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
%------------------------------------------------------------------------------