TSTP Solution File: DAT006_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT006_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 14:36:20 EDT 2022
% Result : Theorem 0.19s 0.56s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT006_1 : TPTP v8.1.0. Released v5.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.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 : Wed Aug 31 01:04:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.56 % SZS status Theorem
% 0.19/0.56 % SZS output start Proof
% 0.19/0.56 tff(read_type, type, (
% 0.19/0.56 read: ( array * $int ) > $int)).
% 0.19/0.56 tff(tptp_fun_U_1_type, type, (
% 0.19/0.56 tptp_fun_U_1: array)).
% 0.19/0.56 tff(write_type, type, (
% 0.19/0.56 write: ( array * $int * $int ) > array)).
% 0.19/0.56 tff(tptp_fun_V_0_type, type, (
% 0.19/0.56 tptp_fun_V_0: array)).
% 0.19/0.56 tff(1,plain,
% 0.19/0.56 (^[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))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(2,plain,
% 0.19/0.56 (![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)),
% 0.19/0.56 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.56 tff(3,plain,
% 0.19/0.56 (^[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)))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(4,plain,
% 0.19/0.56 (![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)),
% 0.19/0.56 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.56 tff(5,plain,
% 0.19/0.56 (^[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))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(6,plain,
% 0.19/0.56 (![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)),
% 0.19/0.56 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.56 tff(7,plain,
% 0.19/0.56 (![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)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(8,axiom,(![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)), file('/export/starexec/sandbox/benchmark/Axioms/DAT001=0.ax','ax1')).
% 0.19/0.56 tff(9,plain,
% 0.19/0.56 (![U: array, V: $int, W: $int] : (read(write(U, V, W), V) = W)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.56 tff(10,plain,
% 0.19/0.56 (![U: array, V: $int, W: $int] : ($sum(read(write(U, V, W), V), $product(-1, W)) = 0)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.19/0.56 tff(11,plain,
% 0.19/0.56 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.19/0.56 tff(12,plain,(
% 0.19/0.56 ![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.19/0.56 inference(skolemize,[status(sab)],[11])).
% 0.19/0.56 tff(13,plain,
% 0.19/0.56 (![U: array, V: $int, W: $int] : ($sum(W, $product(-1, read(write(U, V, W), V))) = 0)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.56 tff(14,plain,
% 0.19/0.56 (((~![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, $product(-1, read(write(U, V, W), V))) = 0)) | (read(write(V!0, 3, 33), 3) = 33))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(15,plain,
% 0.19/0.56 (($sum(33, $product(-1, read(write(V!0, 3, 33), 3))) = 0) <=> (read(write(V!0, 3, 33), 3) = 33)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(16,plain,
% 0.19/0.56 (((~![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))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.56 tff(17,plain,
% 0.19/0.56 (((~![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))),
% 0.19/0.56 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.56 tff(18,plain,
% 0.19/0.56 ((~![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)),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(19,plain,
% 0.19/0.56 ((~![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)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.56 tff(20,plain,
% 0.19/0.56 (read(write(V!0, 3, 33), 3) = 33),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.19/0.56 tff(21,plain,
% 0.19/0.56 (^[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)))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(22,plain,
% 0.19/0.56 (![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))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.56 tff(23,plain,
% 0.19/0.56 (^[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)))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(24,plain,
% 0.19/0.56 (![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))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.56 tff(25,plain,
% 0.19/0.56 (^[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)))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(26,plain,
% 0.19/0.56 (![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))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.56 tff(27,plain,
% 0.19/0.56 (![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)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(28,axiom,(![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/DAT001=0.ax','ax2')).
% 0.19/0.56 tff(29,plain,
% 0.19/0.56 (![X: array, Y: $int, Z: $int, X1: $int] : ((Y = Z) | (read(write(X, Y, X1), Z) = read(X, Z)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.56 tff(30,plain,
% 0.19/0.56 (![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))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.19/0.56 tff(31,plain,
% 0.19/0.56 (![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))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.19/0.56 tff(32,plain,(
% 0.19/0.56 ![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))),
% 0.19/0.56 inference(skolemize,[status(sab)],[31])).
% 0.19/0.56 tff(33,plain,
% 0.19/0.56 (![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))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.19/0.56 tff(34,plain,
% 0.19/0.56 (((~![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), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(35,plain,
% 0.19/0.56 (($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)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(36,plain,
% 0.19/0.56 ((-1 = 0) <=> $false),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(37,plain,
% 0.19/0.56 ($sum(3, -4) = -1),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(38,plain,
% 0.19/0.56 ($product(-1, 4) = -4),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(39,plain,
% 0.19/0.56 ($sum(3, $product(-1, 4)) = $sum(3, -4)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.56 tff(40,plain,
% 0.19/0.56 ($sum(3, $product(-1, 4)) = -1),
% 0.19/0.56 inference(transitivity,[status(thm)],[39, 37])).
% 0.19/0.56 tff(41,plain,
% 0.19/0.56 (($sum(3, $product(-1, 4)) = 0) <=> (-1 = 0)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.56 tff(42,plain,
% 0.19/0.56 (($sum(3, $product(-1, 4)) = 0) <=> $false),
% 0.19/0.56 inference(transitivity,[status(thm)],[41, 36])).
% 0.19/0.56 tff(43,plain,
% 0.19/0.56 ((($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), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.56 tff(44,plain,
% 0.19/0.56 ((($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)),
% 0.19/0.56 inference(transitivity,[status(thm)],[43, 35])).
% 0.19/0.56 tff(45,plain,
% 0.19/0.56 (((~![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))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.56 tff(46,plain,
% 0.19/0.56 (((~![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))),
% 0.19/0.56 inference(transitivity,[status(thm)],[45, 34])).
% 0.19/0.56 tff(47,plain,
% 0.19/0.56 ((~![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))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(48,plain,
% 0.19/0.56 ((~![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), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.56 tff(49,plain,
% 0.19/0.56 ($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))) = 0),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[48, 33])).
% 0.19/0.56 tff(50,plain,
% 0.19/0.56 ((~($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), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))), 0)),
% 0.19/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.56 tff(51,plain,
% 0.19/0.56 ($lesseq($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))), 0)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.56 tff(52,plain,
% 0.19/0.56 ((~($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), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))), 0)),
% 0.19/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.56 tff(53,plain,
% 0.19/0.56 ($greatereq($sum(read(write(V!0, 3, 33), 3), $product(-1, read(write(write(V!0, 3, 33), 4, 444), 3))), 0)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.19/0.56 tff(54,plain,
% 0.19/0.56 (read(write(V!0, 3, 33), 3) = read(write(write(V!0, 3, 33), 4, 444), 3)),
% 0.19/0.56 inference(theory_lemma,[status(thm)],[53, 51])).
% 0.19/0.56 tff(55,plain,
% 0.19/0.56 (read(write(write(V!0, 3, 33), 4, 444), 3) = read(write(V!0, 3, 33), 3)),
% 0.19/0.56 inference(symmetry,[status(thm)],[54])).
% 0.19/0.56 tff(56,plain,
% 0.19/0.56 (((~![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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(57,plain,
% 0.19/0.56 (($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)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(58,plain,
% 0.19/0.56 ((-2 = 0) <=> $false),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(59,plain,
% 0.19/0.56 ($sum(3, -5) = -2),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(60,plain,
% 0.19/0.56 ($product(-1, 5) = -5),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(61,plain,
% 0.19/0.56 ($sum(3, $product(-1, 5)) = $sum(3, -5)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.56 tff(62,plain,
% 0.19/0.56 ($sum(3, $product(-1, 5)) = -2),
% 0.19/0.56 inference(transitivity,[status(thm)],[61, 59])).
% 0.19/0.56 tff(63,plain,
% 0.19/0.56 (($sum(3, $product(-1, 5)) = 0) <=> (-2 = 0)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.56 tff(64,plain,
% 0.19/0.56 (($sum(3, $product(-1, 5)) = 0) <=> $false),
% 0.19/0.56 inference(transitivity,[status(thm)],[63, 58])).
% 0.19/0.56 tff(65,plain,
% 0.19/0.56 ((($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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[64])).
% 0.19/0.56 tff(66,plain,
% 0.19/0.56 ((($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)),
% 0.19/0.56 inference(transitivity,[status(thm)],[65, 57])).
% 0.19/0.56 tff(67,plain,
% 0.19/0.56 (((~![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))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.56 tff(68,plain,
% 0.19/0.56 (((~![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))),
% 0.19/0.56 inference(transitivity,[status(thm)],[67, 56])).
% 0.19/0.56 tff(69,plain,
% 0.19/0.56 ((~![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))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(70,plain,
% 0.19/0.56 ((~![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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.56 tff(71,plain,
% 0.19/0.56 ($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[70, 33])).
% 0.19/0.56 tff(72,plain,
% 0.19/0.56 ((~($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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 0.19/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.56 tff(73,plain,
% 0.19/0.56 ($lesseq($sum(read(write(write(V!0, 3, 33), 4, 444), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.56 tff(74,plain,
% 0.19/0.56 ((~($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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 0.19/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.56 tff(75,plain,
% 0.19/0.56 ($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)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.19/0.56 tff(76,plain,
% 0.19/0.56 (read(write(write(V!0, 3, 33), 4, 444), 3) = read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3)),
% 0.19/0.56 inference(theory_lemma,[status(thm)],[75, 73])).
% 0.19/0.56 tff(77,plain,
% 0.19/0.56 (read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3) = read(write(write(V!0, 3, 33), 4, 444), 3)),
% 0.19/0.56 inference(symmetry,[status(thm)],[76])).
% 0.19/0.56 tff(78,plain,
% 0.19/0.56 (((~![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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(79,plain,
% 0.19/0.56 (($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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(80,plain,
% 0.19/0.56 (($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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(81,plain,
% 0.19/0.56 ($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))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(82,plain,
% 0.19/0.56 (($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($product(-1, read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3)), read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3)) = 0)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.56 tff(83,plain,
% 0.19/0.56 (($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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 0.19/0.56 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.56 tff(84,plain,
% 0.19/0.56 ((($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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[42, 83])).
% 0.19/0.56 tff(85,plain,
% 0.19/0.56 ((($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)),
% 0.19/0.56 inference(transitivity,[status(thm)],[84, 79])).
% 0.19/0.56 tff(86,plain,
% 0.19/0.56 (((~![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))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.56 tff(87,plain,
% 0.19/0.56 (((~![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))),
% 0.19/0.56 inference(transitivity,[status(thm)],[86, 78])).
% 0.19/0.56 tff(88,plain,
% 0.19/0.56 ((~![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))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(89,plain,
% 0.19/0.56 ((~![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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.56 tff(90,plain,
% 0.19/0.56 ($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))) = 0),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[89, 33])).
% 0.19/0.56 tff(91,plain,
% 0.19/0.56 ((~($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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 0.19/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.56 tff(92,plain,
% 0.19/0.56 ($lesseq($sum(read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.56 tff(93,plain,
% 0.19/0.56 ((~($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), $product(-1, read(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 3))), 0)),
% 0.19/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.56 tff(94,plain,
% 0.19/0.56 ($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)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[93, 90])).
% 0.19/0.56 tff(95,plain,
% 0.19/0.56 (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)),
% 0.19/0.56 inference(theory_lemma,[status(thm)],[94, 92])).
% 0.19/0.56 tff(96,plain,
% 0.19/0.56 (((~(~(U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)))) & ![W: $int] : (~(read(U!1, W) = 33))) <=> ((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~(read(U!1, W) = 33)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(97,plain,
% 0.19/0.56 ((~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : (read(U, W) = 33))) <=> (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : (read(U, W) = 33)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(98,plain,
% 0.19/0.56 ((~![U: array, V: array] : ((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) => ?[W: $int] : (read(U, W) = 33))) <=> (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : (read(U, W) = 33)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(99,axiom,(~![U: array, V: array] : ((U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44)) => ?[W: $int] : (read(U, W) = 33))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.19/0.56 tff(100,plain,
% 0.19/0.56 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : (read(U, W) = 33))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.56 tff(101,plain,
% 0.19/0.56 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : (read(U, W) = 33))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[100, 97])).
% 0.19/0.56 tff(102,plain,
% 0.19/0.56 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : (read(U, W) = 33))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.56 tff(103,plain,
% 0.19/0.56 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : (read(U, W) = 33))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[102, 97])).
% 0.19/0.56 tff(104,plain,
% 0.19/0.56 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : (read(U, W) = 33))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[103, 97])).
% 0.19/0.56 tff(105,plain,
% 0.19/0.56 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : (read(U, W) = 33))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.19/0.56 tff(106,plain,
% 0.19/0.56 (~![U: array, V: array] : ((~(U = write(write(write(write(V, 3, 33), 4, 444), 5, 55), 4, 44))) | ?[W: $int] : (read(U, W) = 33))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[105, 97])).
% 0.19/0.56 tff(107,plain,
% 0.19/0.56 ((U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)) & ![W: $int] : (~(read(U!1, W) = 33))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.19/0.56 tff(108,plain,
% 0.19/0.56 (U!1 = write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44)),
% 0.19/0.56 inference(and_elim,[status(thm)],[107])).
% 0.19/0.56 tff(109,plain,
% 0.19/0.56 (read(U!1, 3) = read(write(write(write(write(V!0, 3, 33), 4, 444), 5, 55), 4, 44), 3)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.56 tff(110,plain,
% 0.19/0.56 (read(U!1, 3) = 33),
% 0.19/0.56 inference(transitivity,[status(thm)],[109, 95, 77, 55, 20])).
% 0.19/0.56 tff(111,plain,
% 0.19/0.56 (^[W: $int] : refl((~(read(U!1, W) = 33)) <=> (~(read(U!1, W) = 33)))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(112,plain,
% 0.19/0.56 (![W: $int] : (~(read(U!1, W) = 33)) <=> ![W: $int] : (~(read(U!1, W) = 33))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.56 tff(113,plain,
% 0.19/0.56 (![W: $int] : (~(read(U!1, W) = 33))),
% 0.19/0.56 inference(and_elim,[status(thm)],[107])).
% 0.19/0.56 tff(114,plain,
% 0.19/0.56 (![W: $int] : (~(read(U!1, W) = 33))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.56 tff(115,plain,
% 0.19/0.56 ((~![W: $int] : (~(read(U!1, W) = 33))) | (~(read(U!1, 3) = 33))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(116,plain,
% 0.19/0.56 (~(read(U!1, 3) = 33)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.19/0.56 tff(117,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[116, 110])).
% 0.19/0.56 % SZS output end Proof
%------------------------------------------------------------------------------