TSTP Solution File: ARI618_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI618_1 : TPTP v8.1.0. Released v5.1.0.
% 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 : Tue Sep 6 17:02:18 EDT 2022
% Result : Theorem 0.22s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ARI618_1 : TPTP v8.1.0. Released v5.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 01:05:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.22/0.39 % SZS status Theorem
% 0.22/0.39 % SZS output start Proof
% 0.22/0.39 tff(f_type, type, (
% 0.22/0.39 f: $int > $int)).
% 0.22/0.39 tff(tptp_fun_X_0_type, type, (
% 0.22/0.39 tptp_fun_X_0: $int)).
% 0.22/0.39 tff(1,plain,
% 0.22/0.39 (^[X: $int] : refl((~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0))))) <=> (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0))))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(2,plain,
% 0.22/0.39 (![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0))))) <=> ![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.39 tff(3,plain,
% 0.22/0.39 (^[X: $int] : trans(monotonicity(rewrite(($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)) <=> ($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0))), (($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0))) <=> ($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0))))), rewrite(($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0))) <=> (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))), (($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0))) <=> (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(4,plain,
% 0.22/0.39 (![X: $int] : ($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0))) <=> ![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.39 tff(5,plain,
% 0.22/0.39 (^[X: $int] : rewrite(($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($lesseq($sum(f(X), $product(-1, X)), 0) | $lesseq($sum(f(X), X), 0))) <=> ($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(6,plain,
% 0.22/0.39 (![X: $int] : ($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($lesseq($sum(f(X), $product(-1, X)), 0) | $lesseq($sum(f(X), X), 0))) <=> ![X: $int] : ($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.22/0.39 tff(7,plain,
% 0.22/0.39 (^[X: $int] : rewrite(($lesseq(X, f(X)) & $lesseq($product(-1, X), f(X)) & ($lesseq(f(X), X) | $lesseq(f(X), $product(-1, X)))) <=> ($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($lesseq($sum(f(X), $product(-1, X)), 0) | $lesseq($sum(f(X), X), 0))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(8,plain,
% 0.22/0.39 (![X: $int] : ($lesseq(X, f(X)) & $lesseq($product(-1, X), f(X)) & ($lesseq(f(X), X) | $lesseq(f(X), $product(-1, X)))) <=> ![X: $int] : ($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($lesseq($sum(f(X), $product(-1, X)), 0) | $lesseq($sum(f(X), X), 0)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[7])).
% 0.22/0.39 tff(9,plain,
% 0.22/0.39 (![X: $int] : ($lesseq(X, f(X)) & $lesseq($product(-1, X), f(X)) & ($lesseq(f(X), X) | $lesseq(f(X), $product(-1, X)))) <=> ![X: $int] : ($lesseq(X, f(X)) & $lesseq($product(-1, X), f(X)) & ($lesseq(f(X), X) | $lesseq(f(X), $product(-1, X))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(10,plain,
% 0.22/0.40 ((~(![X: $int] : (($lesseq(X, f(X)) & $lesseq($uminus(X), f(X))) & ($lesseq(f(X), X) | $lesseq(f(X), $uminus(X)))) => ![X: $int] : (f(f(X)) = f(X)))) <=> (~((~![X: $int] : ($lesseq(X, f(X)) & $lesseq($product(-1, X), f(X)) & ($lesseq(f(X), X) | $lesseq(f(X), $product(-1, X))))) | ![X: $int] : (f(f(X)) = f(X))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(11,axiom,(~(![X: $int] : (($lesseq(X, f(X)) & $lesseq($uminus(X), f(X))) & ($lesseq(f(X), X) | $lesseq(f(X), $uminus(X)))) => ![X: $int] : (f(f(X)) = f(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','absolute_value_idempotent')).
% 0.22/0.40 tff(12,plain,
% 0.22/0.40 (~((~![X: $int] : ($lesseq(X, f(X)) & $lesseq($product(-1, X), f(X)) & ($lesseq(f(X), X) | $lesseq(f(X), $product(-1, X))))) | ![X: $int] : (f(f(X)) = f(X)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.22/0.40 tff(13,plain,
% 0.22/0.40 (![X: $int] : ($lesseq(X, f(X)) & $lesseq($product(-1, X), f(X)) & ($lesseq(f(X), X) | $lesseq(f(X), $product(-1, X))))),
% 0.22/0.40 inference(or_elim,[status(thm)],[12])).
% 0.22/0.40 tff(14,plain,
% 0.22/0.40 (![X: $int] : ($lesseq(X, f(X)) & $lesseq($product(-1, X), f(X)) & ($lesseq(f(X), X) | $lesseq(f(X), $product(-1, X))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.22/0.40 tff(15,plain,
% 0.22/0.40 (![X: $int] : ($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($lesseq($sum(f(X), $product(-1, X)), 0) | $lesseq($sum(f(X), X), 0)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.22/0.40 tff(16,plain,
% 0.22/0.40 (![X: $int] : ($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[15, 6])).
% 0.22/0.40 tff(17,plain,(
% 0.22/0.40 ![X: $int] : ($lesseq($sum(X, $product(-1, f(X))), 0) & $greatereq($sum(X, f(X)), 0) & ($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))),
% 0.22/0.40 inference(skolemize,[status(sab)],[16])).
% 0.22/0.40 tff(18,plain,
% 0.22/0.40 (![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[17, 4])).
% 0.22/0.40 tff(19,plain,
% 0.22/0.40 (![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.22/0.40 tff(20,plain,
% 0.22/0.40 ((~![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))) | (~((~$lesseq($sum(X!0, $product(-1, f(X!0))), 0)) | (~$greatereq($sum(X!0, f(X!0)), 0)) | (~($greatereq($sum(X!0, $product(-1, f(X!0))), 0) | $lesseq($sum(X!0, f(X!0)), 0)))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(21,plain,
% 0.22/0.40 (~((~$lesseq($sum(X!0, $product(-1, f(X!0))), 0)) | (~$greatereq($sum(X!0, f(X!0)), 0)) | (~($greatereq($sum(X!0, $product(-1, f(X!0))), 0) | $lesseq($sum(X!0, f(X!0)), 0))))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.22/0.40 tff(22,plain,
% 0.22/0.40 (((~$lesseq($sum(X!0, $product(-1, f(X!0))), 0)) | (~$greatereq($sum(X!0, f(X!0)), 0)) | (~($greatereq($sum(X!0, $product(-1, f(X!0))), 0) | $lesseq($sum(X!0, f(X!0)), 0)))) | $greatereq($sum(X!0, f(X!0)), 0)),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(23,plain,
% 0.22/0.40 ($greatereq($sum(X!0, f(X!0)), 0)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.22/0.40 tff(24,plain,
% 0.22/0.40 (((~$lesseq($sum(X!0, $product(-1, f(X!0))), 0)) | (~$greatereq($sum(X!0, f(X!0)), 0)) | (~($greatereq($sum(X!0, $product(-1, f(X!0))), 0) | $lesseq($sum(X!0, f(X!0)), 0)))) | $lesseq($sum(X!0, $product(-1, f(X!0))), 0)),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(25,plain,
% 0.22/0.40 ($lesseq($sum(X!0, $product(-1, f(X!0))), 0)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.22/0.40 tff(26,plain,
% 0.22/0.40 ((~![X: $int] : ($sum(f(f(X)), $product(-1, f(X))) = 0)) <=> (~![X: $int] : ($sum(f(f(X)), $product(-1, f(X))) = 0))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(27,plain,
% 0.22/0.40 ((~![X: $int] : (f(f(X)) = f(X))) <=> (~![X: $int] : ($sum(f(f(X)), $product(-1, f(X))) = 0))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(28,plain,
% 0.22/0.40 ((~![X: $int] : (f(f(X)) = f(X))) <=> (~![X: $int] : (f(f(X)) = f(X)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(29,plain,
% 0.22/0.40 (~![X: $int] : (f(f(X)) = f(X))),
% 0.22/0.40 inference(or_elim,[status(thm)],[12])).
% 0.22/0.40 tff(30,plain,
% 0.22/0.40 (~![X: $int] : (f(f(X)) = f(X))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.22/0.40 tff(31,plain,
% 0.22/0.40 (~![X: $int] : (f(f(X)) = f(X))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[30, 28])).
% 0.22/0.40 tff(32,plain,
% 0.22/0.40 (~![X: $int] : (f(f(X)) = f(X))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.22/0.40 tff(33,plain,
% 0.22/0.40 (~![X: $int] : ($sum(f(f(X)), $product(-1, f(X))) = 0)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.22/0.40 tff(34,plain,
% 0.22/0.40 (~![X: $int] : ($sum(f(f(X)), $product(-1, f(X))) = 0)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.22/0.40 tff(35,plain,
% 0.22/0.40 (~![X: $int] : ($sum(f(f(X)), $product(-1, f(X))) = 0)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.22/0.40 tff(36,plain,(
% 0.22/0.40 ~($sum(f(f(X!0)), $product(-1, f(X!0))) = 0)),
% 0.22/0.40 inference(skolemize,[status(sab)],[35])).
% 0.22/0.40 tff(37,plain,
% 0.22/0.40 (((~![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))) | (~((~$greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)) | (~$greatereq($sum(f(f(X!0)), f(X!0)), 0)) | (~($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0)))))) <=> ((~![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))) | (~((~$greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)) | (~$greatereq($sum(f(f(X!0)), f(X!0)), 0)) | (~($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0))))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(38,plain,
% 0.22/0.40 ((~((~$lesseq($sum(f(X!0), $product(-1, f(f(X!0)))), 0)) | (~$greatereq($sum(f(X!0), f(f(X!0))), 0)) | (~($greatereq($sum(f(X!0), $product(-1, f(f(X!0)))), 0) | $lesseq($sum(f(X!0), f(f(X!0))), 0))))) <=> (~((~$greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)) | (~$greatereq($sum(f(f(X!0)), f(X!0)), 0)) | (~($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0)))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(39,plain,
% 0.22/0.40 (((~![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))) | (~((~$lesseq($sum(f(X!0), $product(-1, f(f(X!0)))), 0)) | (~$greatereq($sum(f(X!0), f(f(X!0))), 0)) | (~($greatereq($sum(f(X!0), $product(-1, f(f(X!0)))), 0) | $lesseq($sum(f(X!0), f(f(X!0))), 0)))))) <=> ((~![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))) | (~((~$greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)) | (~$greatereq($sum(f(f(X!0)), f(X!0)), 0)) | (~($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0))))))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.22/0.40 tff(40,plain,
% 0.22/0.40 (((~![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))) | (~((~$lesseq($sum(f(X!0), $product(-1, f(f(X!0)))), 0)) | (~$greatereq($sum(f(X!0), f(f(X!0))), 0)) | (~($greatereq($sum(f(X!0), $product(-1, f(f(X!0)))), 0) | $lesseq($sum(f(X!0), f(f(X!0))), 0)))))) <=> ((~![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))) | (~((~$greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)) | (~$greatereq($sum(f(f(X!0)), f(X!0)), 0)) | (~($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0))))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[39, 37])).
% 0.22/0.40 tff(41,plain,
% 0.22/0.40 ((~![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))) | (~((~$lesseq($sum(f(X!0), $product(-1, f(f(X!0)))), 0)) | (~$greatereq($sum(f(X!0), f(f(X!0))), 0)) | (~($greatereq($sum(f(X!0), $product(-1, f(f(X!0)))), 0) | $lesseq($sum(f(X!0), f(f(X!0))), 0)))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(42,plain,
% 0.22/0.40 ((~![X: $int] : (~((~$lesseq($sum(X, $product(-1, f(X))), 0)) | (~$greatereq($sum(X, f(X)), 0)) | (~($greatereq($sum(X, $product(-1, f(X))), 0) | $lesseq($sum(X, f(X)), 0)))))) | (~((~$greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)) | (~$greatereq($sum(f(f(X!0)), f(X!0)), 0)) | (~($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0)))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.22/0.40 tff(43,plain,
% 0.22/0.40 (~((~$greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)) | (~$greatereq($sum(f(f(X!0)), f(X!0)), 0)) | (~($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0))))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[42, 19])).
% 0.22/0.40 tff(44,plain,
% 0.22/0.40 (((~$greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)) | (~$greatereq($sum(f(f(X!0)), f(X!0)), 0)) | (~($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0)))) | $greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(45,plain,
% 0.22/0.40 ($greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.22/0.40 tff(46,plain,
% 0.22/0.40 (($sum(f(f(X!0)), $product(-1, f(X!0))) = 0) | (~$lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)) | (~$greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0))),
% 0.22/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.40 tff(47,plain,
% 0.22/0.40 (~$lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[46, 45, 36])).
% 0.22/0.40 tff(48,plain,
% 0.22/0.40 (((~$greatereq($sum(f(f(X!0)), $product(-1, f(X!0))), 0)) | (~$greatereq($sum(f(f(X!0)), f(X!0)), 0)) | (~($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0)))) | ($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(49,plain,
% 0.22/0.40 ($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[48, 43])).
% 0.22/0.40 tff(50,plain,
% 0.22/0.40 ((~($lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0))) | $lesseq($sum(f(f(X!0)), $product(-1, f(X!0))), 0) | $lesseq($sum(f(f(X!0)), f(X!0)), 0)),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(51,plain,
% 0.22/0.40 ($lesseq($sum(f(f(X!0)), f(X!0)), 0)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[50, 47, 49])).
% 0.22/0.40 tff(52,plain,
% 0.22/0.40 ($false),
% 0.22/0.40 inference(theory_lemma,[status(thm)],[51, 47, 25, 23])).
% 0.22/0.40 % SZS output end Proof
%------------------------------------------------------------------------------