TSTP Solution File: ALG070+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 16:07:45 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 13:28:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(tptp_fun_U_0_type, type, (
% 0.13/0.40 tptp_fun_U_0: $i)).
% 0.13/0.40 tff(op2_type, type, (
% 0.13/0.40 op2: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_V_1_type, type, (
% 0.13/0.40 tptp_fun_V_1: $i)).
% 0.13/0.40 tff(h_type, type, (
% 0.13/0.40 h: $i > $i)).
% 0.13/0.40 tff(j_type, type, (
% 0.13/0.40 j: $i > $i)).
% 0.13/0.40 tff(sorti2_type, type, (
% 0.13/0.40 sorti2: $i > $o)).
% 0.13/0.40 tff(sorti1_type, type, (
% 0.13/0.40 sorti1: $i > $o)).
% 0.13/0.40 tff(op1_type, type, (
% 0.13/0.40 op1: ( $i * $i ) > $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[X1: $i] : refl(((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ((~sorti2(X1)) | (h(j(X1)) = X1)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 ((~((![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))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 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')).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (~((~(![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)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![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))),
% 0.13/0.40 inference(or_elim,[status(thm)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.13/0.40 inference(and_elim,[status(thm)],[7])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.13/0.40 tff(10,plain,(
% 0.13/0.40 ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.13/0.40 inference(skolemize,[status(sab)],[9])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (((~(~sorti2(U!0))) & (~((op2(U!0, V!1) = U!0) | (~(op2(U!0, U!0) = V!1)) | (~sorti2(V!1))))) <=> (sorti2(U!0) & (~((op2(U!0, V!1) = U!0) | (~(op2(U!0, U!0) = V!1)) | (~sorti2(V!1)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~(op2(U, U) = V)) | (~sorti2(V))))) <=> (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~(op2(U, U) = V)) | (~sorti2(V)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 ((~![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => ((~(op2(U, U) = V)) | (op2(U, V) = U))))) <=> (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~(op2(U, U) = V)) | (~sorti2(V)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(15,axiom,(~![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => ((~(op2(U, U) = V)) | (op2(U, V) = U))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax4')).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~(op2(U, U) = V)) | (~sorti2(V))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~(op2(U, U) = V)) | (~sorti2(V))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~(op2(U, U) = V)) | (~sorti2(V))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~(op2(U, U) = V)) | (~sorti2(V))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~(op2(U, U) = V)) | (~sorti2(V))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~(op2(U, U) = V)) | (~sorti2(V))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((op2(U, V) = U) | (~(op2(U, U) = V)) | (~sorti2(V))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (sorti2(U!0) & (~((op2(U!0, V!1) = U!0) | (~(op2(U!0, U!0) = V!1)) | (~sorti2(V!1))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (sorti2(U!0)),
% 0.13/0.40 inference(and_elim,[status(thm)],[23])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!0)) | (h(j(U!0)) = U!0))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!0)) | (h(j(U!0)) = U!0))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!0)) | (h(j(U!0)) = U!0))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!0)) | (h(j(U!0)) = U!0)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (h(j(U!0)) = U!0),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (^[Y: $i] : refl(((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (^[Y: $i] : rewrite(((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[32, 30])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.40 inference(and_elim,[status(thm)],[7])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.40 tff(37,plain,(
% 0.13/0.40 ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[36])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z)))))) <=> ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z)))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[41, 24, 38])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (~((op2(U!0, V!1) = U!0) | (~(op2(U!0, U!0) = V!1)) | (~sorti2(V!1)))),
% 0.13/0.40 inference(and_elim,[status(thm)],[23])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (sorti2(V!1)),
% 0.13/0.40 inference(or_elim,[status(thm)],[43])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | ((~sorti2(V!1)) | (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1))))) <=> ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | (~sorti2(V!1)) | (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | ((~sorti2(V!1)) | (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | (~sorti2(V!1)) | (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (j(op2(U!0, V!1)) = op1(j(U!0), j(V!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[47, 44, 42])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (op1(j(U!0), j(V!1)) = j(op2(U!0, V!1))),
% 0.13/0.40 inference(symmetry,[status(thm)],[48])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (op2(U!0, U!0) = V!1),
% 0.13/0.40 inference(or_elim,[status(thm)],[43])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (V!1 = op2(U!0, U!0)),
% 0.13/0.40 inference(symmetry,[status(thm)],[50])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (j(V!1) = j(op2(U!0, U!0))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[51])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (j(op2(U!0, U!0)) = j(V!1)),
% 0.13/0.40 inference(symmetry,[status(thm)],[52])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | ((~sorti2(U!0)) | (j(op2(U!0, U!0)) = op1(j(U!0), j(U!0))))) <=> ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | (~sorti2(U!0)) | (j(op2(U!0, U!0)) = op1(j(U!0), j(U!0))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | ((~sorti2(U!0)) | (j(op2(U!0, U!0)) = op1(j(U!0), j(U!0))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | (~sorti2(U!0)) | (j(op2(U!0, U!0)) = op1(j(U!0), j(U!0)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (j(op2(U!0, U!0)) = op1(j(U!0), j(U!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[56, 24, 42])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 (op1(j(U!0), j(U!0)) = j(op2(U!0, U!0))),
% 0.13/0.40 inference(symmetry,[status(thm)],[57])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (op1(j(U!0), j(U!0)) = j(V!1)),
% 0.13/0.40 inference(transitivity,[status(thm)],[58, 53])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (op1(j(U!0), op1(j(U!0), j(U!0))) = op1(j(U!0), j(V!1))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[59])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (sorti1(op1(j(U!0), j(U!0))) <=> sorti1(j(V!1))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (sorti1(j(V!1)) <=> sorti1(op1(j(U!0), j(U!0)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[61])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.41 inference(or_elim,[status(thm)],[6])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.41 inference(and_elim,[status(thm)],[66])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.19/0.41 tff(69,plain,(
% 0.19/0.41 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[68])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 64])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (((~![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(V!1)) | sorti1(j(V!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(V!1)) | sorti1(j(V!1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (sorti1(j(V!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[73, 44, 70])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (sorti1(op1(j(U!0), j(U!0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[74, 62])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (((~![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!0)) | sorti1(j(U!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!0)) | sorti1(j(U!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (sorti1(j(U!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[78, 24, 70])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (^[U: $i] : refl(((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V)))) <=> ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (^[U: $i] : rewrite(((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V)))) <=> ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((sorti1(V) => ((~(op1(U, U) = V)) | (op1(U, V) = U))) <=> ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))), (![V: $i] : (sorti1(V) => ((~(op1(U, U) = V)) | (op1(U, V) = U))) <=> ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))), ((sorti1(U) => ![V: $i] : (sorti1(V) => ((~(op1(U, U) = V)) | (op1(U, V) = U)))) <=> (sorti1(U) => ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V)))))), rewrite((sorti1(U) => ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V)))) <=> ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))), ((sorti1(U) => ![V: $i] : (sorti1(V) => ((~(op1(U, U) = V)) | (op1(U, V) = U)))) <=> ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => ((~(op1(U, U) = V)) | (op1(U, V) = U)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.41 tff(88,axiom,(![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => ((~(op1(U, U) = V)) | (op1(U, V) = U))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax3')).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.41 tff(91,plain,(
% 0.19/0.41 ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[90])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))) | ((~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V))))) <=> ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))) | (~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (((~sorti1(j(U!0))) | ![V: $i] : ((op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)) | (~sorti1(V)))) <=> ((~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))) | ((~sorti1(j(U!0))) | ![V: $i] : ((op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)) | (~sorti1(V))))) <=> ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))) | ((~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))) | ((~sorti1(j(U!0))) | ![V: $i] : ((op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)) | (~sorti1(V))))) <=> ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))) | (~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[95, 93])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))) | ((~sorti1(j(U!0))) | ![V: $i] : ((op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)) | (~sorti1(V))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((op1(U, V) = U) | (~(op1(U, U) = V)) | (~sorti1(V))))) | (~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[98, 92, 79])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)))) | ((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)))) <=> ((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)))) | (~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)) | $false) <=> ((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 ((~$true) <=> $false),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 ((op1(j(U!0), j(U!0)) = op1(j(U!0), j(U!0))) <=> $true),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 ((~(op1(j(U!0), j(U!0)) = op1(j(U!0), j(U!0)))) <=> (~$true)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~(op1(j(U!0), j(U!0)) = op1(j(U!0), j(U!0)))) <=> $false),
% 0.19/0.41 inference(transitivity,[status(thm)],[104, 102])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = op1(j(U!0), j(U!0))))) <=> ((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)) | $false)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[105])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = op1(j(U!0), j(U!0))))) <=> ((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[106, 101])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)))) | ((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = op1(j(U!0), j(U!0)))))) <=> ((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)))) | ((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)))) | ((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = op1(j(U!0), j(U!0)))))) <=> ((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)))) | (~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[108, 100])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)))) | ((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = op1(j(U!0), j(U!0)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = j(U!0)) | (~(op1(j(U!0), j(U!0)) = V)))) | (~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 ((~sorti1(op1(j(U!0), j(U!0)))) | (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[111, 99])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (op1(j(U!0), op1(j(U!0), j(U!0))) = j(U!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[112, 75])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (j(U!0) = op1(j(U!0), op1(j(U!0), j(U!0)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[113])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (j(U!0) = j(op2(U!0, V!1))),
% 0.19/0.41 inference(transitivity,[status(thm)],[114, 60, 49])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (h(j(U!0)) = h(j(op2(U!0, V!1)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (h(j(op2(U!0, V!1))) = h(j(U!0))),
% 0.19/0.42 inference(symmetry,[status(thm)],[116])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (^[U: $i] : refl(((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (^[U: $i] : rewrite(((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[120])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[121, 119])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (^[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))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => sorti2(op2(U, V)))) <=> ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.42 tff(126,axiom,(![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => sorti2(op2(U, V))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax2')).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.19/0.42 tff(129,plain,(
% 0.19/0.42 ![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[128])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 (((~![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | ((~sorti2(U!0)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U, V))))) | (~sorti2(U!0)) | ![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[133, 130, 24])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | ((~sorti2(V!1)) | sorti2(op2(U!0, V!1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 ((~![V: $i] : ((~sorti2(V)) | sorti2(op2(U!0, V)))) | (~sorti2(V!1)) | sorti2(op2(U!0, V!1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (sorti2(op2(U!0, V!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[137, 44, 134])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 ((~![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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(op2(U!0, V!1))) | (h(j(op2(U!0, V!1))) = op2(U!0, V!1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (h(j(op2(U!0, V!1))) = op2(U!0, V!1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[141, 11, 138])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (op2(U!0, V!1) = h(j(op2(U!0, V!1)))),
% 0.19/0.42 inference(symmetry,[status(thm)],[142])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (op2(U!0, V!1) = U!0),
% 0.19/0.42 inference(transitivity,[status(thm)],[143, 117, 28])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (~(op2(U!0, V!1) = U!0)),
% 0.19/0.42 inference(or_elim,[status(thm)],[43])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------