TSTP Solution File: DAT032_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT032_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT032_1 : TPTP v8.1.0. Released v5.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 01:39:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(in_type, type, (
% 0.21/0.44 in: ( $int * collection ) > $o)).
% 0.21/0.44 tff(tptp_fun_U_0_type, type, (
% 0.21/0.44 tptp_fun_U_0: collection)).
% 0.21/0.44 tff(count_type, type, (
% 0.21/0.44 count: collection > $int)).
% 0.21/0.44 tff(remove_type, type, (
% 0.21/0.44 remove: ( $int * collection ) > collection)).
% 0.21/0.44 tff(1,assumption,(~$greatereq($sum(count(remove(4, U!0)), $product(-1, count(U!0))), -1)), introduced(assumption)).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 ($greatereq($sum(count(remove(4, U!0)), $product(-1, count(U!0))), -1) | (~$greatereq($sum(count(remove(4, U!0)), $product(-1, count(U!0))), 0))),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (~$greatereq($sum(count(remove(4, U!0)), $product(-1, count(U!0))), 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 ((~($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0)) | $greatereq($sum(count(remove(4, U!0)), $product(-1, count(U!0))), 0)),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (~($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 ((~($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1)) | $greatereq($sum(count(remove(4, U!0)), $product(-1, count(U!0))), -1)),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (~($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (^[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)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (![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))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (^[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)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (![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))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (^[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)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 (![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))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.44 tff(17,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')).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 (![X12: $int, X13: collection] : (in(X12, X13) <=> (count(remove(X12, X13)) = $sum(-1, count(X13))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 (![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(remove(X12, X13)), $product(-1, count(X13))) = -1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 (![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.21/0.44 tff(22,plain,(
% 0.21/0.44 ![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))),
% 0.21/0.44 inference(skolemize,[status(sab)],[21])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[22, 9])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(4, U!0) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(4, U!0) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 ((in(4, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(4, U!0)))) = 1)) <=> (in(4, U!0) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(4, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(4, U!0)))) = 1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(4, U!0) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[25])).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 (((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(4, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(4, U!0)))) = 1))) <=> ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(4, U!0) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[26, 24])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(4, U!0) <=> ($sum(count(U!0), $product(-1, count(remove(4, U!0)))) = 1))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 ((~![X12: $int, X13: collection] : (in(X12, X13) <=> ($sum(count(X13), $product(-1, count(remove(X12, X13)))) = 1))) | (in(4, U!0) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (in(4, U!0) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[29, 23])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 ((~(in(4, U!0) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1))) | (~in(4, U!0)) | ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 ((~in(4, U!0)) | ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = -1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (~in(4, U!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[32, 7])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 (^[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)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (![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))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (^[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)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (![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))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (^[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)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (![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))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(41,axiom,(![X14: $int, X15: collection] : ((~in(X14, X15)) <=> (count(remove(X14, X15)) = count(X15)))), file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax','ax6')).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> (count(remove(X14, X15)) = count(X15)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(remove(X14, X15)), $product(-1, count(X15))) = 0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[42, 39])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[43, 37])).
% 0.21/0.44 tff(45,plain,(
% 0.21/0.44 ![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))),
% 0.21/0.44 inference(skolemize,[status(sab)],[44])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(4, U!0)) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(4, U!0)) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (((~in(4, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(4, U!0)))) = 0)) <=> ((~in(4, U!0)) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(4, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(4, U!0)))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(4, U!0)) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[48])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(4, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(4, U!0)))) = 0))) <=> ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(4, U!0)) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[49, 47])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(4, U!0)) <=> ($sum(count(U!0), $product(-1, count(remove(4, U!0)))) = 0))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 ((~![X14: $int, X15: collection] : ((~in(X14, X15)) <=> ($sum(count(X15), $product(-1, count(remove(X14, X15)))) = 0))) | ((~in(4, U!0)) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 ((~in(4, U!0)) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[52, 46])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 ((~((~in(4, U!0)) <=> ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0))) | in(4, U!0) | ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (in(4, U!0) | ($sum(count(remove(4, U!0)), $product(-1, count(U!0))) = 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[55, 33, 5])).
% 0.21/0.44 tff(57,plain,($greatereq($sum(count(remove(4, U!0)), $product(-1, count(U!0))), -1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 ((~![U: collection] : ((~$greatereq(count(remove(5, U)), 7)) | $greatereq(count(remove(4, U)), 6))) <=> (~![U: collection] : ((~$greatereq(count(remove(5, U)), 7)) | $greatereq(count(remove(4, U)), 6)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 ((~![U: collection] : ($greatereq(count(remove(5, U)), 7) => $greatereq(count(remove(4, U)), 6))) <=> (~![U: collection] : ((~$greatereq(count(remove(5, U)), 7)) | $greatereq(count(remove(4, U)), 6)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(60,axiom,(~![U: collection] : ($greatereq(count(remove(5, U)), 7) => $greatereq(count(remove(4, U)), 6))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 (~![U: collection] : ((~$greatereq(count(remove(5, U)), 7)) | $greatereq(count(remove(4, U)), 6))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (~![U: collection] : ((~$greatereq(count(remove(5, U)), 7)) | $greatereq(count(remove(4, U)), 6))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (~![U: collection] : ((~$greatereq(count(remove(5, U)), 7)) | $greatereq(count(remove(4, U)), 6))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (~![U: collection] : ((~$greatereq(count(remove(5, U)), 7)) | $greatereq(count(remove(4, U)), 6))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (~![U: collection] : ((~$greatereq(count(remove(5, U)), 7)) | $greatereq(count(remove(4, U)), 6))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[64, 58])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (~![U: collection] : ((~$greatereq(count(remove(5, U)), 7)) | $greatereq(count(remove(4, U)), 6))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (~![U: collection] : ((~$greatereq(count(remove(5, U)), 7)) | $greatereq(count(remove(4, U)), 6))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[66, 58])).
% 0.21/0.44 tff(68,plain,(
% 0.21/0.44 ~((~$greatereq(count(remove(5, U!0)), 7)) | $greatereq(count(remove(4, U!0)), 6))),
% 0.21/0.44 inference(skolemize,[status(sab)],[67])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (~$greatereq(count(remove(4, U!0)), 6)),
% 0.21/0.44 inference(or_elim,[status(thm)],[68])).
% 0.21/0.44 tff(70,assumption,($lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), 0)), introduced(assumption)).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 ($greatereq(count(remove(5, U!0)), 7)),
% 0.21/0.44 inference(or_elim,[status(thm)],[68])).
% 0.21/0.44 tff(72,assumption,($greatereq($sum(count(remove(4, U!0)), $product(-1, count(U!0))), -1)), introduced(assumption)).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[72, 71, 70, 69])).
% 0.21/0.44 tff(74,plain,((~$greatereq($sum(count(remove(4, U!0)), $product(-1, count(U!0))), -1)) | (~$lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (~$lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[74, 57])).
% 0.21/0.44 tff(76,plain,
% 0.21/0.44 ((~($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)) | $lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 (~($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 (((~![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)), $product(-1, count(U!0))) = 0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(79,plain,
% 0.21/0.44 (((~in(5, U!0)) <=> ($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))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 (((~![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)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 (((~![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)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[80, 78])).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 ((~![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))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 ((~![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)), $product(-1, count(U!0))) = 0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.44 tff(84,plain,
% 0.21/0.44 ((~in(5, U!0)) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[83, 46])).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 ((~((~in(5, U!0)) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0))) | in(5, U!0) | ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 (in(5, U!0) | ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.44 tff(87,plain,
% 0.21/0.44 (in(5, U!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[86, 77])).
% 0.21/0.44 tff(88,plain,
% 0.21/0.44 ((~$lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), -1)) | $lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), 0)),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.44 tff(89,plain,
% 0.21/0.44 (~$lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), -1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[88, 75])).
% 0.21/0.44 tff(90,plain,
% 0.21/0.44 ((~($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)) | $lesseq($sum(count(remove(5, U!0)), $product(-1, count(U!0))), -1)),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (~($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (((~![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)), $product(-1, count(U!0))) = -1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 ((in(5, U!0) <=> ($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))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (((~![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)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (((~![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)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[94, 92])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 ((~![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))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 ((~![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)), $product(-1, count(U!0))) = -1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 (in(5, U!0) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[97, 23])).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 ((~(in(5, U!0) <=> ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1))) | (~in(5, U!0)) | ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 ((~in(5, U!0)) | ($sum(count(remove(5, U!0)), $product(-1, count(U!0))) = -1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[100, 91, 87])).
% 0.21/0.45 % SZS output end Proof
%------------------------------------------------------------------------------