%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG179+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 04:58:33 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG179+1 : TPTP v9.0.0. Released v2.7.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.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 10:48:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(tptp_fun_U_0_type, type, (
% 0.19/0.39 tptp_fun_U_0: $i)).
% 0.19/0.39 tff(op2_type, type, (
% 0.19/0.39 op2: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_V_1_type, type, (
% 0.19/0.39 tptp_fun_V_1: $i)).
% 0.19/0.39 tff(h_type, type, (
% 0.19/0.39 h: $i > $i)).
% 0.19/0.39 tff(j_type, type, (
% 0.19/0.39 j: $i > $i)).
% 0.19/0.39 tff(sorti2_type, type, (
% 0.19/0.39 sorti2: $i > $o)).
% 0.19/0.39 tff(sorti1_type, type, (
% 0.19/0.39 sorti1: $i > $o)).
% 0.19/0.39 tff(op1_type, type, (
% 0.19/0.39 op1: ( $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[X1: $i] : refl(((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ((~sorti2(X1)) | (h(j(X1)) = X1)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 ((~((![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))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 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')).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (~((~(![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)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(or_elim,[status(thm)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.39 inference(and_elim,[status(thm)],[7])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.19/0.39 tff(10,plain,(
% 0.19/0.39 ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.39 inference(skolemize,[status(sab)],[9])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(op2(U, V), V) = U)))) <=> (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(op2(U, V), V) = U))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 ((~![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => (op2(op2(U, V), V) = U)))) <=> (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(op2(U, V), V) = U))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(14,axiom,(~![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => (op2(op2(U, V), V) = U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax4')).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(op2(U, V), V) = U)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(op2(U, V), V) = U)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(op2(U, V), V) = U)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(op2(U, V), V) = U)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (sorti2(U!0)),
% 0.19/0.39 inference(and_elim,[status(thm)],[18])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!0)) | (h(j(U!0)) = U!0))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!0)) | (h(j(U!0)) = U!0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!0)) | (h(j(U!0)) = U!0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!0)) | (h(j(U!0)) = U!0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (h(j(U!0)) = U!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[22, 19, 11])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.39 inference(or_elim,[status(thm)],[6])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.39 inference(and_elim,[status(thm)],[27])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 26])).
% 0.19/0.39 tff(30,plain,(
% 0.19/0.39 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!0)) | sorti1(j(U!0)))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!0)) | sorti1(j(U!0)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!0)) | sorti1(j(U!0)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!0)) | sorti1(j(U!0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (sorti1(j(U!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 19, 31])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (^[U: $i] : refl(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (^[U: $i] : rewrite(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[39, 37])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((sorti1(V) => (op1(op1(U, V), V) = U)) <=> ((~sorti1(V)) | (op1(op1(U, V), V) = U)))), (![V: $i] : (sorti1(V) => (op1(op1(U, V), V) = U)) <=> ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))), ((sorti1(U) => ![V: $i] : (sorti1(V) => (op1(op1(U, V), V) = U))) <=> (sorti1(U) => ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U))))), rewrite((sorti1(U) => ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))), ((sorti1(U) => ![V: $i] : (sorti1(V) => (op1(op1(U, V), V) = U))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => (op1(op1(U, V), V) = U))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.39 tff(44,axiom,(![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => (op1(op1(U, V), V) = U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax3')).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.39 tff(47,plain,(
% 0.19/0.39 ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))) | ((~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(op1(j(U!0), V), V) = j(U!0))))) <=> ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))) | (~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(op1(j(U!0), V), V) = j(U!0))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))) | ((~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(op1(j(U!0), V), V) = j(U!0))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(op1(U, V), V) = U)))) | (~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(op1(j(U!0), V), V) = j(U!0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![V: $i] : ((~sorti1(V)) | (op1(op1(j(U!0), V), V) = j(U!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[51, 48, 35])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (~((~sorti2(V!1)) | (op2(op2(U!0, V!1), V!1) = U!0))),
% 0.19/0.39 inference(and_elim,[status(thm)],[18])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (sorti2(V!1)),
% 0.19/0.39 inference(or_elim,[status(thm)],[53])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(V!1)) | sorti1(j(V!1)))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(V!1)) | sorti1(j(V!1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(V!1)) | sorti1(j(V!1)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(V!1)) | sorti1(j(V!1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (sorti1(j(V!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[57, 54, 31])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (((~![V: $i] : ((~sorti1(V)) | (op1(op1(j(U!0), V), V) = j(U!0)))) | ((~sorti1(j(V!1))) | (op1(op1(j(U!0), j(V!1)), j(V!1)) = j(U!0)))) <=> ((~![V: $i] : ((~sorti1(V)) | (op1(op1(j(U!0), V), V) = j(U!0)))) | (~sorti1(j(V!1))) | (op1(op1(j(U!0), j(V!1)), j(V!1)) = j(U!0)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((~![V: $i] : ((~sorti1(V)) | (op1(op1(j(U!0), V), V) = j(U!0)))) | ((~sorti1(j(V!1))) | (op1(op1(j(U!0), j(V!1)), j(V!1)) = j(U!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 ((~![V: $i] : ((~sorti1(V)) | (op1(op1(j(U!0), V), V) = j(U!0)))) | (~sorti1(j(V!1))) | (op1(op1(j(U!0), j(V!1)), j(V!1)) = j(U!0))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (op1(op1(j(U!0), j(V!1)), j(V!1)) = j(U!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[61, 58, 52])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[66, 64])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.19/0.40 inference(and_elim,[status(thm)],[7])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,(
% 0.19/0.40 ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[70])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z)))))) <=> ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[75, 19, 72])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | ((~sorti2(V!1)) | (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1))))) <=> ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | (~sorti2(V!1)) | (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | ((~sorti2(V!1)) | (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | (~sorti2(V!1)) | (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[79, 54, 76])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (op1(j(op2(U!0, V!1)), j(V!1)) = op1(op1(j(U!0), j(V!1)), j(V!1))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[80])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (^[U: $i] : refl(((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (^[U: $i] : rewrite(((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((sorti2(V) => sorti2(op2(U, V))) <=> ((~sorti2(V)) | sorti2(op2(U, V))))), (![V: $i] : (sorti2(V) => sorti2(op2(U, V))) <=> ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))), ((sorti2(U) => ![V: $i] : (sorti2(V) => sorti2(op2(U, V)))) <=> (sorti2(U) => ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))))), rewrite((sorti2(U) => ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))), ((sorti2(U) => ![V: $i] : (sorti2(V) => sorti2(op2(U, V)))) <=> ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.40 tff(90,axiom,(![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => sorti2(op2(U, V))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax2')).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.19/0.40 tff(93,plain,(
% 0.19/0.40 ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[92])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | ((~sorti2(U!0)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V))))) <=> ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | (~sorti2(U!0)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | ((~sorti2(U!0)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | (~sorti2(U!0)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[97, 94, 19])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | ((~sorti2(V!1)) | sorti2(op2(U!0, V!1)))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | (~sorti2(V!1)) | sorti2(op2(U!0, V!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | ((~sorti2(V!1)) | sorti2(op2(U!0, V!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | (~sorti2(V!1)) | sorti2(op2(U!0, V!1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (sorti2(op2(U!0, V!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[101, 54, 98])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(op2(U!0, V!1))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(op2(U!0, V!1), Z)) = op1(j(op2(U!0, V!1)), j(Z)))))) <=> ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(op2(U!0, V!1))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(op2(U!0, V!1), Z)) = op1(j(op2(U!0, V!1)), j(Z)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(op2(U!0, V!1))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(op2(U!0, V!1), Z)) = op1(j(op2(U!0, V!1)), j(Z)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(op2(U!0, V!1))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(op2(U!0, V!1), Z)) = op1(j(op2(U!0, V!1)), j(Z))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (![Z: $i] : ((~sorti2(Z)) | (j(op2(op2(U!0, V!1), Z)) = op1(j(op2(U!0, V!1)), j(Z))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[105, 72, 102])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (((~![Z: $i] : ((~sorti2(Z)) | (j(op2(op2(U!0, V!1), Z)) = op1(j(op2(U!0, V!1)), j(Z))))) | ((~sorti2(V!1)) | (j(op2(op2(U!0, V!1), V!1)) = op1(j(op2(U!0, V!1)), j(V!1))))) <=> ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(op2(U!0, V!1), Z)) = op1(j(op2(U!0, V!1)), j(Z))))) | (~sorti2(V!1)) | (j(op2(op2(U!0, V!1), V!1)) = op1(j(op2(U!0, V!1)), j(V!1))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(op2(U!0, V!1), Z)) = op1(j(op2(U!0, V!1)), j(Z))))) | ((~sorti2(V!1)) | (j(op2(op2(U!0, V!1), V!1)) = op1(j(op2(U!0, V!1)), j(V!1))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(op2(U!0, V!1), Z)) = op1(j(op2(U!0, V!1)), j(Z))))) | (~sorti2(V!1)) | (j(op2(op2(U!0, V!1), V!1)) = op1(j(op2(U!0, V!1)), j(V!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (j(op2(op2(U!0, V!1), V!1)) = op1(j(op2(U!0, V!1)), j(V!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[109, 54, 106])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (j(op2(op2(U!0, V!1), V!1)) = j(U!0)),
% 0.19/0.40 inference(transitivity,[status(thm)],[110, 81, 62])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (h(j(op2(op2(U!0, V!1), V!1))) = h(j(U!0))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | ((~sorti2(op2(U!0, V!1))) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(op2(U!0, V!1), V))))) <=> ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | (~sorti2(op2(U!0, V!1))) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(op2(U!0, V!1), V))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | ((~sorti2(op2(U!0, V!1))) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(op2(U!0, V!1), V))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | (~sorti2(op2(U!0, V!1))) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(op2(U!0, V!1), V)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (![V: $i] : ((~sorti2(V)) | sorti2(op2(op2(U!0, V!1), V)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[115, 94, 102])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (((~![V: $i] : ((~sorti2(V)) | sorti2(op2(op2(U!0, V!1), V)))) | ((~sorti2(V!1)) | sorti2(op2(op2(U!0, V!1), V!1)))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(op2(U!0, V!1), V)))) | (~sorti2(V!1)) | sorti2(op2(op2(U!0, V!1), V!1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(op2(U!0, V!1), V)))) | ((~sorti2(V!1)) | sorti2(op2(op2(U!0, V!1), V!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(op2(U!0, V!1), V)))) | (~sorti2(V!1)) | sorti2(op2(op2(U!0, V!1), V!1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (sorti2(op2(op2(U!0, V!1), V!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[119, 54, 116])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(op2(op2(U!0, V!1), V!1))) | (h(j(op2(op2(U!0, V!1), V!1))) = op2(op2(U!0, V!1), V!1)))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(op2(op2(U!0, V!1), V!1))) | (h(j(op2(op2(U!0, V!1), V!1))) = op2(op2(U!0, V!1), V!1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(op2(op2(U!0, V!1), V!1))) | (h(j(op2(op2(U!0, V!1), V!1))) = op2(op2(U!0, V!1), V!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(op2(op2(U!0, V!1), V!1))) | (h(j(op2(op2(U!0, V!1), V!1))) = op2(op2(U!0, V!1), V!1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (h(j(op2(op2(U!0, V!1), V!1))) = op2(op2(U!0, V!1), V!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[123, 11, 120])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (op2(op2(U!0, V!1), V!1) = h(j(op2(op2(U!0, V!1), V!1)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[124])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (op2(op2(U!0, V!1), V!1) = U!0),
% 0.19/0.41 inference(transitivity,[status(thm)],[125, 112, 23])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (~(op2(op2(U!0, V!1), V!1) = U!0)),
% 0.19/0.41 inference(or_elim,[status(thm)],[53])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------