TSTP Solution File: KRS162+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS162+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Sat Sep 17 17:45:02 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS162+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.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 : Thu Sep 1 09:53:22 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.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(tptp_fun_Y0_5_type, type, (
% 0.20/0.41 tptp_fun_Y0_5: $i)).
% 0.20/0.41 tff(tptp_fun_Y1_1_type, type, (
% 0.20/0.41 tptp_fun_Y1_1: $i)).
% 0.20/0.41 tff(cA_type, type, (
% 0.20/0.41 cA: $i > $o)).
% 0.20/0.41 tff(cB_type, type, (
% 0.20/0.41 cB: $i > $o)).
% 0.20/0.41 tff(rq_type, type, (
% 0.20/0.41 rq: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_X_0_type, type, (
% 0.20/0.41 tptp_fun_X_0: $i)).
% 0.20/0.41 tff(rr_type, type, (
% 0.20/0.41 rr: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y2_3_type, type, (
% 0.20/0.41 tptp_fun_Y2_3: $i)).
% 0.20/0.41 tff(tptp_fun_Y1_4_type, type, (
% 0.20/0.41 tptp_fun_Y1_4: $i)).
% 0.20/0.41 tff(tptp_fun_Y0_2_type, type, (
% 0.20/0.41 tptp_fun_Y0_2: $i)).
% 0.20/0.41 tff(rp_type, type, (
% 0.20/0.41 rp: ( $i * $i ) > $o)).
% 0.20/0.41 tff(xsd_integer_type, type, (
% 0.20/0.41 xsd_integer: $i > $o)).
% 0.20/0.41 tff(xsd_string_type, type, (
% 0.20/0.41 xsd_string: $i > $o)).
% 0.20/0.41 tff(cowlNothing_type, type, (
% 0.20/0.41 cowlNothing: $i > $o)).
% 0.20/0.41 tff(cowlThing_type, type, (
% 0.20/0.41 cowlThing: $i > $o)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (((rp(X!0, Y0!2) & rp(X!0, Y1!1) & (~(Y0!2 = Y1!1)) & rq(X!0, Y0!5) & rq(X!0, Y1!4) & rq(X!0, Y2!3) & (~(Y0!5 = Y1!4)) & (~(Y0!5 = Y2!3)) & (~(Y1!4 = Y2!3))) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))) <=> (rp(X!0, Y0!2) & rp(X!0, Y1!1) & (~(Y0!2 = Y1!1)) & rq(X!0, Y0!5) & rq(X!0, Y1!4) & rq(X!0, Y2!3) & (~(Y0!5 = Y1!4)) & (~(Y0!5 = Y2!3)) & (~(Y1!4 = Y2!3)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (((rp(X!0, Y0!2) & rp(X!0, Y1!1) & (~(Y0!2 = Y1!1))) & (rq(X!0, Y0!5) & rq(X!0, Y1!4) & rq(X!0, Y2!3) & (~(Y0!5 = Y1!4)) & (~(Y0!5 = Y2!3)) & (~(Y1!4 = Y2!3)))) <=> (rp(X!0, Y0!2) & rp(X!0, Y1!1) & (~(Y0!2 = Y1!1)) & rq(X!0, Y0!5) & rq(X!0, Y1!4) & rq(X!0, Y2!3) & (~(Y0!5 = Y1!4)) & (~(Y0!5 = Y2!3)) & (~(Y1!4 = Y2!3)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 ((((rp(X!0, Y0!2) & rp(X!0, Y1!1) & (~(Y0!2 = Y1!1))) & (rq(X!0, Y0!5) & rq(X!0, Y1!4) & rq(X!0, Y2!3) & (~(Y0!5 = Y1!4)) & (~(Y0!5 = Y2!3)) & (~(Y1!4 = Y2!3)))) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))) <=> ((rp(X!0, Y0!2) & rp(X!0, Y1!1) & (~(Y0!2 = Y1!1)) & rq(X!0, Y0!5) & rq(X!0, Y1!4) & rq(X!0, Y2!3) & (~(Y0!5 = Y1!4)) & (~(Y0!5 = Y2!3)) & (~(Y1!4 = Y2!3))) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 ((((rp(X!0, Y0!2) & rp(X!0, Y1!1) & (~(Y0!2 = Y1!1))) & (rq(X!0, Y0!5) & rq(X!0, Y1!4) & rq(X!0, Y2!3) & (~(Y0!5 = Y1!4)) & (~(Y0!5 = Y2!3)) & (~(Y1!4 = Y2!3)))) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))) <=> (rp(X!0, Y0!2) & rp(X!0, Y1!1) & (~(Y0!2 = Y1!1)) & rq(X!0, Y0!5) & rq(X!0, Y1!4) & rq(X!0, Y2!3) & (~(Y0!5 = Y1!4)) & (~(Y0!5 = Y2!3)) & (~(Y1!4 = Y2!3)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[3, 1])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 ((~![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))) <=> (~![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))) <=> (~![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[7])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 ((~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : ((?[Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (((((rq(X, Y0) & rq(X, Y1)) & rq(X, Y2)) & (~(Y0 = Y1))) & (~(Y0 = Y2))) & (~(Y1 = Y2)))) => ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((((((((((((((rr(X, Y0) & rr(X, Y1)) & rr(X, Y2)) & rr(X, Y3)) & rr(X, Y4)) & (~(Y0 = Y1))) & (~(Y0 = Y2))) & (~(Y0 = Y3))) & (~(Y0 = Y4))) & (~(Y1 = Y2))) & (~(Y1 = Y3))) & (~(Y1 = Y4))) & (~(Y2 = Y3))) & (~(Y2 = Y4))) & (~(Y3 = Y4)))))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(10,axiom,(~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : ((?[Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (((((rq(X, Y0) & rq(X, Y1)) & rq(X, Y2)) & (~(Y0 = Y1))) & (~(Y0 = Y2))) & (~(Y1 = Y2)))) => ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((((((((((((((rr(X, Y0) & rr(X, Y1)) & rr(X, Y2)) & rr(X, Y3)) & rr(X, Y4)) & (~(Y0 = Y1))) & (~(Y0 = Y2))) & (~(Y0 = Y3))) & (~(Y0 = Y4))) & (~(Y1 = Y2))) & (~(Y1 = Y3))) & (~(Y1 = Y4))) & (~(Y2 = Y3))) & (~(Y2 = Y4))) & (~(Y3 = Y4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (~![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (~![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (~![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[14, 5])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (~![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (~![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[16, 5])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (~![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[17, 5])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (rp(X!0, Y0!2) & rp(X!0, Y1!1) & (~(Y0!2 = Y1!1)) & rq(X!0, Y0!5) & rq(X!0, Y1!4) & rq(X!0, Y2!3) & (~(Y0!5 = Y1!4)) & (~(Y0!5 = Y2!3)) & (~(Y1!4 = Y2!3)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 4])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (rq(X!0, Y0!5)),
% 0.20/0.42 inference(and_elim,[status(thm)],[19])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl((cB(Y) | (~rq(X, Y))) <=> (cB(Y) | (~rq(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y))) <=> ![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y))) <=> ![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : rewrite((rq(X, Y) => cB(Y)) <=> (cB(Y) | (~rq(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (rq(X, Y) => cB(Y)) <=> ![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.42 tff(26,axiom,(![X: $i, Y: $i] : (rq(X, Y) => cB(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_3')).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.42 tff(29,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[28])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | (cB(Y0!5) | (~rq(X!0, Y0!5)))) <=> ((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | cB(Y0!5) | (~rq(X!0, Y0!5)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | (cB(Y0!5) | (~rq(X!0, Y0!5)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | cB(Y0!5) | (~rq(X!0, Y0!5))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (cB(Y0!5)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (^[X: $i] : refl(((~cB(X)) | (~cA(X))) <=> ((~cB(X)) | (~cA(X))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![X: $i] : ((~cB(X)) | (~cA(X))) <=> ![X: $i] : ((~cB(X)) | (~cA(X)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (^[X: $i] : trans(monotonicity(rewrite((cB(X) & cA(X)) <=> (~((~cB(X)) | (~cA(X))))), ((~(cB(X) & cA(X))) <=> (~(~((~cB(X)) | (~cA(X))))))), rewrite((~(~((~cB(X)) | (~cA(X))))) <=> ((~cB(X)) | (~cA(X)))), ((~(cB(X) & cA(X))) <=> ((~cB(X)) | (~cA(X)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![X: $i] : (~(cB(X) & cA(X))) <=> ![X: $i] : ((~cB(X)) | (~cA(X)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![X: $i] : (~(cB(X) & cA(X))) <=> ![X: $i] : (~(cB(X) & cA(X)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(40,axiom,(![X: $i] : (~(cB(X) & cA(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_4')).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![X: $i] : (~(cB(X) & cA(X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.42 tff(42,plain,(
% 0.20/0.42 ![X: $i] : (~(cB(X) & cA(X)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[41])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (![X: $i] : ((~cB(X)) | (~cA(X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![X: $i] : ((~cB(X)) | (~cA(X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (((~![X: $i] : ((~cB(X)) | (~cA(X)))) | ((~cB(Y0!5)) | (~cA(Y0!5)))) <=> ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | (~cB(Y0!5)) | (~cA(Y0!5)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | ((~cB(Y0!5)) | (~cA(Y0!5)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | (~cB(Y0!5)) | (~cA(Y0!5))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (~cA(Y0!5)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[47, 44, 34])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (rp(X!0, Y1!1)),
% 0.20/0.42 inference(and_elim,[status(thm)],[19])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl((cA(Y) | (~rp(X, Y))) <=> (cA(Y) | (~rp(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y))) <=> ![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y))) <=> ![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : rewrite((rp(X, Y) => cA(Y)) <=> (cA(Y) | (~rp(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (rp(X, Y) => cA(Y)) <=> ![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.42 tff(55,axiom,(![X: $i, Y: $i] : (rp(X, Y) => cA(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.42 tff(58,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[57])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))) | (cA(Y1!1) | (~rp(X!0, Y1!1)))) <=> ((~![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))) | cA(Y1!1) | (~rp(X!0, Y1!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))) | (cA(Y1!1) | (~rp(X!0, Y1!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))) | cA(Y1!1) | (~rp(X!0, Y1!1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (cA(Y1!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[62, 59, 49])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (^[A: $i, B: $i] : refl((cA(B) | (~(A = B)) | (~cA(A))) <=> (cA(B) | (~(A = B)) | (~cA(A))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A))) <=> ![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((A = B) & cA(A)) <=> (~((~(A = B)) | (~cA(A))))), ((~((A = B) & cA(A))) <=> (~(~((~(A = B)) | (~cA(A))))))), rewrite((~(~((~(A = B)) | (~cA(A))))) <=> ((~(A = B)) | (~cA(A)))), ((~((A = B) & cA(A))) <=> ((~(A = B)) | (~cA(A))))), ((cA(B) | (~((A = B) & cA(A)))) <=> (cA(B) | ((~(A = B)) | (~cA(A)))))), rewrite((cA(B) | ((~(A = B)) | (~cA(A)))) <=> (cA(B) | (~(A = B)) | (~cA(A)))), ((cA(B) | (~((A = B) & cA(A)))) <=> (cA(B) | (~(A = B)) | (~cA(A)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (![A: $i, B: $i] : (cA(B) | (~((A = B) & cA(A)))) <=> ![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (![A: $i, B: $i] : (cA(B) | (~((A = B) & cA(A)))) <=> ![A: $i, B: $i] : (cA(B) | (~((A = B) & cA(A))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (^[A: $i, B: $i] : rewrite((((A = B) & cA(A)) => cA(B)) <=> (cA(B) | (~((A = B) & cA(A)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (![A: $i, B: $i] : (((A = B) & cA(A)) => cA(B)) <=> ![A: $i, B: $i] : (cA(B) | (~((A = B) & cA(A))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.43 tff(71,axiom,(![A: $i, B: $i] : (((A = B) & cA(A)) => cA(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cA_substitution_1')).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (![A: $i, B: $i] : (cA(B) | (~((A = B) & cA(A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (![A: $i, B: $i] : (cA(B) | (~((A = B) & cA(A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.43 tff(74,plain,(
% 0.20/0.43 ![A: $i, B: $i] : (cA(B) | (~((A = B) & cA(A))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[73])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | ((~cA(Y1!1)) | cA(Y0!5) | (~(Y1!1 = Y0!5)))) <=> ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (~cA(Y1!1)) | cA(Y0!5) | (~(Y1!1 = Y0!5)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 ((cA(Y0!5) | (~(Y1!1 = Y0!5)) | (~cA(Y1!1))) <=> ((~cA(Y1!1)) | cA(Y0!5) | (~(Y1!1 = Y0!5)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (cA(Y0!5) | (~(Y1!1 = Y0!5)) | (~cA(Y1!1)))) <=> ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | ((~cA(Y1!1)) | cA(Y0!5) | (~(Y1!1 = Y0!5))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[78])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (cA(Y0!5) | (~(Y1!1 = Y0!5)) | (~cA(Y1!1)))) <=> ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (~cA(Y1!1)) | cA(Y0!5) | (~(Y1!1 = Y0!5)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[79, 77])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (cA(Y0!5) | (~(Y1!1 = Y0!5)) | (~cA(Y1!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (~cA(Y1!1)) | cA(Y0!5) | (~(Y1!1 = Y0!5))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (~(Y1!1 = Y0!5)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[82, 76, 63, 48])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (rq(X!0, Y1!4)),
% 0.20/0.43 inference(and_elim,[status(thm)],[19])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | (cB(Y1!4) | (~rq(X!0, Y1!4)))) <=> ((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | cB(Y1!4) | (~rq(X!0, Y1!4)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | (cB(Y1!4) | (~rq(X!0, Y1!4)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | cB(Y1!4) | (~rq(X!0, Y1!4))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (cB(Y1!4)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[87, 30, 84])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (((~![X: $i] : ((~cB(X)) | (~cA(X)))) | ((~cB(Y1!4)) | (~cA(Y1!4)))) <=> ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | (~cB(Y1!4)) | (~cA(Y1!4)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | ((~cB(Y1!4)) | (~cA(Y1!4)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | (~cB(Y1!4)) | (~cA(Y1!4))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (~cA(Y1!4)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[91, 44, 88])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | ((~cA(Y1!1)) | cA(Y1!4) | (~(Y1!1 = Y1!4)))) <=> ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (~cA(Y1!1)) | cA(Y1!4) | (~(Y1!1 = Y1!4)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 ((cA(Y1!4) | (~(Y1!1 = Y1!4)) | (~cA(Y1!1))) <=> ((~cA(Y1!1)) | cA(Y1!4) | (~(Y1!1 = Y1!4)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (cA(Y1!4) | (~(Y1!1 = Y1!4)) | (~cA(Y1!1)))) <=> ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | ((~cA(Y1!1)) | cA(Y1!4) | (~(Y1!1 = Y1!4))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[94])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (cA(Y1!4) | (~(Y1!1 = Y1!4)) | (~cA(Y1!1)))) <=> ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (~cA(Y1!1)) | cA(Y1!4) | (~(Y1!1 = Y1!4)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[95, 93])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (cA(Y1!4) | (~(Y1!1 = Y1!4)) | (~cA(Y1!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (~cA(Y1!1)) | cA(Y1!4) | (~(Y1!1 = Y1!4))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (~(Y1!1 = Y1!4)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[98, 76, 63, 92])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (rq(X!0, Y2!3)),
% 0.20/0.43 inference(and_elim,[status(thm)],[19])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | (cB(Y2!3) | (~rq(X!0, Y2!3)))) <=> ((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | cB(Y2!3) | (~rq(X!0, Y2!3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | (cB(Y2!3) | (~rq(X!0, Y2!3)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (cB(Y) | (~rq(X, Y)))) | cB(Y2!3) | (~rq(X!0, Y2!3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (cB(Y2!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[103, 30, 100])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (((~![X: $i] : ((~cB(X)) | (~cA(X)))) | ((~cB(Y2!3)) | (~cA(Y2!3)))) <=> ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | (~cB(Y2!3)) | (~cA(Y2!3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | ((~cB(Y2!3)) | (~cA(Y2!3)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | (~cB(Y2!3)) | (~cA(Y2!3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (~cA(Y2!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[107, 44, 104])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | ((~cA(Y1!1)) | cA(Y2!3) | (~(Y1!1 = Y2!3)))) <=> ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (~cA(Y1!1)) | cA(Y2!3) | (~(Y1!1 = Y2!3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((cA(Y2!3) | (~(Y1!1 = Y2!3)) | (~cA(Y1!1))) <=> ((~cA(Y1!1)) | cA(Y2!3) | (~(Y1!1 = Y2!3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (cA(Y2!3) | (~(Y1!1 = Y2!3)) | (~cA(Y1!1)))) <=> ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | ((~cA(Y1!1)) | cA(Y2!3) | (~(Y1!1 = Y2!3))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (cA(Y2!3) | (~(Y1!1 = Y2!3)) | (~cA(Y1!1)))) <=> ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (~cA(Y1!1)) | cA(Y2!3) | (~(Y1!1 = Y2!3)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[111, 109])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (cA(Y2!3) | (~(Y1!1 = Y2!3)) | (~cA(Y1!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (cA(B) | (~(A = B)) | (~cA(A)))) | (~cA(Y1!1)) | cA(Y2!3) | (~(Y1!1 = Y2!3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (~(Y1!1 = Y2!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[114, 76, 63, 108])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 ((Y1!1 = Y0!2) <=> (Y0!2 = Y1!1)),
% 0.20/0.43 inference(commutativity,[status(thm)],[])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 ((Y0!2 = Y1!1) <=> (Y1!1 = Y0!2)),
% 0.20/0.43 inference(symmetry,[status(thm)],[116])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 ((~(Y0!2 = Y1!1)) <=> (~(Y1!1 = Y0!2))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (~(Y0!2 = Y1!1)),
% 0.20/0.43 inference(and_elim,[status(thm)],[19])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (~(Y1!1 = Y0!2)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (rp(X!0, Y0!2)),
% 0.20/0.43 inference(and_elim,[status(thm)],[19])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))) | (cA(Y0!2) | (~rp(X!0, Y0!2)))) <=> ((~![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))) | cA(Y0!2) | (~rp(X!0, Y0!2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))) | (cA(Y0!2) | (~rp(X!0, Y0!2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (cA(Y) | (~rp(X, Y)))) | cA(Y0!2) | (~rp(X!0, Y0!2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (cA(Y0!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[124, 59, 121])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (((~![X: $i] : ((~cB(X)) | (~cA(X)))) | ((~cB(Y0!2)) | (~cA(Y0!2)))) <=> ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | (~cB(Y0!2)) | (~cA(Y0!2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | ((~cB(Y0!2)) | (~cA(Y0!2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 ((~![X: $i] : ((~cB(X)) | (~cA(X)))) | (~cB(Y0!2)) | (~cA(Y0!2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (~cB(Y0!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[128, 44, 125])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 (^[A: $i, B: $i] : refl((cB(B) | (~(A = B)) | (~cB(A))) <=> (cB(B) | (~(A = B)) | (~cB(A))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 (![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A))) <=> ![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((A = B) & cB(A)) <=> (~((~(A = B)) | (~cB(A))))), ((~((A = B) & cB(A))) <=> (~(~((~(A = B)) | (~cB(A))))))), rewrite((~(~((~(A = B)) | (~cB(A))))) <=> ((~(A = B)) | (~cB(A)))), ((~((A = B) & cB(A))) <=> ((~(A = B)) | (~cB(A))))), ((cB(B) | (~((A = B) & cB(A)))) <=> (cB(B) | ((~(A = B)) | (~cB(A)))))), rewrite((cB(B) | ((~(A = B)) | (~cB(A)))) <=> (cB(B) | (~(A = B)) | (~cB(A)))), ((cB(B) | (~((A = B) & cB(A)))) <=> (cB(B) | (~(A = B)) | (~cB(A)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (![A: $i, B: $i] : (cB(B) | (~((A = B) & cB(A)))) <=> ![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (![A: $i, B: $i] : (cB(B) | (~((A = B) & cB(A)))) <=> ![A: $i, B: $i] : (cB(B) | (~((A = B) & cB(A))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 (^[A: $i, B: $i] : rewrite((((A = B) & cB(A)) => cB(B)) <=> (cB(B) | (~((A = B) & cB(A)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 (![A: $i, B: $i] : (((A = B) & cB(A)) => cB(B)) <=> ![A: $i, B: $i] : (cB(B) | (~((A = B) & cB(A))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.44 tff(137,axiom,(![A: $i, B: $i] : (((A = B) & cB(A)) => cB(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cB_substitution_1')).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (![A: $i, B: $i] : (cB(B) | (~((A = B) & cB(A))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 (![A: $i, B: $i] : (cB(B) | (~((A = B) & cB(A))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.20/0.44 tff(140,plain,(
% 0.20/0.44 ![A: $i, B: $i] : (cB(B) | (~((A = B) & cB(A))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[139])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 (((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~cB(Y0!5)) | (~(Y0!5 = Y0!2)))) <=> ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | cB(Y0!2) | (~cB(Y0!5)) | (~(Y0!5 = Y0!2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 ((cB(Y0!2) | (~(Y0!5 = Y0!2)) | (~cB(Y0!5))) <=> (cB(Y0!2) | (~cB(Y0!5)) | (~(Y0!5 = Y0!2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~(Y0!5 = Y0!2)) | (~cB(Y0!5)))) <=> ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~cB(Y0!5)) | (~(Y0!5 = Y0!2))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 (((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~(Y0!5 = Y0!2)) | (~cB(Y0!5)))) <=> ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | cB(Y0!2) | (~cB(Y0!5)) | (~(Y0!5 = Y0!2)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[145, 143])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~(Y0!5 = Y0!2)) | (~cB(Y0!5)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | cB(Y0!2) | (~cB(Y0!5)) | (~(Y0!5 = Y0!2))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (~(Y0!5 = Y0!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[148, 142, 34, 129])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~cB(Y1!4)) | (~(Y1!4 = Y0!2)))) <=> ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | cB(Y0!2) | (~cB(Y1!4)) | (~(Y1!4 = Y0!2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 ((cB(Y0!2) | (~(Y1!4 = Y0!2)) | (~cB(Y1!4))) <=> (cB(Y0!2) | (~cB(Y1!4)) | (~(Y1!4 = Y0!2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~(Y1!4 = Y0!2)) | (~cB(Y1!4)))) <=> ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~cB(Y1!4)) | (~(Y1!4 = Y0!2))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~(Y1!4 = Y0!2)) | (~cB(Y1!4)))) <=> ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | cB(Y0!2) | (~cB(Y1!4)) | (~(Y1!4 = Y0!2)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[152, 150])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~(Y1!4 = Y0!2)) | (~cB(Y1!4)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | cB(Y0!2) | (~cB(Y1!4)) | (~(Y1!4 = Y0!2))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (~(Y1!4 = Y0!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[155, 142, 88, 129])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~cB(Y2!3)) | (~(Y2!3 = Y0!2)))) <=> ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | cB(Y0!2) | (~cB(Y2!3)) | (~(Y2!3 = Y0!2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 ((cB(Y0!2) | (~(Y2!3 = Y0!2)) | (~cB(Y2!3))) <=> (cB(Y0!2) | (~cB(Y2!3)) | (~(Y2!3 = Y0!2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 (((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~(Y2!3 = Y0!2)) | (~cB(Y2!3)))) <=> ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~cB(Y2!3)) | (~(Y2!3 = Y0!2))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[158])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 (((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~(Y2!3 = Y0!2)) | (~cB(Y2!3)))) <=> ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | cB(Y0!2) | (~cB(Y2!3)) | (~(Y2!3 = Y0!2)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[159, 157])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | (cB(Y0!2) | (~(Y2!3 = Y0!2)) | (~cB(Y2!3)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (cB(B) | (~(A = B)) | (~cB(A)))) | cB(Y0!2) | (~cB(Y2!3)) | (~(Y2!3 = Y0!2))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 (~(Y2!3 = Y0!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[162, 142, 104, 129])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : refl(((~rq(X, Y)) | rr(X, Y)) <=> ((~rq(X, Y)) | rr(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y)) <=> ![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y)) <=> ![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : rewrite((rq(X, Y) => rr(X, Y)) <=> ((~rq(X, Y)) | rr(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rq(X, Y) => rr(X, Y)) <=> ![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.44 tff(169,axiom,(![X: $i, Y: $i] : (rq(X, Y) => rr(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_5')).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.20/0.44 tff(172,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(skolemize,[status(sab)],[171])).
% 0.20/0.44 tff(173,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | ((~rq(X!0, Y2!3)) | rr(X!0, Y2!3))) <=> ((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | (~rq(X!0, Y2!3)) | rr(X!0, Y2!3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | ((~rq(X!0, Y2!3)) | rr(X!0, Y2!3))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(176,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | (~rq(X!0, Y2!3)) | rr(X!0, Y2!3)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.44 tff(177,plain,
% 0.20/0.44 (rr(X!0, Y2!3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[176, 173, 100])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | ((~rq(X!0, Y1!4)) | rr(X!0, Y1!4))) <=> ((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | (~rq(X!0, Y1!4)) | rr(X!0, Y1!4))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | ((~rq(X!0, Y1!4)) | rr(X!0, Y1!4))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(180,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | (~rq(X!0, Y1!4)) | rr(X!0, Y1!4)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.20/0.44 tff(181,plain,
% 0.20/0.44 (rr(X!0, Y1!4)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[180, 173, 84])).
% 0.20/0.44 tff(182,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | ((~rq(X!0, Y0!5)) | rr(X!0, Y0!5))) <=> ((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | (~rq(X!0, Y0!5)) | rr(X!0, Y0!5))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(183,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | ((~rq(X!0, Y0!5)) | rr(X!0, Y0!5))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(184,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rq(X, Y)) | rr(X, Y))) | (~rq(X!0, Y0!5)) | rr(X!0, Y0!5)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.44 tff(185,plain,
% 0.20/0.44 (rr(X!0, Y0!5)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[184, 173, 20])).
% 0.20/0.44 tff(186,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : refl(((~rp(X, Y)) | rr(X, Y)) <=> ((~rp(X, Y)) | rr(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(187,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y)) <=> ![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[186])).
% 0.20/0.44 tff(188,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y)) <=> ![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(189,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : rewrite((rp(X, Y) => rr(X, Y)) <=> ((~rp(X, Y)) | rr(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(190,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rp(X, Y) => rr(X, Y)) <=> ![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.44 tff(191,axiom,(![X: $i, Y: $i] : (rp(X, Y) => rr(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_6')).
% 0.20/0.44 tff(192,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.44 tff(193,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.20/0.44 tff(194,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(skolemize,[status(sab)],[193])).
% 0.20/0.44 tff(195,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.20/0.44 tff(196,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))) | ((~rp(X!0, Y1!1)) | rr(X!0, Y1!1))) <=> ((~![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))) | (~rp(X!0, Y1!1)) | rr(X!0, Y1!1))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(197,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))) | ((~rp(X!0, Y1!1)) | rr(X!0, Y1!1))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(198,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))) | (~rp(X!0, Y1!1)) | rr(X!0, Y1!1)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.20/0.44 tff(199,plain,
% 0.20/0.44 (rr(X!0, Y1!1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[198, 195, 49])).
% 0.20/0.44 tff(200,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))) | ((~rp(X!0, Y0!2)) | rr(X!0, Y0!2))) <=> ((~![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))) | (~rp(X!0, Y0!2)) | rr(X!0, Y0!2))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(201,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))) | ((~rp(X!0, Y0!2)) | rr(X!0, Y0!2))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(202,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rp(X, Y)) | rr(X, Y))) | (~rp(X!0, Y0!2)) | rr(X!0, Y0!2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.44 tff(203,plain,
% 0.20/0.44 (rr(X!0, Y0!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[202, 195, 121])).
% 0.20/0.44 tff(204,plain,
% 0.20/0.44 (^[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : refl(((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4))) <=> ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(205,plain,
% 0.20/0.44 (![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4))) <=> ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[204])).
% 0.20/0.44 tff(206,plain,
% 0.20/0.44 (^[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : trans(monotonicity(rewrite((rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))) <=> (~((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4))))), ((~(rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))) <=> (~(~((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4))))))), rewrite((~(~((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4))))) <=> ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))), ((~(rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))) <=> ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(207,plain,
% 0.20/0.44 (![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))) <=> ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[206])).
% 0.20/0.44 tff(208,plain,
% 0.20/0.44 (![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!0, Y0) & rr(X!0, Y1) & rr(X!0, Y2) & rr(X!0, Y3) & rr(X!0, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(209,plain,
% 0.20/0.44 (![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.20/0.44 tff(210,plain,
% 0.20/0.44 (![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.20/0.44 tff(211,plain,
% 0.20/0.44 (~(Y1!4 = Y2!3)),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(212,plain,
% 0.20/0.44 (~(Y0!5 = Y2!3)),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(213,plain,
% 0.20/0.44 (~(Y0!5 = Y1!4)),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(214,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))) | ((Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (Y1!4 = Y2!3) | (Y2!3 = Y0!2) | (Y1!4 = Y0!2) | (Y0!5 = Y0!2) | (Y1!1 = Y0!2) | (Y1!1 = Y2!3) | (Y1!1 = Y1!4) | (Y1!1 = Y0!5) | (~rr(X!0, Y1!1)) | (~rr(X!0, Y0!5)) | (~rr(X!0, Y1!4)) | (~rr(X!0, Y2!3)) | (~rr(X!0, Y0!2)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (Y1!4 = Y2!3) | (Y2!3 = Y0!2) | (Y1!4 = Y0!2) | (Y0!5 = Y0!2) | (Y1!1 = Y0!2) | (Y1!1 = Y2!3) | (Y1!1 = Y1!4) | (Y1!1 = Y0!5) | (~rr(X!0, Y1!1)) | (~rr(X!0, Y0!5)) | (~rr(X!0, Y1!4)) | (~rr(X!0, Y2!3)) | (~rr(X!0, Y0!2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(215,plain,
% 0.20/0.45 (((Y2!3 = Y0!2) | (Y1!4 = Y2!3) | (Y1!4 = Y0!2) | (Y0!5 = Y0!2) | (Y0!5 = Y2!3) | (Y0!5 = Y1!4) | (Y1!1 = Y0!2) | (Y1!1 = Y2!3) | (Y1!1 = Y1!4) | (Y1!1 = Y0!5) | (~rr(X!0, Y1!1)) | (~rr(X!0, Y0!5)) | (~rr(X!0, Y1!4)) | (~rr(X!0, Y2!3)) | (~rr(X!0, Y0!2))) <=> ((Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (Y1!4 = Y2!3) | (Y2!3 = Y0!2) | (Y1!4 = Y0!2) | (Y0!5 = Y0!2) | (Y1!1 = Y0!2) | (Y1!1 = Y2!3) | (Y1!1 = Y1!4) | (Y1!1 = Y0!5) | (~rr(X!0, Y1!1)) | (~rr(X!0, Y0!5)) | (~rr(X!0, Y1!4)) | (~rr(X!0, Y2!3)) | (~rr(X!0, Y0!2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(216,plain,
% 0.20/0.45 (((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))) | ((Y2!3 = Y0!2) | (Y1!4 = Y2!3) | (Y1!4 = Y0!2) | (Y0!5 = Y0!2) | (Y0!5 = Y2!3) | (Y0!5 = Y1!4) | (Y1!1 = Y0!2) | (Y1!1 = Y2!3) | (Y1!1 = Y1!4) | (Y1!1 = Y0!5) | (~rr(X!0, Y1!1)) | (~rr(X!0, Y0!5)) | (~rr(X!0, Y1!4)) | (~rr(X!0, Y2!3)) | (~rr(X!0, Y0!2)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))) | ((Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (Y1!4 = Y2!3) | (Y2!3 = Y0!2) | (Y1!4 = Y0!2) | (Y0!5 = Y0!2) | (Y1!1 = Y0!2) | (Y1!1 = Y2!3) | (Y1!1 = Y1!4) | (Y1!1 = Y0!5) | (~rr(X!0, Y1!1)) | (~rr(X!0, Y0!5)) | (~rr(X!0, Y1!4)) | (~rr(X!0, Y2!3)) | (~rr(X!0, Y0!2))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[215])).
% 0.20/0.45 tff(217,plain,
% 0.20/0.45 (((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))) | ((Y2!3 = Y0!2) | (Y1!4 = Y2!3) | (Y1!4 = Y0!2) | (Y0!5 = Y0!2) | (Y0!5 = Y2!3) | (Y0!5 = Y1!4) | (Y1!1 = Y0!2) | (Y1!1 = Y2!3) | (Y1!1 = Y1!4) | (Y1!1 = Y0!5) | (~rr(X!0, Y1!1)) | (~rr(X!0, Y0!5)) | (~rr(X!0, Y1!4)) | (~rr(X!0, Y2!3)) | (~rr(X!0, Y0!2)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (Y1!4 = Y2!3) | (Y2!3 = Y0!2) | (Y1!4 = Y0!2) | (Y0!5 = Y0!2) | (Y1!1 = Y0!2) | (Y1!1 = Y2!3) | (Y1!1 = Y1!4) | (Y1!1 = Y0!5) | (~rr(X!0, Y1!1)) | (~rr(X!0, Y0!5)) | (~rr(X!0, Y1!4)) | (~rr(X!0, Y2!3)) | (~rr(X!0, Y0!2)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[216, 214])).
% 0.20/0.45 tff(218,plain,
% 0.20/0.45 ((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))) | ((Y2!3 = Y0!2) | (Y1!4 = Y2!3) | (Y1!4 = Y0!2) | (Y0!5 = Y0!2) | (Y0!5 = Y2!3) | (Y0!5 = Y1!4) | (Y1!1 = Y0!2) | (Y1!1 = Y2!3) | (Y1!1 = Y1!4) | (Y1!1 = Y0!5) | (~rr(X!0, Y1!1)) | (~rr(X!0, Y0!5)) | (~rr(X!0, Y1!4)) | (~rr(X!0, Y2!3)) | (~rr(X!0, Y0!2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(219,plain,
% 0.20/0.45 ((~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!0, Y0)) | (~rr(X!0, Y1)) | (~rr(X!0, Y2)) | (~rr(X!0, Y3)) | (~rr(X!0, Y4)))) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (Y1!4 = Y2!3) | (Y2!3 = Y0!2) | (Y1!4 = Y0!2) | (Y0!5 = Y0!2) | (Y1!1 = Y0!2) | (Y1!1 = Y2!3) | (Y1!1 = Y1!4) | (Y1!1 = Y0!5) | (~rr(X!0, Y1!1)) | (~rr(X!0, Y0!5)) | (~rr(X!0, Y1!4)) | (~rr(X!0, Y2!3)) | (~rr(X!0, Y0!2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.45 tff(220,plain,
% 0.20/0.45 ((Y2!3 = Y0!2) | (Y1!4 = Y0!2) | (Y0!5 = Y0!2) | (Y1!1 = Y0!2) | (Y1!1 = Y2!3) | (Y1!1 = Y1!4) | (Y1!1 = Y0!5)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[219, 213, 212, 211, 210, 203, 199, 185, 181, 177])).
% 0.20/0.45 tff(221,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[220, 163, 156, 149, 120, 115, 99, 83])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------