%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG178+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG178+1 : TPTP v9.0.0. Released v2.7.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.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 10:47:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(tptp_fun_V_1_type, type, (
% 0.12/0.38 tptp_fun_V_1: $i)).
% 0.12/0.38 tff(op2_type, type, (
% 0.12/0.38 op2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_U_0_type, type, (
% 0.12/0.38 tptp_fun_U_0: $i)).
% 0.12/0.38 tff(h_type, type, (
% 0.12/0.38 h: $i > $i)).
% 0.12/0.38 tff(j_type, type, (
% 0.12/0.38 j: $i > $i)).
% 0.12/0.38 tff(sorti2_type, type, (
% 0.12/0.38 sorti2: $i > $o)).
% 0.12/0.38 tff(sorti1_type, type, (
% 0.12/0.38 sorti1: $i > $o)).
% 0.12/0.38 tff(op1_type, type, (
% 0.12/0.38 op1: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X1: $i] : refl(((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ((~sorti2(X1)) | (h(j(X1)) = X1)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 ((~((![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))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 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')).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~((~(![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)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![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))),
% 0.12/0.38 inference(or_elim,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.38 inference(and_elim,[status(thm)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.12/0.38 tff(10,plain,(
% 0.12/0.38 ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.38 inference(skolemize,[status(sab)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, op2(U, V)) = V)))) <=> (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, op2(U, V)) = V))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((~![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => (op2(U, op2(U, V)) = V)))) <=> (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, op2(U, V)) = V))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,axiom,(~![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => (op2(U, op2(U, V)) = V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax4')).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, op2(U, V)) = V)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, op2(U, V)) = V)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, op2(U, V)) = V)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, op2(U, V)) = V)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (~((~sorti2(V!1)) | (op2(U!0, op2(U!0, V!1)) = V!1))),
% 0.12/0.38 inference(and_elim,[status(thm)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (sorti2(V!1)),
% 0.12/0.38 inference(or_elim,[status(thm)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(V!1)) | (h(j(V!1)) = V!1))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(V!1)) | (h(j(V!1)) = V!1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(V!1)) | (h(j(V!1)) = V!1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(V!1)) | (h(j(V!1)) = V!1)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (h(j(V!1)) = V!1),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[23, 20, 11])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.38 inference(or_elim,[status(thm)],[6])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.38 inference(and_elim,[status(thm)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.12/0.38 tff(31,plain,(
% 0.12/0.38 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[30])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (sorti2(U!0)),
% 0.12/0.38 inference(and_elim,[status(thm)],[18])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (((~![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!0)) | sorti1(j(U!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!0)) | sorti1(j(U!0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (sorti1(j(U!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[36, 33, 32])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (^[U: $i] : refl(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (^[U: $i] : rewrite(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[41, 39])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((sorti1(V) => (op1(U, op1(U, V)) = V)) <=> ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))), (![V: $i] : (sorti1(V) => (op1(U, op1(U, V)) = V)) <=> ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))), ((sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, op1(U, V)) = V))) <=> (sorti1(U) => ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V))))), rewrite((sorti1(U) => ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))), ((sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, op1(U, V)) = V))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, op1(U, V)) = V))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.12/0.38 tff(46,axiom,(![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, op1(U, V)) = V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax3')).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.12/0.38 tff(49,plain,(
% 0.12/0.38 ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[48])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))) | ((~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), op1(j(U!0), V)) = V)))) <=> ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))) | (~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), op1(j(U!0), V)) = V)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))) | ((~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), op1(j(U!0), V)) = V)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, op1(U, V)) = V)))) | (~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), op1(j(U!0), V)) = V))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (![V: $i] : ((~sorti1(V)) | (op1(j(U!0), op1(j(U!0), V)) = V))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[53, 50, 37])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (((~![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(V!1)) | sorti1(j(V!1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(V!1)) | sorti1(j(V!1))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (sorti1(j(V!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[57, 20, 32])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), op1(j(U!0), V)) = V))) | ((~sorti1(j(V!1))) | (op1(j(U!0), op1(j(U!0), j(V!1))) = j(V!1)))) <=> ((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), op1(j(U!0), V)) = V))) | (~sorti1(j(V!1))) | (op1(j(U!0), op1(j(U!0), j(V!1))) = j(V!1)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 ((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), op1(j(U!0), V)) = V))) | ((~sorti1(j(V!1))) | (op1(j(U!0), op1(j(U!0), j(V!1))) = j(V!1)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 ((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), op1(j(U!0), V)) = V))) | (~sorti1(j(V!1))) | (op1(j(U!0), op1(j(U!0), j(V!1))) = j(V!1))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (op1(j(U!0), op1(j(U!0), j(V!1))) = j(V!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[61, 58, 54])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[66, 64])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.12/0.39 inference(and_elim,[status(thm)],[7])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.12/0.39 tff(71,plain,(
% 0.12/0.39 ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[70])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (((~![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)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 ((~![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)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 ((~![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))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[75, 33, 72])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (((~![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 ((~![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))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 ((~![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[79, 20, 76])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (op1(j(U!0), j(op2(U!0, V!1))) = op1(j(U!0), op1(j(U!0), j(V!1)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[80])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (^[U: $i] : refl(((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[82])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (^[U: $i] : rewrite(((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[84])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[85, 83])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 (![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[88])).
% 0.12/0.39 tff(90,axiom,(![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => sorti2(op2(U, V))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax2')).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.12/0.39 tff(93,plain,(
% 0.12/0.39 ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[92])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 (((~![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | ((~sorti2(U!0)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | (~sorti2(U!0)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.12/0.39 tff(98,plain,
% 0.12/0.39 (![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[97, 94, 33])).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 (((~![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | ((~sorti2(V!1)) | sorti2(op2(U!0, V!1)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | (~sorti2(V!1)) | sorti2(op2(U!0, V!1))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 (sorti2(op2(U!0, V!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[101, 20, 98])).
% 0.12/0.39 tff(103,plain,
% 0.12/0.39 (((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | ((~sorti2(op2(U!0, V!1))) | (j(op2(U!0, op2(U!0, V!1))) = op1(j(U!0), j(op2(U!0, V!1)))))) <=> ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | (~sorti2(op2(U!0, V!1))) | (j(op2(U!0, op2(U!0, V!1))) = op1(j(U!0), j(op2(U!0, V!1)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(104,plain,
% 0.12/0.39 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | ((~sorti2(op2(U!0, V!1))) | (j(op2(U!0, op2(U!0, V!1))) = op1(j(U!0), j(op2(U!0, V!1)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(105,plain,
% 0.12/0.39 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | (~sorti2(op2(U!0, V!1))) | (j(op2(U!0, op2(U!0, V!1))) = op1(j(U!0), j(op2(U!0, V!1))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.12/0.39 tff(106,plain,
% 0.12/0.39 (j(op2(U!0, op2(U!0, V!1))) = op1(j(U!0), j(op2(U!0, V!1)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[105, 76, 102])).
% 0.12/0.39 tff(107,plain,
% 0.12/0.39 (j(op2(U!0, op2(U!0, V!1))) = j(V!1)),
% 0.12/0.39 inference(transitivity,[status(thm)],[106, 81, 62])).
% 0.12/0.39 tff(108,plain,
% 0.12/0.39 (h(j(op2(U!0, op2(U!0, V!1)))) = h(j(V!1))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[107])).
% 0.12/0.39 tff(109,plain,
% 0.12/0.39 (((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | ((~sorti2(op2(U!0, V!1))) | sorti2(op2(U!0, op2(U!0, V!1))))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | (~sorti2(op2(U!0, V!1))) | sorti2(op2(U!0, op2(U!0, V!1))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(110,plain,
% 0.12/0.39 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | ((~sorti2(op2(U!0, V!1))) | sorti2(op2(U!0, op2(U!0, V!1))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(111,plain,
% 0.12/0.39 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | (~sorti2(op2(U!0, V!1))) | sorti2(op2(U!0, op2(U!0, V!1)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.12/0.39 tff(112,plain,
% 0.12/0.39 (sorti2(op2(U!0, op2(U!0, V!1)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[111, 98, 102])).
% 0.12/0.39 tff(113,plain,
% 0.12/0.39 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(op2(U!0, op2(U!0, V!1)))) | (h(j(op2(U!0, op2(U!0, V!1)))) = op2(U!0, op2(U!0, V!1))))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(op2(U!0, op2(U!0, V!1)))) | (h(j(op2(U!0, op2(U!0, V!1)))) = op2(U!0, op2(U!0, V!1))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(114,plain,
% 0.12/0.39 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(op2(U!0, op2(U!0, V!1)))) | (h(j(op2(U!0, op2(U!0, V!1)))) = op2(U!0, op2(U!0, V!1))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(115,plain,
% 0.12/0.39 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(op2(U!0, op2(U!0, V!1)))) | (h(j(op2(U!0, op2(U!0, V!1)))) = op2(U!0, op2(U!0, V!1)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.12/0.39 tff(116,plain,
% 0.12/0.39 (h(j(op2(U!0, op2(U!0, V!1)))) = op2(U!0, op2(U!0, V!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[115, 11, 112])).
% 0.12/0.39 tff(117,plain,
% 0.12/0.39 (op2(U!0, op2(U!0, V!1)) = h(j(op2(U!0, op2(U!0, V!1))))),
% 0.12/0.39 inference(symmetry,[status(thm)],[116])).
% 0.12/0.39 tff(118,plain,
% 0.12/0.39 (op2(U!0, op2(U!0, V!1)) = V!1),
% 0.12/0.39 inference(transitivity,[status(thm)],[117, 108, 24])).
% 0.12/0.39 tff(119,plain,
% 0.12/0.39 (~(op2(U!0, op2(U!0, V!1)) = V!1)),
% 0.12/0.39 inference(or_elim,[status(thm)],[19])).
% 0.12/0.39 tff(120,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------