%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG029+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 04:57:55 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG029+1 : TPTP v9.0.0. Released v2.7.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n009.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Jun 19 10:41:18 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(op2_type, type, (
% 0.19/0.36 op2: ( $i * $i ) > $i)).
% 0.19/0.36 tff(tptp_fun_U_0_type, type, (
% 0.19/0.36 tptp_fun_U_0: $i)).
% 0.19/0.36 tff(tptp_fun_V_1_type, type, (
% 0.19/0.36 tptp_fun_V_1: $i)).
% 0.19/0.36 tff(h_type, type, (
% 0.19/0.36 h: $i > $i)).
% 0.19/0.36 tff(j_type, type, (
% 0.19/0.36 j: $i > $i)).
% 0.19/0.36 tff(sorti2_type, type, (
% 0.19/0.36 sorti2: $i > $o)).
% 0.19/0.36 tff(sorti1_type, type, (
% 0.19/0.36 sorti1: $i > $o)).
% 0.19/0.36 tff(op1_type, type, (
% 0.19/0.36 op1: ( $i * $i ) > $i)).
% 0.19/0.36 tff(1,plain,
% 0.19/0.36 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))) <=> (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U)))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 ((~![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => (op2(U, V) = op2(V, U))))) <=> (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U)))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(3,axiom,(~![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => (op2(U, V) = op2(V, U))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax4')).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.36 tff(7,plain,
% 0.19/0.36 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 (~((~sorti2(V!1)) | (op2(U!0, V!1) = op2(V!1, U!0)))),
% 0.19/0.36 inference(and_elim,[status(thm)],[7])).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 (sorti2(V!1)),
% 0.19/0.36 inference(or_elim,[status(thm)],[8])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (^[U: $i] : refl(((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 (^[U: $i] : rewrite(((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.36 inference(transitivity,[status(thm)],[13, 11])).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 (^[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))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.36 tff(18,axiom,(![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => sorti2(op2(U, V))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax2')).
% 0.19/0.36 tff(19,plain,
% 0.19/0.36 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.36 tff(20,plain,
% 0.19/0.36 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.36 tff(21,plain,(
% 0.19/0.36 ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.36 inference(skolemize,[status(sab)],[20])).
% 0.19/0.36 tff(22,plain,
% 0.19/0.36 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.36 tff(23,plain,
% 0.19/0.36 (((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | ((~sorti2(V!1)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(V!1, V))))) <=> ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | (~sorti2(V!1)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(V!1, V))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(24,plain,
% 0.19/0.36 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | ((~sorti2(V!1)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(V!1, V))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(25,plain,
% 0.19/0.36 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | (~sorti2(V!1)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(V!1, V)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.36 tff(26,plain,
% 0.19/0.36 (![V: $i] : ((~sorti2(V)) | sorti2(op2(V!1, V)))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 0.19/0.36 tff(27,plain,
% 0.19/0.36 (sorti2(U!0)),
% 0.19/0.36 inference(and_elim,[status(thm)],[7])).
% 0.19/0.36 tff(28,plain,
% 0.19/0.36 (((~![V: $i] : ((~sorti2(V)) | sorti2(op2(V!1, V)))) | ((~sorti2(U!0)) | sorti2(op2(V!1, U!0)))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(V!1, V)))) | (~sorti2(U!0)) | sorti2(op2(V!1, U!0)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(29,plain,
% 0.19/0.36 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(V!1, V)))) | ((~sorti2(U!0)) | sorti2(op2(V!1, U!0)))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(30,plain,
% 0.19/0.36 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(V!1, V)))) | (~sorti2(U!0)) | sorti2(op2(V!1, U!0))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.36 tff(31,plain,
% 0.19/0.36 (sorti2(op2(V!1, U!0))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[30, 27, 26])).
% 0.19/0.36 tff(32,plain,
% 0.19/0.36 (^[X1: $i] : refl(((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ((~sorti2(X1)) | (h(j(X1)) = X1)))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(33,plain,
% 0.19/0.36 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.36 tff(34,plain,
% 0.19/0.36 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(35,plain,
% 0.19/0.36 ((~((![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))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(36,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')).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (~((~(![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)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (![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))),
% 0.19/0.37 inference(or_elim,[status(thm)],[37])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.37 inference(and_elim,[status(thm)],[38])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.19/0.37 tff(41,plain,(
% 0.19/0.37 ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.37 inference(skolemize,[status(sab)],[40])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(op2(V!1, U!0))) | (h(j(op2(V!1, U!0))) = op2(V!1, U!0)))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(op2(V!1, U!0))) | (h(j(op2(V!1, U!0))) = op2(V!1, U!0)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(op2(V!1, U!0))) | (h(j(op2(V!1, U!0))) = op2(V!1, U!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(op2(V!1, U!0))) | (h(j(op2(V!1, U!0))) = op2(V!1, U!0))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (h(j(op2(V!1, U!0))) = op2(V!1, U!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[45, 42, 31])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 (^[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))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 (![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)))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (^[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))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 (![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)))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 (![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)))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[50, 48])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (![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)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.19/0.37 inference(and_elim,[status(thm)],[38])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.37 tff(55,plain,(
% 0.19/0.37 ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[54])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 (((~![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)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(58,plain,
% 0.19/0.37 ((~![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)))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(59,plain,
% 0.19/0.37 ((~![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))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.37 tff(60,plain,
% 0.19/0.37 (![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[59, 27, 56])).
% 0.19/0.37 tff(61,plain,
% 0.19/0.37 (((~![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))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(62,plain,
% 0.19/0.37 ((~![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))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(63,plain,
% 0.19/0.37 ((~![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)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.37 tff(64,plain,
% 0.19/0.37 (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[63, 9, 60])).
% 0.19/0.37 tff(65,plain,
% 0.19/0.37 (op1(j(U!0), j(V!1)) = j(op2(U!0, V!1))),
% 0.19/0.37 inference(symmetry,[status(thm)],[64])).
% 0.19/0.37 tff(66,plain,
% 0.19/0.37 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(67,plain,
% 0.19/0.37 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.37 tff(68,plain,
% 0.19/0.37 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(69,plain,
% 0.19/0.37 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.37 inference(or_elim,[status(thm)],[37])).
% 0.19/0.37 tff(70,plain,
% 0.19/0.37 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.37 inference(and_elim,[status(thm)],[69])).
% 0.19/0.37 tff(71,plain,
% 0.19/0.37 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[70, 68])).
% 0.19/0.37 tff(72,plain,(
% 0.19/0.37 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[71])).
% 0.19/0.37 tff(73,plain,
% 0.19/0.37 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[72, 67])).
% 0.19/0.37 tff(74,plain,
% 0.19/0.37 (((~![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(75,plain,
% 0.19/0.37 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(V!1)) | sorti1(j(V!1)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(76,plain,
% 0.19/0.37 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(V!1)) | sorti1(j(V!1))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.37 tff(77,plain,
% 0.19/0.37 (sorti1(j(V!1))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[76, 9, 73])).
% 0.19/0.37 tff(78,plain,
% 0.19/0.37 (^[U: $i] : refl(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(79,plain,
% 0.19/0.37 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.37 tff(80,plain,
% 0.19/0.37 (^[U: $i] : rewrite(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(81,plain,
% 0.19/0.37 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.37 tff(82,plain,
% 0.19/0.37 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[81, 79])).
% 0.19/0.37 tff(83,plain,
% 0.19/0.37 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(84,plain,
% 0.19/0.37 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((sorti1(V) => (op1(U, V) = op1(V, U))) <=> ((~sorti1(V)) | (op1(U, V) = op1(V, U))))), (![V: $i] : (sorti1(V) => (op1(U, V) = op1(V, U))) <=> ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))), ((sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, V) = op1(V, U)))) <=> (sorti1(U) => ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))))), rewrite((sorti1(U) => ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))), ((sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, V) = op1(V, U)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(85,plain,
% 0.19/0.37 (![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, V) = op1(V, U)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.37 tff(86,axiom,(![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, V) = op1(V, U))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax3')).
% 0.19/0.37 tff(87,plain,
% 0.19/0.37 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.37 tff(88,plain,
% 0.19/0.37 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.37 tff(89,plain,(
% 0.19/0.37 ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[88])).
% 0.19/0.37 tff(90,plain,
% 0.19/0.37 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.19/0.37 tff(91,plain,
% 0.19/0.37 (((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))) | ((~sorti1(j(V!1))) | ![V: $i] : ((~sorti1(V)) | (op1(j(V!1), V) = op1(V, j(V!1)))))) <=> ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))) | (~sorti1(j(V!1))) | ![V: $i] : ((~sorti1(V)) | (op1(j(V!1), V) = op1(V, j(V!1)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(92,plain,
% 0.19/0.37 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))) | ((~sorti1(j(V!1))) | ![V: $i] : ((~sorti1(V)) | (op1(j(V!1), V) = op1(V, j(V!1)))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(93,plain,
% 0.19/0.37 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))) | (~sorti1(j(V!1))) | ![V: $i] : ((~sorti1(V)) | (op1(j(V!1), V) = op1(V, j(V!1))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.37 tff(94,plain,
% 0.19/0.37 (![V: $i] : ((~sorti1(V)) | (op1(j(V!1), V) = op1(V, j(V!1))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[93, 90, 77])).
% 0.19/0.37 tff(95,plain,
% 0.19/0.37 (((~![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(96,plain,
% 0.19/0.37 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!0)) | sorti1(j(U!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(97,plain,
% 0.19/0.37 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!0)) | sorti1(j(U!0))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.37 tff(98,plain,
% 0.19/0.37 (sorti1(j(U!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[97, 27, 73])).
% 0.19/0.37 tff(99,plain,
% 0.19/0.37 (((~![V: $i] : ((~sorti1(V)) | (op1(j(V!1), V) = op1(V, j(V!1))))) | ((~sorti1(j(U!0))) | (op1(j(V!1), j(U!0)) = op1(j(U!0), j(V!1))))) <=> ((~![V: $i] : ((~sorti1(V)) | (op1(j(V!1), V) = op1(V, j(V!1))))) | (~sorti1(j(U!0))) | (op1(j(V!1), j(U!0)) = op1(j(U!0), j(V!1))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(100,plain,
% 0.19/0.37 ((~![V: $i] : ((~sorti1(V)) | (op1(j(V!1), V) = op1(V, j(V!1))))) | ((~sorti1(j(U!0))) | (op1(j(V!1), j(U!0)) = op1(j(U!0), j(V!1))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(101,plain,
% 0.19/0.37 ((~![V: $i] : ((~sorti1(V)) | (op1(j(V!1), V) = op1(V, j(V!1))))) | (~sorti1(j(U!0))) | (op1(j(V!1), j(U!0)) = op1(j(U!0), j(V!1)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.37 tff(102,plain,
% 0.19/0.37 (op1(j(V!1), j(U!0)) = op1(j(U!0), j(V!1))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[101, 98, 94])).
% 0.19/0.37 tff(103,plain,
% 0.19/0.37 (((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(V!1)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(V!1, Z)) = op1(j(V!1), j(Z)))))) <=> ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(V!1)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(V!1, Z)) = op1(j(V!1), j(Z)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(104,plain,
% 0.19/0.37 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(V!1)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(V!1, Z)) = op1(j(V!1), j(Z)))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(105,plain,
% 0.19/0.37 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(V!1)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(V!1, Z)) = op1(j(V!1), j(Z))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.37 tff(106,plain,
% 0.19/0.37 (![Z: $i] : ((~sorti2(Z)) | (j(op2(V!1, Z)) = op1(j(V!1), j(Z))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[105, 9, 56])).
% 0.19/0.37 tff(107,plain,
% 0.19/0.37 (((~![Z: $i] : ((~sorti2(Z)) | (j(op2(V!1, Z)) = op1(j(V!1), j(Z))))) | ((~sorti2(U!0)) | (j(op2(V!1, U!0)) = op1(j(V!1), j(U!0))))) <=> ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(V!1, Z)) = op1(j(V!1), j(Z))))) | (~sorti2(U!0)) | (j(op2(V!1, U!0)) = op1(j(V!1), j(U!0))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(108,plain,
% 0.19/0.37 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(V!1, Z)) = op1(j(V!1), j(Z))))) | ((~sorti2(U!0)) | (j(op2(V!1, U!0)) = op1(j(V!1), j(U!0))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(109,plain,
% 0.19/0.37 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(V!1, Z)) = op1(j(V!1), j(Z))))) | (~sorti2(U!0)) | (j(op2(V!1, U!0)) = op1(j(V!1), j(U!0)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.37 tff(110,plain,
% 0.19/0.37 (j(op2(V!1, U!0)) = op1(j(V!1), j(U!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[109, 27, 106])).
% 0.19/0.37 tff(111,plain,
% 0.19/0.37 (j(op2(V!1, U!0)) = j(op2(U!0, V!1))),
% 0.19/0.37 inference(transitivity,[status(thm)],[110, 102, 65])).
% 0.19/0.37 tff(112,plain,
% 0.19/0.37 (h(j(op2(V!1, U!0))) = h(j(op2(U!0, V!1)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.37 tff(113,plain,
% 0.19/0.37 (h(j(op2(U!0, V!1))) = h(j(op2(V!1, U!0)))),
% 0.19/0.37 inference(symmetry,[status(thm)],[112])).
% 0.19/0.37 tff(114,plain,
% 0.19/0.37 (((~![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))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(115,plain,
% 0.19/0.37 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | ((~sorti2(U!0)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(116,plain,
% 0.19/0.37 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | (~sorti2(U!0)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.38 tff(117,plain,
% 0.19/0.38 (![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[116, 22, 27])).
% 0.19/0.38 tff(118,plain,
% 0.19/0.38 (((~![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(119,plain,
% 0.19/0.38 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | ((~sorti2(V!1)) | sorti2(op2(U!0, V!1)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(120,plain,
% 0.19/0.38 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | (~sorti2(V!1)) | sorti2(op2(U!0, V!1))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.38 tff(121,plain,
% 0.19/0.38 (sorti2(op2(U!0, V!1))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[120, 9, 117])).
% 0.19/0.38 tff(122,plain,
% 0.19/0.38 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(op2(U!0, V!1))) | (h(j(op2(U!0, V!1))) = op2(U!0, V!1)))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(op2(U!0, V!1))) | (h(j(op2(U!0, V!1))) = op2(U!0, V!1)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(123,plain,
% 0.19/0.38 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(op2(U!0, V!1))) | (h(j(op2(U!0, V!1))) = op2(U!0, V!1)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(124,plain,
% 0.19/0.38 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(op2(U!0, V!1))) | (h(j(op2(U!0, V!1))) = op2(U!0, V!1))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.38 tff(125,plain,
% 0.19/0.38 (h(j(op2(U!0, V!1))) = op2(U!0, V!1)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[124, 42, 121])).
% 0.19/0.38 tff(126,plain,
% 0.19/0.38 (op2(U!0, V!1) = h(j(op2(U!0, V!1)))),
% 0.19/0.38 inference(symmetry,[status(thm)],[125])).
% 0.19/0.38 tff(127,plain,
% 0.19/0.38 (op2(U!0, V!1) = op2(V!1, U!0)),
% 0.19/0.38 inference(transitivity,[status(thm)],[126, 113, 46])).
% 0.19/0.38 tff(128,plain,
% 0.19/0.38 (~(op2(U!0, V!1) = op2(V!1, U!0))),
% 0.19/0.38 inference(or_elim,[status(thm)],[8])).
% 0.19/0.38 tff(129,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------