TSTP Solution File: ANA003-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Tue Sep 6 16:23:19 EDT 2022
% Result : Unsatisfiable 37.77s 24.52s
% Output : Proof 37.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.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 : Mon Aug 29 17:52:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 37.77/24.52 % SZS status Unsatisfiable
% 37.77/24.52 % SZS output start Proof
% 37.77/24.52 tff(less_than_type, type, (
% 37.77/24.52 less_than: ( $i * $i ) > $o)).
% 37.77/24.52 tff(minimum_type, type, (
% 37.77/24.52 minimum: ( $i * $i ) > $i)).
% 37.77/24.52 tff(fp32_type, type, (
% 37.77/24.52 fp32: $i > $i)).
% 37.77/24.52 tff(half_type, type, (
% 37.77/24.52 half: $i > $i)).
% 37.77/24.52 tff(b_type, type, (
% 37.77/24.52 b: $i)).
% 37.77/24.52 tff(fp31_type, type, (
% 37.77/24.52 fp31: $i > $i)).
% 37.77/24.52 tff(absolute_type, type, (
% 37.77/24.52 absolute: $i > $i)).
% 37.77/24.52 tff(add_type, type, (
% 37.77/24.52 add: ( $i * $i ) > $i)).
% 37.77/24.52 tff(minus_type, type, (
% 37.77/24.52 minus: $i > $i)).
% 37.77/24.52 tff(a_type, type, (
% 37.77/24.52 a: $i)).
% 37.77/24.52 tff(fp33_type, type, (
% 37.77/24.52 fp33: $i > $i)).
% 37.77/24.52 tff(n0_type, type, (
% 37.77/24.52 n0: $i)).
% 37.77/24.52 tff(l2_type, type, (
% 37.77/24.52 l2: $i)).
% 37.77/24.52 tff(g_type, type, (
% 37.77/24.52 g: $i > $i)).
% 37.77/24.52 tff(l1_type, type, (
% 37.77/24.52 l1: $i)).
% 37.77/24.52 tff(f_type, type, (
% 37.77/24.52 f: $i > $i)).
% 37.77/24.52 tff(1,assumption,(less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))), introduced(assumption)).
% 37.77/24.52 tff(2,plain,
% 37.77/24.52 (less_than(n0, b) <=> less_than(n0, b)),
% 37.77/24.52 inference(rewrite,[status(thm)],[])).
% 37.77/24.52 tff(3,axiom,(less_than(n0, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_14')).
% 37.77/24.52 tff(4,plain,
% 37.77/24.52 (less_than(n0, b)),
% 37.77/24.52 inference(modus_ponens,[status(thm)],[3, 2])).
% 37.77/24.52 tff(5,plain,
% 37.77/24.52 (^[Xa: $i] : refl(((~less_than(n0, Xa)) | less_than(n0, half(Xa))) <=> ((~less_than(n0, Xa)) | less_than(n0, half(Xa))))),
% 37.77/24.52 inference(bind,[status(th)],[])).
% 37.77/24.52 tff(6,plain,
% 37.77/24.52 (![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa))) <=> ![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))),
% 37.77/24.52 inference(quant_intro,[status(thm)],[5])).
% 37.77/24.52 tff(7,plain,
% 37.77/24.52 (![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa))) <=> ![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))),
% 37.77/24.52 inference(rewrite,[status(thm)],[])).
% 37.77/24.52 tff(8,axiom,(![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_7')).
% 37.77/24.52 tff(9,plain,
% 37.77/24.52 (![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))),
% 37.77/24.52 inference(modus_ponens,[status(thm)],[8, 7])).
% 37.77/24.52 tff(10,plain,(
% 37.77/24.52 ![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))),
% 37.77/24.52 inference(skolemize,[status(sab)],[9])).
% 37.77/24.52 tff(11,plain,
% 37.77/24.52 (![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))),
% 37.77/24.52 inference(modus_ponens,[status(thm)],[10, 6])).
% 37.77/24.52 tff(12,plain,
% 37.77/24.52 (((~![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))) | ((~less_than(n0, b)) | less_than(n0, half(b)))) <=> ((~![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))) | (~less_than(n0, b)) | less_than(n0, half(b)))),
% 37.77/24.52 inference(rewrite,[status(thm)],[])).
% 37.77/24.52 tff(13,plain,
% 37.77/24.52 ((~![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))) | ((~less_than(n0, b)) | less_than(n0, half(b)))),
% 37.77/24.52 inference(quant_inst,[status(thm)],[])).
% 37.77/24.52 tff(14,plain,
% 37.77/24.52 ((~![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))) | (~less_than(n0, b)) | less_than(n0, half(b))),
% 37.77/24.52 inference(modus_ponens,[status(thm)],[13, 12])).
% 37.77/24.52 tff(15,plain,
% 37.77/24.52 (less_than(n0, half(b))),
% 37.77/24.52 inference(unit_resolution,[status(thm)],[14, 11, 4])).
% 37.77/24.52 tff(16,plain,
% 37.77/24.52 (^[X: $i] : refl(((~less_than(n0, X)) | less_than(n0, fp31(X))) <=> ((~less_than(n0, X)) | less_than(n0, fp31(X))))),
% 37.77/24.52 inference(bind,[status(th)],[])).
% 37.77/24.52 tff(17,plain,
% 37.77/24.52 (![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X))) <=> ![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X)))),
% 37.77/24.52 inference(quant_intro,[status(thm)],[16])).
% 37.77/24.52 tff(18,plain,
% 37.77/24.52 (![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X))) <=> ![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X)))),
% 37.77/24.52 inference(rewrite,[status(thm)],[])).
% 37.77/24.52 tff(19,axiom,(![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_10')).
% 37.77/24.52 tff(20,plain,
% 37.77/24.52 (![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X)))),
% 37.77/24.52 inference(modus_ponens,[status(thm)],[19, 18])).
% 37.77/24.52 tff(21,plain,(
% 37.77/24.52 ![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X)))),
% 37.77/24.52 inference(skolemize,[status(sab)],[20])).
% 37.77/24.52 tff(22,plain,
% 37.77/24.52 (![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X)))),
% 37.77/24.52 inference(modus_ponens,[status(thm)],[21, 17])).
% 37.77/24.52 tff(23,plain,
% 37.77/24.52 (((~![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X)))) | ((~less_than(n0, half(b))) | less_than(n0, fp31(half(b))))) <=> ((~![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X)))) | (~less_than(n0, half(b))) | less_than(n0, fp31(half(b))))),
% 37.77/24.52 inference(rewrite,[status(thm)],[])).
% 37.77/24.52 tff(24,plain,
% 37.77/24.52 ((~![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X)))) | ((~less_than(n0, half(b))) | less_than(n0, fp31(half(b))))),
% 37.77/24.52 inference(quant_inst,[status(thm)],[])).
% 37.77/24.52 tff(25,plain,
% 37.77/24.52 ((~![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp31(X)))) | (~less_than(n0, half(b))) | less_than(n0, fp31(half(b)))),
% 37.77/24.52 inference(modus_ponens,[status(thm)],[24, 23])).
% 37.77/24.52 tff(26,plain,
% 37.77/24.52 (less_than(n0, fp31(half(b)))),
% 37.77/24.52 inference(unit_resolution,[status(thm)],[25, 22, 15])).
% 37.77/24.52 tff(27,assumption,(~less_than(n0, half(fp31(half(b))))), introduced(assumption)).
% 37.77/24.52 tff(28,plain,
% 37.77/24.52 (((~![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))) | ((~less_than(n0, fp31(half(b)))) | less_than(n0, half(fp31(half(b)))))) <=> ((~![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))) | (~less_than(n0, fp31(half(b)))) | less_than(n0, half(fp31(half(b)))))),
% 37.77/24.52 inference(rewrite,[status(thm)],[])).
% 37.77/24.52 tff(29,plain,
% 37.77/24.52 ((~![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))) | ((~less_than(n0, fp31(half(b)))) | less_than(n0, half(fp31(half(b)))))),
% 37.77/24.52 inference(quant_inst,[status(thm)],[])).
% 37.77/24.52 tff(30,plain,
% 37.77/24.52 ((~![Xa: $i] : ((~less_than(n0, Xa)) | less_than(n0, half(Xa)))) | (~less_than(n0, fp31(half(b)))) | less_than(n0, half(fp31(half(b))))),
% 37.77/24.52 inference(modus_ponens,[status(thm)],[29, 28])).
% 37.77/24.52 tff(31,plain,
% 37.77/24.52 ($false),
% 37.77/24.52 inference(unit_resolution,[status(thm)],[30, 11, 27, 26])).
% 37.77/24.52 tff(32,plain,(less_than(n0, half(fp31(half(b))))), inference(lemma,lemma(discharge,[]))).
% 37.77/24.52 tff(33,assumption,(~less_than(n0, fp32(half(b)))), introduced(assumption)).
% 37.77/24.52 tff(34,plain,
% 37.77/24.52 (^[X: $i] : refl(((~less_than(n0, X)) | less_than(n0, fp32(X))) <=> ((~less_than(n0, X)) | less_than(n0, fp32(X))))),
% 37.81/24.52 inference(bind,[status(th)],[])).
% 37.81/24.52 tff(35,plain,
% 37.81/24.52 (![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X))) <=> ![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X)))),
% 37.81/24.52 inference(quant_intro,[status(thm)],[34])).
% 37.81/24.52 tff(36,plain,
% 37.81/24.52 (![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X))) <=> ![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X)))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(37,axiom,(![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_12')).
% 37.81/24.52 tff(38,plain,
% 37.81/24.52 (![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X)))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[37, 36])).
% 37.81/24.52 tff(39,plain,(
% 37.81/24.52 ![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X)))),
% 37.81/24.52 inference(skolemize,[status(sab)],[38])).
% 37.81/24.52 tff(40,plain,
% 37.81/24.52 (![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X)))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[39, 35])).
% 37.81/24.52 tff(41,plain,
% 37.81/24.52 (((~![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X)))) | ((~less_than(n0, half(b))) | less_than(n0, fp32(half(b))))) <=> ((~![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X)))) | (~less_than(n0, half(b))) | less_than(n0, fp32(half(b))))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(42,plain,
% 37.81/24.52 ((~![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X)))) | ((~less_than(n0, half(b))) | less_than(n0, fp32(half(b))))),
% 37.81/24.52 inference(quant_inst,[status(thm)],[])).
% 37.81/24.52 tff(43,plain,
% 37.81/24.52 ((~![X: $i] : ((~less_than(n0, X)) | less_than(n0, fp32(X)))) | (~less_than(n0, half(b))) | less_than(n0, fp32(half(b)))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[42, 41])).
% 37.81/24.52 tff(44,plain,
% 37.81/24.52 ($false),
% 37.81/24.52 inference(unit_resolution,[status(thm)],[43, 40, 33, 15])).
% 37.81/24.52 tff(45,plain,(less_than(n0, fp32(half(b)))), inference(lemma,lemma(discharge,[]))).
% 37.81/24.52 tff(46,plain,
% 37.81/24.52 (^[Y: $i, X: $i] : refl((less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X))) <=> (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X))))),
% 37.81/24.52 inference(bind,[status(th)],[])).
% 37.81/24.52 tff(47,plain,
% 37.81/24.52 (![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X))) <=> ![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))),
% 37.81/24.52 inference(quant_intro,[status(thm)],[46])).
% 37.81/24.52 tff(48,plain,
% 37.81/24.52 (![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X))) <=> ![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(49,plain,
% 37.81/24.52 (^[Y: $i, X: $i] : rewrite((((~less_than(n0, X)) | (~less_than(n0, Y))) | less_than(n0, minimum(X, Y))) <=> (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X))))),
% 37.81/24.52 inference(bind,[status(th)],[])).
% 37.81/24.52 tff(50,plain,
% 37.81/24.52 (![Y: $i, X: $i] : (((~less_than(n0, X)) | (~less_than(n0, Y))) | less_than(n0, minimum(X, Y))) <=> ![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))),
% 37.81/24.52 inference(quant_intro,[status(thm)],[49])).
% 37.81/24.52 tff(51,axiom,(![Y: $i, X: $i] : (((~less_than(n0, X)) | (~less_than(n0, Y))) | less_than(n0, minimum(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2_1')).
% 37.81/24.52 tff(52,plain,
% 37.81/24.52 (![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[51, 50])).
% 37.81/24.52 tff(53,plain,
% 37.81/24.52 (![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[52, 48])).
% 37.81/24.52 tff(54,plain,(
% 37.81/24.52 ![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))),
% 37.81/24.52 inference(skolemize,[status(sab)],[53])).
% 37.81/24.52 tff(55,plain,
% 37.81/24.52 (![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[54, 47])).
% 37.81/24.52 tff(56,plain,
% 37.81/24.52 (((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | ((~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))) | less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))))) <=> ((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))) | less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(57,plain,
% 37.81/24.52 ((less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))) | (~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b)))))) <=> ((~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))) | less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(58,plain,
% 37.81/24.52 (((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))) | (~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))))) <=> ((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | ((~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))) | less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.52 inference(monotonicity,[status(thm)],[57])).
% 37.81/24.52 tff(59,plain,
% 37.81/24.52 (((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))) | (~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))))) <=> ((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))) | less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.52 inference(transitivity,[status(thm)],[58, 56])).
% 37.81/24.52 tff(60,plain,
% 37.81/24.52 ((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))) | (~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))))),
% 37.81/24.52 inference(quant_inst,[status(thm)],[])).
% 37.81/24.52 tff(61,plain,
% 37.81/24.52 ((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))) | less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[60, 59])).
% 37.81/24.52 tff(62,plain,
% 37.81/24.52 (less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))),
% 37.81/24.52 inference(unit_resolution,[status(thm)],[61, 55, 45, 32])).
% 37.81/24.52 tff(63,plain,
% 37.81/24.52 (((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | ((~less_than(n0, fp31(half(b)))) | less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))))) <=> ((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (~less_than(n0, fp31(half(b)))) | less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(64,plain,
% 37.81/24.52 ((less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b))))) <=> ((~less_than(n0, fp31(half(b)))) | less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(65,plain,
% 37.81/24.52 (((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b)))))) <=> ((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | ((~less_than(n0, fp31(half(b)))) | less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))))))),
% 37.81/24.52 inference(monotonicity,[status(thm)],[64])).
% 37.81/24.52 tff(66,plain,
% 37.81/24.52 (((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b)))))) <=> ((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (~less_than(n0, fp31(half(b)))) | less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.52 inference(transitivity,[status(thm)],[65, 63])).
% 37.81/24.52 tff(67,plain,
% 37.81/24.52 ((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b)))))),
% 37.81/24.52 inference(quant_inst,[status(thm)],[])).
% 37.81/24.52 tff(68,plain,
% 37.81/24.52 ((~![Y: $i, X: $i] : (less_than(n0, minimum(X, Y)) | (~less_than(n0, Y)) | (~less_than(n0, X)))) | (~less_than(n0, fp31(half(b)))) | less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[67, 66])).
% 37.81/24.52 tff(69,plain,
% 37.81/24.52 (less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.52 inference(unit_resolution,[status(thm)],[68, 55, 26, 62])).
% 37.81/24.52 tff(70,plain,
% 37.81/24.52 (^[Y: $i, X: $i] : refl(((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X)) <=> ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X)))),
% 37.81/24.52 inference(bind,[status(th)],[])).
% 37.81/24.52 tff(71,plain,
% 37.81/24.52 (![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X)) <=> ![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))),
% 37.81/24.52 inference(quant_intro,[status(thm)],[70])).
% 37.81/24.52 tff(72,plain,
% 37.81/24.52 (![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X)) <=> ![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(73,plain,
% 37.81/24.52 (^[Y: $i, X: $i] : rewrite((((~less_than(n0, X)) | (~less_than(n0, Y))) | less_than(minimum(X, Y), X)) <=> ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X)))),
% 37.81/24.52 inference(bind,[status(th)],[])).
% 37.81/24.52 tff(74,plain,
% 37.81/24.52 (![Y: $i, X: $i] : (((~less_than(n0, X)) | (~less_than(n0, Y))) | less_than(minimum(X, Y), X)) <=> ![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))),
% 37.81/24.52 inference(quant_intro,[status(thm)],[73])).
% 37.81/24.52 tff(75,axiom,(![Y: $i, X: $i] : (((~less_than(n0, X)) | (~less_than(n0, Y))) | less_than(minimum(X, Y), X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2_2')).
% 37.81/24.52 tff(76,plain,
% 37.81/24.52 (![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[75, 74])).
% 37.81/24.52 tff(77,plain,
% 37.81/24.52 (![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[76, 72])).
% 37.81/24.52 tff(78,plain,(
% 37.81/24.52 ![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))),
% 37.81/24.52 inference(skolemize,[status(sab)],[77])).
% 37.81/24.52 tff(79,plain,
% 37.81/24.52 (![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[78, 71])).
% 37.81/24.52 tff(80,plain,
% 37.81/24.52 (((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))) | ((~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))) | (~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(81,plain,
% 37.81/24.52 (((~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) <=> ((~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(82,plain,
% 37.81/24.52 (((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))) | ((~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b))))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))) | ((~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))))))),
% 37.81/24.52 inference(monotonicity,[status(thm)],[81])).
% 37.81/24.52 tff(83,plain,
% 37.81/24.52 (((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))) | ((~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b))))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))) | (~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.52 inference(transitivity,[status(thm)],[82, 80])).
% 37.81/24.52 tff(84,plain,
% 37.81/24.52 ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))) | ((~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b))))),
% 37.81/24.52 inference(quant_inst,[status(thm)],[])).
% 37.81/24.52 tff(85,plain,
% 37.81/24.52 ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), X))) | (~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[84, 83])).
% 37.81/24.52 tff(86,plain,
% 37.81/24.52 (less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))),
% 37.81/24.52 inference(unit_resolution,[status(thm)],[85, 79, 26, 62])).
% 37.81/24.52 tff(87,assumption,(less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))), introduced(assumption)).
% 37.81/24.52 tff(88,assumption,(less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), introduced(assumption)).
% 37.81/24.52 tff(89,assumption,(less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))), introduced(assumption)).
% 37.81/24.52 tff(90,assumption,(less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), introduced(assumption)).
% 37.81/24.52 tff(91,plain,
% 37.81/24.52 (^[X: $i] : refl(((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b))) <=> ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b))))),
% 37.81/24.52 inference(bind,[status(th)],[])).
% 37.81/24.52 tff(92,plain,
% 37.81/24.52 (![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b))) <=> ![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b)))),
% 37.81/24.52 inference(quant_intro,[status(thm)],[91])).
% 37.81/24.52 tff(93,plain,
% 37.81/24.52 (![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b))) <=> ![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b)))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(94,axiom,(![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_16')).
% 37.81/24.52 tff(95,plain,
% 37.81/24.52 (![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b)))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[94, 93])).
% 37.81/24.52 tff(96,plain,(
% 37.81/24.52 ![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b)))),
% 37.81/24.52 inference(skolemize,[status(sab)],[95])).
% 37.81/24.52 tff(97,plain,
% 37.81/24.52 (![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b)))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[96, 92])).
% 37.81/24.52 tff(98,plain,
% 37.81/24.52 (((~![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b)))) | ((~less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | (~less_than(add(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2)))), b)))) <=> ((~![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b)))) | (~less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | (~less_than(add(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2)))), b)))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(99,plain,
% 37.81/24.52 ((~![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b)))) | ((~less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | (~less_than(add(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2)))), b)))),
% 37.81/24.52 inference(quant_inst,[status(thm)],[])).
% 37.81/24.52 tff(100,plain,
% 37.81/24.52 ((~![X: $i] : ((~less_than(n0, X)) | (~less_than(add(absolute(add(f(fp33(X)), minus(l1))), absolute(add(g(fp33(X)), minus(l2)))), b)))) | (~less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | (~less_than(add(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2)))), b))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[99, 98])).
% 37.81/24.52 tff(101,plain,
% 37.81/24.52 (~less_than(add(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2)))), b)),
% 37.81/24.52 inference(unit_resolution,[status(thm)],[100, 97, 90])).
% 37.81/24.52 tff(102,assumption,(less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))), introduced(assumption)).
% 37.81/24.52 tff(103,assumption,(~less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b))), introduced(assumption)).
% 37.81/24.52 tff(104,plain,
% 37.81/24.52 (^[Y: $i, X: $i] : refl(((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X)))) <=> ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X)))))),
% 37.81/24.52 inference(bind,[status(th)],[])).
% 37.81/24.52 tff(105,plain,
% 37.81/24.52 (![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X)))) <=> ![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))),
% 37.81/24.52 inference(quant_intro,[status(thm)],[104])).
% 37.81/24.52 tff(106,plain,
% 37.81/24.52 (![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X)))) <=> ![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))),
% 37.81/24.52 inference(rewrite,[status(thm)],[])).
% 37.81/24.52 tff(107,plain,
% 37.81/24.52 (^[Y: $i, X: $i] : rewrite((((~less_than(n0, X)) | (~less_than(absolute(add(Y, minus(a))), fp32(X)))) | less_than(absolute(add(g(Y), minus(l2))), X)) <=> ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X)))))),
% 37.81/24.52 inference(bind,[status(th)],[])).
% 37.81/24.52 tff(108,plain,
% 37.81/24.52 (![Y: $i, X: $i] : (((~less_than(n0, X)) | (~less_than(absolute(add(Y, minus(a))), fp32(X)))) | less_than(absolute(add(g(Y), minus(l2))), X)) <=> ![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))),
% 37.81/24.52 inference(quant_intro,[status(thm)],[107])).
% 37.81/24.52 tff(109,axiom,(![Y: $i, X: $i] : (((~less_than(n0, X)) | (~less_than(absolute(add(Y, minus(a))), fp32(X)))) | less_than(absolute(add(g(Y), minus(l2))), X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_13')).
% 37.81/24.52 tff(110,plain,
% 37.81/24.52 (![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))),
% 37.81/24.52 inference(modus_ponens,[status(thm)],[109, 108])).
% 37.81/24.53 tff(111,plain,
% 37.81/24.53 (![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[110, 106])).
% 37.81/24.53 tff(112,plain,(
% 37.81/24.53 ![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))),
% 37.81/24.53 inference(skolemize,[status(sab)],[111])).
% 37.81/24.53 tff(113,plain,
% 37.81/24.53 (![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[112, 105])).
% 37.81/24.53 tff(114,plain,
% 37.81/24.53 (((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))) | ((~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))) | less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b)))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))) | (~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))) | less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b)))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(115,plain,
% 37.81/24.53 (((~less_than(n0, half(b))) | less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b)) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b))))) <=> ((~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))) | less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b)))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(116,plain,
% 37.81/24.53 (((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))) | ((~less_than(n0, half(b))) | less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b)) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))) | ((~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))) | less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b))))),
% 37.81/24.53 inference(monotonicity,[status(thm)],[115])).
% 37.81/24.53 tff(117,plain,
% 37.81/24.53 (((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))) | ((~less_than(n0, half(b))) | less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b)) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))) | (~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))) | less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b)))),
% 37.81/24.53 inference(transitivity,[status(thm)],[116, 114])).
% 37.81/24.53 tff(118,plain,
% 37.81/24.53 ((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))) | ((~less_than(n0, half(b))) | less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b)) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))))),
% 37.81/24.53 inference(quant_inst,[status(thm)],[])).
% 37.81/24.53 tff(119,plain,
% 37.81/24.53 ((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(g(Y), minus(l2))), X) | (~less_than(absolute(add(Y, minus(a))), fp32(X))))) | (~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))) | less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[118, 117])).
% 37.81/24.53 tff(120,plain,
% 37.81/24.53 ($false),
% 37.81/24.53 inference(unit_resolution,[status(thm)],[119, 113, 15, 102, 103])).
% 37.81/24.53 tff(121,plain,(less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b)) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b))))), inference(lemma,lemma(discharge,[]))).
% 37.81/24.53 tff(122,plain,
% 37.81/24.53 (less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b))),
% 37.81/24.53 inference(unit_resolution,[status(thm)],[121, 102])).
% 37.81/24.53 tff(123,assumption,(~less_than(add(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2)))), b)), introduced(assumption)).
% 37.81/24.53 tff(124,plain,
% 37.81/24.53 (^[Y: $i, Xa: $i, X: $i] : refl((less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa)))) <=> (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa)))))),
% 37.81/24.53 inference(bind,[status(th)],[])).
% 37.81/24.53 tff(125,plain,
% 37.81/24.53 (![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa)))) <=> ![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa))))),
% 37.81/24.53 inference(quant_intro,[status(thm)],[124])).
% 37.81/24.53 tff(126,plain,
% 37.81/24.53 (![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa)))) <=> ![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa))))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(127,plain,
% 37.81/24.53 (^[Y: $i, Xa: $i, X: $i] : rewrite((((~less_than(X, half(Xa))) | (~less_than(Y, half(Xa)))) | less_than(add(X, Y), Xa)) <=> (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa)))))),
% 37.81/24.53 inference(bind,[status(th)],[])).
% 37.81/24.53 tff(128,plain,
% 37.81/24.53 (![Y: $i, Xa: $i, X: $i] : (((~less_than(X, half(Xa))) | (~less_than(Y, half(Xa)))) | less_than(add(X, Y), Xa)) <=> ![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa))))),
% 37.81/24.53 inference(quant_intro,[status(thm)],[127])).
% 37.81/24.53 tff(129,axiom,(![Y: $i, Xa: $i, X: $i] : (((~less_than(X, half(Xa))) | (~less_than(Y, half(Xa)))) | less_than(add(X, Y), Xa))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_3')).
% 37.81/24.53 tff(130,plain,
% 37.81/24.53 (![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa))))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[129, 128])).
% 37.81/24.53 tff(131,plain,
% 37.81/24.53 (![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa))))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[130, 126])).
% 37.81/24.53 tff(132,plain,(
% 37.81/24.53 ![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa))))),
% 37.81/24.53 inference(skolemize,[status(sab)],[131])).
% 37.81/24.53 tff(133,plain,
% 37.81/24.53 (![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa))))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[132, 125])).
% 37.81/24.53 tff(134,plain,
% 37.81/24.53 (((~![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa))))) | (less_than(add(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2)))), b) | (~less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b))) | (~less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b))))) <=> ((~![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa))))) | less_than(add(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2)))), b) | (~less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b))) | (~less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b))))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(135,plain,
% 37.81/24.53 ((~![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa))))) | (less_than(add(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2)))), b) | (~less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b))) | (~less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b))))),
% 37.81/24.53 inference(quant_inst,[status(thm)],[])).
% 37.81/24.53 tff(136,plain,
% 37.81/24.53 ((~![Y: $i, Xa: $i, X: $i] : (less_than(add(X, Y), Xa) | (~less_than(Y, half(Xa))) | (~less_than(X, half(Xa))))) | less_than(add(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2)))), b) | (~less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b))) | (~less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b)))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[135, 134])).
% 37.81/24.53 tff(137,plain,
% 37.81/24.53 ((~less_than(absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2))), half(b))) | (~less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b)))),
% 37.81/24.53 inference(unit_resolution,[status(thm)],[136, 133, 123])).
% 37.81/24.53 tff(138,plain,
% 37.81/24.53 (~less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b))),
% 37.81/24.53 inference(unit_resolution,[status(thm)],[137, 122])).
% 37.81/24.53 tff(139,plain,
% 37.81/24.53 (![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(140,plain,
% 37.81/24.53 (![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(141,plain,
% 37.81/24.53 (^[Z: $i, Y: $i, X: $i] : rewrite((((~less_than(X, Y)) | (~less_than(Y, Z))) | less_than(X, Z)) <=> (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y))))),
% 37.81/24.53 inference(bind,[status(th)],[])).
% 37.81/24.53 tff(142,plain,
% 37.81/24.53 (![Z: $i, Y: $i, X: $i] : (((~less_than(X, Y)) | (~less_than(Y, Z))) | less_than(X, Z)) <=> ![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 37.81/24.53 inference(quant_intro,[status(thm)],[141])).
% 37.81/24.53 tff(143,axiom,(![Z: $i, Y: $i, X: $i] : (((~less_than(X, Y)) | (~less_than(Y, Z))) | less_than(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity_of_less_than')).
% 37.81/24.53 tff(144,plain,
% 37.81/24.53 (![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[143, 142])).
% 37.81/24.53 tff(145,plain,
% 37.81/24.53 (![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[144, 140])).
% 37.81/24.53 tff(146,plain,(
% 37.81/24.53 ![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 37.81/24.53 inference(skolemize,[status(sab)],[145])).
% 37.81/24.53 tff(147,plain,
% 37.81/24.53 (![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[146, 139])).
% 37.81/24.53 tff(148,plain,
% 37.81/24.53 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | ((~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b))))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(149,plain,
% 37.81/24.53 ((less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))))) <=> ((~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b))))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(150,plain,
% 37.81/24.53 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | ((~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))))),
% 37.81/24.53 inference(monotonicity,[status(thm)],[149])).
% 37.81/24.53 tff(151,plain,
% 37.81/24.53 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b))))),
% 37.81/24.53 inference(transitivity,[status(thm)],[150, 148])).
% 37.81/24.53 tff(152,plain,
% 37.81/24.53 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))))),
% 37.81/24.53 inference(quant_inst,[status(thm)],[])).
% 37.81/24.53 tff(153,plain,
% 37.81/24.53 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[152, 151])).
% 37.81/24.53 tff(154,plain,
% 37.81/24.53 (less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))),
% 37.81/24.53 inference(unit_resolution,[status(thm)],[153, 147, 89, 88])).
% 37.81/24.53 tff(155,plain,
% 37.81/24.53 (^[Y: $i, X: $i] : refl(((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X)))) <=> ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X)))))),
% 37.81/24.53 inference(bind,[status(th)],[])).
% 37.81/24.53 tff(156,plain,
% 37.81/24.53 (![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X)))) <=> ![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))),
% 37.81/24.53 inference(quant_intro,[status(thm)],[155])).
% 37.81/24.53 tff(157,plain,
% 37.81/24.53 (![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X)))) <=> ![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(158,plain,
% 37.81/24.53 (^[Y: $i, X: $i] : rewrite((((~less_than(n0, X)) | (~less_than(absolute(add(Y, minus(a))), fp31(X)))) | less_than(absolute(add(f(Y), minus(l1))), X)) <=> ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X)))))),
% 37.81/24.53 inference(bind,[status(th)],[])).
% 37.81/24.53 tff(159,plain,
% 37.81/24.53 (![Y: $i, X: $i] : (((~less_than(n0, X)) | (~less_than(absolute(add(Y, minus(a))), fp31(X)))) | less_than(absolute(add(f(Y), minus(l1))), X)) <=> ![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))),
% 37.81/24.53 inference(quant_intro,[status(thm)],[158])).
% 37.81/24.53 tff(160,axiom,(![Y: $i, X: $i] : (((~less_than(n0, X)) | (~less_than(absolute(add(Y, minus(a))), fp31(X)))) | less_than(absolute(add(f(Y), minus(l1))), X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_11')).
% 37.81/24.53 tff(161,plain,
% 37.81/24.53 (![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[160, 159])).
% 37.81/24.53 tff(162,plain,
% 37.81/24.53 (![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[161, 157])).
% 37.81/24.53 tff(163,plain,(
% 37.81/24.53 ![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))),
% 37.81/24.53 inference(skolemize,[status(sab)],[162])).
% 37.81/24.53 tff(164,plain,
% 37.81/24.53 (![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[163, 156])).
% 37.81/24.53 tff(165,plain,
% 37.81/24.53 (((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))) | ((~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))) | less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b)))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))) | (~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))) | less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b)))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(166,plain,
% 37.81/24.53 (((~less_than(n0, half(b))) | less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b)) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b))))) <=> ((~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))) | less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b)))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(167,plain,
% 37.81/24.53 (((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))) | ((~less_than(n0, half(b))) | less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b)) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))) | ((~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))) | less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b))))),
% 37.81/24.53 inference(monotonicity,[status(thm)],[166])).
% 37.81/24.53 tff(168,plain,
% 37.81/24.53 (((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))) | ((~less_than(n0, half(b))) | less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b)) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))) | (~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))) | less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b)))),
% 37.81/24.53 inference(transitivity,[status(thm)],[167, 165])).
% 37.81/24.53 tff(169,plain,
% 37.81/24.53 ((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))) | ((~less_than(n0, half(b))) | less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b)) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))))),
% 37.81/24.53 inference(quant_inst,[status(thm)],[])).
% 37.81/24.53 tff(170,plain,
% 37.81/24.53 ((~![Y: $i, X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(f(Y), minus(l1))), X) | (~less_than(absolute(add(Y, minus(a))), fp31(X))))) | (~less_than(n0, half(b))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp31(half(b)))) | less_than(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), half(b))),
% 37.81/24.53 inference(modus_ponens,[status(thm)],[169, 168])).
% 37.81/24.53 tff(171,plain,
% 37.81/24.53 ($false),
% 37.81/24.53 inference(unit_resolution,[status(thm)],[170, 164, 15, 154, 138])).
% 37.81/24.53 tff(172,plain,((~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))) | less_than(add(absolute(add(f(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l1))), absolute(add(g(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))), minus(l2)))), b) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))))), inference(lemma,lemma(discharge,[]))).
% 37.81/24.53 tff(173,plain,
% 37.81/24.53 (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))),
% 37.81/24.53 inference(unit_resolution,[status(thm)],[172, 101, 89, 88])).
% 37.81/24.53 tff(174,plain,
% 37.81/24.53 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | ((~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b))))),
% 37.81/24.53 inference(rewrite,[status(thm)],[])).
% 37.81/24.53 tff(175,plain,
% 37.81/24.53 ((less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))))) <=> ((~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b))))),
% 37.81/24.54 inference(rewrite,[status(thm)],[])).
% 37.81/24.54 tff(176,plain,
% 37.81/24.54 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | ((~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))))),
% 37.81/24.54 inference(monotonicity,[status(thm)],[175])).
% 37.81/24.54 tff(177,plain,
% 37.81/24.54 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b))))),
% 37.81/24.54 inference(transitivity,[status(thm)],[176, 174])).
% 37.81/24.54 tff(178,plain,
% 37.81/24.54 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))))),
% 37.81/24.54 inference(quant_inst,[status(thm)],[])).
% 37.81/24.54 tff(179,plain,
% 37.81/24.54 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), fp32(half(b)))),
% 37.81/24.54 inference(modus_ponens,[status(thm)],[178, 177])).
% 37.81/24.54 tff(180,plain,
% 37.81/24.54 ($false),
% 37.81/24.54 inference(unit_resolution,[status(thm)],[179, 147, 87, 88, 173])).
% 37.81/24.54 tff(181,plain,((~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp31(half(b)))) | (~less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))))), inference(lemma,lemma(discharge,[]))).
% 37.81/24.54 tff(182,plain,
% 37.81/24.54 (~less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.54 inference(unit_resolution,[status(thm)],[181, 87, 86, 69])).
% 37.81/24.54 tff(183,plain,
% 37.81/24.54 (^[X: $i] : refl(((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X)) <=> ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X)))),
% 37.81/24.54 inference(bind,[status(th)],[])).
% 37.81/24.54 tff(184,plain,
% 37.81/24.54 (![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X)) <=> ![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X))),
% 37.81/24.54 inference(quant_intro,[status(thm)],[183])).
% 37.81/24.54 tff(185,plain,
% 37.81/24.54 (![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X)) <=> ![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X))),
% 37.81/24.54 inference(rewrite,[status(thm)],[])).
% 37.81/24.54 tff(186,axiom,(![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_15')).
% 37.81/24.54 tff(187,plain,
% 37.81/24.54 (![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X))),
% 37.81/24.54 inference(modus_ponens,[status(thm)],[186, 185])).
% 37.81/24.54 tff(188,plain,(
% 37.81/24.54 ![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X))),
% 37.81/24.54 inference(skolemize,[status(sab)],[187])).
% 37.81/24.54 tff(189,plain,
% 37.81/24.54 (![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X))),
% 37.81/24.54 inference(modus_ponens,[status(thm)],[188, 184])).
% 37.81/24.54 tff(190,plain,
% 37.81/24.54 (((~![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X))) | ((~less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))))) <=> ((~![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X))) | (~less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.54 inference(rewrite,[status(thm)],[])).
% 37.81/24.54 tff(191,plain,
% 37.81/24.54 ((~![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X))) | ((~less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.54 inference(quant_inst,[status(thm)],[])).
% 37.81/24.54 tff(192,plain,
% 37.81/24.54 ((~![X: $i] : ((~less_than(n0, X)) | less_than(absolute(add(fp33(X), minus(a))), X))) | (~less_than(n0, minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))) | less_than(absolute(add(fp33(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b))))), minus(a))), minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.54 inference(modus_ponens,[status(thm)],[191, 190])).
% 37.81/24.54 tff(193,plain,
% 37.81/24.54 ($false),
% 37.81/24.54 inference(unit_resolution,[status(thm)],[192, 189, 69, 182])).
% 37.81/24.54 tff(194,plain,(~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b)))), inference(lemma,lemma(discharge,[]))).
% 37.81/24.54 tff(195,plain,
% 37.81/24.54 (^[Y: $i, X: $i] : refl(((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y)) <=> ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y)))),
% 37.81/24.54 inference(bind,[status(th)],[])).
% 37.81/24.54 tff(196,plain,
% 37.81/24.54 (![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y)) <=> ![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))),
% 37.81/24.54 inference(quant_intro,[status(thm)],[195])).
% 37.81/24.54 tff(197,plain,
% 37.81/24.54 (![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y)) <=> ![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))),
% 37.81/24.54 inference(rewrite,[status(thm)],[])).
% 37.81/24.54 tff(198,plain,
% 37.81/24.54 (^[Y: $i, X: $i] : rewrite((((~less_than(n0, X)) | (~less_than(n0, Y))) | less_than(minimum(X, Y), Y)) <=> ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y)))),
% 37.81/24.54 inference(bind,[status(th)],[])).
% 37.81/24.54 tff(199,plain,
% 37.81/24.54 (![Y: $i, X: $i] : (((~less_than(n0, X)) | (~less_than(n0, Y))) | less_than(minimum(X, Y), Y)) <=> ![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))),
% 37.81/24.54 inference(quant_intro,[status(thm)],[198])).
% 37.81/24.54 tff(200,axiom,(![Y: $i, X: $i] : (((~less_than(n0, X)) | (~less_than(n0, Y))) | less_than(minimum(X, Y), Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2_3')).
% 37.81/24.54 tff(201,plain,
% 37.81/24.54 (![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))),
% 37.81/24.54 inference(modus_ponens,[status(thm)],[200, 199])).
% 37.81/24.54 tff(202,plain,
% 37.81/24.54 (![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))),
% 37.81/24.54 inference(modus_ponens,[status(thm)],[201, 197])).
% 37.81/24.54 tff(203,plain,(
% 37.81/24.54 ![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))),
% 37.81/24.54 inference(skolemize,[status(sab)],[202])).
% 37.81/24.54 tff(204,plain,
% 37.81/24.54 (![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))),
% 37.81/24.54 inference(modus_ponens,[status(thm)],[203, 196])).
% 37.81/24.54 tff(205,plain,
% 37.81/24.54 (((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | ((~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))) | less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b))))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | (~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))) | less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b))))),
% 37.81/24.54 inference(rewrite,[status(thm)],[])).
% 37.81/24.54 tff(206,plain,
% 37.81/24.54 ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | ((~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))) | less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b))))),
% 37.81/24.54 inference(quant_inst,[status(thm)],[])).
% 37.81/24.54 tff(207,plain,
% 37.81/24.54 ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | (~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))) | less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))),
% 37.81/24.54 inference(modus_ponens,[status(thm)],[206, 205])).
% 37.81/24.54 tff(208,plain,
% 37.81/24.54 ((~less_than(n0, fp32(half(b)))) | (~less_than(n0, half(fp31(half(b))))) | less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))),
% 37.81/24.54 inference(unit_resolution,[status(thm)],[207, 204])).
% 37.81/24.54 tff(209,plain,
% 37.81/24.54 ((~less_than(n0, fp32(half(b)))) | less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))),
% 37.81/24.54 inference(unit_resolution,[status(thm)],[208, 32])).
% 37.81/24.54 tff(210,plain,
% 37.81/24.54 (less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))),
% 37.81/24.54 inference(unit_resolution,[status(thm)],[209, 45])).
% 37.81/24.54 tff(211,plain,
% 37.81/24.54 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | ((~less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (~less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.54 inference(rewrite,[status(thm)],[])).
% 37.81/24.54 tff(212,plain,
% 37.81/24.54 ((less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b))) | (~less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b)))))) <=> ((~less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.54 inference(rewrite,[status(thm)],[])).
% 37.81/24.54 tff(213,plain,
% 37.81/24.54 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b))) | (~less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | ((~less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b)))))))),
% 37.81/24.54 inference(monotonicity,[status(thm)],[212])).
% 37.81/24.54 tff(214,plain,
% 37.81/24.54 (((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b))) | (~less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))))) <=> ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (~less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.54 inference(transitivity,[status(thm)],[213, 211])).
% 37.81/24.54 tff(215,plain,
% 37.81/24.54 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b))) | (~less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.54 inference(quant_inst,[status(thm)],[])).
% 37.81/24.54 tff(216,plain,
% 37.81/24.54 ((~![Z: $i, Y: $i, X: $i] : (less_than(X, Z) | (~less_than(Y, Z)) | (~less_than(X, Y)))) | (~less_than(minimum(half(fp31(half(b))), fp32(half(b))), fp32(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), fp32(half(b))) | (~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.54 inference(modus_ponens,[status(thm)],[215, 214])).
% 37.81/24.54 tff(217,plain,
% 37.81/24.54 ($false),
% 37.81/24.54 inference(unit_resolution,[status(thm)],[216, 147, 210, 194, 1])).
% 37.81/24.54 tff(218,plain,(~less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))), inference(lemma,lemma(discharge,[]))).
% 37.81/24.54 tff(219,assumption,(~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))), introduced(assumption)).
% 37.81/24.54 tff(220,plain,
% 37.81/24.54 ($false),
% 37.81/24.54 inference(unit_resolution,[status(thm)],[61, 55, 45, 32, 219])).
% 37.81/24.54 tff(221,plain,(less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))), inference(lemma,lemma(discharge,[]))).
% 37.81/24.54 tff(222,plain,
% 37.81/24.54 (((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | ((~less_than(n0, fp31(half(b)))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b)))))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | (~less_than(n0, fp31(half(b)))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.55 inference(rewrite,[status(thm)],[])).
% 37.81/24.55 tff(223,plain,
% 37.81/24.55 (((~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))) <=> ((~less_than(n0, fp31(half(b)))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.55 inference(rewrite,[status(thm)],[])).
% 37.81/24.55 tff(224,plain,
% 37.81/24.55 (((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | ((~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b)))))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | ((~less_than(n0, fp31(half(b)))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))))),
% 37.81/24.55 inference(monotonicity,[status(thm)],[223])).
% 37.81/24.55 tff(225,plain,
% 37.81/24.55 (((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | ((~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b)))))) <=> ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | (~less_than(n0, fp31(half(b)))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.55 inference(transitivity,[status(thm)],[224, 222])).
% 37.81/24.55 tff(226,plain,
% 37.81/24.55 ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | ((~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | (~less_than(n0, fp31(half(b)))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b)))))),
% 37.81/24.55 inference(quant_inst,[status(thm)],[])).
% 37.81/24.55 tff(227,plain,
% 37.81/24.55 ((~![Y: $i, X: $i] : ((~less_than(n0, Y)) | (~less_than(n0, X)) | less_than(minimum(X, Y), Y))) | (~less_than(n0, fp31(half(b)))) | (~less_than(n0, minimum(half(fp31(half(b))), fp32(half(b))))) | less_than(minimum(fp31(half(b)), minimum(half(fp31(half(b))), fp32(half(b)))), minimum(half(fp31(half(b))), fp32(half(b))))),
% 37.81/24.55 inference(modus_ponens,[status(thm)],[226, 225])).
% 37.81/24.55 tff(228,plain,
% 37.81/24.55 ($false),
% 37.81/24.55 inference(unit_resolution,[status(thm)],[227, 204, 26, 221, 218])).
% 37.81/24.55 % SZS output end Proof
%------------------------------------------------------------------------------