TSTP Solution File: ALG071+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG071+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 16:07:45 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG071+1 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 29 13:16:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(j_type, type, (
% 0.14/0.40 j: $i > $i)).
% 0.14/0.40 tff(tptp_fun_U_1_type, type, (
% 0.14/0.40 tptp_fun_U_1: $i)).
% 0.14/0.40 tff(op1_type, type, (
% 0.14/0.40 op1: ( $i * $i ) > $i)).
% 0.14/0.40 tff(tptp_fun_V_0_type, type, (
% 0.14/0.40 tptp_fun_V_0: $i > $i)).
% 0.14/0.40 tff(h_type, type, (
% 0.14/0.40 h: $i > $i)).
% 0.14/0.40 tff(op2_type, type, (
% 0.14/0.40 op2: ( $i * $i ) > $i)).
% 0.14/0.40 tff(sorti1_type, type, (
% 0.14/0.40 sorti1: $i > $o)).
% 0.14/0.40 tff(sorti2_type, type, (
% 0.14/0.40 sorti2: $i > $o)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 ((~((![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))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 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/sandbox/benchmark/theBenchmark.p','co1')).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (~((~(![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)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.40 inference(or_elim,[status(thm)],[6])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.40 inference(and_elim,[status(thm)],[7])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.14/0.40 tff(10,plain,(
% 0.14/0.40 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[9])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (((~(~sorti2(U!1))) & ![V: $i] : (~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V)))) <=> (sorti2(U!1) & ![V: $i] : (~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 ((~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))) <=> (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 ((~![U: $i] : (sorti2(U) => ?[V: $i] : ((sorti2(V) & (~(op2(V, op2(V, U)) = U))) & (op2(U, op2(V, U)) = V)))) <=> (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(15,axiom,(~![U: $i] : (sorti2(U) => ?[V: $i] : ((sorti2(V) & (~(op2(V, op2(V, U)) = U))) & (op2(U, op2(V, U)) = V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax4')).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (sorti2(U!1) & ![V: $i] : (~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (sorti2(U!1)),
% 0.14/0.40 inference(and_elim,[status(thm)],[23])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!1)) | sorti1(j(U!1)))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!1)) | sorti1(j(U!1)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!1)) | sorti1(j(U!1)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!1)) | sorti1(j(U!1))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (sorti1(j(U!1))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (^[U: $i] : refl(((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))))) <=> ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))))) <=> ![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (^[U: $i] : rewrite(((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (~(op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U)) & (op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))) <=> ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (~(op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U)) & (op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))) <=> ![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V))) <=> ![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite(((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V)) <=> (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))), (?[V: $i] : ((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V)) <=> ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))), ((sorti1(U) => ?[V: $i] : ((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V))) <=> (sorti1(U) => ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V))))), rewrite((sorti1(U) => ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V))) <=> ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))), ((sorti1(U) => ?[V: $i] : ((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V))) <=> ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 (![U: $i] : (sorti1(U) => ?[V: $i] : ((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V))) <=> ![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.14/0.40 tff(36,axiom,(![U: $i] : (sorti1(U) => ?[V: $i] : ((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax3')).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.14/0.40 tff(39,plain,(
% 0.14/0.40 ![U: $i] : ((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (~(op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U)) & (op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[38])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (((~![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))) | ((~sorti1(j(U!1))) | (~((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1)))))))) <=> ((~![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))) | (~sorti1(j(U!1))) | (~((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1)))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 ((~![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))) | ((~sorti1(j(U!1))) | (~((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1)))))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 ((~![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))) | (~sorti1(j(U!1))) | (~((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 (~((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1)))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[44, 41, 28])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 (((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1))))) | sorti1(tptp_fun_V_0(j(U!1)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 (sorti1(tptp_fun_V_0(j(U!1)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 (^[U: $i] : refl(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 (^[U: $i] : rewrite(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.14/0.40 tff(52,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[51, 49])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(54,plain,
% 0.14/0.40 (^[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))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 (![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.14/0.40 tff(56,axiom,(![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => sorti1(op1(U, V))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax1')).
% 0.14/0.40 tff(57,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.14/0.40 tff(58,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.14/0.40 tff(59,plain,(
% 0.14/0.40 ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[58])).
% 0.14/0.40 tff(60,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.14/0.40 tff(61,plain,
% 0.14/0.40 (((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V))))) <=> ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(62,plain,
% 0.14/0.41 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(63,plain,
% 0.14/0.41 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.14/0.41 tff(64,plain,
% 0.14/0.41 (![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[63, 60, 47])).
% 0.14/0.41 tff(65,plain,
% 0.14/0.41 (((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | ((~sorti1(j(U!1))) | sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1))))) <=> ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | (~sorti1(j(U!1))) | sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(66,plain,
% 0.14/0.41 ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | ((~sorti1(j(U!1))) | sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(67,plain,
% 0.14/0.41 ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | (~sorti1(j(U!1))) | sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.14/0.41 tff(68,plain,
% 0.14/0.41 (sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[67, 28, 64])).
% 0.14/0.41 tff(69,plain,
% 0.14/0.41 (^[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))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(70,plain,
% 0.14/0.41 (![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)))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.14/0.41 tff(71,plain,
% 0.14/0.41 (^[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))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(72,plain,
% 0.14/0.41 (![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)))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.14/0.41 tff(73,plain,
% 0.14/0.41 (![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)))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[72, 70])).
% 0.14/0.41 tff(74,plain,
% 0.14/0.41 (![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)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(75,plain,
% 0.14/0.41 (![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))),
% 0.14/0.41 inference(or_elim,[status(thm)],[6])).
% 0.14/0.41 tff(76,plain,
% 0.14/0.41 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.14/0.41 inference(and_elim,[status(thm)],[75])).
% 0.14/0.41 tff(77,plain,
% 0.14/0.41 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[76, 74])).
% 0.14/0.41 tff(78,plain,(
% 0.14/0.41 ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[77])).
% 0.14/0.41 tff(79,plain,
% 0.14/0.41 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[78, 73])).
% 0.14/0.41 tff(80,plain,
% 0.14/0.41 (((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X)))))) <=> ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(81,plain,
% 0.14/0.41 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X)))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(82,plain,
% 0.14/0.41 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.14/0.41 tff(83,plain,
% 0.14/0.41 (![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[82, 79, 47])).
% 0.14/0.41 tff(84,plain,
% 0.14/0.41 (((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(85,plain,
% 0.14/0.41 ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(86,plain,
% 0.14/0.41 ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.14/0.41 tff(87,plain,
% 0.14/0.41 (h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[86, 83, 68])).
% 0.14/0.41 tff(88,plain,
% 0.14/0.41 (op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.41 inference(symmetry,[status(thm)],[87])).
% 0.14/0.41 tff(89,plain,
% 0.14/0.41 (((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | ((~sorti1(j(U!1))) | (h(op1(tptp_fun_V_0(j(U!1)), j(U!1))) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1)))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | (~sorti1(j(U!1))) | (h(op1(tptp_fun_V_0(j(U!1)), j(U!1))) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(90,plain,
% 0.14/0.41 ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | ((~sorti1(j(U!1))) | (h(op1(tptp_fun_V_0(j(U!1)), j(U!1))) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1)))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(91,plain,
% 0.14/0.41 ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | (~sorti1(j(U!1))) | (h(op1(tptp_fun_V_0(j(U!1)), j(U!1))) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.14/0.41 tff(92,plain,
% 0.14/0.41 (h(op1(tptp_fun_V_0(j(U!1)), j(U!1))) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[91, 28, 83])).
% 0.14/0.41 tff(93,plain,
% 0.14/0.41 (op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1))) = h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))),
% 0.14/0.41 inference(symmetry,[status(thm)],[92])).
% 0.14/0.41 tff(94,plain,
% 0.14/0.41 (^[X1: $i] : refl(((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ((~sorti2(X1)) | (h(j(X1)) = X1)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(95,plain,
% 0.14/0.41 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[94])).
% 0.14/0.41 tff(96,plain,
% 0.14/0.41 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(97,plain,
% 0.14/0.41 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.14/0.41 inference(and_elim,[status(thm)],[75])).
% 0.14/0.41 tff(98,plain,
% 0.14/0.41 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.14/0.41 tff(99,plain,(
% 0.14/0.41 ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.14/0.41 inference(skolemize,[status(sab)],[98])).
% 0.14/0.41 tff(100,plain,
% 0.14/0.41 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.14/0.41 tff(101,plain,
% 0.14/0.41 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!1)) | (h(j(U!1)) = U!1))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!1)) | (h(j(U!1)) = U!1))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(102,plain,
% 0.14/0.41 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!1)) | (h(j(U!1)) = U!1))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(103,plain,
% 0.14/0.41 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!1)) | (h(j(U!1)) = U!1)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.14/0.41 tff(104,plain,
% 0.14/0.41 (h(j(U!1)) = U!1),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[103, 24, 100])).
% 0.14/0.41 tff(105,plain,
% 0.14/0.41 (U!1 = h(j(U!1))),
% 0.14/0.41 inference(symmetry,[status(thm)],[104])).
% 0.14/0.41 tff(106,plain,
% 0.14/0.41 (op2(h(tptp_fun_V_0(j(U!1))), U!1) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1)))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[105])).
% 0.14/0.41 tff(107,plain,
% 0.14/0.41 (op2(h(tptp_fun_V_0(j(U!1))), U!1) = h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))),
% 0.14/0.41 inference(transitivity,[status(thm)],[106, 93])).
% 0.14/0.41 tff(108,plain,
% 0.14/0.41 (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[107])).
% 0.14/0.41 tff(109,plain,
% 0.14/0.41 (((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1))))) | (op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(110,plain,
% 0.14/0.41 (op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[109, 45])).
% 0.14/0.41 tff(111,plain,
% 0.14/0.41 (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = h(tptp_fun_V_0(j(U!1)))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[110])).
% 0.14/0.41 tff(112,plain,
% 0.14/0.41 (((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(j(U!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X)))))) <=> ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(j(U!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(113,plain,
% 0.14/0.41 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(j(U!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X)))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(114,plain,
% 0.14/0.41 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(j(U!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.14/0.41 tff(115,plain,
% 0.14/0.41 (![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[114, 79, 28])).
% 0.14/0.41 tff(116,plain,
% 0.14/0.41 (((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(117,plain,
% 0.14/0.41 ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(118,plain,
% 0.14/0.41 ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.14/0.41 tff(119,plain,
% 0.14/0.41 ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.14/0.41 tff(120,plain,
% 0.14/0.41 (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[119, 68])).
% 0.14/0.41 tff(121,plain,
% 0.14/0.41 (op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.41 inference(symmetry,[status(thm)],[120])).
% 0.14/0.41 tff(122,plain,
% 0.14/0.41 (op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[105, 107])).
% 0.14/0.41 tff(123,plain,
% 0.14/0.41 (op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1)))),
% 0.14/0.41 inference(transitivity,[status(thm)],[122, 121, 111])).
% 0.14/0.41 tff(124,plain,
% 0.14/0.41 (^[U: $i] : refl(((~sorti1(U)) | sorti2(h(U))) <=> ((~sorti1(U)) | sorti2(h(U))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(125,plain,
% 0.14/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[124])).
% 0.14/0.41 tff(126,plain,
% 0.14/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(127,plain,
% 0.14/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.41 inference(and_elim,[status(thm)],[7])).
% 0.14/0.41 tff(128,plain,
% 0.14/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.14/0.41 tff(129,plain,(
% 0.14/0.41 ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[128])).
% 0.14/0.41 tff(130,plain,
% 0.14/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.14/0.41 tff(131,plain,
% 0.14/0.41 (((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1)))))) <=> ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(132,plain,
% 0.14/0.41 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1)))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(133,plain,
% 0.14/0.41 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.14/0.41 tff(134,plain,
% 0.14/0.41 (sorti2(h(tptp_fun_V_0(j(U!1))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[133, 130, 47])).
% 0.14/0.41 tff(135,plain,
% 0.14/0.41 (^[V: $i] : refl(((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))) <=> ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(136,plain,
% 0.14/0.42 (![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))) <=> ![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[135])).
% 0.14/0.42 tff(137,plain,
% 0.14/0.42 (^[V: $i] : trans(monotonicity(rewrite((sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V)) <=> (~((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))))), ((~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V))) <=> (~(~((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))))))), rewrite((~(~((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))))) <=> ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))), ((~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V))) <=> ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(138,plain,
% 0.14/0.42 (![V: $i] : (~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V))) <=> ![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[137])).
% 0.14/0.42 tff(139,plain,
% 0.14/0.42 (![V: $i] : (~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V)))),
% 0.14/0.42 inference(and_elim,[status(thm)],[23])).
% 0.14/0.42 tff(140,plain,
% 0.14/0.42 (![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.14/0.42 tff(141,plain,
% 0.14/0.42 (![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.14/0.42 tff(142,plain,
% 0.14/0.42 (((~![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1) | (~(op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1))))))) <=> ((~![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1) | (~(op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(143,plain,
% 0.14/0.42 ((~![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1) | (~(op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1))))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(144,plain,
% 0.14/0.42 ((~![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1) | (~(op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.14/0.42 tff(145,plain,
% 0.14/0.42 ((op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1) | (~(op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1)))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[144, 141, 134])).
% 0.14/0.42 tff(146,plain,
% 0.14/0.42 (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[145, 123])).
% 0.14/0.42 tff(147,plain,
% 0.14/0.42 (U!1 = op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1))),
% 0.14/0.42 inference(symmetry,[status(thm)],[146])).
% 0.14/0.42 tff(148,plain,
% 0.14/0.42 (U!1 = h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[147, 108, 88])).
% 0.14/0.42 tff(149,plain,
% 0.14/0.42 (j(U!1) = j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[148])).
% 0.14/0.42 tff(150,plain,
% 0.14/0.42 (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = j(U!1)),
% 0.14/0.42 inference(symmetry,[status(thm)],[149])).
% 0.14/0.42 tff(151,plain,
% 0.14/0.42 (((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))) <=> ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(152,plain,
% 0.14/0.42 ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(153,plain,
% 0.14/0.42 ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.14/0.42 tff(154,plain,
% 0.14/0.42 (sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[153, 64, 68])).
% 0.14/0.42 tff(155,plain,
% 0.14/0.42 (^[X2: $i] : refl(((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ((~sorti1(X2)) | (j(h(X2)) = X2)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(156,plain,
% 0.14/0.42 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[155])).
% 0.14/0.42 tff(157,plain,
% 0.14/0.42 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(158,plain,
% 0.14/0.42 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.42 inference(and_elim,[status(thm)],[75])).
% 0.14/0.42 tff(159,plain,
% 0.14/0.42 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.14/0.42 tff(160,plain,(
% 0.14/0.42 ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.42 inference(skolemize,[status(sab)],[159])).
% 0.14/0.42 tff(161,plain,
% 0.14/0.42 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.14/0.42 tff(162,plain,
% 0.14/0.42 (((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) | (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))) <=> ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) | (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(163,plain,
% 0.14/0.42 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) | (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(164,plain,
% 0.14/0.42 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) | (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.14/0.42 tff(165,plain,
% 0.14/0.42 (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[164, 161, 154])).
% 0.14/0.42 tff(166,plain,
% 0.14/0.42 (op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.14/0.42 inference(symmetry,[status(thm)],[165])).
% 0.14/0.42 tff(167,plain,
% 0.14/0.42 (op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)),
% 0.14/0.42 inference(transitivity,[status(thm)],[166, 150])).
% 0.14/0.42 tff(168,plain,
% 0.14/0.42 (((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1))))) | (~(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(169,plain,
% 0.21/0.42 (~(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[168, 45])).
% 0.21/0.42 tff(170,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[169, 167])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------