U!0)))) = 0))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(3, U!0)) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 ((~in(3, U!0)) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[105, 87])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 ((~((~in(3, U!0)) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0))) | in(3, U!0) | ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 (in(3, U!0) | ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[108, 19])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 ((~($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0)) | $lesseq($sum(count(remove(3, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 ($lesseq($sum(count(remove(3, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.49 tff(112,assumption,(~$greatereq($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))), 0)), introduced(assumption)).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 ((~($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = 0)) | $greatereq($sum(count(remove(3, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 ($greatereq($sum(count(remove(3, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[113, 109])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 ((~$lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), 0)) | $greatereq($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))), 0) | (~$greatereq($sum(count(remove(3, U!0)), $product(-1, count(U!0))), 0))),
% 0.20/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 (~$lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[115, 114, 112])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 ((~($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)) | $lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 (~($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.20/0.49 tff(119,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[96, 74, 118])).
% 0.20/0.49 tff(120,plain,(in(3, U!0) | $greatereq($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(121,plain,
% 0.20/0.49 (in(3, U!0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[120, 112])).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 (^[X12: $int, X13: collection] : refl((in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1)) <=> (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 (![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1)) <=> ![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 (^[X12: $int, X13: collection] : rewrite((in(X12, X13) <=> ($sum(count(remove(X12, X13)), $product(-1, count(X13))) = -1)) <=> (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 (![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(remove(X12, X13)), $product(-1, count(X13))) = -1)) <=> ![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.49 tff(126,plain,
% 0.20/0.49 (^[X12: $int, X13: collection] : rewrite((in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13)))) <=> (in(X12, X13) <=> ($sum(count(remove(X12, X13)), $product(-1, count(X13))) = -1)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 (![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13)))) <=> ![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(remove(X12, X13)), $product(-1, count(X13))) = -1))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.49 tff(128,plain,
% 0.20/0.49 (![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13)))) <=> ![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 (^[X12: $int, X13: collection] : rewrite((in(X12, X13) <=> (count(remove(X12, X13)) = $difference(count(X13), 1))) <=> (in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 (![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $difference(count(X13), 1))) <=> ![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.49 tff(131,axiom,(![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $difference(count(X13), 1)))), file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax','ax5')).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 (![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(remove(X12, X13)), $product(-1, count(X13))) = -1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[133, 127])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 (![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[134, 125])).
% 0.20/0.49 tff(136,plain,(
% 0.20/0.49 ![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))),
% 0.20/0.49 inference(skolemize,[status(sab)],[135])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 (![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[136, 123])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(3, U!0) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(3, U!0) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 ((in(3, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(3, U!0)))) = 1)) <=> (in(3, U!0) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(3, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(3, U!0)))) = 1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(3, U!0) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(3, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(3, U!0)))) = 1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(3, U!0) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[140, 138])).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(3, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(3, U!0)))) = 1))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(3, U!0) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 (in(3, U!0) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[143, 137])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 ((~(in(3, U!0) <=> ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1))) | (~in(3, U!0)) | ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(146,plain,
% 0.20/0.49 ((~in(3, U!0)) | ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[146, 121])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 ((~($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1)) | $greatereq($sum(count(remove(3, U!0)), $product(-1, count(U!0))), -1)),
% 0.20/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.49 tff(149,plain,
% 0.20/0.49 ($greatereq($sum(count(remove(3, U!0)), $product(-1, count(U!0))), -1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.20/0.49 tff(150,plain,
% 0.20/0.49 ((~$lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), -1)) | $greatereq($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))), 0) | (~$greatereq($sum(count(remove(3, U!0)), $product(-1, count(U!0))), -1))),
% 0.20/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.49 tff(151,plain,
% 0.20/0.49 (~$lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), -1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[150, 149, 112])).
% 0.20/0.49 tff(152,plain,
% 0.20/0.49 ((~($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)) | $lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), -1)),
% 0.20/0.49 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.49 tff(153,plain,
% 0.20/0.49 (~($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.20/0.49 tff(154,plain,
% 0.20/0.49 (((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(3, U!0) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0))) <=> ((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(3, U!0) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(155,plain,
% 0.20/0.50 ((in(3, U!0) <=> ($sum(count(U!0), $product(-1, count(add(3, U!0)))) = 0)) <=> (in(3, U!0) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(156,plain,
% 0.20/0.50 (((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(3, U!0) <=> ($sum(count(U!0), $product(-1, count(add(3, U!0)))) = 0))) <=> ((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(3, U!0) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[155])).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 (((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(3, U!0) <=> ($sum(count(U!0), $product(-1, count(add(3, U!0)))) = 0))) <=> ((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(3, U!0) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[156, 154])).
% 0.20/0.50 tff(158,plain,
% 0.20/0.50 ((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(3, U!0) <=> ($sum(count(U!0), $product(-1, count(add(3, U!0)))) = 0))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 ((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(3, U!0) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.50 tff(160,plain,
% 0.20/0.50 (in(3, U!0) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[159, 64])).
% 0.20/0.50 tff(161,plain,
% 0.20/0.50 ((~(in(3, U!0) <=> ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0))) | (~in(3, U!0)) | ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(162,plain,
% 0.20/0.50 ((~in(3, U!0)) | ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[162, 121])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 ((~($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0)) | $greatereq($sum(count(add(3, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 ($greatereq($sum(count(add(3, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.20/0.50 tff(166,plain,
% 0.20/0.50 ($greatereq($sum(count(add(5, U!0)), $product(-1, count(U!0))), 0) | (~$greatereq($sum(count(add(3, U!0)), $product(-1, count(U!0))), 0)) | (~$lesseq($sum(count(add(3, U!0)), $product(-1, count(add(5, U!0)))), 0))),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 ($greatereq($sum(count(add(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[166, 165, 18])).
% 0.20/0.50 tff(168,plain,
% 0.20/0.50 ((~($sum(count(add(3, U!0)), $product(-1, count(add(5, U!0)))) = 0)) | $greatereq($sum(count(add(3, U!0)), $product(-1, count(add(5, U!0)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 ($greatereq($sum(count(add(3, U!0)), $product(-1, count(add(5, U!0)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[168, 16])).
% 0.20/0.50 tff(170,plain,
% 0.20/0.50 ((~($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0)) | $lesseq($sum(count(add(3, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 ($lesseq($sum(count(add(3, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[170, 163])).
% 0.20/0.50 tff(172,plain,
% 0.20/0.50 ($lesseq($sum(count(add(5, U!0)), $product(-1, count(U!0))), 0) | (~$lesseq($sum(count(add(3, U!0)), $product(-1, count(U!0))), 0)) | (~$greatereq($sum(count(add(3, U!0)), $product(-1, count(add(5, U!0)))), 0))),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(173,plain,
% 0.20/0.50 ($lesseq($sum(count(add(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[172, 171, 169])).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 (($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0) | (~$lesseq($sum(count(add(5, U!0)), $product(-1, count(U!0))), 0)) | (~$greatereq($sum(count(add(5, U!0)), $product(-1, count(U!0))), 0))),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(175,plain,
% 0.20/0.50 ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[174, 173, 167])).
% 0.20/0.50 tff(176,plain,
% 0.20/0.50 ((~(in(5, U!0) <=> ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0))) | in(5, U!0) | (~($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(177,plain,
% 0.20/0.50 (in(5, U!0) | (~($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[176, 71])).
% 0.20/0.50 tff(178,plain,
% 0.20/0.50 (in(5, U!0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[177, 175])).
% 0.20/0.50 tff(179,plain,
% 0.20/0.50 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(5, U!0) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(5, U!0) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(180,plain,
% 0.20/0.50 ((in(5, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(5, U!0)))) = 1)) <=> (in(5, U!0) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(181,plain,
% 0.20/0.50 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(5, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(5, U!0)))) = 1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(5, U!0) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[180])).
% 0.20/0.50 tff(182,plain,
% 0.20/0.50 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(5, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(5, U!0)))) = 1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(5, U!0) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[181, 179])).
% 0.20/0.50 tff(183,plain,
% 0.20/0.50 ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(5, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(5, U!0)))) = 1))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(184,plain,
% 0.20/0.50 ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(5, U!0) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.50 tff(185,plain,
% 0.20/0.50 (in(5, U!0) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[184, 137])).
% 0.20/0.50 tff(186,plain,
% 0.20/0.50 ((~(in(5, U!0) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1))) | (~in(5, U!0)) | ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(187,plain,
% 0.20/0.50 ((~in(5, U!0)) | ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.20/0.50 tff(188,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[187, 178, 153])).
% 0.20/0.50 tff(189,plain,($greatereq($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(190,plain,
% 0.20/0.50 (~($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))) = 0)),
% 0.20/0.50 inference(or_elim,[status(thm)],[15])).
% 0.20/0.51 tff(191,plain,
% 0.20/0.51 (($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))) = 0) | (~$lesseq($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))), 0)) | (~$greatereq($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))), 0))),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(192,plain,
% 0.20/0.51 ((~$lesseq($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))), 0)) | (~$greatereq($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))), 0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.20/0.51 tff(193,plain,
% 0.20/0.51 (~$lesseq($sum(count(remove(3, U!0)), $product(-1, count(remove(5, U!0)))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[192, 189])).
% 0.20/0.51 tff(194,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[193, 111, 99])).
% 0.20/0.51 tff(195,plain,(in(3, U!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(196,plain,
% 0.20/0.51 ($sum(count(add(3, U!0)), $product(-1, count(U!0))) = 0),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[162, 195])).
% 0.20/0.51 tff(197,plain,
% 0.20/0.51 ($greatereq($sum(count(add(3, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[164, 196])).
% 0.20/0.51 tff(198,plain,
% 0.20/0.51 ($greatereq($sum(count(add(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[166, 197, 18])).
% 0.20/0.51 tff(199,plain,
% 0.20/0.51 ($lesseq($sum(count(add(3, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[170, 196])).
% 0.20/0.51 tff(200,plain,
% 0.20/0.51 ($lesseq($sum(count(add(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[172, 199, 169])).
% 0.20/0.51 tff(201,plain,
% 0.20/0.51 ($sum(count(add(5, U!0)), $product(-1, count(U!0))) = 0),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[174, 200, 198])).
% 0.20/0.51 tff(202,plain,
% 0.20/0.51 (in(5, U!0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[177, 201])).
% 0.20/0.51 tff(203,plain,
% 0.20/0.51 ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[187, 202])).
% 0.20/0.51 tff(204,plain,
% 0.20/0.51 ((~($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)) | $greatereq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), -1)),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(205,plain,
% 0.20/0.51 ($greatereq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), -1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.20/0.51 tff(206,plain,
% 0.20/0.51 ($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[146, 195])).
% 0.20/0.51 tff(207,plain,
% 0.20/0.51 ((~($sum(count(remove(3, U!0)), $product(-1, count(U!0))) = -1)) | $lesseq($sum(count(remove(3, U!0)), $product(-1, count(U!0))), -1)),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(208,plain,
% 0.20/0.51 ($lesseq($sum(count(remove(3, U!0)), $product(-1, count(U!0))), -1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.20/0.51 tff(209,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[193, 208, 205])).
% 0.20/0.51 % SZS output end Proof
%------------------------------------------------------------------------------