TSTP Solution File: ALG073+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 : Tue Sep 6 16:07:46 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 13:41:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 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(op1_type, type, (
% 0.12/0.38 op1: ( $i * $i ) > $i)).
% 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(j_type, type, (
% 0.12/0.38 j: $i > $i)).
% 0.12/0.38 tff(h_type, type, (
% 0.12/0.38 h: $i > $i)).
% 0.12/0.38 tff(sorti1_type, type, (
% 0.12/0.38 sorti1: $i > $o)).
% 0.12/0.38 tff(sorti2_type, type, (
% 0.12/0.38 sorti2: $i > $o)).
% 0.12/0.38 tff(op2_type, type, (
% 0.12/0.38 op2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X2: $i] : refl(((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ((~sorti1(X2)) | (j(h(X2)) = X2)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 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/sandbox2/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 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.12/0.38 inference(and_elim,[status(thm)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.12/0.38 tff(10,plain,(
% 0.12/0.38 ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.12/0.38 inference(skolemize,[status(sab)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 ((sorti1(U!0) & (sorti1(V!1) & (op1(U!0, U!0) = V!1) & (op1(V!1, V!1) = U!0) & (~(op1(U!0, V!1) = U!0)))) <=> (sorti1(U!0) & sorti1(V!1) & (op1(U!0, U!0) = V!1) & (op1(V!1, V!1) = U!0) & (~(op1(U!0, V!1) = U!0)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (?[U: $i] : (sorti1(U) & ?[V: $i] : (sorti1(V) & (op1(U, U) = V) & (op1(V, V) = U) & (~(op1(U, V) = U)))) <=> ?[U: $i] : (sorti1(U) & ?[V: $i] : (sorti1(V) & (op1(U, U) = V) & (op1(V, V) = U) & (~(op1(U, V) = U))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (^[U: $i] : rewrite((sorti1(U) & ?[V: $i] : (((sorti1(V) & (op1(U, U) = V)) & (op1(V, V) = U)) & (~(op1(U, V) = U)))) <=> (sorti1(U) & ?[V: $i] : (sorti1(V) & (op1(U, U) = V) & (op1(V, V) = U) & (~(op1(U, V) = U)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (?[U: $i] : (sorti1(U) & ?[V: $i] : (((sorti1(V) & (op1(U, U) = V)) & (op1(V, V) = U)) & (~(op1(U, V) = U)))) <=> ?[U: $i] : (sorti1(U) & ?[V: $i] : (sorti1(V) & (op1(U, U) = V) & (op1(V, V) = U) & (~(op1(U, V) = U))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.38 tff(16,axiom,(?[U: $i] : (sorti1(U) & ?[V: $i] : (((sorti1(V) & (op1(U, U) = V)) & (op1(V, V) = U)) & (~(op1(U, V) = U))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax3')).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (?[U: $i] : (sorti1(U) & ?[V: $i] : (sorti1(V) & (op1(U, U) = V) & (op1(V, V) = U) & (~(op1(U, V) = U))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (?[U: $i] : (sorti1(U) & ?[V: $i] : (sorti1(V) & (op1(U, U) = V) & (op1(V, V) = U) & (~(op1(U, V) = U))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (sorti1(U!0) & sorti1(V!1) & (op1(U!0, U!0) = V!1) & (op1(V!1, V!1) = U!0) & (~(op1(U!0, V!1) = U!0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (sorti1(U!0)),
% 0.12/0.38 inference(and_elim,[status(thm)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(U!0)) | (j(h(U!0)) = U!0))) <=> ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(U!0)) | (j(h(U!0)) = U!0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(U!0)) | (j(h(U!0)) = U!0))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(U!0)) | (j(h(U!0)) = U!0)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (j(h(U!0)) = U!0),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[23, 20, 11])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (^[W: $i] : refl(((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (^[W: $i] : rewrite(((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[28, 26])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.38 inference(and_elim,[status(thm)],[7])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.38 tff(33,plain,(
% 0.12/0.38 ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[32])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(U!0)) | ![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X)))))) <=> ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(U!0)) | ![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(U!0)) | ![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(U!0)) | ![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[37, 20, 34])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (sorti1(V!1)),
% 0.12/0.39 inference(and_elim,[status(thm)],[19])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (((~![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X))))) | ((~sorti1(V!1)) | (h(op1(U!0, V!1)) = op2(h(U!0), h(V!1))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X))))) | (~sorti1(V!1)) | (h(op1(U!0, V!1)) = op2(h(U!0), h(V!1))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X))))) | ((~sorti1(V!1)) | (h(op1(U!0, V!1)) = op2(h(U!0), h(V!1))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X))))) | (~sorti1(V!1)) | (h(op1(U!0, V!1)) = op2(h(U!0), h(V!1)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (h(op1(U!0, V!1)) = op2(h(U!0), h(V!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[42, 39, 38])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (op2(h(U!0), h(V!1)) = h(op1(U!0, V!1))),
% 0.12/0.39 inference(symmetry,[status(thm)],[43])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (((~![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X))))) | ((~sorti1(U!0)) | (h(op1(U!0, U!0)) = op2(h(U!0), h(U!0))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X))))) | (~sorti1(U!0)) | (h(op1(U!0, U!0)) = op2(h(U!0), h(U!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X))))) | ((~sorti1(U!0)) | (h(op1(U!0, U!0)) = op2(h(U!0), h(U!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(U!0, X)) = op2(h(U!0), h(X))))) | (~sorti1(U!0)) | (h(op1(U!0, U!0)) = op2(h(U!0), h(U!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (h(op1(U!0, U!0)) = op2(h(U!0), h(U!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[47, 20, 38])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (op1(U!0, U!0) = V!1),
% 0.12/0.39 inference(and_elim,[status(thm)],[19])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (V!1 = op1(U!0, U!0)),
% 0.12/0.39 inference(symmetry,[status(thm)],[49])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (h(V!1) = h(op1(U!0, U!0))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (h(V!1) = op2(h(U!0), h(U!0))),
% 0.12/0.39 inference(transitivity,[status(thm)],[51, 48])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (op2(h(U!0), h(V!1)) = op2(h(U!0), op2(h(U!0), h(U!0)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[52])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (op2(h(U!0), op2(h(U!0), h(U!0))) = op2(h(U!0), h(V!1))),
% 0.12/0.39 inference(symmetry,[status(thm)],[53])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (op1(V!1, V!1) = U!0),
% 0.12/0.39 inference(and_elim,[status(thm)],[19])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (U!0 = op1(V!1, V!1)),
% 0.12/0.39 inference(symmetry,[status(thm)],[55])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (h(U!0) = h(op1(V!1, V!1))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[56])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (h(op1(V!1, V!1)) = h(U!0)),
% 0.12/0.39 inference(symmetry,[status(thm)],[57])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(V!1)) | ![X: $i] : ((~sorti1(X)) | (h(op1(V!1, X)) = op2(h(V!1), h(X)))))) <=> ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(V!1)) | ![X: $i] : ((~sorti1(X)) | (h(op1(V!1, X)) = op2(h(V!1), h(X)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(V!1)) | ![X: $i] : ((~sorti1(X)) | (h(op1(V!1, X)) = op2(h(V!1), h(X)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(V!1)) | ![X: $i] : ((~sorti1(X)) | (h(op1(V!1, X)) = op2(h(V!1), h(X))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![X: $i] : ((~sorti1(X)) | (h(op1(V!1, X)) = op2(h(V!1), h(X))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[61, 39, 34])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (((~![X: $i] : ((~sorti1(X)) | (h(op1(V!1, X)) = op2(h(V!1), h(X))))) | ((~sorti1(V!1)) | (h(op1(V!1, V!1)) = op2(h(V!1), h(V!1))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(V!1, X)) = op2(h(V!1), h(X))))) | (~sorti1(V!1)) | (h(op1(V!1, V!1)) = op2(h(V!1), h(V!1))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(V!1, X)) = op2(h(V!1), h(X))))) | ((~sorti1(V!1)) | (h(op1(V!1, V!1)) = op2(h(V!1), h(V!1))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(V!1, X)) = op2(h(V!1), h(X))))) | (~sorti1(V!1)) | (h(op1(V!1, V!1)) = op2(h(V!1), h(V!1)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (h(op1(V!1, V!1)) = op2(h(V!1), h(V!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[65, 39, 62])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (op2(h(V!1), h(V!1)) = h(op1(V!1, V!1))),
% 0.19/0.39 inference(symmetry,[status(thm)],[66])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (h(op1(U!0, U!0)) = h(V!1)),
% 0.19/0.39 inference(symmetry,[status(thm)],[51])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (op2(h(U!0), h(U!0)) = h(op1(U!0, U!0))),
% 0.19/0.39 inference(symmetry,[status(thm)],[48])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (op2(h(U!0), h(U!0)) = h(V!1)),
% 0.19/0.39 inference(transitivity,[status(thm)],[69, 68])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = op2(h(V!1), h(V!1))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[70, 70])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0)),
% 0.19/0.39 inference(transitivity,[status(thm)],[71, 67, 58])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (sorti2(op2(h(U!0), h(U!0))) <=> sorti2(h(V!1))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[70])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (sorti2(h(V!1)) <=> sorti2(op2(h(U!0), h(U!0)))),
% 0.19/0.39 inference(symmetry,[status(thm)],[73])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (^[U: $i] : refl(((~sorti1(U)) | sorti2(h(U))) <=> ((~sorti1(U)) | sorti2(h(U))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(78,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(79,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.19/0.39 inference(and_elim,[status(thm)],[78])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[79, 77])).
% 0.19/0.39 tff(81,plain,(
% 0.19/0.39 ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[80])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[81, 76])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(V!1)) | sorti2(h(V!1)))) <=> ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(V!1)) | sorti2(h(V!1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(V!1)) | sorti2(h(V!1)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(V!1)) | sorti2(h(V!1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (sorti2(h(V!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[85, 39, 82])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 (sorti2(op2(h(U!0), h(U!0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[86, 74])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 (((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(U!0)) | sorti2(h(U!0)))) <=> ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(U!0)) | sorti2(h(U!0)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(U!0)) | sorti2(h(U!0)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(U!0)) | sorti2(h(U!0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 (sorti2(h(U!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[90, 20, 82])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (^[U: $i] : refl(((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U)))) <=> ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 (^[U: $i] : rewrite(((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U)))) <=> ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[95, 93])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (^[U: $i] : rewrite(((~sorti2(U)) | ![V: $i] : (~(sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))) <=> ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 (![U: $i] : ((~sorti2(U)) | ![V: $i] : (~(sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 ((~?[U: $i] : (sorti2(U) & ?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))) <=> (~?[U: $i] : (sorti2(U) & ?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 ((~?[U: $i] : (sorti2(U) & ?[V: $i] : (((sorti2(V) & (op2(U, U) = V)) & (op2(V, V) = U)) & (~(op2(U, V) = U))))) <=> (~?[U: $i] : (sorti2(U) & ?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(101,axiom,(~?[U: $i] : (sorti2(U) & ?[V: $i] : (((sorti2(V) & (op2(U, U) = V)) & (op2(V, V) = U)) & (~(op2(U, V) = U))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax4')).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (~?[U: $i] : (sorti2(U) & ?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 (~?[U: $i] : (sorti2(U) & ?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 (~?[U: $i] : (sorti2(U) & ?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (~?[U: $i] : (sorti2(U) & ?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[104, 99])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (~?[U: $i] : (sorti2(U) & ?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[105, 99])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (~?[U: $i] : (sorti2(U) & ?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (~?[U: $i] : (sorti2(U) & ?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[107, 99])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (^[U: $i] : nnf_neg(refl($oeq((~sorti2(U)), (~sorti2(U)))), nnf_neg(proof_bind(^[V: $i] : refl($oeq((~(sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U)))), (~(sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))))), $oeq((~?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U)))), ![V: $i] : (~(sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U)))))), $oeq((~(sorti2(U) & ?[V: $i] : (sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U))))), ((~sorti2(U)) | ![V: $i] : (~(sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(110,plain,(
% 0.19/0.40 ![U: $i] : ((~sorti2(U)) | ![V: $i] : (~(sorti2(V) & (op2(U, U) = V) & (op2(V, V) = U) & (~(op2(U, V) = U)))))),
% 0.19/0.40 inference(nnf-neg,[status(sab)],[108, 109])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[110, 98])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[111, 96])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))) | ((~sorti2(h(U!0))) | ![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0)))))) <=> ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))) | (~sorti2(h(U!0))) | ![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (((~sorti2(h(U!0))) | ![V: $i] : ((op2(h(U!0), V) = h(U!0)) | (~sorti2(V)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))) <=> ((~sorti2(h(U!0))) | ![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))) | ((~sorti2(h(U!0))) | ![V: $i] : ((op2(h(U!0), V) = h(U!0)) | (~sorti2(V)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0)))))) <=> ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))) | ((~sorti2(h(U!0))) | ![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[114])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 (((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))) | ((~sorti2(h(U!0))) | ![V: $i] : ((op2(h(U!0), V) = h(U!0)) | (~sorti2(V)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0)))))) <=> ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))) | (~sorti2(h(U!0))) | ![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[115, 113])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))) | ((~sorti2(h(U!0))) | ![V: $i] : ((op2(h(U!0), V) = h(U!0)) | (~sorti2(V)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~sorti2(V)) | (~(op2(U, U) = V)) | (~(op2(V, V) = U))))) | (~sorti2(h(U!0))) | ![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[118, 112, 91])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 (((~![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))) | ((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0))))) <=> ((~![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))) | (~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | $false | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0)))) <=> ((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 ((~$true) <=> $false),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 ((op2(h(U!0), h(U!0)) = op2(h(U!0), h(U!0))) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 ((~(op2(h(U!0), h(U!0)) = op2(h(U!0), h(U!0)))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[123])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 ((~(op2(h(U!0), h(U!0)) = op2(h(U!0), h(U!0)))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[124, 122])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 (((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = op2(h(U!0), h(U!0)))) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0)))) <=> ((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | $false | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 (((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = op2(h(U!0), h(U!0)))) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0)))) <=> ((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[126, 121])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 (((~![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))) | ((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = op2(h(U!0), h(U!0)))) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0))))) <=> ((~![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))) | ((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[127])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 (((~![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))) | ((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = op2(h(U!0), h(U!0)))) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0))))) <=> ((~![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))) | (~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[128, 120])).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 ((~![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))) | ((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = op2(h(U!0), h(U!0)))) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 ((~![V: $i] : ((~sorti2(V)) | (op2(h(U!0), V) = h(U!0)) | (~(op2(h(U!0), h(U!0)) = V)) | (~(op2(V, V) = h(U!0))))) | (~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 ((~sorti2(op2(h(U!0), h(U!0)))) | (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)) | (~(op2(op2(h(U!0), h(U!0)), op2(h(U!0), h(U!0))) = h(U!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[131, 119])).
% 0.19/0.40 tff(133,plain,
% 0.19/0.40 (op2(h(U!0), op2(h(U!0), h(U!0))) = h(U!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[132, 87, 72])).
% 0.19/0.40 tff(134,plain,
% 0.19/0.40 (h(U!0) = op2(h(U!0), op2(h(U!0), h(U!0)))),
% 0.19/0.40 inference(symmetry,[status(thm)],[133])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 (h(U!0) = h(op1(U!0, V!1))),
% 0.19/0.40 inference(transitivity,[status(thm)],[134, 54, 44])).
% 0.19/0.40 tff(136,plain,
% 0.19/0.40 (j(h(U!0)) = j(h(op1(U!0, V!1)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[135])).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 (j(h(op1(U!0, V!1))) = j(h(U!0))),
% 0.19/0.40 inference(symmetry,[status(thm)],[136])).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 (^[U: $i] : refl(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(139,plain,
% 0.19/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 (^[U: $i] : rewrite(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.40 tff(142,plain,
% 0.19/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[141, 139])).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(144,plain,
% 0.19/0.40 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((sorti1(V) => sorti1(op1(U, V))) <=> ((~sorti1(V)) | sorti1(op1(U, V))))), (![V: $i] : (sorti1(V) => sorti1(op1(U, V))) <=> ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))), ((sorti1(U) => ![V: $i] : (sorti1(V) => sorti1(op1(U, V)))) <=> (sorti1(U) => ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))))), rewrite((sorti1(U) => ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))), ((sorti1(U) => ![V: $i] : (sorti1(V) => sorti1(op1(U, V)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(145,plain,
% 0.19/0.40 (![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[144])).
% 0.19/0.40 tff(146,axiom,(![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => sorti1(op1(U, V))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax1')).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.19/0.41 tff(149,plain,(
% 0.19/0.41 ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[148])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.19/0.41 tff(151,plain,
% 0.19/0.41 (((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | ((~sorti1(U!0)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U!0, V))))) <=> ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | (~sorti1(U!0)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U!0, V))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | ((~sorti1(U!0)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U!0, V))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | (~sorti1(U!0)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U!0, V)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.41 tff(154,plain,
% 0.19/0.41 (![V: $i] : ((~sorti1(V)) | sorti1(op1(U!0, V)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[153, 150, 20])).
% 0.19/0.41 tff(155,plain,
% 0.19/0.41 (((~![V: $i] : ((~sorti1(V)) | sorti1(op1(U!0, V)))) | ((~sorti1(V!1)) | sorti1(op1(U!0, V!1)))) <=> ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(U!0, V)))) | (~sorti1(V!1)) | sorti1(op1(U!0, V!1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(156,plain,
% 0.19/0.41 ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(U!0, V)))) | ((~sorti1(V!1)) | sorti1(op1(U!0, V!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(157,plain,
% 0.19/0.41 ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(U!0, V)))) | (~sorti1(V!1)) | sorti1(op1(U!0, V!1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.41 tff(158,plain,
% 0.19/0.41 (sorti1(op1(U!0, V!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[157, 39, 154])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 (((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(op1(U!0, V!1))) | (j(h(op1(U!0, V!1))) = op1(U!0, V!1)))) <=> ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(op1(U!0, V!1))) | (j(h(op1(U!0, V!1))) = op1(U!0, V!1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(op1(U!0, V!1))) | (j(h(op1(U!0, V!1))) = op1(U!0, V!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(161,plain,
% 0.19/0.41 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(op1(U!0, V!1))) | (j(h(op1(U!0, V!1))) = op1(U!0, V!1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.41 tff(162,plain,
% 0.19/0.41 (j(h(op1(U!0, V!1))) = op1(U!0, V!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[161, 11, 158])).
% 0.19/0.41 tff(163,plain,
% 0.19/0.41 (op1(U!0, V!1) = j(h(op1(U!0, V!1)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[162])).
% 0.19/0.41 tff(164,plain,
% 0.19/0.41 (op1(U!0, V!1) = U!0),
% 0.19/0.41 inference(transitivity,[status(thm)],[163, 137, 24])).
% 0.19/0.41 tff(165,plain,
% 0.19/0.41 (~(op1(U!0, V!1) = U!0)),
% 0.19/0.41 inference(and_elim,[status(thm)],[19])).
% 0.19/0.41 tff(166,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------