TSTP Solution File: DAT084_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT084_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 14:36:39 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT084_1 : TPTP v8.1.0. Released v6.1.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.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 02:11:32 EDT 2022
% 0.19/0.35 % CPUTime :
% 0.19/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35 Usage: tptp [options] [-file:]file
% 0.19/0.35 -h, -? prints this message.
% 0.19/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.35 -m, -model generate model.
% 0.19/0.35 -p, -proof generate proof.
% 0.19/0.35 -c, -core generate unsat core of named formulas.
% 0.19/0.35 -st, -statistics display statistics.
% 0.19/0.35 -t:timeout set timeout (in second).
% 0.19/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35 -<param>:<value> configuration parameter and value.
% 0.19/0.35 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(length_type, type, (
% 0.19/0.40 length: list > $int)).
% 0.19/0.40 tff(cons_type, type, (
% 0.19/0.40 cons: ( $int * list ) > list)).
% 0.19/0.40 tff(tptp_fun_L_6_type, type, (
% 0.19/0.40 tptp_fun_L_6: list)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[L: list] : rewrite((length(L) = length(cons(1, L))) <=> ($sum(length(L), $product(-1, length(cons(1, L)))) = 0))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (?[L: list] : (length(L) = length(cons(1, L))) <=> ?[L: list] : ($sum(length(L), $product(-1, length(cons(1, L)))) = 0)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (?[L: list] : (length(L) = length(cons(1, L))) <=> ?[L: list] : (length(L) = length(cons(1, L)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 ((~(~?[L: list] : (length(L) = length(cons(1, L))))) <=> ?[L: list] : (length(L) = length(cons(1, L)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 ((~?[L: list] : (length(L) = length(cons(1, L)))) <=> (~?[L: list] : (length(L) = length(cons(1, L))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 ((~(~?[L: list] : (length(L) = length(cons(1, L))))) <=> (~(~?[L: list] : (length(L) = length(cons(1, L)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[5])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 ((~(~?[L: list] : (length(L) = length(cons(1, L))))) <=> ?[L: list] : (length(L) = length(cons(1, L)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[6, 4])).
% 0.19/0.40 tff(8,axiom,(~(~?[L: list] : (length(L) = length(cons(1, L))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c')).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (?[L: list] : (length(L) = length(cons(1, L)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (?[L: list] : (length(L) = length(cons(1, L)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (?[L: list] : ($sum(length(L), $product(-1, length(cons(1, L)))) = 0)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.19/0.40 tff(12,plain,(
% 0.19/0.40 $sum(length(L!6), $product(-1, length(cons(1, L!6)))) = 0),
% 0.19/0.40 inference(skolemize,[status(sab)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 ((~($sum(length(L!6), $product(-1, length(cons(1, L!6)))) = 0)) | $greatereq($sum(length(L!6), $product(-1, length(cons(1, L!6)))), 0)),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 ($greatereq($sum(length(L!6), $product(-1, length(cons(1, L!6)))), 0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 ((~$lesseq($sum(length(L!6), $product(-1, length(cons(1, L!6)))), -1)) | (~$greatereq($sum(length(L!6), $product(-1, length(cons(1, L!6)))), 0))),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (~$lesseq($sum(length(L!6), $product(-1, length(cons(1, L!6)))), -1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 ((~($sum(length(L!6), $product(-1, length(cons(1, L!6)))) = -1)) | $lesseq($sum(length(L!6), $product(-1, length(cons(1, L!6)))), -1)),
% 0.19/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (~($sum(length(L!6), $product(-1, length(cons(1, L!6)))) = -1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (^[H: $int, T: list] : refl(($sum(length(cons(H, T)), $product(-1, length(T))) = 1) <=> ($sum(length(cons(H, T)), $product(-1, length(T))) = 1))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1) <=> ![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (^[H: $int, T: list] : rewrite((length(cons(H, T)) = $sum(1, length(T))) <=> ($sum(length(cons(H, T)), $product(-1, length(T))) = 1))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![H: $int, T: list] : (length(cons(H, T)) = $sum(1, length(T))) <=> ![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![H: $int, T: list] : (length(cons(H, T)) = $sum(1, length(T))) <=> ![H: $int, T: list] : (length(cons(H, T)) = $sum(1, length(T)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(24,axiom,(![H: $int, T: list] : (length(cons(H, T)) = $sum(1, length(T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l_1')).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![H: $int, T: list] : (length(cons(H, T)) = $sum(1, length(T)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.19/0.40 tff(27,plain,(
% 0.19/0.40 ![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)),
% 0.19/0.40 inference(skolemize,[status(sab)],[26])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (((~![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)) | ($sum(length(L!6), $product(-1, length(cons(1, L!6)))) = -1)) <=> ((~![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)) | ($sum(length(L!6), $product(-1, length(cons(1, L!6)))) = -1))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (($sum($product(-1, length(L!6)), length(cons(1, L!6))) = 1) <=> ($sum(length(L!6), $product(-1, length(cons(1, L!6)))) = -1)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 ($sum(length(cons(1, L!6)), $product(-1, length(L!6))) = $sum($product(-1, length(L!6)), length(cons(1, L!6)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (($sum(length(cons(1, L!6)), $product(-1, length(L!6))) = 1) <=> ($sum($product(-1, length(L!6)), length(cons(1, L!6))) = 1)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (($sum(length(cons(1, L!6)), $product(-1, length(L!6))) = 1) <=> ($sum(length(L!6), $product(-1, length(cons(1, L!6)))) = -1)),
% 0.19/0.40 inference(transitivity,[status(thm)],[32, 30])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (((~![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)) | ($sum(length(cons(1, L!6)), $product(-1, length(L!6))) = 1)) <=> ((~![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)) | ($sum(length(L!6), $product(-1, length(cons(1, L!6)))) = -1))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (((~![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)) | ($sum(length(cons(1, L!6)), $product(-1, length(L!6))) = 1)) <=> ((~![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)) | ($sum(length(L!6), $product(-1, length(cons(1, L!6)))) = -1))),
% 0.19/0.40 inference(transitivity,[status(thm)],[34, 29])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 ((~![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)) | ($sum(length(cons(1, L!6)), $product(-1, length(L!6))) = 1)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 ((~![H: $int, T: list] : ($sum(length(cons(H, T)), $product(-1, length(T))) = 1)) | ($sum(length(L!6), $product(-1, length(cons(1, L!6)))) = -1)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[37, 28, 18])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------