TSTP Solution File: SYN381+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN381+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : Thu Sep 29 23:55:04 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN381+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 03:08:40 EDT 2022
% 0.13/0.33 % 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.
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(big_q_type, type, (
% 0.13/0.38 big_q: ( $i * $i ) > $o)).
% 0.13/0.38 tff(tptp_fun_U_0_type, type, (
% 0.13/0.38 tptp_fun_U_0: $i > $i)).
% 0.13/0.38 tff(tptp_fun_Z_1_type, type, (
% 0.13/0.38 tptp_fun_Z_1: $i)).
% 0.13/0.38 tff(big_p_type, type, (
% 0.13/0.38 big_p: $i > $o)).
% 0.13/0.38 tff(1,assumption,(big_q(Z!1, Z!1)), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((~![Z: $i] : big_p(Z)) <=> (~![Z: $i] : big_p(Z))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 ((~(((![X: $i] : (?[Y: $i] : big_q(X, Y) => big_p(X)) & ![V: $i] : ?[U: $i] : big_q(U, V)) & ![W: $i, Z: $i] : (big_q(W, Z) => (big_q(Z, W) | big_q(Z, Z)))) => ![Z: $i] : big_p(Z))) <=> (~((~(![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y))) & ![V: $i] : ?[U: $i] : big_q(U, V) & ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))))) | ![Z: $i] : big_p(Z)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(4,axiom,(~(((![X: $i] : (?[Y: $i] : big_q(X, Y) => big_p(X)) & ![V: $i] : ?[U: $i] : big_q(U, V)) & ![W: $i, Z: $i] : (big_q(W, Z) => (big_q(Z, W) | big_q(Z, Z)))) => ![Z: $i] : big_p(Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2133')).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (~((~(![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y))) & ![V: $i] : ?[U: $i] : big_q(U, V) & ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))))) | ![Z: $i] : big_p(Z))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (~![Z: $i] : big_p(Z)),
% 0.13/0.38 inference(or_elim,[status(thm)],[5])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (~![Z: $i] : big_p(Z)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (~![Z: $i] : big_p(Z)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (~![Z: $i] : big_p(Z)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (~![Z: $i] : big_p(Z)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (~![Z: $i] : big_p(Z)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (~![Z: $i] : big_p(Z)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.13/0.38 tff(13,plain,(
% 0.13/0.38 ~big_p(Z!1)),
% 0.13/0.38 inference(skolemize,[status(sab)],[12])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (^[X: $i] : refl((big_p(X) | ![Y: $i] : (~big_q(X, Y))) <=> (big_p(X) | ![Y: $i] : (~big_q(X, Y))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y))) <=> ![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (^[X: $i] : rewrite((big_p(X) | ![Y: $i] : (~big_q(X, Y))) <=> (big_p(X) | ![Y: $i] : (~big_q(X, Y))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y))) <=> ![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y))) <=> ![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))),
% 0.13/0.38 inference(transitivity,[status(thm)],[17, 15])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y))) <=> ![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y))) & ![V: $i] : ?[U: $i] : big_q(U, V) & ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.13/0.38 inference(or_elim,[status(thm)],[5])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y)))),
% 0.13/0.38 inference(and_elim,[status(thm)],[20])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (![X: $i] : (big_p(X) | (~?[Y: $i] : big_q(X, Y)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[21, 19])).
% 0.13/0.38 tff(23,plain,(
% 0.13/0.38 ![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[22])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (((~![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))) | (big_p(Z!1) | ![Y: $i] : (~big_q(Z!1, Y)))) <=> ((~![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))) | big_p(Z!1) | ![Y: $i] : (~big_q(Z!1, Y)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 ((~![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))) | (big_p(Z!1) | ![Y: $i] : (~big_q(Z!1, Y)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 ((~![X: $i] : (big_p(X) | ![Y: $i] : (~big_q(X, Y)))) | big_p(Z!1) | ![Y: $i] : (~big_q(Z!1, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![Y: $i] : (~big_q(Z!1, Y))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[27, 24, 13])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~![Y: $i] : (~big_q(Z!1, Y))) | (~big_q(Z!1, Z!1))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 28, 1])).
% 0.13/0.39 tff(31,plain,(~big_q(Z!1, Z!1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![V: $i] : ?[U: $i] : big_q(U, V) <=> ![V: $i] : ?[U: $i] : big_q(U, V)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![V: $i] : ?[U: $i] : big_q(U, V)),
% 0.13/0.39 inference(and_elim,[status(thm)],[20])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![V: $i] : ?[U: $i] : big_q(U, V)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.39 tff(35,plain,(
% 0.13/0.39 ![V: $i] : big_q(tptp_fun_U_0(V), V)),
% 0.13/0.39 inference(skolemize,[status(sab)],[34])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~![V: $i] : big_q(tptp_fun_U_0(V), V)) | big_q(tptp_fun_U_0(Z!1), Z!1)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (big_q(tptp_fun_U_0(Z!1), Z!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (^[W: $i, Z: $i] : refl((big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))) <=> (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))) <=> ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z))) <=> ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.13/0.39 inference(and_elim,[status(thm)],[20])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.39 tff(43,plain,(
% 0.13/0.39 ![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[42])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | (big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1)))) <=> ((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 ((big_q(Z!1, tptp_fun_U_0(Z!1)) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1))) <=> (big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | (big_q(Z!1, tptp_fun_U_0(Z!1)) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)))) <=> ((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | (big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | (big_q(Z!1, tptp_fun_U_0(Z!1)) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)))) <=> ((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[47, 45])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 ((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | (big_q(Z!1, tptp_fun_U_0(Z!1)) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 ((~![W: $i, Z: $i] : (big_q(Z, W) | big_q(Z, Z) | (~big_q(W, Z)))) | big_q(Z!1, Z!1) | (~big_q(tptp_fun_U_0(Z!1), Z!1)) | big_q(Z!1, tptp_fun_U_0(Z!1))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (big_q(Z!1, Z!1) | big_q(Z!1, tptp_fun_U_0(Z!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[50, 44, 37])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 (big_q(Z!1, tptp_fun_U_0(Z!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[51, 31])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 ((~![Y: $i] : (~big_q(Z!1, Y))) | (~big_q(Z!1, tptp_fun_U_0(Z!1)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[53, 28, 52])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------