TSTP Solution File: DAT026_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT026_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:36:25 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : DAT026_1 : TPTP v8.1.0. Released v5.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 01:53:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(in_type, type, (
% 0.19/0.39 in: ( $int * collection ) > $o)).
% 0.19/0.39 tff(tptp_fun_V_1_type, type, (
% 0.19/0.39 tptp_fun_V_1: collection)).
% 0.19/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.39 tptp_fun_Y_3: $int)).
% 0.19/0.39 tff(tptp_fun_W_0_type, type, (
% 0.19/0.39 tptp_fun_W_0: $int)).
% 0.19/0.39 tff(remove_type, type, (
% 0.19/0.39 remove: ( $int * collection ) > collection)).
% 0.19/0.39 tff(add_type, type, (
% 0.19/0.39 add: ( $int * collection ) > collection)).
% 0.19/0.39 tff(tptp_fun_U_2_type, type, (
% 0.19/0.39 tptp_fun_U_2: collection)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[X3: $int, X4: collection, X5: $int] : refl(((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4))) <=> ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4))) <=> ![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[X3: $int, X4: collection, X5: $int] : rewrite(((in(X3, X4) & (~($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4))) <=> ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4))) <=> ![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (^[X3: $int, X4: collection, X5: $int] : rewrite(((in(X3, X4) & (~($sum(X3, $product(-1, X5)) = 0))) <=> in(X3, remove(X5, X4))) <=> ((in(X3, X4) & (~($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~($sum(X3, $product(-1, X5)) = 0))) <=> in(X3, remove(X5, X4))) <=> ![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (^[X3: $int, X4: collection, X5: $int] : rewrite(((in(X3, X4) & (~(X3 = X5))) <=> in(X3, remove(X5, X4))) <=> ((in(X3, X4) & (~($sum(X3, $product(-1, X5)) = 0))) <=> in(X3, remove(X5, X4))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~(X3 = X5))) <=> in(X3, remove(X5, X4))) <=> ![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~($sum(X3, $product(-1, X5)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~(X3 = X5))) <=> in(X3, remove(X5, X4))) <=> ![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~(X3 = X5))) <=> in(X3, remove(X5, X4)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(10,axiom,(![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~(X3 = X5))) <=> in(X3, remove(X5, X4)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=0.ax','ax5')).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~(X3 = X5))) <=> in(X3, remove(X5, X4)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~($sum(X3, $product(-1, X5)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.19/0.39 tff(14,plain,(
% 0.19/0.39 ![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 ((~![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))) | ((~((~in(Y!3, V!1)) | ($sum(W!0, $product(-1, Y!3)) = 0))) <=> in(Y!3, remove(W!0, V!1)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~((~in(Y!3, V!1)) | ($sum(W!0, $product(-1, Y!3)) = 0))) <=> in(Y!3, remove(W!0, V!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (^[Z: $int, X1: collection, X2: $int] : refl(((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1))) <=> ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1))) <=> ![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (^[Z: $int, X1: collection, X2: $int] : rewrite(((in(Z, X1) | ($sum(Z, $product(-1, X2)) = 0)) <=> in(Z, add(X2, X1))) <=> ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(Z, $product(-1, X2)) = 0)) <=> in(Z, add(X2, X1))) <=> ![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (^[Z: $int, X1: collection, X2: $int] : rewrite((((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1))) <=> ((in(Z, X1) | ($sum(Z, $product(-1, X2)) = 0)) <=> in(Z, add(X2, X1))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1))) <=> ![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(Z, $product(-1, X2)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1))) <=> ![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[Z: $int, X1: collection, X2: $int] : rewrite(((in(Z, X1) | (Z = X2)) <=> in(Z, add(X2, X1))) <=> (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | (Z = X2)) <=> in(Z, add(X2, X1))) <=> ![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,axiom,(![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | (Z = X2)) <=> in(Z, add(X2, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=0.ax','ax4')).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(Z, $product(-1, X2)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 22])).
% 0.19/0.39 tff(33,plain,(
% 0.19/0.39 ![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[32])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 20])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1))))) <=> ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (((in(Y!3, remove(W!0, V!1)) | ($sum($sum(2, W!0), $product(-1, Y!3)) = 0)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1)))) <=> ((in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(Y!3, remove(W!0, V!1)) | ($sum($sum(2, W!0), $product(-1, Y!3)) = 0)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1))))) <=> ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(Y!3, remove(W!0, V!1)) | ($sum($sum(2, W!0), $product(-1, Y!3)) = 0)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1))))) <=> ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[37, 35])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(Y!3, remove(W!0, V!1)) | ($sum($sum(2, W!0), $product(-1, Y!3)) = 0)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1))) & in(W!0, V!1) & (U!2 = add($sum(2, W!0), remove(W!0, V!1)))) & (~((~$lesseq(Y!3, 0)) | (~in(Y!3, U!2))))) <=> (![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1))) & in(W!0, V!1) & (U!2 = add($sum(2, W!0), remove(W!0, V!1))) & (~((~$lesseq(Y!3, 0)) | (~in(Y!3, U!2)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1))) & in(W!0, V!1) & (U!2 = add($sum(2, W!0), remove(W!0, V!1)))) <=> (![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1))) & in(W!0, V!1) & (U!2 = add($sum(2, W!0), remove(W!0, V!1))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (((![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1))) & in(W!0, V!1) & (U!2 = add($sum(2, W!0), remove(W!0, V!1)))) & (~((~$lesseq(Y!3, 0)) | (~in(Y!3, U!2))))) <=> ((![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1))) & in(W!0, V!1) & (U!2 = add($sum(2, W!0), remove(W!0, V!1)))) & (~((~$lesseq(Y!3, 0)) | (~in(Y!3, U!2)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (((![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1))) & in(W!0, V!1) & (U!2 = add($sum(2, W!0), remove(W!0, V!1)))) & (~((~$lesseq(Y!3, 0)) | (~in(Y!3, U!2))))) <=> (![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1))) & in(W!0, V!1) & (U!2 = add($sum(2, W!0), remove(W!0, V!1))) & (~((~$lesseq(Y!3, 0)) | (~in(Y!3, U!2)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[44, 42])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((~![U: collection, V: collection, W: $int] : ((~(![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V))) & in(W, V) & (U = add($sum(2, W), remove(W, V))))) | ![Y: $int] : ((~$lesseq(Y, 0)) | (~in(Y, U))))) <=> (~![U: collection, V: collection, W: $int] : ((~(![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V))) & in(W, V) & (U = add($sum(2, W), remove(W, V))))) | ![Y: $int] : ((~$lesseq(Y, 0)) | (~in(Y, U)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((~![U: collection, V: collection, W: $int] : (((![X: $int] : (in(X, V) => $greater(X, 0)) & in(W, V)) & (U = add($sum(W, 2), remove(W, V)))) => ![Y: $int] : (in(Y, U) => $greater(Y, 0)))) <=> (~![U: collection, V: collection, W: $int] : ((~(![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V))) & in(W, V) & (U = add($sum(2, W), remove(W, V))))) | ![Y: $int] : ((~$lesseq(Y, 0)) | (~in(Y, U)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(48,axiom,(~![U: collection, V: collection, W: $int] : (((![X: $int] : (in(X, V) => $greater(X, 0)) & in(W, V)) & (U = add($sum(W, 2), remove(W, V)))) => ![Y: $int] : (in(Y, U) => $greater(Y, 0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (~![U: collection, V: collection, W: $int] : ((~(![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V))) & in(W, V) & (U = add($sum(2, W), remove(W, V))))) | ![Y: $int] : ((~$lesseq(Y, 0)) | (~in(Y, U))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (~![U: collection, V: collection, W: $int] : ((~(![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V))) & in(W, V) & (U = add($sum(2, W), remove(W, V))))) | ![Y: $int] : ((~$lesseq(Y, 0)) | (~in(Y, U))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (~![U: collection, V: collection, W: $int] : ((~(![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V))) & in(W, V) & (U = add($sum(2, W), remove(W, V))))) | ![Y: $int] : ((~$lesseq(Y, 0)) | (~in(Y, U))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (~![U: collection, V: collection, W: $int] : ((~(![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V))) & in(W, V) & (U = add($sum(2, W), remove(W, V))))) | ![Y: $int] : ((~$lesseq(Y, 0)) | (~in(Y, U))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[51, 46])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (~![U: collection, V: collection, W: $int] : ((~(![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V))) & in(W, V) & (U = add($sum(2, W), remove(W, V))))) | ![Y: $int] : ((~$lesseq(Y, 0)) | (~in(Y, U))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[52, 46])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (~![U: collection, V: collection, W: $int] : ((~(![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V))) & in(W, V) & (U = add($sum(2, W), remove(W, V))))) | ![Y: $int] : ((~$lesseq(Y, 0)) | (~in(Y, U))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (~![U: collection, V: collection, W: $int] : ((~(![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V))) & in(W, V) & (U = add($sum(2, W), remove(W, V))))) | ![Y: $int] : ((~$lesseq(Y, 0)) | (~in(Y, U))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[54, 46])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1))) & in(W!0, V!1) & (U!2 = add($sum(2, W!0), remove(W!0, V!1))) & (~((~$lesseq(Y!3, 0)) | (~in(Y!3, U!2))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (U!2 = add($sum(2, W!0), remove(W!0, V!1))),
% 0.19/0.39 inference(and_elim,[status(thm)],[56])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (add($sum(2, W!0), remove(W!0, V!1)) = U!2),
% 0.19/0.39 inference(symmetry,[status(thm)],[57])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (in(Y!3, add($sum(2, W!0), remove(W!0, V!1))) <=> in(Y!3, U!2)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (in(Y!3, U!2) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1)))),
% 0.19/0.39 inference(symmetry,[status(thm)],[59])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (~((~$lesseq(Y!3, 0)) | (~in(Y!3, U!2)))),
% 0.19/0.39 inference(and_elim,[status(thm)],[56])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.40 (in(Y!3, U!2)),
% 0.19/0.40 inference(or_elim,[status(thm)],[61])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (in(Y!3, add($sum(2, W!0), remove(W!0, V!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 60])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 ((~((in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2)) <=> in(Y!3, add($sum(2, W!0), remove(W!0, V!1))))) | (in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2)) | (~in(Y!3, add($sum(2, W!0), remove(W!0, V!1))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[64, 63, 41])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (in(W!0, V!1)),
% 0.19/0.40 inference(and_elim,[status(thm)],[56])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (^[X: $int] : refl(((~$lesseq(X, 0)) | (~in(X, V!1))) <=> ((~$lesseq(X, 0)) | (~in(X, V!1))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1))) <=> ![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1)))),
% 0.19/0.40 inference(and_elim,[status(thm)],[56])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (((~![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1)))) | ((~$lesseq(W!0, 0)) | (~in(W!0, V!1)))) <=> ((~![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1)))) | (~$lesseq(W!0, 0)) | (~in(W!0, V!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((~![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1)))) | ((~$lesseq(W!0, 0)) | (~in(W!0, V!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((~![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1)))) | (~$lesseq(W!0, 0)) | (~in(W!0, V!1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (~$lesseq(W!0, 0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[73, 70, 66])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ($lesseq(Y!3, 0)),
% 0.19/0.40 inference(or_elim,[status(thm)],[61])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~$lesseq($sum(W!0, $product(-1, Y!3)), -2)) | $lesseq(W!0, 0) | (~$lesseq(Y!3, 0))),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (~$lesseq($sum(W!0, $product(-1, Y!3)), -2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 75, 74])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ((~($sum(W!0, $product(-1, Y!3)) = -2)) | $lesseq($sum(W!0, $product(-1, Y!3)), -2)),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (~($sum(W!0, $product(-1, Y!3)) = -2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 ((~(in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2))) | in(Y!3, remove(W!0, V!1)) | ($sum(W!0, $product(-1, Y!3)) = -2)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (in(Y!3, remove(W!0, V!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[80, 79, 65])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~((~((~in(Y!3, V!1)) | ($sum(W!0, $product(-1, Y!3)) = 0))) <=> in(Y!3, remove(W!0, V!1)))) | (~((~in(Y!3, V!1)) | ($sum(W!0, $product(-1, Y!3)) = 0))) | (~in(Y!3, remove(W!0, V!1)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ((~((~((~in(Y!3, V!1)) | ($sum(W!0, $product(-1, Y!3)) = 0))) <=> in(Y!3, remove(W!0, V!1)))) | (~((~in(Y!3, V!1)) | ($sum(W!0, $product(-1, Y!3)) = 0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (~((~in(Y!3, V!1)) | ($sum(W!0, $product(-1, Y!3)) = 0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[83, 18])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (((~in(Y!3, V!1)) | ($sum(W!0, $product(-1, Y!3)) = 0)) | in(Y!3, V!1)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (in(Y!3, V!1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (((~![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1)))) | ((~$lesseq(Y!3, 0)) | (~in(Y!3, V!1)))) <=> ((~![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1)))) | (~$lesseq(Y!3, 0)) | (~in(Y!3, V!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1)))) | ((~$lesseq(Y!3, 0)) | (~in(Y!3, V!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ((~![X: $int] : ((~$lesseq(X, 0)) | (~in(X, V!1)))) | (~$lesseq(Y!3, 0)) | (~in(Y!3, V!1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[89, 70, 75, 86])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------