TSTP Solution File: DAT022_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT022_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:36:24 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT022_1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n022.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 01:44:29 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.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(in_type, type, (
% 0.21/0.39 in: ( $int * collection ) > $o)).
% 0.21/0.39 tff(tptp_fun_V_0_type, type, (
% 0.21/0.39 tptp_fun_V_0: collection)).
% 0.21/0.39 tff(tptp_fun_X_2_type, type, (
% 0.21/0.39 tptp_fun_X_2: $int)).
% 0.21/0.39 tff(remove_type, type, (
% 0.21/0.39 remove: ( $int * collection ) > collection)).
% 0.21/0.39 tff(add_type, type, (
% 0.21/0.39 add: ( $int * collection ) > collection)).
% 0.21/0.39 tff(tptp_fun_U_1_type, type, (
% 0.21/0.39 tptp_fun_U_1: collection)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 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')).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~(X3 = X5))) <=> in(X3, remove(X5, X4)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~($sum(X3, $product(-1, X5)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.21/0.39 tff(14,plain,(
% 0.21/0.39 ![X3: $int, X4: collection, X5: $int] : ((in(X3, X4) & (~($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[13])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (((~![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))) | ((~((~in(X!2, V!0)) | (X!2 = 7))) <=> in(X!2, remove(7, V!0)))) <=> ((~![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))) | ((~((~in(X!2, V!0)) | (X!2 = 7))) <=> in(X!2, remove(7, V!0))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (((~((~in(X!2, V!0)) | ($sum(7, $product(-1, X!2)) = 0))) <=> in(X!2, remove(7, V!0))) <=> ((~((~in(X!2, V!0)) | (X!2 = 7))) <=> in(X!2, remove(7, V!0)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (((~![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))) | ((~((~in(X!2, V!0)) | ($sum(7, $product(-1, X!2)) = 0))) <=> in(X!2, remove(7, V!0)))) <=> ((~![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))) | ((~((~in(X!2, V!0)) | (X!2 = 7))) <=> in(X!2, remove(7, V!0))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[18])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (((~![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))) | ((~((~in(X!2, V!0)) | ($sum(7, $product(-1, X!2)) = 0))) <=> in(X!2, remove(7, V!0)))) <=> ((~![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))) | ((~((~in(X!2, V!0)) | (X!2 = 7))) <=> in(X!2, remove(7, V!0))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[19, 17])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 ((~![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))) | ((~((~in(X!2, V!0)) | ($sum(7, $product(-1, X!2)) = 0))) <=> in(X!2, remove(7, V!0)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 ((~![X3: $int, X4: collection, X5: $int] : ((~((~in(X3, X4)) | ($sum(X5, $product(-1, X3)) = 0))) <=> in(X3, remove(X5, X4)))) | ((~((~in(X!2, V!0)) | (X!2 = 7))) <=> in(X!2, remove(7, V!0)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 ((~((~in(X!2, V!0)) | (X!2 = 7))) <=> in(X!2, remove(7, V!0))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.39 tff(33,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')).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (![Z: $int, X1: collection, X2: $int] : (((Z = X2) | in(Z, X1)) <=> in(Z, add(X2, X1)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(Z, $product(-1, X2)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[36, 27])).
% 0.21/0.39 tff(38,plain,(
% 0.21/0.39 ![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[37])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 25])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(X!2, remove(7, V!0)) | (X!2 = 2)) <=> in(X!2, add(2, remove(7, V!0))))) <=> ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(X!2, remove(7, V!0)) | (X!2 = 2)) <=> in(X!2, add(2, remove(7, V!0)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (((in(X!2, remove(7, V!0)) | ($sum(2, $product(-1, X!2)) = 0)) <=> in(X!2, add(2, remove(7, V!0)))) <=> ((in(X!2, remove(7, V!0)) | (X!2 = 2)) <=> in(X!2, add(2, remove(7, V!0))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(X!2, remove(7, V!0)) | ($sum(2, $product(-1, X!2)) = 0)) <=> in(X!2, add(2, remove(7, V!0))))) <=> ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(X!2, remove(7, V!0)) | (X!2 = 2)) <=> in(X!2, add(2, remove(7, V!0)))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(X!2, remove(7, V!0)) | ($sum(2, $product(-1, X!2)) = 0)) <=> in(X!2, add(2, remove(7, V!0))))) <=> ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(X!2, remove(7, V!0)) | (X!2 = 2)) <=> in(X!2, add(2, remove(7, V!0)))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[42, 40])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(X!2, remove(7, V!0)) | ($sum(2, $product(-1, X!2)) = 0)) <=> in(X!2, add(2, remove(7, V!0))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 ((~![Z: $int, X1: collection, X2: $int] : ((in(Z, X1) | ($sum(X2, $product(-1, Z)) = 0)) <=> in(Z, add(X2, X1)))) | ((in(X!2, remove(7, V!0)) | (X!2 = 2)) <=> in(X!2, add(2, remove(7, V!0))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 ((in(X!2, remove(7, V!0)) | (X!2 = 2)) <=> in(X!2, add(2, remove(7, V!0)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[45, 39])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & (U!1 = add(2, remove(7, V!0)))) & (~((~$lesseq(X!2, 0)) | (~in(X!2, U!1))))) <=> (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & (U!1 = add(2, remove(7, V!0))) & (~((~$lesseq(X!2, 0)) | (~in(X!2, U!1)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 ((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & (U!1 = add(2, remove(7, V!0)))) <=> (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & (U!1 = add(2, remove(7, V!0))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & (U!1 = add(2, remove(7, V!0)))) & (~((~$lesseq(X!2, 0)) | (~in(X!2, U!1))))) <=> ((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & (U!1 = add(2, remove(7, V!0)))) & (~((~$lesseq(X!2, 0)) | (~in(X!2, U!1)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[48])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (((![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & (U!1 = add(2, remove(7, V!0)))) & (~((~$lesseq(X!2, 0)) | (~in(X!2, U!1))))) <=> (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & (U!1 = add(2, remove(7, V!0))) & (~((~$lesseq(X!2, 0)) | (~in(X!2, U!1)))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[49, 47])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 ((~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & (U = add(2, remove(7, V))))) | ![X: $int] : ((~$lesseq(X, 0)) | (~in(X, U))))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & (U = add(2, remove(7, V))))) | ![X: $int] : ((~$lesseq(X, 0)) | (~in(X, U)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 ((~![U: collection, V: collection] : ((![W: $int] : (in(W, V) => $greater(W, 0)) & (U = add(2, remove(7, V)))) => ![X: $int] : (in(X, U) => $greater(X, 0)))) <=> (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & (U = add(2, remove(7, V))))) | ![X: $int] : ((~$lesseq(X, 0)) | (~in(X, U)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(53,axiom,(~![U: collection, V: collection] : ((![W: $int] : (in(W, V) => $greater(W, 0)) & (U = add(2, remove(7, V)))) => ![X: $int] : (in(X, U) => $greater(X, 0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & (U = add(2, remove(7, V))))) | ![X: $int] : ((~$lesseq(X, 0)) | (~in(X, U))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & (U = add(2, remove(7, V))))) | ![X: $int] : ((~$lesseq(X, 0)) | (~in(X, U))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & (U = add(2, remove(7, V))))) | ![X: $int] : ((~$lesseq(X, 0)) | (~in(X, U))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & (U = add(2, remove(7, V))))) | ![X: $int] : ((~$lesseq(X, 0)) | (~in(X, U))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & (U = add(2, remove(7, V))))) | ![X: $int] : ((~$lesseq(X, 0)) | (~in(X, U))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[57, 51])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & (U = add(2, remove(7, V))))) | ![X: $int] : ((~$lesseq(X, 0)) | (~in(X, U))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (~![U: collection, V: collection] : ((~(![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V))) & (U = add(2, remove(7, V))))) | ![X: $int] : ((~$lesseq(X, 0)) | (~in(X, U))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[59, 51])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) & (U!1 = add(2, remove(7, V!0))) & (~((~$lesseq(X!2, 0)) | (~in(X!2, U!1))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (U!1 = add(2, remove(7, V!0))),
% 0.21/0.40 inference(and_elim,[status(thm)],[61])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (add(2, remove(7, V!0)) = U!1),
% 0.21/0.40 inference(symmetry,[status(thm)],[62])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (in(X!2, add(2, remove(7, V!0))) <=> in(X!2, U!1)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[63])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (in(X!2, U!1) <=> in(X!2, add(2, remove(7, V!0)))),
% 0.21/0.40 inference(symmetry,[status(thm)],[64])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (~((~$lesseq(X!2, 0)) | (~in(X!2, U!1)))),
% 0.21/0.40 inference(and_elim,[status(thm)],[61])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (in(X!2, U!1)),
% 0.21/0.40 inference(or_elim,[status(thm)],[66])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (in(X!2, add(2, remove(7, V!0)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 ((~((in(X!2, remove(7, V!0)) | (X!2 = 2)) <=> in(X!2, add(2, remove(7, V!0))))) | (in(X!2, remove(7, V!0)) | (X!2 = 2)) | (~in(X!2, add(2, remove(7, V!0))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 (in(X!2, remove(7, V!0)) | (X!2 = 2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[69, 68, 46])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 ($lesseq(X!2, 0)),
% 0.21/0.40 inference(or_elim,[status(thm)],[66])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 ((~$greatereq(X!2, 2)) | (~$lesseq(X!2, 0))),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (~$greatereq(X!2, 2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 ((~(X!2 = 2)) | $greatereq(X!2, 2)),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (~(X!2 = 2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 ((~(in(X!2, remove(7, V!0)) | (X!2 = 2))) | in(X!2, remove(7, V!0)) | (X!2 = 2)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 ((~(in(X!2, remove(7, V!0)) | (X!2 = 2))) | in(X!2, remove(7, V!0))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (in(X!2, remove(7, V!0))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[77, 70])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 ((~((~((~in(X!2, V!0)) | (X!2 = 7))) <=> in(X!2, remove(7, V!0)))) | (~((~in(X!2, V!0)) | (X!2 = 7))) | (~in(X!2, remove(7, V!0)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 ((~((~((~in(X!2, V!0)) | (X!2 = 7))) <=> in(X!2, remove(7, V!0)))) | (~((~in(X!2, V!0)) | (X!2 = 7)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (~((~in(X!2, V!0)) | (X!2 = 7))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[80, 23])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 (((~in(X!2, V!0)) | (X!2 = 7)) | in(X!2, V!0)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 (in(X!2, V!0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (^[W: $int] : refl(((~$lesseq(W, 0)) | (~in(W, V!0))) <=> ((~$lesseq(W, 0)) | (~in(W, V!0))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0))) <=> ![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.21/0.40 inference(and_elim,[status(thm)],[61])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 (((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | ((~$lesseq(X!2, 0)) | (~in(X!2, V!0)))) <=> ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | (~$lesseq(X!2, 0)) | (~in(X!2, V!0)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | ((~$lesseq(X!2, 0)) | (~in(X!2, V!0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 ((~![W: $int] : ((~$lesseq(W, 0)) | (~in(W, V!0)))) | (~$lesseq(X!2, 0)) | (~in(X!2, V!0))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.40 tff(91,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[90, 87, 71, 83])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------