TSTP Solution File: ARI615_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI615_1 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 17:02:17 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ARI615_1 : TPTP v8.1.0. Released v5.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 00:51:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(tptp_fun_X_3_type, type, (
% 0.12/0.38 tptp_fun_X_3: $int)).
% 0.12/0.38 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.38 tptp_fun_Y_2: $int)).
% 0.12/0.38 tff(tptp_fun_Z_1_type, type, (
% 0.12/0.38 tptp_fun_Z_1: $int)).
% 0.12/0.38 tff(p_type, type, (
% 0.12/0.38 p: ( $int * $int * $int ) > $o)).
% 0.12/0.38 tff(tptp_fun_W_0_type, type, (
% 0.12/0.38 tptp_fun_W_0: $int)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X: $int, Y: $int, Z: $int] : refl(((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z)) <=> ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z)) <=> ![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[X: $int, Y: $int, Z: $int] : rewrite((($greatereq($sum(X, $sum($product(-1, Y), Z)), 0) & $lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)) <=> p(X, Y, Z)) <=> ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![X: $int, Y: $int, Z: $int] : (($greatereq($sum(X, $sum($product(-1, Y), Z)), 0) & $lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)) <=> p(X, Y, Z)) <=> ![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (^[X: $int, Y: $int, Z: $int] : rewrite((($lesseq($sum(Y, $sum($product(-1, Z), $product(-1, X))), 0) & $lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)) <=> p(X, Y, Z)) <=> (($greatereq($sum(X, $sum($product(-1, Y), Z)), 0) & $lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)) <=> p(X, Y, Z)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $sum($product(-1, Z), $product(-1, X))), 0) & $lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)) <=> p(X, Y, Z)) <=> ![X: $int, Y: $int, Z: $int] : (($greatereq($sum(X, $sum($product(-1, Y), Z)), 0) & $lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)) <=> p(X, Y, Z))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (^[X: $int, Y: $int, Z: $int] : rewrite((($lesseq($sum(Y, $product(-1, Z)), X) & $lesseq(X, $sum(Y, Z))) <=> p(X, Y, Z)) <=> (($lesseq($sum(Y, $sum($product(-1, Z), $product(-1, X))), 0) & $lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)) <=> p(X, Y, Z)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $product(-1, Z)), X) & $lesseq(X, $sum(Y, Z))) <=> p(X, Y, Z)) <=> ![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $sum($product(-1, Z), $product(-1, X))), 0) & $lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)) <=> p(X, Y, Z))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $product(-1, Z)), X) & $lesseq(X, $sum(Y, Z))) <=> p(X, Y, Z)) <=> ![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $product(-1, Z)), X) & $lesseq(X, $sum(Y, Z))) <=> p(X, Y, Z))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ((~(![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $uminus(Z)), X) & $lesseq(X, $sum(Y, Z))) <=> p(X, Y, Z)) => ![X: $int, Y: $int, Z: $int, W: $int] : ($lesseq(Z, W) => (p(X, Y, Z) => p(X, Y, W))))) <=> (~((~![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $product(-1, Z)), X) & $lesseq(X, $sum(Y, Z))) <=> p(X, Y, Z))) | ![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq(Z, W)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(11,axiom,(~(![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $uminus(Z)), X) & $lesseq(X, $sum(Y, Z))) <=> p(X, Y, Z)) => ![X: $int, Y: $int, Z: $int, W: $int] : ($lesseq(Z, W) => (p(X, Y, Z) => p(X, Y, W))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','interv_with_smaller_radius_contained')).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~((~![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $product(-1, Z)), X) & $lesseq(X, $sum(Y, Z))) <=> p(X, Y, Z))) | ![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq(Z, W))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $product(-1, Z)), X) & $lesseq(X, $sum(Y, Z))) <=> p(X, Y, Z))),
% 0.12/0.39 inference(or_elim,[status(thm)],[12])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $product(-1, Z)), X) & $lesseq(X, $sum(Y, Z))) <=> p(X, Y, Z))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![X: $int, Y: $int, Z: $int] : (($lesseq($sum(Y, $sum($product(-1, Z), $product(-1, X))), 0) & $lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)) <=> p(X, Y, Z))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![X: $int, Y: $int, Z: $int] : (($greatereq($sum(X, $sum($product(-1, Y), Z)), 0) & $lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)) <=> p(X, Y, Z))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 6])).
% 0.12/0.39 tff(17,plain,(
% 0.12/0.39 ![X: $int, Y: $int, Z: $int] : (($greatereq($sum(X, $sum($product(-1, Y), Z)), 0) & $lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)) <=> p(X, Y, Z))),
% 0.12/0.39 inference(skolemize,[status(sab)],[16])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[17, 4])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, Z!1))) <=> ((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, Z!1)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (((~((~$greatereq($sum(X!3, $sum($product(-1, Y!2), Z!1)), 0)) | (~$lesseq($sum(X!3, $sum($product(-1, Y!2), $product(-1, Z!1))), 0)))) <=> p(X!3, Y!2, Z!1)) <=> ((~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, Z!1))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(X!3, $sum($product(-1, Y!2), Z!1)), 0)) | (~$lesseq($sum(X!3, $sum($product(-1, Y!2), $product(-1, Z!1))), 0)))) <=> p(X!3, Y!2, Z!1))) <=> ((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, Z!1)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[21])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(X!3, $sum($product(-1, Y!2), Z!1)), 0)) | (~$lesseq($sum(X!3, $sum($product(-1, Y!2), $product(-1, Z!1))), 0)))) <=> p(X!3, Y!2, Z!1))) <=> ((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, Z!1)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[22, 20])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 ((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(X!3, $sum($product(-1, Y!2), Z!1)), 0)) | (~$lesseq($sum(X!3, $sum($product(-1, Y!2), $product(-1, Z!1))), 0)))) <=> p(X!3, Y!2, Z!1))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 ((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, Z!1))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 ((~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, Z!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 ((~(p(X!3, Y!2, W!0) | (~p(X!3, Y!2, Z!1)) | (~$lesseq($sum(Z!1, $product(-1, W!0)), 0)))) <=> (~(p(X!3, Y!2, W!0) | (~p(X!3, Y!2, Z!1)) | (~$greatereq($sum(W!0, $product(-1, Z!1)), 0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 ((~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq($sum(Z, $product(-1, W)), 0)))) <=> (~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq($sum(Z, $product(-1, W)), 0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 ((~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq(Z, W)))) <=> (~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq($sum(Z, $product(-1, W)), 0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 ((~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq(Z, W)))) <=> (~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq(Z, W))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq(Z, W)))),
% 0.12/0.39 inference(or_elim,[status(thm)],[12])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq(Z, W)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq(Z, W)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[32, 30])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq(Z, W)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq($sum(Z, $product(-1, W)), 0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq($sum(Z, $product(-1, W)), 0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (~![X: $int, Y: $int, Z: $int, W: $int] : (p(X, Y, W) | (~p(X, Y, Z)) | (~$lesseq($sum(Z, $product(-1, W)), 0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[36, 28])).
% 0.12/0.39 tff(38,plain,(
% 0.12/0.39 ~(p(X!3, Y!2, W!0) | (~p(X!3, Y!2, Z!1)) | (~$lesseq($sum(Z!1, $product(-1, W!0)), 0)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[37])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (~(p(X!3, Y!2, W!0) | (~p(X!3, Y!2, Z!1)) | (~$greatereq($sum(W!0, $product(-1, Z!1)), 0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[38, 27])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (p(X!3, Y!2, Z!1)),
% 0.12/0.39 inference(or_elim,[status(thm)],[39])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 ((~((~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, Z!1))) | (~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)))) | (~p(X!3, Y!2, Z!1))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 ((~((~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, Z!1))) | (~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (~((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[42, 26])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0))) | $greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 ($greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (((~$greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(Z!1, $sum(Y!2, $product(-1, X!3))), 0))) | $greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 ($greatereq($sum(Z!1, $sum($product(-1, Y!2), X!3)), 0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.12/0.39 tff(48,assumption,(~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)), introduced(assumption)).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 ($greatereq($sum(W!0, $product(-1, Z!1)), 0)),
% 0.12/0.39 inference(or_elim,[status(thm)],[39])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(theory_lemma,[status(thm)],[49, 48, 47])).
% 0.12/0.39 tff(51,plain,($greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, W!0))) <=> ((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, W!0)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (((~((~$greatereq($sum(X!3, $sum($product(-1, Y!2), W!0)), 0)) | (~$lesseq($sum(X!3, $sum($product(-1, Y!2), $product(-1, W!0))), 0)))) <=> p(X!3, Y!2, W!0)) <=> ((~((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, W!0))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(X!3, $sum($product(-1, Y!2), W!0)), 0)) | (~$lesseq($sum(X!3, $sum($product(-1, Y!2), $product(-1, W!0))), 0)))) <=> p(X!3, Y!2, W!0))) <=> ((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, W!0)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(X!3, $sum($product(-1, Y!2), W!0)), 0)) | (~$lesseq($sum(X!3, $sum($product(-1, Y!2), $product(-1, W!0))), 0)))) <=> p(X!3, Y!2, W!0))) <=> ((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, W!0)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[54, 52])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 ((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(X!3, $sum($product(-1, Y!2), W!0)), 0)) | (~$lesseq($sum(X!3, $sum($product(-1, Y!2), $product(-1, W!0))), 0)))) <=> p(X!3, Y!2, W!0))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 ((~![X: $int, Y: $int, Z: $int] : ((~((~$greatereq($sum(X, $sum($product(-1, Y), Z)), 0)) | (~$lesseq($sum(X, $sum($product(-1, Y), $product(-1, Z))), 0)))) <=> p(X, Y, Z))) | ((~((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, W!0))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 ((~((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, W!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[57, 19])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (~p(X!3, Y!2, W!0)),
% 0.12/0.39 inference(or_elim,[status(thm)],[39])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 ((~((~((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, W!0))) | ((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0))) | p(X!3, Y!2, W!0)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 ((~((~((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)))) <=> p(X!3, Y!2, W!0))) | ((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 ((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)))) | (~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 ((~$greatereq($sum(W!0, $sum($product(-1, Y!2), X!3)), 0)) | (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (~$greatereq($sum(W!0, $sum(Y!2, $product(-1, X!3))), 0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[64, 51])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(theory_lemma,[status(thm)],[49, 65, 45])).
% 0.12/0.39 % SZS output end Proof
%------------------------------------------------------------------------------