%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG069+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 04:58:05 AM UTC 2025
% Result : Theorem 0.17s 0.35s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : ALG069+1 : TPTP v9.0.0. Released v2.7.0.
% 0.06/0.10 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n011.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Jun 19 10:47:41 EDT 2025
% 0.10/0.31 % CPUTime :
% 0.17/0.35 % SZS status Theorem
% 0.17/0.35 % SZS output start Proof
% 0.17/0.35 tff(tptp_fun_U_1_type, type, (
% 0.17/0.35 tptp_fun_U_1: $i)).
% 0.17/0.35 tff(op2_type, type, (
% 0.17/0.35 op2: ( $i * $i ) > $i)).
% 0.17/0.35 tff(h_type, type, (
% 0.17/0.35 h: $i > $i)).
% 0.17/0.35 tff(tptp_fun_V_0_type, type, (
% 0.17/0.35 tptp_fun_V_0: $i > $i)).
% 0.17/0.35 tff(j_type, type, (
% 0.17/0.35 j: $i > $i)).
% 0.17/0.35 tff(sorti2_type, type, (
% 0.17/0.35 sorti2: $i > $o)).
% 0.17/0.35 tff(sorti1_type, type, (
% 0.17/0.35 sorti1: $i > $o)).
% 0.17/0.35 tff(op1_type, type, (
% 0.17/0.35 op1: ( $i * $i ) > $i)).
% 0.17/0.35 tff(1,plain,
% 0.17/0.35 (^[X1: $i] : refl(((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ((~sorti2(X1)) | (h(j(X1)) = X1)))),
% 0.17/0.35 inference(bind,[status(th)],[])).
% 0.17/0.35 tff(2,plain,
% 0.17/0.35 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.17/0.35 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.35 tff(3,plain,
% 0.17/0.35 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(4,plain,
% 0.17/0.35 ((~((![U: $i] : (sorti1(U) => sorti2(h(U))) & ![V: $i] : (sorti2(V) => sorti1(j(V)))) => (~(((![W: $i] : (sorti1(W) => ![X: $i] : (sorti1(X) => (h(op1(W, X)) = op2(h(W), h(X))))) & ![Y: $i] : (sorti2(Y) => ![Z: $i] : (sorti2(Z) => (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) & ![X1: $i] : (sorti2(X1) => (h(j(X1)) = X1))) & ![X2: $i] : (sorti1(X2) => (j(h(X2)) = X2)))))) <=> (~((~(![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V))))) | (~(![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) & ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) & ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) & ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))))))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(5,axiom,(~((![U: $i] : (sorti1(U) => sorti2(h(U))) & ![V: $i] : (sorti2(V) => sorti1(j(V)))) => (~(((![W: $i] : (sorti1(W) => ![X: $i] : (sorti1(X) => (h(op1(W, X)) = op2(h(W), h(X))))) & ![Y: $i] : (sorti2(Y) => ![Z: $i] : (sorti2(Z) => (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) & ![X1: $i] : (sorti2(X1) => (h(j(X1)) = X1))) & ![X2: $i] : (sorti1(X2) => (j(h(X2)) = X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.17/0.35 tff(6,plain,
% 0.17/0.35 (~((~(![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V))))) | (~(![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) & ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) & ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) & ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)))))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.17/0.35 tff(7,plain,
% 0.17/0.35 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) & ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) & ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) & ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.17/0.35 inference(or_elim,[status(thm)],[6])).
% 0.17/0.35 tff(8,plain,
% 0.17/0.35 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.17/0.35 inference(and_elim,[status(thm)],[7])).
% 0.17/0.35 tff(9,plain,
% 0.17/0.35 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.17/0.35 tff(10,plain,(
% 0.17/0.35 ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.17/0.35 inference(skolemize,[status(sab)],[9])).
% 0.17/0.35 tff(11,plain,
% 0.17/0.35 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.17/0.35 tff(12,plain,
% 0.17/0.35 ((sorti2(U!1) & ![V: $i] : (~(sorti2(V) & (op2(V, V) = U!1)))) <=> (sorti2(U!1) & ![V: $i] : (~(sorti2(V) & (op2(V, V) = U!1))))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(13,plain,
% 0.17/0.35 ((~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))) <=> (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U))))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(14,plain,
% 0.17/0.35 ((~![U: $i] : (sorti2(U) => ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))) <=> (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U))))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(15,axiom,(~![U: $i] : (sorti2(U) => ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax4')).
% 0.17/0.35 tff(16,plain,
% 0.17/0.35 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.17/0.35 tff(17,plain,
% 0.17/0.35 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.17/0.35 tff(18,plain,
% 0.17/0.35 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.17/0.35 tff(19,plain,
% 0.17/0.35 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.17/0.35 tff(20,plain,
% 0.17/0.35 (sorti2(U!1) & ![V: $i] : (~(sorti2(V) & (op2(V, V) = U!1)))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.17/0.35 tff(21,plain,
% 0.17/0.35 (sorti2(U!1)),
% 0.17/0.35 inference(and_elim,[status(thm)],[20])).
% 0.17/0.35 tff(22,plain,
% 0.17/0.35 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!1)) | (h(j(U!1)) = U!1))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!1)) | (h(j(U!1)) = U!1))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(23,plain,
% 0.17/0.35 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!1)) | (h(j(U!1)) = U!1))),
% 0.17/0.35 inference(quant_inst,[status(thm)],[])).
% 0.17/0.35 tff(24,plain,
% 0.17/0.35 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!1)) | (h(j(U!1)) = U!1)),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.17/0.35 tff(25,plain,
% 0.17/0.35 (h(j(U!1)) = U!1),
% 0.17/0.35 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.17/0.35 tff(26,plain,
% 0.17/0.35 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.17/0.35 inference(bind,[status(th)],[])).
% 0.17/0.35 tff(27,plain,
% 0.17/0.35 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.17/0.35 inference(quant_intro,[status(thm)],[26])).
% 0.17/0.35 tff(28,plain,
% 0.17/0.35 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(29,plain,
% 0.17/0.35 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.17/0.35 inference(or_elim,[status(thm)],[6])).
% 0.17/0.35 tff(30,plain,
% 0.17/0.35 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.17/0.35 inference(and_elim,[status(thm)],[29])).
% 0.17/0.35 tff(31,plain,
% 0.17/0.35 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[30, 28])).
% 0.17/0.35 tff(32,plain,(
% 0.17/0.35 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.17/0.35 inference(skolemize,[status(sab)],[31])).
% 0.17/0.35 tff(33,plain,
% 0.17/0.35 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.17/0.35 tff(34,plain,
% 0.17/0.35 (((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!1)) | sorti1(j(U!1)))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!1)) | sorti1(j(U!1)))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(35,plain,
% 0.17/0.35 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!1)) | sorti1(j(U!1)))),
% 0.17/0.35 inference(quant_inst,[status(thm)],[])).
% 0.17/0.35 tff(36,plain,
% 0.17/0.35 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!1)) | sorti1(j(U!1))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.17/0.35 tff(37,plain,
% 0.17/0.35 (sorti1(j(U!1))),
% 0.17/0.35 inference(unit_resolution,[status(thm)],[36, 21, 33])).
% 0.17/0.35 tff(38,plain,
% 0.17/0.35 (^[U: $i] : refl(((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))) <=> ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))))),
% 0.17/0.35 inference(bind,[status(th)],[])).
% 0.17/0.35 tff(39,plain,
% 0.17/0.35 (![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))) <=> ![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))),
% 0.17/0.35 inference(quant_intro,[status(thm)],[38])).
% 0.17/0.35 tff(40,plain,
% 0.17/0.35 (^[U: $i] : rewrite(((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))) <=> ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))))),
% 0.17/0.35 inference(bind,[status(th)],[])).
% 0.17/0.35 tff(41,plain,
% 0.17/0.35 (![U: $i] : ((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))) <=> ![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))),
% 0.17/0.35 inference(quant_intro,[status(thm)],[40])).
% 0.17/0.35 tff(42,plain,
% 0.17/0.35 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U))) <=> ![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U)))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(43,plain,
% 0.17/0.35 (^[U: $i] : rewrite((sorti1(U) => ?[V: $i] : (sorti1(V) & (op1(V, V) = U))) <=> ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U))))),
% 0.17/0.35 inference(bind,[status(th)],[])).
% 0.17/0.35 tff(44,plain,
% 0.17/0.35 (![U: $i] : (sorti1(U) => ?[V: $i] : (sorti1(V) & (op1(V, V) = U))) <=> ![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U)))),
% 0.17/0.35 inference(quant_intro,[status(thm)],[43])).
% 0.17/0.35 tff(45,axiom,(![U: $i] : (sorti1(U) => ?[V: $i] : (sorti1(V) & (op1(V, V) = U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax3')).
% 0.17/0.35 tff(46,plain,
% 0.17/0.35 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U)))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.17/0.35 tff(47,plain,
% 0.17/0.35 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U)))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.17/0.35 tff(48,plain,(
% 0.17/0.35 ![U: $i] : ((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))),
% 0.17/0.35 inference(skolemize,[status(sab)],[47])).
% 0.17/0.35 tff(49,plain,
% 0.17/0.35 (![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.17/0.35 tff(50,plain,
% 0.17/0.35 (![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.17/0.35 tff(51,plain,
% 0.17/0.35 (((~![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))) | ((~sorti1(j(U!1))) | (~((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))))))) <=> ((~![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))) | (~sorti1(j(U!1))) | (~((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))))))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(52,plain,
% 0.17/0.35 ((~![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))) | ((~sorti1(j(U!1))) | (~((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))))))),
% 0.17/0.35 inference(quant_inst,[status(thm)],[])).
% 0.17/0.35 tff(53,plain,
% 0.17/0.35 ((~![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))) | (~sorti1(j(U!1))) | (~((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1)))))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.17/0.35 tff(54,plain,
% 0.17/0.35 (~((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))))),
% 0.17/0.35 inference(unit_resolution,[status(thm)],[53, 50, 37])).
% 0.17/0.35 tff(55,plain,
% 0.17/0.35 (((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1)))) | (op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))),
% 0.17/0.35 inference(tautology,[status(thm)],[])).
% 0.17/0.35 tff(56,plain,
% 0.17/0.35 (op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1)),
% 0.17/0.35 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.17/0.35 tff(57,plain,
% 0.17/0.35 (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = h(j(U!1))),
% 0.17/0.35 inference(monotonicity,[status(thm)],[56])).
% 0.17/0.35 tff(58,plain,
% 0.17/0.35 (((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1)))) | sorti1(tptp_fun_V_0(j(U!1)))),
% 0.17/0.35 inference(tautology,[status(thm)],[])).
% 0.17/0.35 tff(59,plain,
% 0.17/0.35 (sorti1(tptp_fun_V_0(j(U!1)))),
% 0.17/0.35 inference(unit_resolution,[status(thm)],[58, 54])).
% 0.17/0.35 tff(60,plain,
% 0.17/0.35 (^[W: $i] : refl(((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))))),
% 0.17/0.35 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(61,plain,
% 0.17/0.36 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[60])).
% 0.17/0.36 tff(62,plain,
% 0.17/0.36 (^[W: $i] : rewrite(((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(63,plain,
% 0.17/0.36 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[62])).
% 0.17/0.36 tff(64,plain,
% 0.17/0.36 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.17/0.36 inference(transitivity,[status(thm)],[63, 61])).
% 0.17/0.36 tff(65,plain,
% 0.17/0.36 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(66,plain,
% 0.17/0.36 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.17/0.36 inference(and_elim,[status(thm)],[7])).
% 0.17/0.36 tff(67,plain,
% 0.17/0.36 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.17/0.36 tff(68,plain,(
% 0.17/0.36 ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.17/0.36 inference(skolemize,[status(sab)],[67])).
% 0.17/0.36 tff(69,plain,
% 0.17/0.36 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.17/0.36 tff(70,plain,
% 0.17/0.36 (((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X)))))) <=> ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X)))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(71,plain,
% 0.17/0.36 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X)))))),
% 0.17/0.36 inference(quant_inst,[status(thm)],[])).
% 0.17/0.36 tff(72,plain,
% 0.17/0.36 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.17/0.36 tff(73,plain,
% 0.17/0.36 (![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[72, 69, 59])).
% 0.17/0.36 tff(74,plain,
% 0.17/0.36 (((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(75,plain,
% 0.17/0.36 ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))))),
% 0.17/0.36 inference(quant_inst,[status(thm)],[])).
% 0.17/0.36 tff(76,plain,
% 0.17/0.36 ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.17/0.36 tff(77,plain,
% 0.17/0.36 (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[76, 59, 73])).
% 0.17/0.36 tff(78,plain,
% 0.17/0.36 (op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))))),
% 0.17/0.36 inference(symmetry,[status(thm)],[77])).
% 0.17/0.36 tff(79,plain,
% 0.17/0.36 (op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1),
% 0.17/0.36 inference(transitivity,[status(thm)],[78, 57, 25])).
% 0.17/0.36 tff(80,plain,
% 0.17/0.36 (^[U: $i] : refl(((~sorti1(U)) | sorti2(h(U))) <=> ((~sorti1(U)) | sorti2(h(U))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(81,plain,
% 0.17/0.36 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[80])).
% 0.17/0.36 tff(82,plain,
% 0.17/0.36 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(83,plain,
% 0.17/0.36 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.17/0.36 inference(and_elim,[status(thm)],[29])).
% 0.17/0.36 tff(84,plain,
% 0.17/0.36 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.17/0.36 tff(85,plain,(
% 0.17/0.36 ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.17/0.36 inference(skolemize,[status(sab)],[84])).
% 0.17/0.36 tff(86,plain,
% 0.17/0.36 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.17/0.36 tff(87,plain,
% 0.17/0.36 (((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1)))))) <=> ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1)))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(88,plain,
% 0.17/0.36 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1)))))),
% 0.17/0.36 inference(quant_inst,[status(thm)],[])).
% 0.17/0.36 tff(89,plain,
% 0.17/0.36 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.17/0.36 tff(90,plain,
% 0.17/0.36 (sorti2(h(tptp_fun_V_0(j(U!1))))),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[89, 86, 59])).
% 0.17/0.36 tff(91,plain,
% 0.17/0.36 (^[V: $i] : refl(((~sorti2(V)) | (~(op2(V, V) = U!1))) <=> ((~sorti2(V)) | (~(op2(V, V) = U!1))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(92,plain,
% 0.17/0.36 (![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1))) <=> ![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[91])).
% 0.17/0.36 tff(93,plain,
% 0.17/0.36 (^[V: $i] : trans(monotonicity(rewrite((sorti2(V) & (op2(V, V) = U!1)) <=> (~((~sorti2(V)) | (~(op2(V, V) = U!1))))), ((~(sorti2(V) & (op2(V, V) = U!1))) <=> (~(~((~sorti2(V)) | (~(op2(V, V) = U!1))))))), rewrite((~(~((~sorti2(V)) | (~(op2(V, V) = U!1))))) <=> ((~sorti2(V)) | (~(op2(V, V) = U!1)))), ((~(sorti2(V) & (op2(V, V) = U!1))) <=> ((~sorti2(V)) | (~(op2(V, V) = U!1)))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(94,plain,
% 0.17/0.36 (![V: $i] : (~(sorti2(V) & (op2(V, V) = U!1))) <=> ![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[93])).
% 0.17/0.36 tff(95,plain,
% 0.17/0.36 (![V: $i] : (~(sorti2(V) & (op2(V, V) = U!1)))),
% 0.17/0.36 inference(and_elim,[status(thm)],[20])).
% 0.17/0.36 tff(96,plain,
% 0.17/0.36 (![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.17/0.36 tff(97,plain,
% 0.17/0.36 (![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.17/0.36 tff(98,plain,
% 0.17/0.36 (((~![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | (~(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1)))) <=> ((~![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | (~(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1)))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(99,plain,
% 0.17/0.36 ((~![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | (~(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1)))),
% 0.17/0.36 inference(quant_inst,[status(thm)],[])).
% 0.17/0.36 tff(100,plain,
% 0.17/0.36 ((~![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | (~(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.17/0.36 tff(101,plain,
% 0.17/0.36 (~(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1)),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[100, 97, 90])).
% 0.17/0.36 tff(102,plain,
% 0.17/0.36 ($false),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[101, 79])).
% 0.17/0.36 % SZS output end Proof
% 0.17/0.36 % E exiting
%------------------------------------------------------------------------------