TSTP Solution File: MSC017+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MSC017+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Sun Sep 18 05:34:07 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : MSC017+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 03:11:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(outcome_type, type, (
% 0.12/0.38 outcome: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_O_1_type, type, (
% 0.12/0.38 tptp_fun_O_1: $i)).
% 0.12/0.38 tff(tptp_fun_D_0_type, type, (
% 0.12/0.38 tptp_fun_D_0: $i)).
% 0.12/0.38 tff(dci_type, type, (
% 0.12/0.38 dci: $i)).
% 0.12/0.38 tff(bad_type, type, (
% 0.12/0.38 bad: $i > $o)).
% 0.12/0.38 tff(dive_type, type, (
% 0.12/0.38 dive: $i > $o)).
% 0.12/0.38 tff(greater_type, type, (
% 0.12/0.38 greater: ( $i * $i ) > $o)).
% 0.12/0.38 tff(nitrogen_limit_type, type, (
% 0.12/0.38 nitrogen_limit: $i)).
% 0.12/0.38 tff(nitrogen_type, type, (
% 0.12/0.38 nitrogen: $i > $i)).
% 0.12/0.38 tff(time_limit_type, type, (
% 0.12/0.38 time_limit: $i)).
% 0.12/0.38 tff(time_type, type, (
% 0.12/0.38 time: $i > $i)).
% 0.12/0.38 tff(depth_limit_type, type, (
% 0.12/0.38 depth_limit: $i)).
% 0.12/0.38 tff(depth_type, type, (
% 0.12/0.38 depth: $i > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (((~(~dive(D!0))) & (~((~bad(O!1)) | (~outcome(D!0, O!1))))) <=> (dive(D!0) & (~((~bad(O!1)) | (~outcome(D!0, O!1)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))) <=> (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 ((~![D: $i] : (dive(D) => ![O: $i] : (outcome(D, O) => (~bad(O))))) <=> (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(~![D: $i] : (dive(D) => ![O: $i] : (outcome(D, O) => (~bad(O))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_bad')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (dive(D!0) & (~((~bad(O!1)) | (~outcome(D!0, O!1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (dive(D!0)),
% 0.12/0.38 inference(and_elim,[status(thm)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (^[D: $i] : refl(((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O)))) <=> ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O)))) <=> ![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (^[D: $i] : rewrite(((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O)))) <=> ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O)))) <=> ![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O)))) <=> ![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[17, 15])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (^[D: $i] : rewrite(((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci))) <=> ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![D: $i] : ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci))) <=> ![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![D: $i] : ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci))) <=> ![D: $i] : ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[O: $i] : rewrite(((outcome(D, O) & bad(O)) => (O = dci)) <=> ((~(outcome(D, O) & bad(O))) | (O = dci)))), (![O: $i] : ((outcome(D, O) & bad(O)) => (O = dci)) <=> ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci)))), ((dive(D) => ![O: $i] : ((outcome(D, O) & bad(O)) => (O = dci))) <=> (dive(D) => ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci))))), rewrite((dive(D) => ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci))) <=> ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci)))), ((dive(D) => ![O: $i] : ((outcome(D, O) & bad(O)) => (O = dci))) <=> ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![D: $i] : (dive(D) => ![O: $i] : ((outcome(D, O) & bad(O)) => (O = dci))) <=> ![D: $i] : ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.39 tff(24,axiom,(![D: $i] : (dive(D) => ![O: $i] : ((outcome(D, O) & bad(O)) => (O = dci)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dci_is_the_only_bad_outcome')).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![D: $i] : ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![D: $i] : ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.39 tff(27,plain,(
% 0.12/0.39 ![D: $i] : ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[26])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (((~![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))) | ((~dive(D!0)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O))))) <=> ((~![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))) | (~dive(D!0)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 ((~![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))) | ((~dive(D!0)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ((~![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))) | (~dive(D!0)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[32, 29, 13])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (~((~bad(O!1)) | (~outcome(D!0, O!1)))),
% 0.12/0.39 inference(and_elim,[status(thm)],[12])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (outcome(D!0, O!1)),
% 0.12/0.39 inference(or_elim,[status(thm)],[34])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (bad(O!1)),
% 0.12/0.39 inference(or_elim,[status(thm)],[34])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (((~![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))) | ((~bad(O!1)) | (~outcome(D!0, O!1)) | (O!1 = dci))) <=> ((~![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))) | (~bad(O!1)) | (~outcome(D!0, O!1)) | (O!1 = dci))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (((O!1 = dci) | (~bad(O!1)) | (~outcome(D!0, O!1))) <=> ((~bad(O!1)) | (~outcome(D!0, O!1)) | (O!1 = dci))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (((~![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))) | ((O!1 = dci) | (~bad(O!1)) | (~outcome(D!0, O!1)))) <=> ((~![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))) | ((~bad(O!1)) | (~outcome(D!0, O!1)) | (O!1 = dci)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (((~![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))) | ((O!1 = dci) | (~bad(O!1)) | (~outcome(D!0, O!1)))) <=> ((~![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))) | (~bad(O!1)) | (~outcome(D!0, O!1)) | (O!1 = dci))),
% 0.12/0.40 inference(transitivity,[status(thm)],[39, 37])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 ((~![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))) | ((O!1 = dci) | (~bad(O!1)) | (~outcome(D!0, O!1)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 ((~![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))) | (~bad(O!1)) | (~outcome(D!0, O!1)) | (O!1 = dci)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (O!1 = dci),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[42, 36, 35, 33])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (outcome(D!0, O!1) <=> outcome(D!0, dci)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (outcome(D!0, dci) <=> outcome(D!0, O!1)),
% 0.12/0.40 inference(symmetry,[status(thm)],[44])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 ((~outcome(D!0, dci)) <=> (~outcome(D!0, O!1))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[45])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (^[D: $i] : refl(((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))) <=> ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))) <=> ![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))) <=> ![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (^[D: $i] : rewrite((dive(D) => (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))) <=> ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (![D: $i] : (dive(D) => (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))) <=> ![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.40 tff(52,axiom,(![D: $i] : (dive(D) => (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','too_much_nitrogen')).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.12/0.40 tff(55,plain,(
% 0.12/0.40 ![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[54])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (((~![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))) | ((~dive(D!0)) | (greater(nitrogen(D!0), nitrogen_limit) <=> outcome(D!0, dci)))) <=> ((~![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))) | (~dive(D!0)) | (greater(nitrogen(D!0), nitrogen_limit) <=> outcome(D!0, dci)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 ((~![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))) | ((~dive(D!0)) | (greater(nitrogen(D!0), nitrogen_limit) <=> outcome(D!0, dci)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 ((~![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))) | (~dive(D!0)) | (greater(nitrogen(D!0), nitrogen_limit) <=> outcome(D!0, dci))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (greater(nitrogen(D!0), nitrogen_limit) <=> outcome(D!0, dci)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[59, 56, 13])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (^[D: $i] : refl(((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit))) <=> ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit))) <=> ![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit))) <=> ![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (^[D: $i] : rewrite((dive(D) => ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit))) <=> ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (![D: $i] : (dive(D) => ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit))) <=> ![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.12/0.40 tff(66,axiom,(![D: $i] : (dive(D) => ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','depth_and_time_and_nitrogen')).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.12/0.40 tff(69,plain,(
% 0.12/0.40 ![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[68])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (((~![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))) | ((~dive(D!0)) | ((greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) <=> greater(nitrogen(D!0), nitrogen_limit)))) <=> ((~![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))) | (~dive(D!0)) | ((greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) <=> greater(nitrogen(D!0), nitrogen_limit)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 ((~![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))) | ((~dive(D!0)) | ((greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) <=> greater(nitrogen(D!0), nitrogen_limit)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 ((~![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))) | (~dive(D!0)) | ((greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) <=> greater(nitrogen(D!0), nitrogen_limit))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.12/0.41 tff(74,plain,
% 0.12/0.41 ((greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) <=> greater(nitrogen(D!0), nitrogen_limit)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[73, 70, 13])).
% 0.12/0.41 tff(75,plain,
% 0.12/0.41 (^[D: $i] : refl(((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit)))) <=> ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(76,plain,
% 0.12/0.41 (![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit)))) <=> ![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.12/0.41 tff(77,plain,
% 0.12/0.41 (^[D: $i] : rewrite(((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit)))) <=> ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(78,plain,
% 0.12/0.41 (![D: $i] : ((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit)))) <=> ![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[77])).
% 0.12/0.41 tff(79,plain,
% 0.12/0.41 (![D: $i] : ((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit)))) <=> ![D: $i] : ((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(80,plain,
% 0.12/0.41 (^[D: $i] : rewrite((dive(D) => ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit)))) <=> ((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(81,plain,
% 0.12/0.41 (![D: $i] : (dive(D) => ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit)))) <=> ![D: $i] : ((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.12/0.41 tff(82,axiom,(![D: $i] : (dive(D) => ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_deep_long')).
% 0.12/0.41 tff(83,plain,
% 0.12/0.41 (![D: $i] : ((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.12/0.41 tff(84,plain,
% 0.12/0.41 (![D: $i] : ((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.12/0.41 tff(85,plain,(
% 0.12/0.41 ![D: $i] : ((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[84])).
% 0.12/0.41 tff(86,plain,
% 0.12/0.41 (![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.12/0.41 tff(87,plain,
% 0.12/0.41 (![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.12/0.41 tff(88,plain,
% 0.12/0.41 (((~![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit))))) | ((~dive(D!0)) | (~(greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit))))) <=> ((~![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit))))) | (~dive(D!0)) | (~(greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(89,plain,
% 0.12/0.41 ((~![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit))))) | ((~dive(D!0)) | (~(greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(90,plain,
% 0.12/0.41 ((~![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit))))) | (~dive(D!0)) | (~(greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.12/0.41 tff(91,plain,
% 0.12/0.41 (~(greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[90, 87, 13])).
% 0.12/0.41 tff(92,plain,
% 0.12/0.41 ((~((greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) <=> greater(nitrogen(D!0), nitrogen_limit))) | (greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) | (~greater(nitrogen(D!0), nitrogen_limit))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(93,plain,
% 0.12/0.41 ((~((greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) <=> greater(nitrogen(D!0), nitrogen_limit))) | (~greater(nitrogen(D!0), nitrogen_limit))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.12/0.41 tff(94,plain,
% 0.12/0.41 (~greater(nitrogen(D!0), nitrogen_limit)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[93, 74])).
% 0.12/0.41 tff(95,plain,
% 0.12/0.41 ((~(greater(nitrogen(D!0), nitrogen_limit) <=> outcome(D!0, dci))) | greater(nitrogen(D!0), nitrogen_limit) | (~outcome(D!0, dci))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(96,plain,
% 0.12/0.41 (~outcome(D!0, dci)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[95, 94, 60])).
% 0.12/0.41 tff(97,plain,
% 0.12/0.41 (~outcome(D!0, O!1)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[96, 46])).
% 0.12/0.41 tff(98,plain,
% 0.12/0.41 ($false),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[35, 97])).
% 0.12/0.41 % SZS output end Proof
%------------------------------------------------------------------------------