TSTP Solution File: ARI620_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI620_1 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 17:02:19 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ARI620_1 : TPTP v8.1.0. Released v5.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 01:10:30 EDT 2022
% 0.14/0.34 % 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.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(pow2_type, type, (
% 0.14/0.40 pow2: $int > $o)).
% 0.14/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.14/0.40 tptp_fun_Y_0: $int > $int)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (^[X: $int] : refl((~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0))))))))))) <=> (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0))))))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0))))))))))) <=> ![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (^[X: $int] : rewrite((~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0))))))))))) <=> (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0))))))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0))))))))))) <=> ![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0))))))))))) <=> ![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (^[X: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq(X, 2) & ($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X))) <=> (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X)))))), (((X = 1) | (~pow2(X)) | ($greatereq(X, 2) & ($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X)))) <=> ((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X)))))))), rewrite(((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X)))))) <=> ((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))), (((X = 1) | (~pow2(X)) | ($greatereq(X, 2) & ($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X)))) <=> ((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X)))))))), rewrite((pow2(X) | ((~(X = 1)) & ((~$greatereq(X, 2)) | ![Y: $int] : (~(($sum(X, $product(-2, Y)) = 0) & pow2(Y)))))) <=> (pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0))))))))), ((((X = 1) | (~pow2(X)) | ($greatereq(X, 2) & ($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X)))) & (pow2(X) | ((~(X = 1)) & ((~$greatereq(X, 2)) | ![Y: $int] : (~(($sum(X, $product(-2, Y)) = 0) & pow2(Y))))))) <=> (((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X)))))) & (pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0))))))))))), rewrite((((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X)))))) & (pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0))))))))) <=> (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))), ((((X = 1) | (~pow2(X)) | ($greatereq(X, 2) & ($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X)))) & (pow2(X) | ((~(X = 1)) & ((~$greatereq(X, 2)) | ![Y: $int] : (~(($sum(X, $product(-2, Y)) = 0) & pow2(Y))))))) <=> (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (![X: $int] : (((X = 1) | (~pow2(X)) | ($greatereq(X, 2) & ($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X)))) & (pow2(X) | ((~(X = 1)) & ((~$greatereq(X, 2)) | ![Y: $int] : (~(($sum(X, $product(-2, Y)) = 0) & pow2(Y))))))) <=> ![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (^[X: $int] : rewrite((((~pow2(X)) | ((X = 1) | ($greatereq(X, 2) & (($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X)))))) & (pow2(X) | ((~(X = 1)) & ((~$greatereq(X, 2)) | ![Y: $int] : (~(($sum(X, $product(-2, Y)) = 0) & pow2(Y))))))) <=> (((X = 1) | (~pow2(X)) | ($greatereq(X, 2) & ($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X)))) & (pow2(X) | ((~(X = 1)) & ((~$greatereq(X, 2)) | ![Y: $int] : (~(($sum(X, $product(-2, Y)) = 0) & pow2(Y))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (![X: $int] : (((~pow2(X)) | ((X = 1) | ($greatereq(X, 2) & (($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X)))))) & (pow2(X) | ((~(X = 1)) & ((~$greatereq(X, 2)) | ![Y: $int] : (~(($sum(X, $product(-2, Y)) = 0) & pow2(Y))))))) <=> ![X: $int] : (((X = 1) | (~pow2(X)) | ($greatereq(X, 2) & ($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X)))) & (pow2(X) | ((~(X = 1)) & ((~$greatereq(X, 2)) | ![Y: $int] : (~(($sum(X, $product(-2, Y)) = 0) & pow2(Y)))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (^[X: $int] : rewrite((pow2(X) <=> ((X = 1) | ($greatereq(X, 2) & ?[Y: $int] : (($sum($product(2, Y), $product(-1, X)) = 0) & pow2(Y))))) <=> (pow2(X) <=> ((X = 1) | ($greatereq(X, 2) & ?[Y: $int] : (($sum(X, $product(-2, Y)) = 0) & pow2(Y))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (![X: $int] : (pow2(X) <=> ((X = 1) | ($greatereq(X, 2) & ?[Y: $int] : (($sum($product(2, Y), $product(-1, X)) = 0) & pow2(Y))))) <=> ![X: $int] : (pow2(X) <=> ((X = 1) | ($greatereq(X, 2) & ?[Y: $int] : (($sum(X, $product(-2, Y)) = 0) & pow2(Y)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (^[X: $int] : rewrite((pow2(X) <=> ((X = 1) | ($lesseq(2, X) & ?[Y: $int] : (($product(2, Y) = X) & pow2(Y))))) <=> (pow2(X) <=> ((X = 1) | ($greatereq(X, 2) & ?[Y: $int] : (($sum($product(2, Y), $product(-1, X)) = 0) & pow2(Y))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (![X: $int] : (pow2(X) <=> ((X = 1) | ($lesseq(2, X) & ?[Y: $int] : (($product(2, Y) = X) & pow2(Y))))) <=> ![X: $int] : (pow2(X) <=> ((X = 1) | ($greatereq(X, 2) & ?[Y: $int] : (($sum($product(2, Y), $product(-1, X)) = 0) & pow2(Y)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (![X: $int] : (pow2(X) <=> ((X = 1) | ($lesseq(2, X) & ?[Y: $int] : (($product(2, Y) = X) & pow2(Y))))) <=> ![X: $int] : (pow2(X) <=> ((X = 1) | ($lesseq(2, X) & ?[Y: $int] : (($product(2, Y) = X) & pow2(Y)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 ((~(![X: $int] : (pow2(X) <=> ((X = 1) | ($lesseq(2, X) & ?[Y: $int] : (($product(2, Y) = X) & pow2(Y))))) => pow2(8))) <=> (~(pow2(8) | (~![X: $int] : (pow2(X) <=> ((X = 1) | ($lesseq(2, X) & ?[Y: $int] : (($product(2, Y) = X) & pow2(Y))))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(16,axiom,(~(![X: $int] : (pow2(X) <=> ((X = 1) | ($lesseq(2, X) & ?[Y: $int] : (($product(2, Y) = X) & pow2(Y))))) => pow2(8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pow_of_2_8')).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (~(pow2(8) | (~![X: $int] : (pow2(X) <=> ((X = 1) | ($lesseq(2, X) & ?[Y: $int] : (($product(2, Y) = X) & pow2(Y)))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (![X: $int] : (pow2(X) <=> ((X = 1) | ($lesseq(2, X) & ?[Y: $int] : (($product(2, Y) = X) & pow2(Y)))))),
% 0.14/0.40 inference(or_elim,[status(thm)],[17])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (![X: $int] : (pow2(X) <=> ((X = 1) | ($lesseq(2, X) & ?[Y: $int] : (($product(2, Y) = X) & pow2(Y)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (![X: $int] : (pow2(X) <=> ((X = 1) | ($greatereq(X, 2) & ?[Y: $int] : (($sum($product(2, Y), $product(-1, X)) = 0) & pow2(Y)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (![X: $int] : (pow2(X) <=> ((X = 1) | ($greatereq(X, 2) & ?[Y: $int] : (($sum(X, $product(-2, Y)) = 0) & pow2(Y)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.14/0.40 tff(22,plain,(
% 0.14/0.40 ![X: $int] : (((~pow2(X)) | ((X = 1) | ($greatereq(X, 2) & (($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X)))))) & (pow2(X) | ((~(X = 1)) & ((~$greatereq(X, 2)) | ![Y: $int] : (~(($sum(X, $product(-2, Y)) = 0) & pow2(Y)))))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[21])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (![X: $int] : (((X = 1) | (~pow2(X)) | ($greatereq(X, 2) & ($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0) & pow2(tptp_fun_Y_0(X)))) & (pow2(X) | ((~(X = 1)) & ((~$greatereq(X, 2)) | ![Y: $int] : (~(($sum(X, $product(-2, Y)) = 0) & pow2(Y)))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[22, 9])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[23, 7])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~(pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2))))) | (~((~pow2(4)) | (~((~(tptp_fun_Y_0(4) = 2)) | (~pow2(tptp_fun_Y_0(4)))))))))) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~(pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2))))) | (~((~pow2(4)) | (~((~(tptp_fun_Y_0(4) = 2)) | (~pow2(tptp_fun_Y_0(4))))))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 ((~((~((4 = 1) | (~pow2(4)) | (~((~$greatereq(4, 2)) | (~($sum(4, $product(-2, tptp_fun_Y_0(4))) = 0)) | (~pow2(tptp_fun_Y_0(4))))))) | (~(pow2(4) | (~((4 = 1) | (~((~$greatereq(4, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(4, $product(-2, Y)) = 0))))))))))) <=> (~((~(pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2))))) | (~((~pow2(4)) | (~((~(tptp_fun_Y_0(4) = 2)) | (~pow2(tptp_fun_Y_0(4)))))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((4 = 1) | (~pow2(4)) | (~((~$greatereq(4, 2)) | (~($sum(4, $product(-2, tptp_fun_Y_0(4))) = 0)) | (~pow2(tptp_fun_Y_0(4))))))) | (~(pow2(4) | (~((4 = 1) | (~((~$greatereq(4, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(4, $product(-2, Y)) = 0)))))))))))) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~(pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2))))) | (~((~pow2(4)) | (~((~(tptp_fun_Y_0(4) = 2)) | (~pow2(tptp_fun_Y_0(4))))))))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((4 = 1) | (~pow2(4)) | (~((~$greatereq(4, 2)) | (~($sum(4, $product(-2, tptp_fun_Y_0(4))) = 0)) | (~pow2(tptp_fun_Y_0(4))))))) | (~(pow2(4) | (~((4 = 1) | (~((~$greatereq(4, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(4, $product(-2, Y)) = 0)))))))))))) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~(pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2))))) | (~((~pow2(4)) | (~((~(tptp_fun_Y_0(4) = 2)) | (~pow2(tptp_fun_Y_0(4))))))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[28, 26])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((4 = 1) | (~pow2(4)) | (~((~$greatereq(4, 2)) | (~($sum(4, $product(-2, tptp_fun_Y_0(4))) = 0)) | (~pow2(tptp_fun_Y_0(4))))))) | (~(pow2(4) | (~((4 = 1) | (~((~$greatereq(4, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(4, $product(-2, Y)) = 0)))))))))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~(pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2))))) | (~((~pow2(4)) | (~((~(tptp_fun_Y_0(4) = 2)) | (~pow2(tptp_fun_Y_0(4)))))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 (~((~(pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2))))) | (~((~pow2(4)) | (~((~(tptp_fun_Y_0(4) = 2)) | (~pow2(tptp_fun_Y_0(4))))))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (((~(pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2))))) | (~((~pow2(4)) | (~((~(tptp_fun_Y_0(4) = 2)) | (~pow2(tptp_fun_Y_0(4)))))))) | (pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.14/0.40 tff(35,assumption,(![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))), introduced(assumption)).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((~pow2(2)) | (~((~pow2(tptp_fun_Y_0(2))) | (~(tptp_fun_Y_0(2) = 1)))))) | (~(pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))))))) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((~pow2(2)) | (~((~pow2(tptp_fun_Y_0(2))) | (~(tptp_fun_Y_0(2) = 1)))))) | (~(pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1))))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 ((~((~((2 = 1) | (~pow2(2)) | (~((~$greatereq(2, 2)) | (~($sum(2, $product(-2, tptp_fun_Y_0(2))) = 0)) | (~pow2(tptp_fun_Y_0(2))))))) | (~(pow2(2) | (~((2 = 1) | (~((~$greatereq(2, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(2, $product(-2, Y)) = 0))))))))))) <=> (~((~((~pow2(2)) | (~((~pow2(tptp_fun_Y_0(2))) | (~(tptp_fun_Y_0(2) = 1)))))) | (~(pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((2 = 1) | (~pow2(2)) | (~((~$greatereq(2, 2)) | (~($sum(2, $product(-2, tptp_fun_Y_0(2))) = 0)) | (~pow2(tptp_fun_Y_0(2))))))) | (~(pow2(2) | (~((2 = 1) | (~((~$greatereq(2, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(2, $product(-2, Y)) = 0)))))))))))) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((~pow2(2)) | (~((~pow2(tptp_fun_Y_0(2))) | (~(tptp_fun_Y_0(2) = 1)))))) | (~(pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1))))))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((2 = 1) | (~pow2(2)) | (~((~$greatereq(2, 2)) | (~($sum(2, $product(-2, tptp_fun_Y_0(2))) = 0)) | (~pow2(tptp_fun_Y_0(2))))))) | (~(pow2(2) | (~((2 = 1) | (~((~$greatereq(2, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(2, $product(-2, Y)) = 0)))))))))))) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((~pow2(2)) | (~((~pow2(tptp_fun_Y_0(2))) | (~(tptp_fun_Y_0(2) = 1)))))) | (~(pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1))))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[38, 36])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((2 = 1) | (~pow2(2)) | (~((~$greatereq(2, 2)) | (~($sum(2, $product(-2, tptp_fun_Y_0(2))) = 0)) | (~pow2(tptp_fun_Y_0(2))))))) | (~(pow2(2) | (~((2 = 1) | (~((~$greatereq(2, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(2, $product(-2, Y)) = 0)))))))))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(41,plain,
% 0.14/0.41 ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((~pow2(2)) | (~((~pow2(tptp_fun_Y_0(2))) | (~(tptp_fun_Y_0(2) = 1)))))) | (~(pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.14/0.41 tff(42,plain,
% 0.14/0.41 (~((~((~pow2(2)) | (~((~pow2(tptp_fun_Y_0(2))) | (~(tptp_fun_Y_0(2) = 1)))))) | (~(pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1))))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[41, 25])).
% 0.14/0.41 tff(43,plain,
% 0.14/0.41 (((~((~pow2(2)) | (~((~pow2(tptp_fun_Y_0(2))) | (~(tptp_fun_Y_0(2) = 1)))))) | (~(pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))))) | (pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1))))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(44,plain,
% 0.14/0.41 (pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.14/0.41 tff(45,assumption,(![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))), introduced(assumption)).
% 0.14/0.41 tff(46,plain,
% 0.14/0.41 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | pow2(1)) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | pow2(1))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(47,plain,
% 0.14/0.41 ((~(~pow2(1))) <=> pow2(1)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(48,plain,
% 0.14/0.41 (($false | (~pow2(1))) <=> (~pow2(1))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(49,plain,
% 0.14/0.41 ((~(pow2($sum(2, $product(-1, 1))) | (~(($sum(2, $product(-1, 1)) = 1) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, Y)) = 0))))))))) <=> (~pow2(1))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(50,plain,
% 0.14/0.41 ((~$true) <=> $false),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(51,plain,
% 0.14/0.41 (($true | (~pow2(1)) | $false) <=> $true),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(52,plain,
% 0.14/0.41 (($true | $true | (~pow2(tptp_fun_Y_0(1)))) <=> $true),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(53,plain,
% 0.14/0.41 ((~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))) <=> (~pow2(tptp_fun_Y_0(1)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(54,plain,
% 0.14/0.41 ((~$false) <=> $true),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(55,plain,
% 0.14/0.41 (($sum(1, $product(-2, tptp_fun_Y_0(1))) = 0) <=> $false),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(56,plain,
% 0.14/0.41 ($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = $sum(1, $product(-2, tptp_fun_Y_0(1)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(57,plain,
% 0.14/0.41 (($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0) <=> ($sum(1, $product(-2, tptp_fun_Y_0(1))) = 0)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[56])).
% 0.14/0.41 tff(58,plain,
% 0.14/0.41 (($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0) <=> $false),
% 0.14/0.41 inference(transitivity,[status(thm)],[57, 55])).
% 0.14/0.41 tff(59,plain,
% 0.14/0.41 ((~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) <=> (~$false)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[58])).
% 0.14/0.41 tff(60,plain,
% 0.14/0.41 ((~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) <=> $true),
% 0.14/0.41 inference(transitivity,[status(thm)],[59, 54])).
% 0.14/0.41 tff(61,plain,
% 0.14/0.41 ($greatereq(1, 2) <=> $false),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(62,plain,
% 0.14/0.41 ($sum(2, -1) = 1),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(63,plain,
% 0.14/0.41 ($product(-1, 1) = -1),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(64,plain,
% 0.14/0.41 ($sum(2, $product(-1, 1)) = $sum(2, -1)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.14/0.41 tff(65,plain,
% 0.14/0.41 ($sum(2, $product(-1, 1)) = 1),
% 0.14/0.41 inference(transitivity,[status(thm)],[64, 62])).
% 0.14/0.41 tff(66,plain,
% 0.14/0.41 ($greatereq($sum(2, $product(-1, 1)), 2) <=> $greatereq(1, 2)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[65])).
% 0.14/0.41 tff(67,plain,
% 0.14/0.41 ($greatereq($sum(2, $product(-1, 1)), 2) <=> $false),
% 0.14/0.41 inference(transitivity,[status(thm)],[66, 61])).
% 0.14/0.41 tff(68,plain,
% 0.14/0.41 ((~$greatereq($sum(2, $product(-1, 1)), 2)) <=> (~$false)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[67])).
% 0.14/0.41 tff(69,plain,
% 0.14/0.41 ((~$greatereq($sum(2, $product(-1, 1)), 2)) <=> $true),
% 0.14/0.41 inference(transitivity,[status(thm)],[68, 54])).
% 0.14/0.41 tff(70,plain,
% 0.14/0.41 (((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1)))))) <=> ($true | $true | (~pow2(tptp_fun_Y_0(1))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[69, 60, 53])).
% 0.14/0.41 tff(71,plain,
% 0.14/0.41 (((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1)))))) <=> $true),
% 0.14/0.41 inference(transitivity,[status(thm)],[70, 52])).
% 0.14/0.41 tff(72,plain,
% 0.14/0.41 ((~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))))) <=> (~$true)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[71])).
% 0.14/0.41 tff(73,plain,
% 0.14/0.41 ((~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))))) <=> $false),
% 0.14/0.41 inference(transitivity,[status(thm)],[72, 50])).
% 0.14/0.41 tff(74,plain,
% 0.14/0.41 ((~pow2($sum(2, $product(-1, 1)))) <=> (~pow2(1))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(75,plain,
% 0.14/0.41 ((1 = 1) <=> $true),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(76,plain,
% 0.14/0.41 (($sum(2, $product(-1, 1)) = 1) <=> (1 = 1)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[65])).
% 0.14/0.41 tff(77,plain,
% 0.14/0.41 (($sum(2, $product(-1, 1)) = 1) <=> $true),
% 0.14/0.41 inference(transitivity,[status(thm)],[76, 75])).
% 0.14/0.41 tff(78,plain,
% 0.14/0.41 ((($sum(2, $product(-1, 1)) = 1) | (~pow2($sum(2, $product(-1, 1)))) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1)))))))) <=> ($true | (~pow2(1)) | $false)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[77, 74, 73])).
% 0.14/0.41 tff(79,plain,
% 0.14/0.41 ((($sum(2, $product(-1, 1)) = 1) | (~pow2($sum(2, $product(-1, 1)))) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1)))))))) <=> $true),
% 0.14/0.41 inference(transitivity,[status(thm)],[78, 51])).
% 0.14/0.41 tff(80,plain,
% 0.14/0.41 ((~(($sum(2, $product(-1, 1)) = 1) | (~pow2($sum(2, $product(-1, 1)))) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))))))) <=> (~$true)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[79])).
% 0.14/0.41 tff(81,plain,
% 0.14/0.41 ((~(($sum(2, $product(-1, 1)) = 1) | (~pow2($sum(2, $product(-1, 1)))) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))))))) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[80, 50])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (((~(($sum(2, $product(-1, 1)) = 1) | (~pow2($sum(2, $product(-1, 1)))) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))))))) | (~(pow2($sum(2, $product(-1, 1))) | (~(($sum(2, $product(-1, 1)) = 1) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, Y)) = 0)))))))))) <=> ($false | (~pow2(1)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[81, 49])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (((~(($sum(2, $product(-1, 1)) = 1) | (~pow2($sum(2, $product(-1, 1)))) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))))))) | (~(pow2($sum(2, $product(-1, 1))) | (~(($sum(2, $product(-1, 1)) = 1) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, Y)) = 0)))))))))) <=> (~pow2(1))),
% 0.21/0.41 inference(transitivity,[status(thm)],[82, 48])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 ((~((~(($sum(2, $product(-1, 1)) = 1) | (~pow2($sum(2, $product(-1, 1)))) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))))))) | (~(pow2($sum(2, $product(-1, 1))) | (~(($sum(2, $product(-1, 1)) = 1) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, Y)) = 0))))))))))) <=> (~(~pow2(1)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 ((~((~(($sum(2, $product(-1, 1)) = 1) | (~pow2($sum(2, $product(-1, 1)))) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))))))) | (~(pow2($sum(2, $product(-1, 1))) | (~(($sum(2, $product(-1, 1)) = 1) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, Y)) = 0))))))))))) <=> pow2(1)),
% 0.21/0.41 inference(transitivity,[status(thm)],[84, 47])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~(($sum(2, $product(-1, 1)) = 1) | (~pow2($sum(2, $product(-1, 1)))) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))))))) | (~(pow2($sum(2, $product(-1, 1))) | (~(($sum(2, $product(-1, 1)) = 1) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, Y)) = 0)))))))))))) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | pow2(1))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[85])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~(($sum(2, $product(-1, 1)) = 1) | (~pow2($sum(2, $product(-1, 1)))) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))))))) | (~(pow2($sum(2, $product(-1, 1))) | (~(($sum(2, $product(-1, 1)) = 1) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, Y)) = 0)))))))))))) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | pow2(1))),
% 0.21/0.41 inference(transitivity,[status(thm)],[86, 46])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~(($sum(2, $product(-1, 1)) = 1) | (~pow2($sum(2, $product(-1, 1)))) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, tptp_fun_Y_0($sum(2, $product(-1, 1))))) = 0)) | (~pow2(tptp_fun_Y_0($sum(2, $product(-1, 1))))))))) | (~(pow2($sum(2, $product(-1, 1))) | (~(($sum(2, $product(-1, 1)) = 1) | (~((~$greatereq($sum(2, $product(-1, 1)), 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum($sum(2, $product(-1, 1)), $product(-2, Y)) = 0)))))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | pow2(1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (pow2(1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[89, 25])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 (((~![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))) | (~pow2(1))) <=> ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))) | (~pow2(1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (((~pow2(1)) | $false) <=> (~pow2(1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 ((~(1 = 1)) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 ((~(1 = 1)) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[93, 50])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 (((~pow2(1)) | (~(1 = 1))) <=> ((~pow2(1)) | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[94])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 (((~pow2(1)) | (~(1 = 1))) <=> (~pow2(1))),
% 0.21/0.41 inference(transitivity,[status(thm)],[95, 92])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (((~![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))) | ((~pow2(1)) | (~(1 = 1)))) <=> ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))) | (~pow2(1)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[96])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 (((~![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))) | ((~pow2(1)) | (~(1 = 1)))) <=> ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))) | (~pow2(1)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[97, 91])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))) | ((~pow2(1)) | (~(1 = 1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))) | (~pow2(1))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[100, 90, 45])).
% 0.21/0.41 tff(102,plain,(~![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 ((~(pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1))))) | pow2(2) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 1)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 (pow2(2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[103, 102, 44])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 (((~![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))) | (~pow2(2))) <=> ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))) | (~pow2(2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 (((~pow2(2)) | $false) <=> (~pow2(2))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 ((2 = 2) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 ((~(2 = 2)) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[107])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 ((~(2 = 2)) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[108, 50])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 (((~pow2(2)) | (~(2 = 2))) <=> ((~pow2(2)) | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 (((~pow2(2)) | (~(2 = 2))) <=> (~pow2(2))),
% 0.21/0.41 inference(transitivity,[status(thm)],[110, 106])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 (((~![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))) | ((~pow2(2)) | (~(2 = 2)))) <=> ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))) | (~pow2(2)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[111])).
% 0.21/0.41 tff(113,plain,
% 0.21/0.41 (((~![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))) | ((~pow2(2)) | (~(2 = 2)))) <=> ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))) | (~pow2(2)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[112, 105])).
% 0.21/0.41 tff(114,plain,
% 0.21/0.41 ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))) | ((~pow2(2)) | (~(2 = 2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(115,plain,
% 0.21/0.41 ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))) | (~pow2(2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.41 tff(116,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[115, 104, 35])).
% 0.21/0.41 tff(117,plain,(~![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 ((~(pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2))))) | pow2(4) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 2)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 (pow2(4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[118, 117, 34])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((~pow2(8)) | (~((~pow2(tptp_fun_Y_0(8))) | (~(tptp_fun_Y_0(8) = 4)))))) | (~(pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))))))) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((~pow2(8)) | (~((~pow2(tptp_fun_Y_0(8))) | (~(tptp_fun_Y_0(8) = 4)))))) | (~(pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(121,plain,
% 0.21/0.41 ((~((~((8 = 1) | (~pow2(8)) | (~((~$greatereq(8, 2)) | (~($sum(8, $product(-2, tptp_fun_Y_0(8))) = 0)) | (~pow2(tptp_fun_Y_0(8))))))) | (~(pow2(8) | (~((8 = 1) | (~((~$greatereq(8, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(8, $product(-2, Y)) = 0))))))))))) <=> (~((~((~pow2(8)) | (~((~pow2(tptp_fun_Y_0(8))) | (~(tptp_fun_Y_0(8) = 4)))))) | (~(pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(122,plain,
% 0.21/0.41 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((8 = 1) | (~pow2(8)) | (~((~$greatereq(8, 2)) | (~($sum(8, $product(-2, tptp_fun_Y_0(8))) = 0)) | (~pow2(tptp_fun_Y_0(8))))))) | (~(pow2(8) | (~((8 = 1) | (~((~$greatereq(8, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(8, $product(-2, Y)) = 0)))))))))))) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((~pow2(8)) | (~((~pow2(tptp_fun_Y_0(8))) | (~(tptp_fun_Y_0(8) = 4)))))) | (~(pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4))))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[121])).
% 0.21/0.41 tff(123,plain,
% 0.21/0.41 (((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((8 = 1) | (~pow2(8)) | (~((~$greatereq(8, 2)) | (~($sum(8, $product(-2, tptp_fun_Y_0(8))) = 0)) | (~pow2(tptp_fun_Y_0(8))))))) | (~(pow2(8) | (~((8 = 1) | (~((~$greatereq(8, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(8, $product(-2, Y)) = 0)))))))))))) <=> ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((~pow2(8)) | (~((~pow2(tptp_fun_Y_0(8))) | (~(tptp_fun_Y_0(8) = 4)))))) | (~(pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4))))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[122, 120])).
% 0.21/0.41 tff(124,plain,
% 0.21/0.41 ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((8 = 1) | (~pow2(8)) | (~((~$greatereq(8, 2)) | (~($sum(8, $product(-2, tptp_fun_Y_0(8))) = 0)) | (~pow2(tptp_fun_Y_0(8))))))) | (~(pow2(8) | (~((8 = 1) | (~((~$greatereq(8, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(8, $product(-2, Y)) = 0)))))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(125,plain,
% 0.21/0.41 ((~![X: $int] : (~((~((X = 1) | (~pow2(X)) | (~((~$greatereq(X, 2)) | (~($sum(X, $product(-2, tptp_fun_Y_0(X))) = 0)) | (~pow2(tptp_fun_Y_0(X))))))) | (~(pow2(X) | (~((X = 1) | (~((~$greatereq(X, 2)) | ![Y: $int] : ((~pow2(Y)) | (~($sum(X, $product(-2, Y)) = 0)))))))))))) | (~((~((~pow2(8)) | (~((~pow2(tptp_fun_Y_0(8))) | (~(tptp_fun_Y_0(8) = 4)))))) | (~(pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.41 tff(126,plain,
% 0.21/0.41 (~((~((~pow2(8)) | (~((~pow2(tptp_fun_Y_0(8))) | (~(tptp_fun_Y_0(8) = 4)))))) | (~(pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[125, 25])).
% 0.21/0.41 tff(127,plain,
% 0.21/0.41 (((~((~pow2(8)) | (~((~pow2(tptp_fun_Y_0(8))) | (~(tptp_fun_Y_0(8) = 4)))))) | (~(pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))))) | (pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(128,plain,
% 0.21/0.41 (pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.21/0.41 tff(129,plain,
% 0.21/0.41 ((~pow2(8)) <=> (~pow2(8))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(130,plain,
% 0.21/0.41 (~pow2(8)),
% 0.21/0.41 inference(or_elim,[status(thm)],[17])).
% 0.21/0.41 tff(131,plain,
% 0.21/0.41 (~pow2(8)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.41 tff(132,plain,
% 0.21/0.41 ((~(pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4))))) | pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(133,plain,
% 0.21/0.41 ((~(pow2(8) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4))))) | ![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.21/0.41 tff(134,plain,
% 0.21/0.41 (![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[133, 128])).
% 0.21/0.41 tff(135,plain,
% 0.21/0.41 (((~![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))) | (~pow2(4))) <=> ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))) | (~pow2(4)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 (((~pow2(4)) | $false) <=> (~pow2(4))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(137,plain,
% 0.21/0.41 ((4 = 4) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(138,plain,
% 0.21/0.41 ((~(4 = 4)) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[137])).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 ((~(4 = 4)) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[138, 50])).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 (((~pow2(4)) | (~(4 = 4))) <=> ((~pow2(4)) | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[139])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 (((~pow2(4)) | (~(4 = 4))) <=> (~pow2(4))),
% 0.21/0.41 inference(transitivity,[status(thm)],[140, 136])).
% 0.21/0.41 tff(142,plain,
% 0.21/0.41 (((~![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))) | ((~pow2(4)) | (~(4 = 4)))) <=> ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))) | (~pow2(4)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[141])).
% 0.21/0.41 tff(143,plain,
% 0.21/0.41 (((~![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))) | ((~pow2(4)) | (~(4 = 4)))) <=> ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))) | (~pow2(4)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[142, 135])).
% 0.21/0.41 tff(144,plain,
% 0.21/0.41 ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))) | ((~pow2(4)) | (~(4 = 4)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(145,plain,
% 0.21/0.41 ((~![Y: $int] : ((~pow2(Y)) | (~(Y = 4)))) | (~pow2(4))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.41 tff(146,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[145, 134, 119])).
% 0.21/0.41 % SZS output end Proof
%------------------------------------------------------------------------------