%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG041+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 04:57:59 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : ALG041+1 : TPTP v9.0.0. Released v2.7.0.
% 0.01/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.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 : Thu Jun 19 10:45:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(j_type, type, (
% 0.20/0.38 j: $i > $i)).
% 0.20/0.38 tff(tptp_fun_U_1_type, type, (
% 0.20/0.38 tptp_fun_U_1: $i)).
% 0.20/0.38 tff(op1_type, type, (
% 0.20/0.38 op1: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_V_0_type, type, (
% 0.20/0.38 tptp_fun_V_0: $i > $i)).
% 0.20/0.38 tff(op2_type, type, (
% 0.20/0.38 op2: ( $i * $i ) > $i)).
% 0.20/0.38 tff(h_type, type, (
% 0.20/0.38 h: $i > $i)).
% 0.20/0.38 tff(sorti2_type, type, (
% 0.20/0.38 sorti2: $i > $o)).
% 0.20/0.38 tff(sorti1_type, type, (
% 0.20/0.38 sorti1: $i > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 ((~((![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))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 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/sandbox/benchmark/theBenchmark.p','co1')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (~((~(![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)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.38 inference(or_elim,[status(thm)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.38 inference(and_elim,[status(thm)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.20/0.38 tff(10,plain,(
% 0.20/0.38 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[9])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 ((sorti2(U!1) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U!1))) <=> (sorti2(U!1) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U!1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U))) <=> ?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 ((~(~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U))))) <=> ?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 ((~?[U: $i] : (sorti2(U) & ![V: $i] : (sorti2(V) => (op2(V, V) = U)))) <=> (~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 ((~(~?[U: $i] : (sorti2(U) & ![V: $i] : (sorti2(V) => (op2(V, V) = U))))) <=> (~(~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[15])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ((~(~?[U: $i] : (sorti2(U) & ![V: $i] : (sorti2(V) => (op2(V, V) = U))))) <=> ?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.38 tff(18,axiom,(~(~?[U: $i] : (sorti2(U) & ![V: $i] : (sorti2(V) => (op2(V, V) = U))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax4')).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (sorti2(U!1) & ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U!1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (sorti2(U!1)),
% 0.20/0.38 inference(and_elim,[status(thm)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (((~![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)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!1)) | sorti1(j(U!1)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!1)) | sorti1(j(U!1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (sorti1(j(U!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[25, 22, 11])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (^[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)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((~?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (op1(V, V) = U)))) <=> (~?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (op1(V, V) = U))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 ((~?[U: $i] : (sorti1(U) & ![V: $i] : (sorti1(V) => (op1(V, V) = U)))) <=> (~?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (op1(V, V) = U))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(31,axiom,(~?[U: $i] : (sorti1(U) & ![V: $i] : (sorti1(V) => (op1(V, V) = U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax3')).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (~?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (op1(V, V) = U)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (~?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (op1(V, V) = U)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (~?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (op1(V, V) = U)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (~?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (op1(V, V) = U)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (^[U: $i] : nnf_neg(refl($oeq((~sorti1(U)), (~sorti1(U)))), sk($oeq((~![V: $i] : ((~sorti1(V)) | (op1(V, V) = U))), (~((~sorti1(tptp_fun_V_0(U))) | (op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))), $oeq((~(sorti1(U) & ![V: $i] : ((~sorti1(V)) | (op1(V, V) = U)))), ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(37,plain,(
% 0.20/0.38 ![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))),
% 0.20/0.38 inference(nnf-neg,[status(sab)],[35, 36])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[37, 28])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (((~![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)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 ((~![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)))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 ((~![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (~((~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)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[41, 38, 26])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (((~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)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (sorti1(tptp_fun_V_0(j(U!1)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (^[U: $i] : refl(((~sorti1(U)) | sorti2(h(U))) <=> ((~sorti1(U)) | sorti2(h(U))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.20/0.38 inference(and_elim,[status(thm)],[7])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.38 tff(50,plain,(
% 0.20/0.38 ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[49])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (((~![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)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1)))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (sorti2(h(tptp_fun_V_0(j(U!1))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[54, 51, 44])).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 (^[V: $i] : refl(((~sorti2(V)) | (op2(V, V) = U!1)) <=> ((~sorti2(V)) | (op2(V, V) = U!1)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 (![V: $i] : ((~sorti2(V)) | (op2(V, V) = U!1)) <=> ![V: $i] : ((~sorti2(V)) | (op2(V, V) = U!1))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (![V: $i] : ((~sorti2(V)) | (op2(V, V) = U!1))),
% 0.20/0.38 inference(and_elim,[status(thm)],[21])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (![V: $i] : ((~sorti2(V)) | (op2(V, V) = U!1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (((~![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))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 ((~![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))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((~![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)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[62, 59, 55])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (j(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))) = j(U!1)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[63])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (^[Y: $i] : refl(((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (^[Y: $i] : rewrite(((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[68, 66])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (![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))),
% 0.20/0.39 inference(or_elim,[status(thm)],[6])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.20/0.39 inference(and_elim,[status(thm)],[71])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[72, 70])).
% 0.20/0.39 tff(74,plain,(
% 0.20/0.39 ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[73])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[74, 69])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(h(tptp_fun_V_0(j(U!1))), Z)) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(Z)))))) <=> ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(h(tptp_fun_V_0(j(U!1))), Z)) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(Z)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(h(tptp_fun_V_0(j(U!1))), Z)) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(Z)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(h(tptp_fun_V_0(j(U!1))), Z)) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(Z))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (![Z: $i] : ((~sorti2(Z)) | (j(op2(h(tptp_fun_V_0(j(U!1))), Z)) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(Z))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[78, 75, 55])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (((~![Z: $i] : ((~sorti2(Z)) | (j(op2(h(tptp_fun_V_0(j(U!1))), Z)) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(Z))))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | (j(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(h(tptp_fun_V_0(j(U!1)))))))) <=> ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(h(tptp_fun_V_0(j(U!1))), Z)) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(Z))))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | (j(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(h(tptp_fun_V_0(j(U!1)))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(h(tptp_fun_V_0(j(U!1))), Z)) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(Z))))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | (j(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(h(tptp_fun_V_0(j(U!1)))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(h(tptp_fun_V_0(j(U!1))), Z)) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(Z))))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | (j(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(h(tptp_fun_V_0(j(U!1))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (j(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(h(tptp_fun_V_0(j(U!1)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[82, 55, 79])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (op1(j(h(tptp_fun_V_0(j(U!1)))), j(h(tptp_fun_V_0(j(U!1))))) = j(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))))),
% 0.20/0.39 inference(symmetry,[status(thm)],[83])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 (^[X2: $i] : refl(((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ((~sorti1(X2)) | (j(h(X2)) = X2)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.20/0.39 inference(and_elim,[status(thm)],[71])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.39 tff(90,plain,(
% 0.20/0.39 ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.20/0.39 inference(skolemize,[status(sab)],[89])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 (((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | (j(h(tptp_fun_V_0(j(U!1)))) = tptp_fun_V_0(j(U!1))))) <=> ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (j(h(tptp_fun_V_0(j(U!1)))) = tptp_fun_V_0(j(U!1))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | (j(h(tptp_fun_V_0(j(U!1)))) = tptp_fun_V_0(j(U!1))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (j(h(tptp_fun_V_0(j(U!1)))) = tptp_fun_V_0(j(U!1)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 (j(h(tptp_fun_V_0(j(U!1)))) = tptp_fun_V_0(j(U!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[94, 91, 44])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 (tptp_fun_V_0(j(U!1)) = j(h(tptp_fun_V_0(j(U!1))))),
% 0.20/0.39 inference(symmetry,[status(thm)],[95])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 (op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = op1(j(h(tptp_fun_V_0(j(U!1)))), j(h(tptp_fun_V_0(j(U!1)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[96, 96])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 (op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1)),
% 0.20/0.39 inference(transitivity,[status(thm)],[97, 84, 64])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 (((~sorti1(tptp_fun_V_0(j(U!1)))) | (op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[99, 42])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[100, 98])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------