TSTP Solution File: DAT031_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT031_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:36:26 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : DAT031_1 : TPTP v8.1.0. Released v5.0.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 01:28:31 EDT 2022
% 0.13/0.35 % 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.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(in_type, type, (
% 0.20/0.46 in: ( $int * collection ) > $o)).
% 0.20/0.46 tff(tptp_fun_U_0_type, type, (
% 0.20/0.46 tptp_fun_U_0: collection)).
% 0.20/0.46 tff(add_type, type, (
% 0.20/0.46 add: ( $int * collection ) > collection)).
% 0.20/0.46 tff(empty_type, type, (
% 0.20/0.46 empty: collection)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (((~(~(U!0 = add(10, add(30, add(50, empty)))))) & ![V: $int] : (~($greatereq(V, 20) & $lesseq(V, 40) & in(V, U!0)))) <=> ((U!0 = add(10, add(30, add(50, empty)))) & ![V: $int] : (~($greatereq(V, 20) & $lesseq(V, 40) & in(V, U!0))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 ((~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($greatereq(V, 20) & $lesseq(V, 40) & in(V, U)))) <=> (~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($greatereq(V, 20) & $lesseq(V, 40) & in(V, U))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 ((~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($lesseq(20, V) & $lesseq(V, 40) & in(V, U)))) <=> (~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($greatereq(V, 20) & $lesseq(V, 40) & in(V, U))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 ((~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($lesseq(20, V) & $lesseq(V, 40) & in(V, U)))) <=> (~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($lesseq(20, V) & $lesseq(V, 40) & in(V, U))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 ((~![U: collection] : ((U = add(10, add(30, add(50, empty)))) => ?[V: $int] : (($lesseq(20, V) & $lesseq(V, 40)) & in(V, U)))) <=> (~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($lesseq(20, V) & $lesseq(V, 40) & in(V, U))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(6,axiom,(~![U: collection] : ((U = add(10, add(30, add(50, empty)))) => ?[V: $int] : (($lesseq(20, V) & $lesseq(V, 40)) & in(V, U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($lesseq(20, V) & $lesseq(V, 40) & in(V, U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 (~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($lesseq(20, V) & $lesseq(V, 40) & in(V, U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($lesseq(20, V) & $lesseq(V, 40) & in(V, U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($lesseq(20, V) & $lesseq(V, 40) & in(V, U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($greatereq(V, 20) & $lesseq(V, 40) & in(V, U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($greatereq(V, 20) & $lesseq(V, 40) & in(V, U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (~![U: collection] : ((~(U = add(10, add(30, add(50, empty))))) | ?[V: $int] : ($greatereq(V, 20) & $lesseq(V, 40) & in(V, U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 ((U!0 = add(10, add(30, add(50, empty)))) & ![V: $int] : (~($greatereq(V, 20) & $lesseq(V, 40) & in(V, U!0)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[13, 1])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (U!0 = add(10, add(30, add(50, empty)))),
% 0.20/0.46 inference(and_elim,[status(thm)],[14])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (in(30, U!0) <=> in(30, add(10, add(30, add(50, empty))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[15])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (in(30, add(10, add(30, add(50, empty)))) <=> in(30, U!0)),
% 0.20/0.46 inference(symmetry,[status(thm)],[16])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (^[Z: $int, X1: collection, X2: $int] : refl(((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1))) <=> ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1))) <=> ![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 (^[Z: $int, X1: collection, X2: $int] : rewrite(((in(Z, X1) | ($sum(Z, $product(-1, X2)) = 0)) <=> in(Z, add(X2, X1))) <=> ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(Z, $product(-1, X2)) = 0)) <=> in(Z, add(X2, X1))) <=> ![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 (^[Z: $int, X1: collection, X2: $int] : rewrite((((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1))) <=> ((in(Z, X1) | ($sum(Z, $product(-1, X2)) = 0)) <=> in(Z, add(X2, X1))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1))) <=> ![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(Z, $product(-1, X2)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1))) <=> ![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (^[Z: $int, X1: collection, X2: $int] : rewrite(((in(Z, X1) | (Z = X2)) <=> in(Z, add(X2, X1))) <=> (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | (Z = X2)) <=> in(Z, add(X2, X1))) <=> ![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.47 tff(27,axiom,(![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | (Z = X2)) <=> in(Z, add(X2, X1)))), file('/export/starexec/sandbox/benchmark/Axioms/DAT002=0.ax','ax4')).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(Z, $product(-1, X2)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[30, 21])).
% 0.20/0.47 tff(32,plain,(
% 0.20/0.47 ![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[31])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[32, 19])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | (in(30, add(30, add(50, empty))) <=> in(30, add(10, add(30, add(50, empty)))))) <=> ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | (in(30, add(30, add(50, empty))) <=> in(30, add(10, add(30, add(50, empty))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (((in(30, add(30, add(50, empty))) | ($sum(10, $product(-1, 30)) = 0)) <=> in(30, add(10, add(30, add(50, empty))))) <=> (in(30, add(30, add(50, empty))) <=> in(30, add(10, add(30, add(50, empty)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(30, add(30, add(50, empty))) | ($sum(10, $product(-1, 30)) = 0)) <=> in(30, add(10, add(30, add(50, empty)))))) <=> ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | (in(30, add(30, add(50, empty))) <=> in(30, add(10, add(30, add(50, empty))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 (((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(30, add(30, add(50, empty))) | ($sum(10, $product(-1, 30)) = 0)) <=> in(30, add(10, add(30, add(50, empty)))))) <=> ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | (in(30, add(30, add(50, empty))) <=> in(30, add(10, add(30, add(50, empty))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[36, 34])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(30, add(30, add(50, empty))) | ($sum(10, $product(-1, 30)) = 0)) <=> in(30, add(10, add(30, add(50, empty)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | (in(30, add(30, add(50, empty))) <=> in(30, add(10, add(30, add(50, empty)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (in(30, add(30, add(50, empty))) <=> in(30, add(10, add(30, add(50, empty))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[39, 33])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (^[V: $int, W: collection] : refl(in(V, add(V, W)) <=> in(V, add(V, W)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 (![V: $int, W: collection] : in(V, add(V, W)) <=> ![V: $int, W: collection] : in(V, add(V, W))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 (![V: $int, W: collection] : in(V, add(V, W)) <=> ![V: $int, W: collection] : in(V, add(V, W))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(44,axiom,(![V: $int, W: collection] : in(V, add(V, W))), file('/export/starexec/sandbox/benchmark/Axioms/DAT002=0.ax','ax2')).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (![V: $int, W: collection] : in(V, add(V, W))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.47 tff(46,plain,(
% 0.20/0.47 ![V: $int, W: collection] : in(V, add(V, W))),
% 0.20/0.47 inference(skolemize,[status(sab)],[45])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (![V: $int, W: collection] : in(V, add(V, W))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 ((~![V: $int, W: collection] : in(V, add(V, W))) | in(30, add(30, add(50, empty)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (in(30, add(30, add(50, empty)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 ((~(in(30, add(30, add(50, empty))) <=> in(30, add(10, add(30, add(50, empty)))))) | (~in(30, add(30, add(50, empty)))) | in(30, add(10, add(30, add(50, empty))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 ((~(in(30, add(30, add(50, empty))) <=> in(30, add(10, add(30, add(50, empty)))))) | in(30, add(10, add(30, add(50, empty))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (in(30, add(10, add(30, add(50, empty))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[51, 40])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (in(30, U!0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[52, 17])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (^[V: $int] : refl(((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0))) <=> ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0))) <=> ![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (^[V: $int] : trans(monotonicity(rewrite(($greatereq(V, 20) & $lesseq(V, 40) & in(V, U!0)) <=> (~((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0))))), ((~($greatereq(V, 20) & $lesseq(V, 40) & in(V, U!0))) <=> (~(~((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0))))))), rewrite((~(~((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0))))) <=> ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))), ((~($greatereq(V, 20) & $lesseq(V, 40) & in(V, U!0))) <=> ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (![V: $int] : (~($greatereq(V, 20) & $lesseq(V, 40) & in(V, U!0))) <=> ![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (![V: $int] : (~($greatereq(V, 20) & $lesseq(V, 40) & in(V, U!0)))),
% 0.20/0.47 inference(and_elim,[status(thm)],[14])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (((~![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))) | (~in(30, U!0))) <=> ((~![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))) | (~in(30, U!0)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 (($false | $false | (~in(30, U!0))) <=> (~in(30, U!0))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 ((~$true) <=> $false),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 ($lesseq(30, 40) <=> $true),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 ((~$lesseq(30, 40)) <=> (~$true)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 ((~$lesseq(30, 40)) <=> $false),
% 0.20/0.47 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 ($greatereq(30, 20) <=> $true),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 ((~$greatereq(30, 20)) <=> (~$true)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 ((~$greatereq(30, 20)) <=> $false),
% 0.20/0.47 inference(transitivity,[status(thm)],[68, 63])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (((~$greatereq(30, 20)) | (~$lesseq(30, 40)) | (~in(30, U!0))) <=> ($false | $false | (~in(30, U!0)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[69, 66])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (((~$greatereq(30, 20)) | (~$lesseq(30, 40)) | (~in(30, U!0))) <=> (~in(30, U!0))),
% 0.20/0.47 inference(transitivity,[status(thm)],[70, 62])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (((~![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))) | ((~$greatereq(30, 20)) | (~$lesseq(30, 40)) | (~in(30, U!0)))) <=> ((~![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))) | (~in(30, U!0)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 (((~![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))) | ((~$greatereq(30, 20)) | (~$lesseq(30, 40)) | (~in(30, U!0)))) <=> ((~![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))) | (~in(30, U!0)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[72, 61])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 ((~![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))) | ((~$greatereq(30, 20)) | (~$lesseq(30, 40)) | (~in(30, U!0)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 ((~![V: $int] : ((~$greatereq(V, 20)) | (~$lesseq(V, 40)) | (~in(V, U!0)))) | (~in(30, U!0))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (~in(30, U!0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[75, 60])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[76, 53])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------