%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV400+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 05:32:22 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV400+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:44:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(pair_in_list_type, type, (
% 0.12/0.38 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_W_1_type, type, (
% 0.12/0.38 tptp_fun_W_1: $i)).
% 0.12/0.38 tff(tptp_fun_V_2_type, type, (
% 0.12/0.38 tptp_fun_V_2: $i)).
% 0.12/0.38 tff(create_slb_type, type, (
% 0.12/0.38 create_slb: $i)).
% 0.12/0.38 tff(less_than_type, type, (
% 0.12/0.38 less_than: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: $i)).
% 0.12/0.38 tff(update_slb_type, type, (
% 0.12/0.38 update_slb: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((~![V: $i, W: $i, X: $i] : ((~(pair_in_list(create_slb, V, W) & less_than(X, W))) | pair_in_list(update_slb(create_slb, X), V, W))) <=> (~![V: $i, W: $i, X: $i] : ((~(pair_in_list(create_slb, V, W) & less_than(X, W))) | pair_in_list(update_slb(create_slb, X), V, W)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(create_slb, V, W) & less_than(X, W)) => pair_in_list(update_slb(create_slb, X), V, W))) <=> (~![V: $i, W: $i, X: $i] : ((~(pair_in_list(create_slb, V, W) & less_than(X, W))) | pair_in_list(update_slb(create_slb, X), V, W)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,axiom,(~![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(create_slb, V, W) & less_than(X, W)) => pair_in_list(update_slb(create_slb, X), V, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l36_co')).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (~![V: $i, W: $i, X: $i] : ((~(pair_in_list(create_slb, V, W) & less_than(X, W))) | pair_in_list(update_slb(create_slb, X), V, W))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![V: $i, W: $i, X: $i] : ((~(pair_in_list(create_slb, V, W) & less_than(X, W))) | pair_in_list(update_slb(create_slb, X), V, W))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![V: $i, W: $i, X: $i] : ((~(pair_in_list(create_slb, V, W) & less_than(X, W))) | pair_in_list(update_slb(create_slb, X), V, W))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![V: $i, W: $i, X: $i] : ((~(pair_in_list(create_slb, V, W) & less_than(X, W))) | pair_in_list(update_slb(create_slb, X), V, W))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.38 tff(8,plain,(
% 0.12/0.38 ~((~(pair_in_list(create_slb, V!2, W!1) & less_than(X!0, W!1))) | pair_in_list(update_slb(create_slb, X!0), V!2, W!1))),
% 0.12/0.38 inference(skolemize,[status(sab)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (pair_in_list(create_slb, V!2, W!1) & less_than(X!0, W!1)),
% 0.12/0.38 inference(or_elim,[status(thm)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (pair_in_list(create_slb, V!2, W!1)),
% 0.12/0.38 inference(and_elim,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (^[U: $i, V: $i] : refl((~pair_in_list(create_slb, U, V)) <=> (~pair_in_list(create_slb, U, V)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V)) <=> ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V)) <=> ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,axiom,(![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax22')).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.38 tff(16,plain,(
% 0.12/0.38 ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.12/0.38 inference(skolemize,[status(sab)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((~![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))) | (~pair_in_list(create_slb, V!2, W!1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------