TSTP Solution File: SYN722+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN722+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n005.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 : Thu Sep 29 23:57:05 EDT 2022

% Result   : Theorem 0.19s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYN722+1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Sep  5 06:45:03 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.19/0.39  % SZS status Theorem
% 0.19/0.39  % SZS output start Proof
% 0.19/0.39  tff(r_type, type, (
% 0.19/0.39     r: $i > $o)).
% 0.19/0.39  tff(a_type, type, (
% 0.19/0.39     a: $i)).
% 0.19/0.39  tff(p_type, type, (
% 0.19/0.39     p: $i > $o)).
% 0.19/0.39  tff(q_type, type, (
% 0.19/0.39     q: $i > $o)).
% 0.19/0.39  tff(b_type, type, (
% 0.19/0.39     b: $i)).
% 0.19/0.39  tff(d_type, type, (
% 0.19/0.39     d: $i)).
% 0.19/0.39  tff(c_type, type, (
% 0.19/0.39     c: $i)).
% 0.19/0.39  tff(tptp_fun_Y_0_type, type, (
% 0.19/0.39     tptp_fun_Y_0: $i > $i)).
% 0.19/0.39  tff(1,plain,
% 0.19/0.39      (^[Z: $i] : refl((~((~q(Z)) | (~(p(Z) | r(Z))))) <=> (~((~q(Z)) | (~(p(Z) | r(Z))))))),
% 0.19/0.39      inference(bind,[status(th)],[])).
% 0.19/0.39  tff(2,plain,
% 0.19/0.39      (![Z: $i] : (~((~q(Z)) | (~(p(Z) | r(Z))))) <=> ![Z: $i] : (~((~q(Z)) | (~(p(Z) | r(Z)))))),
% 0.19/0.39      inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39  tff(3,plain,
% 0.19/0.39      (^[Z: $i] : rewrite(((p(Z) | r(Z)) & q(Z)) <=> (~((~q(Z)) | (~(p(Z) | r(Z))))))),
% 0.19/0.39      inference(bind,[status(th)],[])).
% 0.19/0.39  tff(4,plain,
% 0.19/0.39      (![Z: $i] : ((p(Z) | r(Z)) & q(Z)) <=> ![Z: $i] : (~((~q(Z)) | (~(p(Z) | r(Z)))))),
% 0.19/0.39      inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39  tff(5,plain,
% 0.19/0.39      (![Z: $i] : ((p(Z) | r(Z)) & q(Z)) <=> ![Z: $i] : ((p(Z) | r(Z)) & q(Z))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(6,plain,
% 0.19/0.39      ((~(~(![Z: $i] : ((p(Z) | r(Z)) & q(Z)) & ![X: $i] : ?[Y: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(Y))) & ((~p(a)) | (~p(b)))))) <=> (![Z: $i] : ((p(Z) | r(Z)) & q(Z)) & ![X: $i] : ?[Y: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(Y))) & ((~p(a)) | (~p(b))))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(7,plain,
% 0.19/0.39      ((~((![Z: $i] : ((p(Z) | r(Z)) & q(Z)) & ![X: $i] : ?[Y: $i] : ((((p(X) | (~q(X))) | (~q(Y))) | (~q(c))) | (~q(d)))) & ((~p(a)) | (~p(b))))) <=> (~(![Z: $i] : ((p(Z) | r(Z)) & q(Z)) & ![X: $i] : ?[Y: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(Y))) & ((~p(a)) | (~p(b)))))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(8,plain,
% 0.19/0.39      ((~(~((![Z: $i] : ((p(Z) | r(Z)) & q(Z)) & ![X: $i] : ?[Y: $i] : ((((p(X) | (~q(X))) | (~q(Y))) | (~q(c))) | (~q(d)))) & ((~p(a)) | (~p(b)))))) <=> (~(~(![Z: $i] : ((p(Z) | r(Z)) & q(Z)) & ![X: $i] : ?[Y: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(Y))) & ((~p(a)) | (~p(b))))))),
% 0.19/0.39      inference(monotonicity,[status(thm)],[7])).
% 0.19/0.39  tff(9,plain,
% 0.19/0.39      ((~(~((![Z: $i] : ((p(Z) | r(Z)) & q(Z)) & ![X: $i] : ?[Y: $i] : ((((p(X) | (~q(X))) | (~q(Y))) | (~q(c))) | (~q(d)))) & ((~p(a)) | (~p(b)))))) <=> (![Z: $i] : ((p(Z) | r(Z)) & q(Z)) & ![X: $i] : ?[Y: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(Y))) & ((~p(a)) | (~p(b))))),
% 0.19/0.39      inference(transitivity,[status(thm)],[8, 6])).
% 0.19/0.39  tff(10,axiom,(~(~((![Z: $i] : ((p(Z) | r(Z)) & q(Z)) & ![X: $i] : ?[Y: $i] : ((((p(X) | (~q(X))) | (~q(Y))) | (~q(c))) | (~q(d)))) & ((~p(a)) | (~p(b)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm119')).
% 0.19/0.39  tff(11,plain,
% 0.19/0.39      (![Z: $i] : ((p(Z) | r(Z)) & q(Z)) & ![X: $i] : ?[Y: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(Y))) & ((~p(a)) | (~p(b)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.39  tff(12,plain,
% 0.19/0.39      (![Z: $i] : ((p(Z) | r(Z)) & q(Z))),
% 0.19/0.39      inference(and_elim,[status(thm)],[11])).
% 0.19/0.39  tff(13,plain,
% 0.19/0.39      (![Z: $i] : ((p(Z) | r(Z)) & q(Z))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.39  tff(14,plain,(
% 0.19/0.39      ![Z: $i] : ((p(Z) | r(Z)) & q(Z))),
% 0.19/0.39      inference(skolemize,[status(sab)],[13])).
% 0.19/0.39  tff(15,plain,
% 0.19/0.39      (![Z: $i] : (~((~q(Z)) | (~(p(Z) | r(Z)))))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[14, 4])).
% 0.19/0.39  tff(16,plain,
% 0.19/0.39      (![Z: $i] : (~((~q(Z)) | (~(p(Z) | r(Z)))))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[15, 2])).
% 0.19/0.39  tff(17,plain,
% 0.19/0.39      ((~![Z: $i] : (~((~q(Z)) | (~(p(Z) | r(Z)))))) | (~((~q(a)) | (~(p(a) | r(a)))))),
% 0.19/0.39      inference(quant_inst,[status(thm)],[])).
% 0.19/0.39  tff(18,plain,
% 0.19/0.39      (~((~q(a)) | (~(p(a) | r(a))))),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.39  tff(19,assumption,((~q(tptp_fun_Y_0(a))) | (~(p(tptp_fun_Y_0(a)) | r(tptp_fun_Y_0(a))))), introduced(assumption)).
% 0.19/0.39  tff(20,plain,
% 0.19/0.39      ((~![Z: $i] : (~((~q(Z)) | (~(p(Z) | r(Z)))))) | (~((~q(tptp_fun_Y_0(a))) | (~(p(tptp_fun_Y_0(a)) | r(tptp_fun_Y_0(a))))))),
% 0.19/0.39      inference(quant_inst,[status(thm)],[])).
% 0.19/0.39  tff(21,plain,
% 0.19/0.39      ($false),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[20, 16, 19])).
% 0.19/0.39  tff(22,plain,(~((~q(tptp_fun_Y_0(a))) | (~(p(tptp_fun_Y_0(a)) | r(tptp_fun_Y_0(a)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39  tff(23,plain,
% 0.19/0.39      (((~q(tptp_fun_Y_0(a))) | (~(p(tptp_fun_Y_0(a)) | r(tptp_fun_Y_0(a))))) | q(tptp_fun_Y_0(a))),
% 0.19/0.39      inference(tautology,[status(thm)],[])).
% 0.19/0.39  tff(24,plain,
% 0.19/0.39      (q(tptp_fun_Y_0(a))),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.39  tff(25,assumption,((~q(c)) | (~(p(c) | r(c)))), introduced(assumption)).
% 0.19/0.39  tff(26,plain,
% 0.19/0.39      ((~![Z: $i] : (~((~q(Z)) | (~(p(Z) | r(Z)))))) | (~((~q(c)) | (~(p(c) | r(c)))))),
% 0.19/0.39      inference(quant_inst,[status(thm)],[])).
% 0.19/0.39  tff(27,plain,
% 0.19/0.39      ($false),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[26, 16, 25])).
% 0.19/0.39  tff(28,plain,(~((~q(c)) | (~(p(c) | r(c))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39  tff(29,plain,
% 0.19/0.39      (((~q(c)) | (~(p(c) | r(c)))) | q(c)),
% 0.19/0.39      inference(tautology,[status(thm)],[])).
% 0.19/0.39  tff(30,plain,
% 0.19/0.39      (q(c)),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[29, 28])).
% 0.19/0.39  tff(31,assumption,((~q(d)) | (~(p(d) | r(d)))), introduced(assumption)).
% 0.19/0.39  tff(32,plain,
% 0.19/0.39      ((~![Z: $i] : (~((~q(Z)) | (~(p(Z) | r(Z)))))) | (~((~q(d)) | (~(p(d) | r(d)))))),
% 0.19/0.39      inference(quant_inst,[status(thm)],[])).
% 0.19/0.39  tff(33,plain,
% 0.19/0.39      ($false),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[32, 16, 31])).
% 0.19/0.39  tff(34,plain,(~((~q(d)) | (~(p(d) | r(d))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39  tff(35,plain,
% 0.19/0.39      (((~q(d)) | (~(p(d) | r(d)))) | q(d)),
% 0.19/0.39      inference(tautology,[status(thm)],[])).
% 0.19/0.39  tff(36,plain,
% 0.19/0.39      (q(d)),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.39  tff(37,plain,
% 0.19/0.39      ((~![Z: $i] : (~((~q(Z)) | (~(p(Z) | r(Z)))))) | (~((~q(b)) | (~(p(b) | r(b)))))),
% 0.19/0.39      inference(quant_inst,[status(thm)],[])).
% 0.19/0.39  tff(38,plain,
% 0.19/0.39      (~((~q(b)) | (~(p(b) | r(b))))),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[37, 16])).
% 0.19/0.39  tff(39,assumption,((~q(tptp_fun_Y_0(b))) | (~(p(tptp_fun_Y_0(b)) | r(tptp_fun_Y_0(b))))), introduced(assumption)).
% 0.19/0.39  tff(40,plain,
% 0.19/0.39      ((~![Z: $i] : (~((~q(Z)) | (~(p(Z) | r(Z)))))) | (~((~q(tptp_fun_Y_0(b))) | (~(p(tptp_fun_Y_0(b)) | r(tptp_fun_Y_0(b))))))),
% 0.19/0.39      inference(quant_inst,[status(thm)],[])).
% 0.19/0.39  tff(41,plain,
% 0.19/0.39      ($false),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[40, 16, 39])).
% 0.19/0.39  tff(42,plain,(~((~q(tptp_fun_Y_0(b))) | (~(p(tptp_fun_Y_0(b)) | r(tptp_fun_Y_0(b)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39  tff(43,plain,
% 0.19/0.39      (((~q(tptp_fun_Y_0(b))) | (~(p(tptp_fun_Y_0(b)) | r(tptp_fun_Y_0(b))))) | q(tptp_fun_Y_0(b))),
% 0.19/0.39      inference(tautology,[status(thm)],[])).
% 0.19/0.39  tff(44,plain,
% 0.19/0.39      (q(tptp_fun_Y_0(b))),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.39  tff(45,assumption,(~p(b)), introduced(assumption)).
% 0.19/0.39  tff(46,plain,
% 0.19/0.39      (^[X: $i] : refl((p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X)))) <=> (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X)))))),
% 0.19/0.39      inference(bind,[status(th)],[])).
% 0.19/0.39  tff(47,plain,
% 0.19/0.39      (![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X)))) <=> ![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))),
% 0.19/0.39      inference(quant_intro,[status(thm)],[46])).
% 0.19/0.39  tff(48,plain,
% 0.19/0.39      (^[X: $i] : rewrite(((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(tptp_fun_Y_0(X)))) <=> (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X)))))),
% 0.19/0.39      inference(bind,[status(th)],[])).
% 0.19/0.39  tff(49,plain,
% 0.19/0.39      (![X: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(tptp_fun_Y_0(X)))) <=> ![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))),
% 0.19/0.39      inference(quant_intro,[status(thm)],[48])).
% 0.19/0.39  tff(50,plain,
% 0.19/0.39      (![X: $i] : ?[Y: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(Y))) <=> ![X: $i] : ?[Y: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(Y)))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(51,plain,
% 0.19/0.39      (![X: $i] : ?[Y: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(Y)))),
% 0.19/0.39      inference(and_elim,[status(thm)],[11])).
% 0.19/0.39  tff(52,plain,
% 0.19/0.39      (![X: $i] : ?[Y: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(Y)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.39  tff(53,plain,(
% 0.19/0.39      ![X: $i] : ((~q(X)) | p(X) | (~q(c)) | (~q(d)) | (~q(tptp_fun_Y_0(X))))),
% 0.19/0.39      inference(skolemize,[status(sab)],[52])).
% 0.19/0.39  tff(54,plain,
% 0.19/0.39      (![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[53, 49])).
% 0.19/0.40  tff(55,plain,
% 0.19/0.40      (![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.40  tff(56,plain,
% 0.19/0.40      (((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | ((~q(c)) | (~q(d)) | p(b) | (~q(b)) | (~q(tptp_fun_Y_0(b))))) <=> ((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | (~q(c)) | (~q(d)) | p(b) | (~q(b)) | (~q(tptp_fun_Y_0(b))))),
% 0.19/0.40      inference(rewrite,[status(thm)],[])).
% 0.19/0.40  tff(57,plain,
% 0.19/0.40      ((p(b) | (~q(c)) | (~q(d)) | (~q(b)) | (~q(tptp_fun_Y_0(b)))) <=> ((~q(c)) | (~q(d)) | p(b) | (~q(b)) | (~q(tptp_fun_Y_0(b))))),
% 0.19/0.40      inference(rewrite,[status(thm)],[])).
% 0.19/0.40  tff(58,plain,
% 0.19/0.40      (((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | (p(b) | (~q(c)) | (~q(d)) | (~q(b)) | (~q(tptp_fun_Y_0(b))))) <=> ((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | ((~q(c)) | (~q(d)) | p(b) | (~q(b)) | (~q(tptp_fun_Y_0(b)))))),
% 0.19/0.40      inference(monotonicity,[status(thm)],[57])).
% 0.19/0.40  tff(59,plain,
% 0.19/0.40      (((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | (p(b) | (~q(c)) | (~q(d)) | (~q(b)) | (~q(tptp_fun_Y_0(b))))) <=> ((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | (~q(c)) | (~q(d)) | p(b) | (~q(b)) | (~q(tptp_fun_Y_0(b))))),
% 0.19/0.40      inference(transitivity,[status(thm)],[58, 56])).
% 0.19/0.40  tff(60,plain,
% 0.19/0.40      ((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | (p(b) | (~q(c)) | (~q(d)) | (~q(b)) | (~q(tptp_fun_Y_0(b))))),
% 0.19/0.40      inference(quant_inst,[status(thm)],[])).
% 0.19/0.40  tff(61,plain,
% 0.19/0.40      ((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | (~q(c)) | (~q(d)) | p(b) | (~q(b)) | (~q(tptp_fun_Y_0(b)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.40  tff(62,plain,
% 0.19/0.40      (~q(b)),
% 0.19/0.40      inference(unit_resolution,[status(thm)],[61, 55, 45, 36, 30, 44])).
% 0.19/0.40  tff(63,plain,
% 0.19/0.40      (((~q(b)) | (~(p(b) | r(b)))) | q(b)),
% 0.19/0.40      inference(tautology,[status(thm)],[])).
% 0.19/0.40  tff(64,plain,
% 0.19/0.40      ($false),
% 0.19/0.40      inference(unit_resolution,[status(thm)],[63, 62, 38])).
% 0.19/0.40  tff(65,plain,(p(b)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40  tff(66,plain,
% 0.19/0.40      (((~p(a)) | (~p(b))) <=> ((~p(a)) | (~p(b)))),
% 0.19/0.40      inference(rewrite,[status(thm)],[])).
% 0.19/0.40  tff(67,plain,
% 0.19/0.40      ((~p(a)) | (~p(b))),
% 0.19/0.40      inference(and_elim,[status(thm)],[11])).
% 0.19/0.40  tff(68,plain,
% 0.19/0.40      ((~p(a)) | (~p(b))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.40  tff(69,plain,
% 0.19/0.40      (~p(a)),
% 0.19/0.40      inference(unit_resolution,[status(thm)],[68, 65])).
% 0.19/0.40  tff(70,plain,
% 0.19/0.40      (((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | (p(a) | (~q(c)) | (~q(d)) | (~q(a)) | (~q(tptp_fun_Y_0(a))))) <=> ((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | p(a) | (~q(c)) | (~q(d)) | (~q(a)) | (~q(tptp_fun_Y_0(a))))),
% 0.19/0.40      inference(rewrite,[status(thm)],[])).
% 0.19/0.40  tff(71,plain,
% 0.19/0.40      ((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | (p(a) | (~q(c)) | (~q(d)) | (~q(a)) | (~q(tptp_fun_Y_0(a))))),
% 0.19/0.40      inference(quant_inst,[status(thm)],[])).
% 0.19/0.40  tff(72,plain,
% 0.19/0.40      ((~![X: $i] : (p(X) | (~q(c)) | (~q(d)) | (~q(X)) | (~q(tptp_fun_Y_0(X))))) | p(a) | (~q(c)) | (~q(d)) | (~q(a)) | (~q(tptp_fun_Y_0(a)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.40  tff(73,plain,
% 0.19/0.40      (~q(a)),
% 0.19/0.40      inference(unit_resolution,[status(thm)],[72, 55, 69, 36, 30, 24])).
% 0.19/0.40  tff(74,plain,
% 0.19/0.40      (((~q(a)) | (~(p(a) | r(a)))) | q(a)),
% 0.19/0.40      inference(tautology,[status(thm)],[])).
% 0.19/0.40  tff(75,plain,
% 0.19/0.40      ($false),
% 0.19/0.40      inference(unit_resolution,[status(thm)],[74, 73, 18])).
% 0.19/0.40  % SZS output end Proof
%------------------------------------------------------------------------------