TSTP Solution File: DAT007_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT007_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 14:36:21 EDT 2022
% Result : Theorem 1.11s 0.98s
% Output : Proof 1.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : DAT007_1 : TPTP v8.1.0. Released v5.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n015.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 01:52:37 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.
% 1.11/0.98 % SZS status Theorem
% 1.11/0.98 % SZS output start Proof
% 1.11/0.98 tff(read_type, type, (
% 1.11/0.98 read: ( array * $int ) > $int)).
% 1.11/0.98 tff(tptp_fun_U_1_type, type, (
% 1.11/0.98 tptp_fun_U_1: array)).
% 1.11/0.98 tff(write_type, type, (
% 1.11/0.98 write: ( array * $int * $int ) > array)).
% 1.11/0.98 tff(tptp_fun_V_0_type, type, (
% 1.11/0.98 tptp_fun_V_0: array)).
% 1.11/0.98 tff(1,plain,
% 1.11/0.98 (^[X: array, Y: $int, Z: $int, X1: $int] : refl((($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0)) <=> (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0)))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(2,plain,
% 1.11/0.98 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0)) <=> ![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 1.11/0.98 inference(quant_intro,[status(thm)],[1])).
% 1.11/0.98 tff(3,plain,
% 1.11/0.98 (^[X: array, Y: $int, Z: $int, X1: $int] : rewrite((($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0)) <=> (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0)))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(4,plain,
% 1.11/0.98 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0)) <=> ![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 1.11/0.98 inference(quant_intro,[status(thm)],[3])).
% 1.11/0.98 tff(5,plain,
% 1.11/0.98 (^[X: array, Y: $int, Z: $int, X1: $int] : rewrite(((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z))) <=> (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0)))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(6,plain,
% 1.11/0.98 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z))) <=> ![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0))),
% 1.11/0.98 inference(quant_intro,[status(thm)],[5])).
% 1.11/0.98 tff(7,plain,
% 1.11/0.98 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z))) <=> ![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(8,axiom,(![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT001=0.ax','ax2')).
% 1.11/0.98 tff(9,plain,
% 1.11/0.98 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[8, 7])).
% 1.11/0.98 tff(10,plain,
% 1.11/0.98 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Y, $product(-1, Z)) = 0) | ($sum(read(write(X, Y, X1), Z), $product(-1, read(X, Z))) = 0))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[9, 6])).
% 1.11/0.98 tff(11,plain,
% 1.11/0.98 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[10, 4])).
% 1.11/0.98 tff(12,plain,(
% 1.11/0.98 ![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 1.11/0.98 inference(skolemize,[status(sab)],[11])).
% 1.11/0.98 tff(13,plain,
% 1.11/0.98 (![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[12, 2])).
% 1.11/0.98 tff(14,plain,
% 1.11/0.98 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(15,plain,
% 1.11/0.98 (($false | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)) <=> ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(16,plain,
% 1.11/0.98 ((-2 = 0) <=> $false),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(17,plain,
% 1.11/0.98 ($sum(3, -5) = -2),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(18,plain,
% 1.11/0.98 ($product(-1, 5) = -5),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(19,plain,
% 1.11/0.98 ($sum(3, $product(-1, 5)) = $sum(3, -5)),
% 1.11/0.98 inference(monotonicity,[status(thm)],[18])).
% 1.11/0.98 tff(20,plain,
% 1.11/0.98 ($sum(3, $product(-1, 5)) = -2),
% 1.11/0.98 inference(transitivity,[status(thm)],[19, 17])).
% 1.11/0.98 tff(21,plain,
% 1.11/0.98 (($sum(3, $product(-1, 5)) = 0) <=> (-2 = 0)),
% 1.11/0.98 inference(monotonicity,[status(thm)],[20])).
% 1.11/0.98 tff(22,plain,
% 1.11/0.98 (($sum(3, $product(-1, 5)) = 0) <=> $false),
% 1.11/0.98 inference(transitivity,[status(thm)],[21, 16])).
% 1.11/0.98 tff(23,plain,
% 1.11/0.98 ((($sum(3, $product(-1, 5)) = 0) | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)) <=> ($false | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 1.11/0.98 inference(monotonicity,[status(thm)],[22])).
% 1.11/0.98 tff(24,plain,
% 1.11/0.98 ((($sum(3, $product(-1, 5)) = 0) | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)) <=> ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 1.11/0.98 inference(transitivity,[status(thm)],[23, 15])).
% 1.11/0.98 tff(25,plain,
% 1.11/0.98 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(3, $product(-1, 5)) = 0) | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 1.11/0.98 inference(monotonicity,[status(thm)],[24])).
% 1.11/0.98 tff(26,plain,
% 1.11/0.98 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(3, $product(-1, 5)) = 0) | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 1.11/0.98 inference(transitivity,[status(thm)],[25, 14])).
% 1.11/0.98 tff(27,plain,
% 1.11/0.98 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(3, $product(-1, 5)) = 0) | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 1.11/0.98 inference(quant_inst,[status(thm)],[])).
% 1.11/0.98 tff(28,plain,
% 1.11/0.98 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.11/0.98 tff(29,plain,
% 1.11/0.98 ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[28, 13])).
% 1.11/0.98 tff(30,plain,
% 1.11/0.98 ((~($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)) | $greatereq($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 1.11/0.98 inference(theory_lemma,[status(thm)],[])).
% 1.11/0.98 tff(31,plain,
% 1.11/0.98 ($greatereq($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[30, 29])).
% 1.11/0.98 tff(32,plain,
% 1.11/0.98 (((~(~(U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)))) & ![W: $int] : (~((~$greatereq(read(U!1, W), 40)) & (~$lesseq(read(U!1, W), 30))))) <=> ((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~((~$greatereq(read(U!1, W), 40)) & (~$lesseq(read(U!1, W), 30)))))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(33,plain,
% 1.11/0.98 ((~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$greatereq(read(U, W), 40)) & (~$lesseq(read(U, W), 30))))) <=> (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$greatereq(read(U, W), 40)) & (~$lesseq(read(U, W), 30)))))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(34,plain,
% 1.11/0.98 ((~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$lesseq(40, read(U, W))) & (~$lesseq(read(U, W), 30))))) <=> (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$greatereq(read(U, W), 40)) & (~$lesseq(read(U, W), 30)))))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(35,plain,
% 1.11/0.98 ((~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$lesseq(40, read(U, W))) & (~$lesseq(read(U, W), 30))))) <=> (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$lesseq(40, read(U, W))) & (~$lesseq(read(U, W), 30)))))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(36,plain,
% 1.11/0.98 ((~![U: array, V: array] : ((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) => ?[W: $int] : ($less(read(U, W), 40) & $less(30, read(U, W))))) <=> (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$lesseq(40, read(U, W))) & (~$lesseq(read(U, W), 30)))))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(37,axiom,(~![U: array, V: array] : ((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) => ?[W: $int] : ($less(read(U, W), 40) & $less(30, read(U, W))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 1.11/0.98 tff(38,plain,
% 1.11/0.98 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$lesseq(40, read(U, W))) & (~$lesseq(read(U, W), 30))))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.11/0.98 tff(39,plain,
% 1.11/0.98 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$lesseq(40, read(U, W))) & (~$lesseq(read(U, W), 30))))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[38, 35])).
% 1.11/0.98 tff(40,plain,
% 1.11/0.98 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$lesseq(40, read(U, W))) & (~$lesseq(read(U, W), 30))))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.11/0.98 tff(41,plain,
% 1.11/0.98 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$lesseq(40, read(U, W))) & (~$lesseq(read(U, W), 30))))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[40, 35])).
% 1.11/0.98 tff(42,plain,
% 1.11/0.98 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$greatereq(read(U, W), 40)) & (~$lesseq(read(U, W), 30))))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.11/0.98 tff(43,plain,
% 1.11/0.98 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$greatereq(read(U, W), 40)) & (~$lesseq(read(U, W), 30))))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[42, 33])).
% 1.11/0.98 tff(44,plain,
% 1.11/0.98 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : ((~$greatereq(read(U, W), 40)) & (~$lesseq(read(U, W), 30))))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[43, 33])).
% 1.11/0.98 tff(45,plain,
% 1.11/0.98 ((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~((~$greatereq(read(U!1, W), 40)) & (~$lesseq(read(U!1, W), 30))))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[44, 32])).
% 1.11/0.98 tff(46,plain,
% 1.11/0.98 (U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)),
% 1.11/0.98 inference(and_elim,[status(thm)],[45])).
% 1.11/0.98 tff(47,plain,
% 1.11/0.98 (write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44) = U!1),
% 1.11/0.98 inference(symmetry,[status(thm)],[46])).
% 1.11/0.98 tff(48,plain,
% 1.11/0.98 (read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3) = read(U!1, 3)),
% 1.11/0.98 inference(monotonicity,[status(thm)],[47])).
% 1.11/0.98 tff(49,plain,
% 1.11/0.98 ((~(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3) = read(U!1, 3))) | $greatereq($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(U!1, 3))), 0)),
% 1.11/0.98 inference(theory_lemma,[status(thm)],[])).
% 1.11/0.98 tff(50,plain,
% 1.11/0.98 ($greatereq($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(U!1, 3))), 0)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[49, 48])).
% 1.11/0.98 tff(51,assumption,($greatereq(read(U!1, 3), 40)), introduced(assumption)).
% 1.11/0.98 tff(52,plain,
% 1.11/0.98 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(53,plain,
% 1.11/0.98 (($false | ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)) <=> ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(54,plain,
% 1.11/0.98 (($sum($product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3)), read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3)) = 0) <=> ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(55,plain,
% 1.11/0.98 ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3))) = $sum($product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3)), read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(56,plain,
% 1.11/0.98 (($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3))) = 0) <=> ($sum($product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3)), read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3)) = 0)),
% 1.11/0.98 inference(monotonicity,[status(thm)],[55])).
% 1.11/0.98 tff(57,plain,
% 1.11/0.98 (($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3))) = 0) <=> ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 1.11/0.98 inference(transitivity,[status(thm)],[56, 54])).
% 1.11/0.98 tff(58,plain,
% 1.11/0.98 ((-1 = 0) <=> $false),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(59,plain,
% 1.11/0.98 ($sum(3, -4) = -1),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(60,plain,
% 1.11/0.98 ($product(-1, 4) = -4),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(61,plain,
% 1.11/0.98 ($sum(3, $product(-1, 4)) = $sum(3, -4)),
% 1.11/0.98 inference(monotonicity,[status(thm)],[60])).
% 1.11/0.98 tff(62,plain,
% 1.11/0.98 ($sum(3, $product(-1, 4)) = -1),
% 1.11/0.98 inference(transitivity,[status(thm)],[61, 59])).
% 1.11/0.98 tff(63,plain,
% 1.11/0.98 (($sum(3, $product(-1, 4)) = 0) <=> (-1 = 0)),
% 1.11/0.98 inference(monotonicity,[status(thm)],[62])).
% 1.11/0.98 tff(64,plain,
% 1.11/0.98 (($sum(3, $product(-1, 4)) = 0) <=> $false),
% 1.11/0.98 inference(transitivity,[status(thm)],[63, 58])).
% 1.11/0.98 tff(65,plain,
% 1.11/0.98 ((($sum(3, $product(-1, 4)) = 0) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3))) = 0)) <=> ($false | ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 1.11/0.98 inference(monotonicity,[status(thm)],[64, 57])).
% 1.11/0.98 tff(66,plain,
% 1.11/0.98 ((($sum(3, $product(-1, 4)) = 0) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3))) = 0)) <=> ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 1.11/0.98 inference(transitivity,[status(thm)],[65, 53])).
% 1.11/0.98 tff(67,plain,
% 1.11/0.98 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(3, $product(-1, 4)) = 0) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 1.11/0.98 inference(monotonicity,[status(thm)],[66])).
% 1.11/0.98 tff(68,plain,
% 1.11/0.98 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(3, $product(-1, 4)) = 0) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 1.11/0.98 inference(transitivity,[status(thm)],[67, 52])).
% 1.11/0.98 tff(69,plain,
% 1.11/0.98 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(3, $product(-1, 4)) = 0) | ($sum(read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3), $product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3))) = 0))),
% 1.11/0.98 inference(quant_inst,[status(thm)],[])).
% 1.11/0.98 tff(70,plain,
% 1.11/0.98 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.11/0.98 tff(71,plain,
% 1.11/0.98 ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[70, 13])).
% 1.11/0.98 tff(72,plain,
% 1.11/0.98 ((~($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)) | $lesseq($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 1.11/0.98 inference(theory_lemma,[status(thm)],[])).
% 1.11/0.98 tff(73,plain,
% 1.11/0.98 ($lesseq($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[72, 71])).
% 1.11/0.98 tff(74,plain,
% 1.11/0.98 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0)) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(75,plain,
% 1.11/0.98 (($false | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0)) <=> ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0)),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(76,plain,
% 1.11/0.98 ((($sum(3, $product(-1, 4)) = 0) | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0)) <=> ($false | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0))),
% 1.11/0.98 inference(monotonicity,[status(thm)],[64])).
% 1.11/0.98 tff(77,plain,
% 1.11/0.98 ((($sum(3, $product(-1, 4)) = 0) | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0)) <=> ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0)),
% 1.11/0.98 inference(transitivity,[status(thm)],[76, 75])).
% 1.11/0.98 tff(78,plain,
% 1.11/0.98 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(3, $product(-1, 4)) = 0) | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0))),
% 1.11/0.98 inference(monotonicity,[status(thm)],[77])).
% 1.11/0.98 tff(79,plain,
% 1.11/0.98 (((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(3, $product(-1, 4)) = 0) | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0))) <=> ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0))),
% 1.11/0.98 inference(transitivity,[status(thm)],[78, 74])).
% 1.11/0.98 tff(80,plain,
% 1.11/0.98 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | (($sum(3, $product(-1, 4)) = 0) | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0))),
% 1.11/0.98 inference(quant_inst,[status(thm)],[])).
% 1.11/0.98 tff(81,plain,
% 1.11/0.98 ((~![X: array, Y: $int, Z: $int, X1: $int] : (($sum(Z, $product(-1, Y)) = 0) | ($sum(read(X, Z), $product(-1, read(write(X, Y, X1), Z))) = 0))) | ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.11/0.98 tff(82,plain,
% 1.11/0.98 ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[81, 13])).
% 1.11/0.98 tff(83,plain,
% 1.11/0.98 ((~($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0)) | $greatereq($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))), 0)),
% 1.11/0.98 inference(theory_lemma,[status(thm)],[])).
% 1.11/0.98 tff(84,plain,
% 1.11/0.98 ($greatereq($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))), 0)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[83, 82])).
% 1.11/0.98 tff(85,plain,
% 1.11/0.98 (^[U: array, V: $int, W: $int] : refl(($sum(W, $product(-1, read(write(U, V, W), V))) = 0) <=> ($sum(W, $product(-1, read(write(U, V, W), V))) = 0))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(86,plain,
% 1.11/0.98 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0) <=> ![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 1.11/0.98 inference(quant_intro,[status(thm)],[85])).
% 1.11/0.98 tff(87,plain,
% 1.11/0.98 (^[U: array, V: $int, W: $int] : trans(monotonicity(rewrite($sum(read(write(U, V, W), V), $product(-1, W)) = $sum($product(-1, W), read(write(U, V, W), V))), (($sum(read(write(U, V, W), V), $product(-1, W)) = 0) <=> ($sum($product(-1, W), read(write(U, V, W), V)) = 0))), rewrite(($sum($product(-1, W), read(write(U, V, W), V)) = 0) <=> ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)), (($sum(read(write(U, V, W), V), $product(-1, W)) = 0) <=> ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(88,plain,
% 1.11/0.98 (![U: array, V: $int, W: $int] : ($sum(read(write(U, V, W), V), $product(-1, W)) = 0) <=> ![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 1.11/0.98 inference(quant_intro,[status(thm)],[87])).
% 1.11/0.98 tff(89,plain,
% 1.11/0.98 (^[U: array, V: $int, W: $int] : rewrite((read(write(U, V, W), V) = W) <=> ($sum(read(write(U, V, W), V), $product(-1, W)) = 0))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(90,plain,
% 1.11/0.98 (![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W) <=> ![U: array, V: $int, W: $int] : ($sum(read(write(U, V, W), V), $product(-1, W)) = 0)),
% 1.11/0.98 inference(quant_intro,[status(thm)],[89])).
% 1.11/0.98 tff(91,plain,
% 1.11/0.98 (![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W) <=> ![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(92,axiom,(![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)), file('/export/starexec/sandbox2/benchmark/Axioms/DAT001=0.ax','ax1')).
% 1.11/0.98 tff(93,plain,
% 1.11/0.98 (![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.11/0.98 tff(94,plain,
% 1.11/0.98 (![U: array, V: $int, W: $int] : ($sum(read(write(U, V, W), V), $product(-1, W)) = 0)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[93, 90])).
% 1.11/0.98 tff(95,plain,
% 1.11/0.98 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[94, 88])).
% 1.11/0.98 tff(96,plain,(
% 1.11/0.98 ![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 1.11/0.98 inference(skolemize,[status(sab)],[95])).
% 1.11/0.98 tff(97,plain,
% 1.11/0.98 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[96, 86])).
% 1.11/0.98 tff(98,plain,
% 1.11/0.98 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 33), 3) = 33)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 33), 3) = 33))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(99,plain,
% 1.11/0.98 (($sum(33, $product(-1, read(write(V!0, 3, 33), 3))) = 0) <=> (read(write(V!0, 3, 33), 3) = 33)),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(100,plain,
% 1.11/0.98 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(33, $product(-1, read(write(V!0, 3, 33), 3))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 33), 3) = 33))),
% 1.11/0.98 inference(monotonicity,[status(thm)],[99])).
% 1.11/0.98 tff(101,plain,
% 1.11/0.98 (((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(33, $product(-1, read(write(V!0, 3, 33), 3))) = 0)) <=> ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 33), 3) = 33))),
% 1.11/0.98 inference(transitivity,[status(thm)],[100, 98])).
% 1.11/0.98 tff(102,plain,
% 1.11/0.98 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | ($sum(33, $product(-1, read(write(V!0, 3, 33), 3))) = 0)),
% 1.11/0.98 inference(quant_inst,[status(thm)],[])).
% 1.11/0.98 tff(103,plain,
% 1.11/0.98 ((~![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 33), 3) = 33)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.11/0.98 tff(104,plain,
% 1.11/0.98 (read(write(V!0, 3, 33), 3) = 33),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[103, 97])).
% 1.11/0.98 tff(105,plain,
% 1.11/0.98 ((~(read(write(V!0, 3, 33), 3) = 33)) | $lesseq(read(write(V!0, 3, 33), 3), 33)),
% 1.11/0.98 inference(theory_lemma,[status(thm)],[])).
% 1.11/0.98 tff(106,plain,
% 1.11/0.98 ($lesseq(read(write(V!0, 3, 33), 3), 33)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[105, 104])).
% 1.11/0.98 tff(107,plain,
% 1.11/0.98 ($false),
% 1.11/0.98 inference(theory_lemma,[status(thm)],[106, 84, 73, 51, 50, 31])).
% 1.11/0.98 tff(108,plain,(~$greatereq(read(U!1, 3), 40)), inference(lemma,lemma(discharge,[]))).
% 1.11/0.98 tff(109,plain,
% 1.11/0.98 (^[W: $int] : refl(($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30)) <=> ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30)))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(110,plain,
% 1.11/0.98 (![W: $int] : ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30)) <=> ![W: $int] : ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30))),
% 1.11/0.98 inference(quant_intro,[status(thm)],[109])).
% 1.11/0.98 tff(111,plain,
% 1.11/0.98 (^[W: $int] : trans(monotonicity(rewrite(((~$greatereq(read(U!1, W), 40)) & (~$lesseq(read(U!1, W), 30))) <=> (~($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30)))), ((~((~$greatereq(read(U!1, W), 40)) & (~$lesseq(read(U!1, W), 30)))) <=> (~(~($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30)))))), rewrite((~(~($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30)))) <=> ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30))), ((~((~$greatereq(read(U!1, W), 40)) & (~$lesseq(read(U!1, W), 30)))) <=> ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30))))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(112,plain,
% 1.11/0.98 (![W: $int] : (~((~$greatereq(read(U!1, W), 40)) & (~$lesseq(read(U!1, W), 30)))) <=> ![W: $int] : ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30))),
% 1.11/0.98 inference(quant_intro,[status(thm)],[111])).
% 1.11/0.98 tff(113,plain,
% 1.11/0.98 (![W: $int] : (~((~$greatereq(read(U!1, W), 40)) & (~$lesseq(read(U!1, W), 30))))),
% 1.11/0.98 inference(and_elim,[status(thm)],[45])).
% 1.11/0.98 tff(114,plain,
% 1.11/0.98 (![W: $int] : ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.11/0.98 tff(115,plain,
% 1.11/0.98 (![W: $int] : ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[114, 110])).
% 1.11/0.98 tff(116,plain,
% 1.11/0.98 (((~![W: $int] : ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30))) | ($greatereq(read(U!1, 3), 40) | $lesseq(read(U!1, 3), 30))) <=> ((~![W: $int] : ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30))) | $greatereq(read(U!1, 3), 40) | $lesseq(read(U!1, 3), 30))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(117,plain,
% 1.11/0.98 ((~![W: $int] : ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30))) | ($greatereq(read(U!1, 3), 40) | $lesseq(read(U!1, 3), 30))),
% 1.11/0.98 inference(quant_inst,[status(thm)],[])).
% 1.11/0.98 tff(118,plain,
% 1.11/0.98 ((~![W: $int] : ($greatereq(read(U!1, W), 40) | $lesseq(read(U!1, W), 30))) | $greatereq(read(U!1, 3), 40) | $lesseq(read(U!1, 3), 30)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.11/0.98 tff(119,plain,
% 1.11/0.98 ($greatereq(read(U!1, 3), 40) | $lesseq(read(U!1, 3), 30)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[118, 115])).
% 1.11/0.98 tff(120,plain,
% 1.11/0.98 ($lesseq(read(U!1, 3), 30)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[119, 108])).
% 1.11/0.98 tff(121,plain,
% 1.11/0.98 ((~($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0)) | $lesseq($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))), 0)),
% 1.11/0.99 inference(theory_lemma,[status(thm)],[])).
% 1.11/0.99 tff(122,plain,
% 1.11/0.99 ($lesseq($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))), 0)),
% 1.11/0.99 inference(unit_resolution,[status(thm)],[121, 82])).
% 1.11/0.99 tff(123,plain,
% 1.11/0.99 ((~(read(write(V!0, 3, 33), 3) = 33)) | $greatereq(read(write(V!0, 3, 33), 3), 33)),
% 1.11/0.99 inference(theory_lemma,[status(thm)],[])).
% 1.11/0.99 tff(124,plain,
% 1.11/0.99 ($greatereq(read(write(V!0, 3, 33), 3), 33)),
% 1.11/0.99 inference(unit_resolution,[status(thm)],[123, 104])).
% 1.11/0.99 tff(125,plain,
% 1.11/0.99 ((~($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)) | $lesseq($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 1.11/0.99 inference(theory_lemma,[status(thm)],[])).
% 1.11/0.99 tff(126,plain,
% 1.11/0.99 ($lesseq($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 1.11/0.99 inference(unit_resolution,[status(thm)],[125, 29])).
% 1.11/0.99 tff(127,plain,
% 1.11/0.99 ((~($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)) | $greatereq($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 1.11/0.99 inference(theory_lemma,[status(thm)],[])).
% 1.11/0.99 tff(128,plain,
% 1.11/0.99 ($greatereq($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 1.11/0.99 inference(unit_resolution,[status(thm)],[127, 71])).
% 1.11/0.99 tff(129,plain,
% 1.11/0.99 ((~(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3) = read(U!1, 3))) | $lesseq($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(U!1, 3))), 0)),
% 1.11/0.99 inference(theory_lemma,[status(thm)],[])).
% 1.11/0.99 tff(130,plain,
% 1.11/0.99 ($lesseq($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(U!1, 3))), 0)),
% 1.11/0.99 inference(unit_resolution,[status(thm)],[129, 48])).
% 1.11/0.99 tff(131,plain,
% 1.11/0.99 ($false),
% 1.11/0.99 inference(theory_lemma,[status(thm)],[130, 128, 126, 124, 122, 120])).
% 1.11/0.99 % SZS output end Proof
%------------------------------------------------------------------------------