%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MSC017+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:17:33 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MSC017+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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 : Thu Jun 19 23:36:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(outcome_type, type, (
% 0.19/0.37 outcome: ( $i * $i ) > $o)).
% 0.19/0.37 tff(tptp_fun_O_1_type, type, (
% 0.19/0.37 tptp_fun_O_1: $i)).
% 0.19/0.37 tff(tptp_fun_D_0_type, type, (
% 0.19/0.37 tptp_fun_D_0: $i)).
% 0.19/0.37 tff(dci_type, type, (
% 0.19/0.37 dci: $i)).
% 0.19/0.37 tff(bad_type, type, (
% 0.19/0.37 bad: $i > $o)).
% 0.19/0.37 tff(dive_type, type, (
% 0.19/0.37 dive: $i > $o)).
% 0.19/0.37 tff(greater_type, type, (
% 0.19/0.37 greater: ( $i * $i ) > $o)).
% 0.19/0.37 tff(nitrogen_limit_type, type, (
% 0.19/0.37 nitrogen_limit: $i)).
% 0.19/0.37 tff(nitrogen_type, type, (
% 0.19/0.37 nitrogen: $i > $i)).
% 0.19/0.37 tff(time_limit_type, type, (
% 0.19/0.37 time_limit: $i)).
% 0.19/0.37 tff(time_type, type, (
% 0.19/0.37 time: $i > $i)).
% 0.19/0.37 tff(depth_limit_type, type, (
% 0.19/0.37 depth_limit: $i)).
% 0.19/0.37 tff(depth_type, type, (
% 0.19/0.37 depth: $i > $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 ((~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))) <=> (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 ((~![D: $i] : (dive(D) => ![O: $i] : (outcome(D, O) => (~bad(O))))) <=> (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(3,axiom,(~![D: $i] : (dive(D) => ![O: $i] : (outcome(D, O) => (~bad(O))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_bad')).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (~![D: $i] : ((~dive(D)) | ![O: $i] : ((~bad(O)) | (~outcome(D, O))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (dive(D!0)),
% 0.19/0.37 inference(and_elim,[status(thm)],[7])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (^[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)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (^[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)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[12, 10])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (^[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)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (^[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)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.37 tff(19,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')).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (![D: $i] : ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (![D: $i] : ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.37 tff(22,plain,(
% 0.19/0.37 ![D: $i] : ((~dive(D)) | ![O: $i] : ((~(outcome(D, O) & bad(O))) | (O = dci)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[21])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (![D: $i] : ((~dive(D)) | ![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D, O))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (((~![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))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 ((~![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))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 ((~![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)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[27, 24, 8])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (~((~bad(O!1)) | (~outcome(D!0, O!1)))),
% 0.19/0.37 inference(and_elim,[status(thm)],[7])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (outcome(D!0, O!1)),
% 0.19/0.37 inference(or_elim,[status(thm)],[29])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (bad(O!1)),
% 0.19/0.37 inference(or_elim,[status(thm)],[29])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (((~![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))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (((O!1 = dci) | (~bad(O!1)) | (~outcome(D!0, O!1))) <=> ((~bad(O!1)) | (~outcome(D!0, O!1)) | (O!1 = dci))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (((~![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)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (((~![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))),
% 0.19/0.37 inference(transitivity,[status(thm)],[34, 32])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 ((~![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))) | ((O!1 = dci) | (~bad(O!1)) | (~outcome(D!0, O!1)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 ((~![O: $i] : ((O = dci) | (~bad(O)) | (~outcome(D!0, O)))) | (~bad(O!1)) | (~outcome(D!0, O!1)) | (O!1 = dci)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (O!1 = dci),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[37, 31, 30, 28])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (outcome(D!0, O!1) <=> outcome(D!0, dci)),
% 0.19/0.37 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (outcome(D!0, dci) <=> outcome(D!0, O!1)),
% 0.19/0.37 inference(symmetry,[status(thm)],[39])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 ((~outcome(D!0, dci)) <=> (~outcome(D!0, O!1))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (^[D: $i] : refl(((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))) <=> ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))) <=> ![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))) <=> ![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (^[D: $i] : rewrite((dive(D) => (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))) <=> ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (![D: $i] : (dive(D) => (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci))) <=> ![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.37 tff(47,axiom,(![D: $i] : (dive(D) => (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','too_much_nitrogen')).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 (![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.37 tff(50,plain,(
% 0.19/0.37 ![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[49])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 (![D: $i] : ((~dive(D)) | (greater(nitrogen(D), nitrogen_limit) <=> outcome(D, dci)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (((~![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 ((~![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)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 ((~![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))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 (greater(nitrogen(D!0), nitrogen_limit) <=> outcome(D!0, dci)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[54, 51, 8])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 (^[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))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.38 tff(61,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')).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 (![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.38 tff(64,plain,(
% 0.19/0.38 ![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[63])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 (![D: $i] : ((~dive(D)) | ((greater(depth(D), depth_limit) | greater(time(D), time_limit)) <=> greater(nitrogen(D), nitrogen_limit)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (((~![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 ((~![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)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 ((~![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))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 ((greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) <=> greater(nitrogen(D!0), nitrogen_limit)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[68, 65, 8])).
% 0.19/0.38 tff(70,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(76,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.38 tff(77,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')).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 (![D: $i] : ((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 (![D: $i] : ((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.38 tff(80,plain,(
% 0.19/0.38 ![D: $i] : ((~dive(D)) | ((~greater(depth(D), depth_limit)) & (~greater(time(D), time_limit))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[79])).
% 0.19/0.38 tff(81,plain,
% 0.19/0.38 (![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.19/0.38 tff(82,plain,
% 0.19/0.38 (![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.19/0.38 tff(83,plain,
% 0.19/0.38 (((~![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(84,plain,
% 0.19/0.38 ((~![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))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(85,plain,
% 0.19/0.38 ((~![D: $i] : ((~dive(D)) | (~(greater(depth(D), depth_limit) | greater(time(D), time_limit))))) | (~dive(D!0)) | (~(greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.38 tff(86,plain,
% 0.19/0.38 (~(greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[85, 82, 8])).
% 0.19/0.38 tff(87,plain,
% 0.19/0.38 ((~((greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) <=> greater(nitrogen(D!0), nitrogen_limit))) | (greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) | (~greater(nitrogen(D!0), nitrogen_limit))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(88,plain,
% 0.19/0.38 ((~((greater(depth(D!0), depth_limit) | greater(time(D!0), time_limit)) <=> greater(nitrogen(D!0), nitrogen_limit))) | (~greater(nitrogen(D!0), nitrogen_limit))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.38 tff(89,plain,
% 0.19/0.38 (~greater(nitrogen(D!0), nitrogen_limit)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[88, 69])).
% 0.19/0.38 tff(90,plain,
% 0.19/0.38 ((~(greater(nitrogen(D!0), nitrogen_limit) <=> outcome(D!0, dci))) | greater(nitrogen(D!0), nitrogen_limit) | (~outcome(D!0, dci))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(91,plain,
% 0.19/0.38 (~outcome(D!0, dci)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[90, 89, 55])).
% 0.19/0.38 tff(92,plain,
% 0.19/0.38 (~outcome(D!0, O!1)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[91, 41])).
% 0.19/0.38 tff(93,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[30, 92])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------