TSTP Solution File: SWV412+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV412+1 : TPTP v8.1.0. Released v3.3.0.
% 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 15:11:41 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV412+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 03:03:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(pair_in_list_type, type, (
% 0.12/0.39 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_X_0_type, type, (
% 0.12/0.39 tptp_fun_X_0: $i)).
% 0.12/0.39 tff(tptp_fun_V_2_type, type, (
% 0.12/0.39 tptp_fun_V_2: $i)).
% 0.12/0.39 tff(update_slb_type, type, (
% 0.12/0.39 update_slb: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_U_3_type, type, (
% 0.12/0.39 tptp_fun_U_3: $i)).
% 0.12/0.39 tff(strictly_less_than_type, type, (
% 0.12/0.39 strictly_less_than: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_W_1_type, type, (
% 0.12/0.39 tptp_fun_W_1: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : (((pair_in_list(U, V, W) & strictly_less_than(V, X)) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,axiom,(~![U: $i, V: $i, W: $i, X: $i] : (((pair_in_list(U, V, W) & strictly_less_than(V, X)) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l48_co')).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.39 tff(11,plain,(
% 0.12/0.39 ~((~(pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & strictly_less_than(W!1, X!0))) | pair_in_list(update_slb(U!3, X!0), V!2, X!0))),
% 0.12/0.39 inference(skolemize,[status(sab)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~pair_in_list(update_slb(U!3, X!0), V!2, X!0)),
% 0.12/0.39 inference(or_elim,[status(thm)],[11])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & strictly_less_than(W!1, X!0)),
% 0.12/0.39 inference(or_elim,[status(thm)],[11])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (strictly_less_than(W!1, X!0)),
% 0.12/0.39 inference(and_elim,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (pair_in_list(U!3, V!2, W!1)),
% 0.12/0.39 inference(and_elim,[status(thm)],[13])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (^[U: $i, V: $i, W: $i, X: $i] : refl((pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U, V, W) & strictly_less_than(W, X)) <=> (~((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))), ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) <=> (~(~((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))))), rewrite((~(~((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))) <=> ((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))), ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) <=> ((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))), (((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))), rewrite((((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))), (((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.39 tff(23,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l48_li3839')).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.39 tff(26,plain,(
% 0.12/0.39 ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.12/0.39 inference(skolemize,[status(sab)],[25])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!3, X!0), V!2, X!0) | (~pair_in_list(U!3, V!2, W!1)) | (~strictly_less_than(W!1, X!0)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | pair_in_list(update_slb(U!3, X!0), V!2, X!0) | (~pair_in_list(U!3, V!2, W!1)) | (~strictly_less_than(W!1, X!0)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!3, X!0), V!2, X!0) | (~pair_in_list(U!3, V!2, W!1)) | (~strictly_less_than(W!1, X!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | pair_in_list(update_slb(U!3, X!0), V!2, X!0) | (~pair_in_list(U!3, V!2, W!1)) | (~strictly_less_than(W!1, X!0))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[31, 28, 15, 14, 12])).
% 0.12/0.39 % SZS output end Proof
%------------------------------------------------------------------------------