%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Tue May 5 07:08:14 PM UTC 2026
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.13/0.32 % Computer : n028.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 09:38:17 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(cons_type, type, (
% 0.19/0.37 cons: ( $i * $i ) > $i)).
% 0.19/0.37 tff(nil_type, type, (
% 0.19/0.37 nil: $i)).
% 0.19/0.37 tff(elem_1_type, type, (
% 0.19/0.37 elem_1: $i)).
% 0.19/0.37 tff(inj_0_type, type, (
% 0.19/0.37 inj_0: ( $i * $i ) > $i)).
% 0.19/0.37 tff(drop_type, type, (
% 0.19/0.37 drop: ( $i * $i ) > $i)).
% 0.19/0.37 tff(s_type, type, (
% 0.19/0.37 s: $i > $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (![N: $i, Xs: $i, Ys: $i] : ((~(drop(N, Xs) = drop(N, Ys))) | (Xs = Ys)) <=> ![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!1, drop(Xk!1, Xk!0)) = Xk!0)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 ((~?[N: $i, Xs: $i, Ys: $i] : (~((~(drop(N, Xs) = drop(N, Ys))) | (Xs = Ys)))) <=> (~?[N: $i, Xs: $i, Ys: $i] : (~((~(drop(N, Xs) = drop(N, Ys))) | (Xs = Ys))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 ((~?[N: $i, Xs: $i, Ys: $i] : (~((drop(N, Xs) = drop(N, Ys)) => (Xs = Ys)))) <=> (~?[N: $i, Xs: $i, Ys: $i] : (~((~(drop(N, Xs) = drop(N, Ys))) | (Xs = Ys))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(4,axiom,(~?[N: $i, Xs: $i, Ys: $i] : (~((drop(N, Xs) = drop(N, Ys)) => (Xs = Ys)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goal_009')).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (~?[N: $i, Xs: $i, Ys: $i] : (~((~(drop(N, Xs) = drop(N, Ys))) | (Xs = Ys)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (~?[N: $i, Xs: $i, Ys: $i] : (~((~(drop(N, Xs) = drop(N, Ys))) | (Xs = Ys)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (~?[N: $i, Xs: $i, Ys: $i] : (~((~(drop(N, Xs) = drop(N, Ys))) | (Xs = Ys)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (~?[N: $i, Xs: $i, Ys: $i] : (~((~(drop(N, Xs) = drop(N, Ys))) | (Xs = Ys)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (^[N: $i, Xs: $i, Ys: $i] : refl($oeq(((~(drop(N, Xs) = drop(N, Ys))) | (Xs = Ys)), ((~(drop(N, Xs) = drop(N, Ys))) | (Xs = Ys))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(10,plain,(
% 0.19/0.37 ![N: $i, Xs: $i, Ys: $i] : ((~(drop(N, Xs) = drop(N, Ys))) | (Xs = Ys))),
% 0.19/0.37 inference(nnf-neg,[status(sab)],[8, 9])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!1, drop(Xk!1, Xk!0)) = Xk!0)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!1, drop(Xk!1, Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1)), drop(s(s(elem!1)), cons(elem!1, nil))) = cons(elem!1, nil))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (inj_0(s(s(elem!1)), drop(s(s(elem!1)), cons(elem!1, nil))) = cons(elem!1, nil)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (^[Z: $i] : refl((drop(s(Z), nil) = nil) <=> (drop(s(Z), nil) = nil))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (![Z: $i] : (drop(s(Z), nil) = nil) <=> ![Z: $i] : (drop(s(Z), nil) = nil)),
% 0.19/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![Z: $i] : (drop(s(Z), nil) = nil) <=> ![Z: $i] : (drop(s(Z), nil) = nil)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(17,axiom,(![Z: $i] : (drop(s(Z), nil) = nil)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_006')).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (![Z: $i] : (drop(s(Z), nil) = nil)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.37 tff(19,plain,(
% 0.19/0.37 ![Z: $i] : (drop(s(Z), nil) = nil)),
% 0.19/0.37 inference(skolemize,[status(sab)],[18])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (![Z: $i] : (drop(s(Z), nil) = nil)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 ((~![Z: $i] : (drop(s(Z), nil) = nil)) | (drop(s(s(elem!1)), nil) = nil)),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (drop(s(s(elem!1)), nil) = nil),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (nil = drop(s(s(elem!1)), nil)),
% 0.19/0.37 inference(symmetry,[status(thm)],[22])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 ((~![Z: $i] : (drop(s(Z), nil) = nil)) | (drop(s(elem!1), nil) = nil)),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (drop(s(elem!1), nil) = nil),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[24, 20])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (^[Z: $i, X2: $i, X3: $i] : refl((drop(s(Z), cons(X2, X3)) = drop(Z, X3)) <=> (drop(s(Z), cons(X2, X3)) = drop(Z, X3)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (![Z: $i, X2: $i, X3: $i] : (drop(s(Z), cons(X2, X3)) = drop(Z, X3)) <=> ![Z: $i, X2: $i, X3: $i] : (drop(s(Z), cons(X2, X3)) = drop(Z, X3))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (![Z: $i, X2: $i, X3: $i] : (drop(s(Z), cons(X2, X3)) = drop(Z, X3)) <=> ![Z: $i, X2: $i, X3: $i] : (drop(s(Z), cons(X2, X3)) = drop(Z, X3))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(29,axiom,(![Z: $i, X2: $i, X3: $i] : (drop(s(Z), cons(X2, X3)) = drop(Z, X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_007')).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (![Z: $i, X2: $i, X3: $i] : (drop(s(Z), cons(X2, X3)) = drop(Z, X3))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.37 tff(31,plain,(
% 0.19/0.37 ![Z: $i, X2: $i, X3: $i] : (drop(s(Z), cons(X2, X3)) = drop(Z, X3))),
% 0.19/0.37 inference(skolemize,[status(sab)],[30])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (![Z: $i, X2: $i, X3: $i] : (drop(s(Z), cons(X2, X3)) = drop(Z, X3))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 ((~![Z: $i, X2: $i, X3: $i] : (drop(s(Z), cons(X2, X3)) = drop(Z, X3))) | (drop(s(s(elem!1)), cons(elem!1, nil)) = drop(s(elem!1), nil))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (drop(s(s(elem!1)), cons(elem!1, nil)) = drop(s(elem!1), nil)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (drop(s(s(elem!1)), cons(elem!1, nil)) = drop(s(s(elem!1)), nil)),
% 0.19/0.37 inference(transitivity,[status(thm)],[34, 25, 23])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (inj_0(s(s(elem!1)), drop(s(s(elem!1)), cons(elem!1, nil))) = inj_0(s(s(elem!1)), drop(s(s(elem!1)), nil))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (inj_0(s(s(elem!1)), drop(s(s(elem!1)), nil)) = inj_0(s(s(elem!1)), drop(s(s(elem!1)), cons(elem!1, nil)))),
% 0.19/0.37 inference(symmetry,[status(thm)],[36])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!1, drop(Xk!1, Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1)), drop(s(s(elem!1)), nil)) = nil)),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (inj_0(s(s(elem!1)), drop(s(s(elem!1)), nil)) = nil),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[38, 11])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (nil = inj_0(s(s(elem!1)), drop(s(s(elem!1)), nil))),
% 0.19/0.37 inference(symmetry,[status(thm)],[39])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (nil = cons(elem!1, nil)),
% 0.19/0.37 inference(transitivity,[status(thm)],[40, 37, 13])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (^[X: $i, X2: $i] : refl((~(nil = cons(X, X2))) <=> (~(nil = cons(X, X2))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (![X: $i, X2: $i] : (~(nil = cons(X, X2))) <=> ![X: $i, X2: $i] : (~(nil = cons(X, X2)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (![X: $i, X2: $i] : (~(nil = cons(X, X2))) <=> ![X: $i, X2: $i] : (~(nil = cons(X, X2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(45,axiom,(![X: $i, X2: $i] : (~(nil = cons(X, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_003')).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (![X: $i, X2: $i] : (~(nil = cons(X, X2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.37 tff(47,plain,(
% 0.19/0.37 ![X: $i, X2: $i] : (~(nil = cons(X, X2)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[46])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 (![X: $i, X2: $i] : (~(nil = cons(X, X2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 ((~![X: $i, X2: $i] : (~(nil = cons(X, X2)))) | (~(nil = cons(elem!1, nil)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 (~(nil = cons(elem!1, nil))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[50, 41])).
% 0.19/0.37 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------