TSTP Solution File: DAT049_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT049_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 14:36:31 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : DAT049_1 : TPTP v8.1.0. Released v5.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 02:08:17 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(count_type, type, (
% 0.20/0.42 count: collection > $int)).
% 0.20/0.42 tff(add_type, type, (
% 0.20/0.42 add: ( $int * collection ) > collection)).
% 0.20/0.42 tff(tptp_fun_U_1_type, type, (
% 0.20/0.42 tptp_fun_U_1: collection)).
% 0.20/0.42 tff(tptp_fun_V_0_type, type, (
% 0.20/0.42 tptp_fun_V_0: $int)).
% 0.20/0.42 tff(in_type, type, (
% 0.20/0.42 in: ( $int * collection ) > $o)).
% 0.20/0.42 tff(remove_type, type, (
% 0.20/0.42 remove: ( $int * collection ) > collection)).
% 0.20/0.42 tff(1,assumption,(~in(V!0, U!1)), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.42 tff(11,axiom,(![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(count(X9), 1)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax','ax3')).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> (count(add(X8, X9)) = $sum(1, count(X9))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(add(X8, X9)), $product(-1, count(X9))) = 1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[14, 5])).
% 0.20/0.42 tff(16,plain,(
% 0.20/0.42 ![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.20/0.42 inference(skolemize,[status(sab)],[15])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[16, 3])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 ((~![X8: $int, X9: collection] : ((~in(X8, X9)) <=> ($sum(count(X9), $product(-1, count(add(X8, X9)))) = -1))) | ((~in(V!0, U!1)) <=> ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 ((~in(V!0, U!1)) <=> ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 ((~((~in(V!0, U!1)) <=> ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1))) | in(V!0, U!1) | ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (in(V!0, U!1) | ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[21, 1])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((~($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1)) | $lesseq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), -1)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 ($lesseq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), -1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.42 tff(25,assumption,(~$greatereq($sum(count(remove(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))), 0)), introduced(assumption)).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(33,axiom,(![X14: $int, X15: collection] : ((~in(X14, X15)) <=> (count(remove(X14, X15)) = count(X15)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax','ax6')).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> (count(remove(X14, X15)) = count(X15)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(remove(X14, X15)), $product(-1, count(X15))) = 0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.20/0.42 tff(37,plain,(
% 0.20/0.42 ![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))),
% 0.20/0.42 inference(skolemize,[status(sab)],[36])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(V!0, U!1)) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(V!0, U!1)) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (((~in(V!0, U!1)) <=> ($sum(count(U!1), $product(-1, count(remove(V!0, U!1)))) = 0)) <=> ((~in(V!0, U!1)) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(V!0, U!1)) <=> ($sum(count(U!1), $product(-1, count(remove(V!0, U!1)))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(V!0, U!1)) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(V!0, U!1)) <=> ($sum(count(U!1), $product(-1, count(remove(V!0, U!1)))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(V!0, U!1)) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(V!0, U!1)) <=> ($sum(count(U!1), $product(-1, count(remove(V!0, U!1)))) = 0))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(V!0, U!1)) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~in(V!0, U!1)) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[44, 38])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 ((~((~in(V!0, U!1)) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0))) | in(V!0, U!1) | ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (in(V!0, U!1) | ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[47, 1])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 ((~($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0)) | $greatereq($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))), 0)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 ($greatereq($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.42 tff(60,axiom,(![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $difference(count(X13), 1)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax','ax5')).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(remove(X12, X13)), $product(-1, count(X13))) = -1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[62, 56])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[63, 54])).
% 0.20/0.42 tff(65,plain,(
% 0.20/0.42 ![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))),
% 0.20/0.42 inference(skolemize,[status(sab)],[64])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[65, 52])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, add(V!0, U!1)) <=> ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, add(V!0, U!1)) <=> ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 ((in(V!0, add(V!0, U!1)) <=> ($sum(count(add(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))) = 1)) <=> (in(V!0, add(V!0, U!1)) <=> ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, add(V!0, U!1)) <=> ($sum(count(add(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))) = 1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, add(V!0, U!1)) <=> ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, add(V!0, U!1)) <=> ($sum(count(add(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))) = 1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, add(V!0, U!1)) <=> ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, add(V!0, U!1)) <=> ($sum(count(add(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))) = 1))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, add(V!0, U!1)) <=> ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (in(V!0, add(V!0, U!1)) <=> ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[72, 66])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (^[V: $int, W: collection] : refl(in(V, add(V, W)) <=> in(V, add(V, W)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (![V: $int, W: collection] : in(V, add(V, W)) <=> ![V: $int, W: collection] : in(V, add(V, W))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![V: $int, W: collection] : in(V, add(V, W)) <=> ![V: $int, W: collection] : in(V, add(V, W))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(77,axiom,(![V: $int, W: collection] : in(V, add(V, W))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=0.ax','ax2')).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![V: $int, W: collection] : in(V, add(V, W))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.43 tff(79,plain,(
% 0.20/0.43 ![V: $int, W: collection] : in(V, add(V, W))),
% 0.20/0.43 inference(skolemize,[status(sab)],[78])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (![V: $int, W: collection] : in(V, add(V, W))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 ((~![V: $int, W: collection] : in(V, add(V, W))) | in(V!0, add(V!0, U!1))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (in(V!0, add(V!0, U!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 ((~(in(V!0, add(V!0, U!1)) <=> ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1))) | (~in(V!0, add(V!0, U!1))) | ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 ((~(in(V!0, add(V!0, U!1)) <=> ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1))) | ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 ($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[84, 73])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 ((~($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1)) | $lesseq($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))), -1)),
% 0.20/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 ($lesseq($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))), -1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 ((~($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = -1)) | $greatereq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), -1)),
% 0.20/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 ($greatereq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), -1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[88, 22])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(theory_lemma,[status(thm)],[89, 87, 25, 50])).
% 0.20/0.43 tff(91,plain,(in(V!0, U!1) | $greatereq($sum(count(remove(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (in(V!0, U!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[91, 25])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, U!1) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, U!1) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 ((in(V!0, U!1) <=> ($sum(count(U!1), $product(-1, count(remove(V!0, U!1)))) = 1)) <=> (in(V!0, U!1) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, U!1) <=> ($sum(count(U!1), $product(-1, count(remove(V!0, U!1)))) = 1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, U!1) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[94])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, U!1) <=> ($sum(count(U!1), $product(-1, count(remove(V!0, U!1)))) = 1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, U!1) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[95, 93])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, U!1) <=> ($sum(count(U!1), $product(-1, count(remove(V!0, U!1)))) = 1))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(V!0, U!1) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (in(V!0, U!1) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[98, 66])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 ((~(in(V!0, U!1) <=> ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1))) | (~in(V!0, U!1)) | ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 ((~in(V!0, U!1)) | ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[101, 92])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 ((~($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1)) | $greatereq($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))), -1)),
% 0.20/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 ($greatereq($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))), -1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (^[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)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (^[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)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (^[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)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(112,axiom,(![X10: $int, X11: collection] : (in(X10, X11) <=> (count(add(X10, X11)) = count(X11)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax','ax4')).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (![X10: $int, X11: collection] : (in(X10, X11) <=> (count(add(X10, X11)) = count(X11)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(add(X10, X11)), $product(-1, count(X11))) = 0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[114, 108])).
% 0.20/0.43 tff(116,plain,(
% 0.20/0.43 ![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))),
% 0.20/0.43 inference(skolemize,[status(sab)],[115])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 ((~![X10: $int, X11: collection] : (in(X10, X11) <=> ($sum(count(X11), $product(-1, count(add(X10, X11)))) = 0))) | (in(V!0, U!1) <=> ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = 0))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (in(V!0, U!1) <=> ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = 0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 ((~(in(V!0, U!1) <=> ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = 0))) | (~in(V!0, U!1)) | ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = 0)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 ((~in(V!0, U!1)) | ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = 0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = 0),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[121, 92])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 ((~($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = 0)) | $greatereq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), 0)),
% 0.20/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 ($greatereq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), 0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(theory_lemma,[status(thm)],[124, 87, 25, 104])).
% 0.20/0.43 tff(126,plain,($greatereq($sum(count(remove(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 ((~![U: collection, V: $int] : ($sum(count(remove(V, U)), $product(-1, count(remove(V, add(V, U))))) = 0)) <=> (~![U: collection, V: $int] : ($sum(count(remove(V, U)), $product(-1, count(remove(V, add(V, U))))) = 0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 ((~![U: collection, V: $int] : ($sum(count(remove(V, add(V, U))), $product(-1, count(remove(V, U)))) = 0)) <=> (~![U: collection, V: $int] : ($sum(count(remove(V, U)), $product(-1, count(remove(V, add(V, U))))) = 0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 ((~![U: collection, V: $int] : (count(remove(V, add(V, U))) = count(remove(V, U)))) <=> (~![U: collection, V: $int] : ($sum(count(remove(V, add(V, U))), $product(-1, count(remove(V, U)))) = 0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 ((~![U: collection, V: $int] : (count(remove(V, add(V, U))) = count(remove(V, U)))) <=> (~![U: collection, V: $int] : (count(remove(V, add(V, U))) = count(remove(V, U))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(131,axiom,(~![U: collection, V: $int] : (count(remove(V, add(V, U))) = count(remove(V, U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (~![U: collection, V: $int] : (count(remove(V, add(V, U))) = count(remove(V, U)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (~![U: collection, V: $int] : (count(remove(V, add(V, U))) = count(remove(V, U)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[132, 130])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 (~![U: collection, V: $int] : (count(remove(V, add(V, U))) = count(remove(V, U)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[133, 130])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (~![U: collection, V: $int] : (count(remove(V, add(V, U))) = count(remove(V, U)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (~![U: collection, V: $int] : ($sum(count(remove(V, add(V, U))), $product(-1, count(remove(V, U)))) = 0)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[135, 129])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (~![U: collection, V: $int] : ($sum(count(remove(V, U)), $product(-1, count(remove(V, add(V, U))))) = 0)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[136, 128])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (~![U: collection, V: $int] : ($sum(count(remove(V, U)), $product(-1, count(remove(V, add(V, U))))) = 0)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[137, 127])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 (~![U: collection, V: $int] : ($sum(count(remove(V, U)), $product(-1, count(remove(V, add(V, U))))) = 0)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[138, 127])).
% 0.20/0.43 tff(140,plain,(
% 0.20/0.43 ~($sum(count(remove(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))) = 0)),
% 0.20/0.43 inference(skolemize,[status(sab)],[139])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 (($sum(count(remove(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))) = 0) | (~$lesseq($sum(count(remove(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))), 0)) | (~$greatereq($sum(count(remove(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))), 0))),
% 0.20/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 ((~$lesseq($sum(count(remove(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))), 0)) | (~$greatereq($sum(count(remove(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))), 0))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (~$lesseq($sum(count(remove(V!0, U!1)), $product(-1, count(remove(V!0, add(V!0, U!1))))), 0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[142, 126])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 ((~($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = 0)) | $lesseq($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))), 0)),
% 0.20/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 ($lesseq($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))), 0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[144, 48])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.44 ((~($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))) = -1)) | $greatereq($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))), -1)),
% 0.20/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 ($greatereq($sum(count(remove(V!0, add(V!0, U!1))), $product(-1, count(add(V!0, U!1)))), -1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[146, 85])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(theory_lemma,[status(thm)],[147, 145, 143, 24])).
% 0.20/0.44 tff(149,plain,(in(V!0, U!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 ($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = 0),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[121, 149])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 ((~($sum(count(U!1), $product(-1, count(add(V!0, U!1)))) = 0)) | $lesseq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), 0)),
% 0.20/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 ($lesseq($sum(count(U!1), $product(-1, count(add(V!0, U!1)))), 0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 ($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[101, 149])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 ((~($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))) = -1)) | $lesseq($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))), -1)),
% 0.20/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 ($lesseq($sum(count(remove(V!0, U!1)), $product(-1, count(U!1))), -1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(theory_lemma,[status(thm)],[147, 155, 143, 152])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------