TSTP Solution File: SYO606+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO606+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Fri Sep 30 01:41:02 EDT 2022
% Result : Theorem 0.15s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO606+1 : TPTP v8.1.0. Released v7.0.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n029.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Sep 5 15:23:46 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.15/0.40 % SZS status Theorem
% 0.15/0.40 % SZS output start Proof
% 0.15/0.40 tff(g_false_type, type, (
% 0.15/0.40 g_false: ( $i * $i ) > $o)).
% 0.15/0.40 tff(tptp_fun_B_13_type, type, (
% 0.15/0.40 tptp_fun_B_13: $i > $i)).
% 0.15/0.40 tff(tptp_fun_A_0_type, type, (
% 0.15/0.40 tptp_fun_A_0: $i)).
% 0.15/0.40 tff(g_true_type, type, (
% 0.15/0.40 g_true: ( $i * $i ) > $o)).
% 0.15/0.40 tff(g_true_only_type, type, (
% 0.15/0.40 g_true_only: ( $i * $i ) > $o)).
% 0.15/0.40 tff(g_both_type, type, (
% 0.15/0.40 g_both: ( $i * $i ) > $o)).
% 0.15/0.40 tff(g_false_only_type, type, (
% 0.15/0.40 g_false_only: ( $i * $i ) > $o)).
% 0.15/0.40 tff(tptp_fun_B_1_type, type, (
% 0.15/0.40 tptp_fun_B_1: $i)).
% 0.15/0.40 tff(h_true_only_type, type, (
% 0.15/0.40 h_true_only: ( $i * $i ) > $o)).
% 0.15/0.40 tff(tptp_fun_A_3_type, type, (
% 0.15/0.40 tptp_fun_A_3: $i)).
% 0.15/0.40 tff(tptp_fun_B_2_type, type, (
% 0.15/0.40 tptp_fun_B_2: $i)).
% 0.15/0.40 tff(h_false_only_type, type, (
% 0.15/0.40 h_false_only: ( $i * $i ) > $o)).
% 0.15/0.40 tff(tptp_fun_C_7_type, type, (
% 0.15/0.40 tptp_fun_C_7: ( $i * $i ) > $i)).
% 0.15/0.40 tff(h_both_type, type, (
% 0.15/0.40 h_both: ( $i * $i ) > $o)).
% 0.15/0.40 tff(tptp_fun_B_6_type, type, (
% 0.15/0.40 tptp_fun_B_6: $i > $i)).
% 0.15/0.40 tff(tptp_fun_B_5_type, type, (
% 0.15/0.40 tptp_fun_B_5: $i > $i)).
% 0.15/0.40 tff(tptp_fun_B_4_type, type, (
% 0.15/0.40 tptp_fun_B_4: $i > $i)).
% 0.15/0.40 tff(tptp_fun_B_9_type, type, (
% 0.15/0.40 tptp_fun_B_9: $i)).
% 0.15/0.40 tff(tptp_fun_A_15_type, type, (
% 0.15/0.40 tptp_fun_A_15: $i)).
% 0.15/0.40 tff(tptp_fun_B_14_type, type, (
% 0.15/0.40 tptp_fun_B_14: $i)).
% 0.15/0.40 tff(h_true_type, type, (
% 0.15/0.40 h_true: ( $i * $i ) > $o)).
% 0.15/0.40 tff(h_false_type, type, (
% 0.15/0.40 h_false: ( $i * $i ) > $o)).
% 0.15/0.40 tff(tptp_fun_A_8_type, type, (
% 0.15/0.40 tptp_fun_A_8: $i)).
% 0.15/0.40 tff(tptp_fun_B_10_type, type, (
% 0.15/0.40 tptp_fun_B_10: $i)).
% 0.15/0.40 tff(tptp_fun_B_11_type, type, (
% 0.15/0.40 tptp_fun_B_11: $i)).
% 0.15/0.40 tff(tptp_fun_C_12_type, type, (
% 0.15/0.40 tptp_fun_C_12: ( $i * $i ) > $i)).
% 0.15/0.40 tff(1,assumption,(![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))), introduced(assumption)).
% 0.15/0.40 tff(2,assumption,((~((~g_both(A!0, B!1)) | (~h_false_only(A!0, tptp_fun_B_5(A!0))) | g_true_only(A!0, tptp_fun_B_6(A!0)))) | (~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0))))))), introduced(assumption)).
% 0.15/0.40 tff(3,plain,
% 0.15/0.40 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!0, B!1)) | (~h_false_only(A!0, tptp_fun_B_5(A!0))) | g_true_only(A!0, tptp_fun_B_6(A!0)))) | (~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0))))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!0, B!1)) | (~h_false_only(A!0, tptp_fun_B_5(A!0))) | g_true_only(A!0, tptp_fun_B_6(A!0)))) | (~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0)))))))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(4,plain,
% 0.15/0.40 ((~((~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0)))))) | (~((~h_false_only(A!0, tptp_fun_B_5(A!0))) | (~g_both(A!0, B!1)) | g_true_only(A!0, tptp_fun_B_6(A!0)))))) <=> (~((~((~g_both(A!0, B!1)) | (~h_false_only(A!0, tptp_fun_B_5(A!0))) | g_true_only(A!0, tptp_fun_B_6(A!0)))) | (~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0))))))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(5,plain,
% 0.15/0.40 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0)))))) | (~((~h_false_only(A!0, tptp_fun_B_5(A!0))) | (~g_both(A!0, B!1)) | g_true_only(A!0, tptp_fun_B_6(A!0))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!0, B!1)) | (~h_false_only(A!0, tptp_fun_B_5(A!0))) | g_true_only(A!0, tptp_fun_B_6(A!0)))) | (~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0)))))))))),
% 0.15/0.40 inference(monotonicity,[status(thm)],[4])).
% 0.15/0.40 tff(6,plain,
% 0.15/0.40 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0)))))) | (~((~h_false_only(A!0, tptp_fun_B_5(A!0))) | (~g_both(A!0, B!1)) | g_true_only(A!0, tptp_fun_B_6(A!0))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!0, B!1)) | (~h_false_only(A!0, tptp_fun_B_5(A!0))) | g_true_only(A!0, tptp_fun_B_6(A!0)))) | (~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0)))))))))),
% 0.15/0.40 inference(transitivity,[status(thm)],[5, 3])).
% 0.15/0.40 tff(7,plain,
% 0.15/0.40 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0)))))) | (~((~h_false_only(A!0, tptp_fun_B_5(A!0))) | (~g_both(A!0, B!1)) | g_true_only(A!0, tptp_fun_B_6(A!0))))))),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(8,plain,
% 0.15/0.40 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!0, B!1)) | (~h_false_only(A!0, tptp_fun_B_5(A!0))) | g_true_only(A!0, tptp_fun_B_6(A!0)))) | (~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0))))))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.15/0.40 tff(9,plain,
% 0.15/0.40 ($false),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[8, 1, 2])).
% 0.15/0.40 tff(10,plain,((~((~((~g_both(A!0, B!1)) | (~h_false_only(A!0, tptp_fun_B_5(A!0))) | g_true_only(A!0, tptp_fun_B_6(A!0)))) | (~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0)))))))) | (~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.40 tff(11,plain,
% 0.15/0.40 (~((~((~g_both(A!0, B!1)) | (~h_false_only(A!0, tptp_fun_B_5(A!0))) | g_true_only(A!0, tptp_fun_B_6(A!0)))) | (~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0)))))))),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[10, 1])).
% 0.15/0.40 tff(12,plain,
% 0.15/0.40 (((~((~g_both(A!0, B!1)) | (~h_false_only(A!0, tptp_fun_B_5(A!0))) | g_true_only(A!0, tptp_fun_B_6(A!0)))) | (~((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0))))))) | ((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0)))))),
% 0.15/0.40 inference(tautology,[status(thm)],[])).
% 0.15/0.40 tff(13,plain,
% 0.15/0.40 ((~g_true_only(A!0, tptp_fun_B_13(A!0))) | (~((~((~h_both(A!0, tptp_fun_B_5(A!0))) | h_true_only(A!0, tptp_fun_B_4(A!0)))) | h_false_only(A!0, tptp_fun_B_5(A!0))))),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.15/0.40 tff(14,assumption,((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))), introduced(assumption)).
% 0.15/0.40 tff(15,plain,
% 0.15/0.40 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(16,plain,
% 0.15/0.40 ((~((~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3)))))) <=> (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(17,plain,
% 0.15/0.40 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[16])).
% 0.15/0.41 tff(18,plain,
% 0.15/0.41 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.15/0.41 tff(19,plain,
% 0.15/0.41 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(20,plain,
% 0.15/0.41 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.15/0.41 tff(21,plain,
% 0.15/0.41 ($false),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[20, 1, 14])).
% 0.15/0.41 tff(22,plain,((~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))) | (~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.41 tff(23,plain,
% 0.15/0.41 (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[22, 1])).
% 0.15/0.41 tff(24,plain,
% 0.15/0.41 (((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))) | ((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))),
% 0.15/0.41 inference(tautology,[status(thm)],[])).
% 0.15/0.41 tff(25,plain,
% 0.15/0.41 ((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.15/0.41 tff(26,assumption,((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))), introduced(assumption)).
% 0.15/0.41 tff(27,plain,
% 0.15/0.41 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(28,plain,
% 0.15/0.41 ((~((~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3)))))) <=> (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(29,plain,
% 0.15/0.41 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[28])).
% 0.15/0.41 tff(30,plain,
% 0.15/0.41 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.41 inference(transitivity,[status(thm)],[29, 27])).
% 0.15/0.41 tff(31,plain,
% 0.15/0.41 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(32,plain,
% 0.15/0.41 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.15/0.41 tff(33,plain,
% 0.15/0.41 ($false),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[32, 1, 26])).
% 0.15/0.41 tff(34,plain,((~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))) | (~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.41 tff(35,plain,
% 0.15/0.41 (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[34, 1])).
% 0.15/0.41 tff(36,plain,
% 0.15/0.41 (((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))) | ((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))),
% 0.15/0.41 inference(tautology,[status(thm)],[])).
% 0.15/0.41 tff(37,plain,
% 0.15/0.41 ((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.15/0.41 tff(38,assumption,((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))), introduced(assumption)).
% 0.15/0.41 tff(39,plain,
% 0.15/0.41 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(40,plain,
% 0.15/0.42 ((~((~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3)))))) <=> (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(41,plain,
% 0.15/0.42 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.42 inference(monotonicity,[status(thm)],[40])).
% 0.15/0.42 tff(42,plain,
% 0.15/0.42 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[41, 39])).
% 0.15/0.42 tff(43,plain,
% 0.15/0.42 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(44,plain,
% 0.15/0.42 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.15/0.42 tff(45,plain,
% 0.15/0.42 ($false),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[44, 1, 38])).
% 0.15/0.42 tff(46,plain,((~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))) | (~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.42 tff(47,plain,
% 0.15/0.42 (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[46, 1])).
% 0.15/0.42 tff(48,plain,
% 0.15/0.42 (((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))) | ((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))),
% 0.15/0.42 inference(tautology,[status(thm)],[])).
% 0.15/0.42 tff(49,plain,
% 0.15/0.42 ((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.15/0.42 tff(50,assumption,((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))), introduced(assumption)).
% 0.15/0.42 tff(51,plain,
% 0.15/0.42 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(52,plain,
% 0.15/0.42 ((~((~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3)))))) <=> (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(53,plain,
% 0.15/0.42 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.42 inference(monotonicity,[status(thm)],[52])).
% 0.15/0.42 tff(54,plain,
% 0.15/0.42 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[53, 51])).
% 0.15/0.42 tff(55,plain,
% 0.15/0.42 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~h_false_only(A!3, tptp_fun_B_5(A!3))) | (~g_both(A!3, B!2)) | g_true_only(A!3, tptp_fun_B_6(A!3))))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(56,plain,
% 0.15/0.42 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.15/0.42 tff(57,plain,
% 0.15/0.42 ($false),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[56, 1, 50])).
% 0.15/0.42 tff(58,plain,((~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))) | (~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.43 tff(59,plain,
% 0.15/0.43 (~((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[58, 1])).
% 0.15/0.43 tff(60,plain,
% 0.15/0.43 (((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))) | (g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(61,plain,
% 0.15/0.43 (g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3)))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.15/0.43 tff(62,assumption,((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))), introduced(assumption)).
% 0.15/0.43 tff(63,plain,
% 0.15/0.43 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(64,plain,
% 0.15/0.43 ((~((~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15)))))) <=> (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(65,plain,
% 0.15/0.43 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))))),
% 0.15/0.43 inference(monotonicity,[status(thm)],[64])).
% 0.15/0.43 tff(66,plain,
% 0.15/0.43 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))))),
% 0.15/0.43 inference(transitivity,[status(thm)],[65, 63])).
% 0.15/0.43 tff(67,plain,
% 0.15/0.43 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15))))))),
% 0.15/0.43 inference(quant_inst,[status(thm)],[])).
% 0.15/0.43 tff(68,plain,
% 0.15/0.43 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.15/0.43 tff(69,plain,
% 0.15/0.43 ($false),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[68, 1, 62])).
% 0.15/0.43 tff(70,plain,((~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))) | (~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.43 tff(71,plain,
% 0.15/0.43 (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[70, 1])).
% 0.15/0.43 tff(72,plain,
% 0.15/0.43 (((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))) | ((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(73,plain,
% 0.15/0.43 ((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.15/0.43 tff(74,plain,
% 0.15/0.43 (((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))) | ((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(75,plain,
% 0.15/0.43 ((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.15/0.43 tff(76,assumption,((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))), introduced(assumption)).
% 0.15/0.43 tff(77,assumption,((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15))), introduced(assumption)).
% 0.15/0.43 tff(78,assumption,(~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))))), introduced(assumption)).
% 0.15/0.43 tff(79,plain,
% 0.15/0.43 (((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15)))) | g_both(A!15, B!14)),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(80,plain,
% 0.15/0.43 (g_both(A!15, B!14)),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.15/0.43 tff(81,plain,
% 0.15/0.43 (((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(82,plain,
% 0.15/0.43 (h_false_only(A!15, tptp_fun_B_5(A!15))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[81, 78])).
% 0.15/0.43 tff(83,plain,
% 0.15/0.43 ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(84,plain,
% 0.15/0.43 (g_true_only(A!15, tptp_fun_B_6(A!15))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[83, 82, 80, 77])).
% 0.15/0.43 tff(85,plain,
% 0.15/0.43 (((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))) | (~h_false_only(A!15, tptp_fun_B_5(A!15)))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(86,plain,
% 0.15/0.43 ((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.15/0.43 tff(87,plain,
% 0.15/0.43 ((~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))),
% 0.15/0.43 inference(tautology,[status(thm)],[])).
% 0.15/0.43 tff(88,plain,
% 0.15/0.43 ($false),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[87, 86, 84, 76])).
% 0.15/0.43 tff(89,plain,(((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15)))) | (~((~g_true_only(A!15, tptp_fun_B_6(A!15))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.43 tff(90,plain,
% 0.15/0.43 ((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15)))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[89, 75, 73])).
% 0.15/0.43 tff(91,assumption,(![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))), introduced(assumption)).
% 0.15/0.43 tff(92,plain,
% 0.15/0.43 (^[X_2: $i, X_1: $i] : refl((h_both(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | (~h_true(X_2, X_1))))) <=> (h_both(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | (~h_true(X_2, X_1))))))),
% 0.15/0.43 inference(bind,[status(th)],[])).
% 0.15/0.43 tff(93,plain,
% 0.15/0.43 (![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | (~h_true(X_2, X_1))))) <=> ![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | (~h_true(X_2, X_1)))))),
% 0.15/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.15/0.43 tff(94,plain,
% 0.15/0.43 (^[X_2: $i, X_1: $i] : rewrite((h_both(X_2, X_1) <=> (h_true(X_2, X_1) & h_false(X_2, X_1))) <=> (h_both(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | (~h_true(X_2, X_1))))))),
% 0.15/0.43 inference(bind,[status(th)],[])).
% 0.15/0.43 tff(95,plain,
% 0.15/0.43 (![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (h_true(X_2, X_1) & h_false(X_2, X_1))) <=> ![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | (~h_true(X_2, X_1)))))),
% 0.15/0.43 inference(quant_intro,[status(thm)],[94])).
% 0.15/0.43 tff(96,plain,
% 0.15/0.43 (![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (h_true(X_2, X_1) & h_false(X_2, X_1))) <=> ![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (h_true(X_2, X_1) & h_false(X_2, X_1)))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(97,axiom,(![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (h_true(X_2, X_1) & h_false(X_2, X_1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','both_h')).
% 0.15/0.43 tff(98,plain,
% 0.15/0.43 (![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (h_true(X_2, X_1) & h_false(X_2, X_1)))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.15/0.43 tff(99,plain,(
% 0.15/0.43 ![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (h_true(X_2, X_1) & h_false(X_2, X_1)))),
% 0.15/0.43 inference(skolemize,[status(sab)],[98])).
% 0.15/0.43 tff(100,plain,
% 0.15/0.43 (![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | (~h_true(X_2, X_1)))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.15/0.43 tff(101,plain,
% 0.15/0.43 (![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | (~h_true(X_2, X_1)))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.15/0.43 tff(102,plain,
% 0.15/0.43 ((~![X_2: $i, X_1: $i] : (h_both(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | (~h_true(X_2, X_1)))))) | (h_both(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_false(A!15, tptp_fun_B_4(A!15))) | (~h_true(A!15, tptp_fun_B_4(A!15))))))),
% 0.15/0.43 inference(quant_inst,[status(thm)],[])).
% 0.15/0.43 tff(103,plain,
% 0.15/0.43 (h_both(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_false(A!15, tptp_fun_B_4(A!15))) | (~h_true(A!15, tptp_fun_B_4(A!15)))))),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.15/0.43 tff(104,plain,
% 0.15/0.43 (^[X_2: $i, X_1: $i] : refl((h_true_only(X_2, X_1) <=> (~((~h_true(X_2, X_1)) | h_false(X_2, X_1)))) <=> (h_true_only(X_2, X_1) <=> (~((~h_true(X_2, X_1)) | h_false(X_2, X_1)))))),
% 0.15/0.43 inference(bind,[status(th)],[])).
% 0.15/0.43 tff(105,plain,
% 0.15/0.43 (![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (~((~h_true(X_2, X_1)) | h_false(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (~((~h_true(X_2, X_1)) | h_false(X_2, X_1))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[104])).
% 0.15/0.44 tff(106,plain,
% 0.15/0.44 (^[X_2: $i, X_1: $i] : rewrite((h_true_only(X_2, X_1) <=> (h_true(X_2, X_1) & (~h_false(X_2, X_1)))) <=> (h_true_only(X_2, X_1) <=> (~((~h_true(X_2, X_1)) | h_false(X_2, X_1)))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(107,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (h_true(X_2, X_1) & (~h_false(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (~((~h_true(X_2, X_1)) | h_false(X_2, X_1))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[106])).
% 0.15/0.44 tff(108,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (h_true(X_2, X_1) & (~h_false(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (h_true(X_2, X_1) & (~h_false(X_2, X_1))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(109,axiom,(![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (h_true(X_2, X_1) & (~h_false(X_2, X_1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','true_only_h')).
% 0.15/0.44 tff(110,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (h_true(X_2, X_1) & (~h_false(X_2, X_1))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.15/0.44 tff(111,plain,(
% 0.15/0.44 ![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (h_true(X_2, X_1) & (~h_false(X_2, X_1))))),
% 0.15/0.44 inference(skolemize,[status(sab)],[110])).
% 0.15/0.44 tff(112,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (~((~h_true(X_2, X_1)) | h_false(X_2, X_1))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.15/0.44 tff(113,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (~((~h_true(X_2, X_1)) | h_false(X_2, X_1))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.15/0.44 tff(114,plain,
% 0.15/0.44 ((~![X_2: $i, X_1: $i] : (h_true_only(X_2, X_1) <=> (~((~h_true(X_2, X_1)) | h_false(X_2, X_1))))) | (h_true_only(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_true(A!15, tptp_fun_B_4(A!15))) | h_false(A!15, tptp_fun_B_4(A!15)))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(115,plain,
% 0.15/0.44 (h_true_only(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_true(A!15, tptp_fun_B_4(A!15))) | h_false(A!15, tptp_fun_B_4(A!15))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.15/0.44 tff(116,plain,
% 0.15/0.44 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(117,plain,
% 0.15/0.44 ((~((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15)))))) <=> (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(118,plain,
% 0.15/0.44 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))))),
% 0.15/0.44 inference(monotonicity,[status(thm)],[117])).
% 0.15/0.44 tff(119,plain,
% 0.15/0.44 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))))),
% 0.15/0.44 inference(transitivity,[status(thm)],[118, 116])).
% 0.15/0.44 tff(120,plain,
% 0.15/0.44 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15))))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(121,plain,
% 0.15/0.44 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.15/0.44 tff(122,plain,
% 0.15/0.44 (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[121, 1])).
% 0.15/0.44 tff(123,plain,
% 0.15/0.44 (((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))) | ((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(124,plain,
% 0.15/0.44 ((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.15/0.44 tff(125,assumption,(g_true_only(A!15, B!14)), introduced(assumption)).
% 0.15/0.44 tff(126,plain,
% 0.15/0.44 ((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(127,plain,
% 0.15/0.44 ((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.15/0.44 tff(128,plain,
% 0.15/0.44 (~((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[127, 124])).
% 0.15/0.44 tff(129,plain,
% 0.15/0.44 (((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))) | ((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(130,plain,
% 0.15/0.44 ((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.15/0.44 tff(131,plain,
% 0.15/0.44 (^[X_2: $i, X_1: $i] : refl((g_both(X_2, X_1) <=> (~((~g_false(X_2, X_1)) | (~g_true(X_2, X_1))))) <=> (g_both(X_2, X_1) <=> (~((~g_false(X_2, X_1)) | (~g_true(X_2, X_1))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(132,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (~((~g_false(X_2, X_1)) | (~g_true(X_2, X_1))))) <=> ![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (~((~g_false(X_2, X_1)) | (~g_true(X_2, X_1)))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[131])).
% 0.15/0.44 tff(133,plain,
% 0.15/0.44 (^[X_2: $i, X_1: $i] : rewrite((g_both(X_2, X_1) <=> (g_true(X_2, X_1) & g_false(X_2, X_1))) <=> (g_both(X_2, X_1) <=> (~((~g_false(X_2, X_1)) | (~g_true(X_2, X_1))))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(134,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (g_true(X_2, X_1) & g_false(X_2, X_1))) <=> ![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (~((~g_false(X_2, X_1)) | (~g_true(X_2, X_1)))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[133])).
% 0.15/0.44 tff(135,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (g_true(X_2, X_1) & g_false(X_2, X_1))) <=> ![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (g_true(X_2, X_1) & g_false(X_2, X_1)))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(136,axiom,(![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (g_true(X_2, X_1) & g_false(X_2, X_1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','both_g')).
% 0.15/0.44 tff(137,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (g_true(X_2, X_1) & g_false(X_2, X_1)))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.15/0.44 tff(138,plain,(
% 0.15/0.44 ![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (g_true(X_2, X_1) & g_false(X_2, X_1)))),
% 0.15/0.44 inference(skolemize,[status(sab)],[137])).
% 0.15/0.44 tff(139,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (~((~g_false(X_2, X_1)) | (~g_true(X_2, X_1)))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.15/0.44 tff(140,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (~((~g_false(X_2, X_1)) | (~g_true(X_2, X_1)))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.15/0.44 tff(141,plain,
% 0.15/0.44 ((~![X_2: $i, X_1: $i] : (g_both(X_2, X_1) <=> (~((~g_false(X_2, X_1)) | (~g_true(X_2, X_1)))))) | (g_both(A!15, B!14) <=> (~((~g_false(A!15, B!14)) | (~g_true(A!15, B!14)))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(142,plain,
% 0.15/0.44 (g_both(A!15, B!14) <=> (~((~g_false(A!15, B!14)) | (~g_true(A!15, B!14))))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.15/0.44 tff(143,plain,
% 0.15/0.44 (^[X_2: $i, X_1: $i] : refl((g_true_only(X_2, X_1) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1)))) <=> (g_true_only(X_2, X_1) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1)))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(144,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[143])).
% 0.15/0.44 tff(145,plain,
% 0.15/0.44 (^[X_2: $i, X_1: $i] : rewrite((g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1)))) <=> (g_true_only(X_2, X_1) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1)))))),
% 0.15/0.44 inference(bind,[status(th)],[])).
% 0.15/0.44 tff(146,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1))))),
% 0.15/0.44 inference(quant_intro,[status(thm)],[145])).
% 0.15/0.44 tff(147,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(148,axiom,(![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','true_only_g')).
% 0.15/0.44 tff(149,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.15/0.44 tff(150,plain,(
% 0.15/0.44 ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1))))),
% 0.15/0.44 inference(skolemize,[status(sab)],[149])).
% 0.15/0.44 tff(151,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.15/0.44 tff(152,plain,
% 0.15/0.44 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1))))),
% 0.15/0.44 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.15/0.44 tff(153,plain,
% 0.15/0.44 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1))))) | (g_true_only(A!15, B!14) <=> (~((~g_true(A!15, B!14)) | g_false(A!15, B!14))))),
% 0.15/0.44 inference(quant_inst,[status(thm)],[])).
% 0.15/0.44 tff(154,plain,
% 0.15/0.44 (g_true_only(A!15, B!14) <=> (~((~g_true(A!15, B!14)) | g_false(A!15, B!14)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.15/0.44 tff(155,plain,
% 0.15/0.44 ((~(g_true_only(A!15, B!14) <=> (~((~g_true(A!15, B!14)) | g_false(A!15, B!14))))) | (~g_true_only(A!15, B!14)) | (~((~g_true(A!15, B!14)) | g_false(A!15, B!14)))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(156,plain,
% 0.15/0.44 ((~(g_true_only(A!15, B!14) <=> (~((~g_true(A!15, B!14)) | g_false(A!15, B!14))))) | (~((~g_true(A!15, B!14)) | g_false(A!15, B!14)))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[155, 125])).
% 0.15/0.44 tff(157,plain,
% 0.15/0.44 (~((~g_true(A!15, B!14)) | g_false(A!15, B!14))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[156, 154])).
% 0.15/0.44 tff(158,plain,
% 0.15/0.44 (((~g_true(A!15, B!14)) | g_false(A!15, B!14)) | (~g_false(A!15, B!14))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(159,plain,
% 0.15/0.44 (~g_false(A!15, B!14)),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.15/0.44 tff(160,plain,
% 0.15/0.44 (((~g_false(A!15, B!14)) | (~g_true(A!15, B!14))) | g_false(A!15, B!14)),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.44 tff(161,plain,
% 0.15/0.44 ((~g_false(A!15, B!14)) | (~g_true(A!15, B!14))),
% 0.15/0.44 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.15/0.44 tff(162,plain,
% 0.15/0.44 ((~(g_both(A!15, B!14) <=> (~((~g_false(A!15, B!14)) | (~g_true(A!15, B!14)))))) | (~g_both(A!15, B!14)) | (~((~g_false(A!15, B!14)) | (~g_true(A!15, B!14))))),
% 0.15/0.44 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(163,plain,
% 0.15/0.45 ((~(g_both(A!15, B!14) <=> (~((~g_false(A!15, B!14)) | (~g_true(A!15, B!14)))))) | (~g_both(A!15, B!14))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.15/0.45 tff(164,plain,
% 0.15/0.45 (~g_both(A!15, B!14)),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[163, 142])).
% 0.15/0.45 tff(165,plain,
% 0.15/0.45 ((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15)))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[79, 164])).
% 0.15/0.45 tff(166,plain,
% 0.15/0.45 (((~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))) | ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))) <=> ((~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))) | (~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(167,plain,
% 0.15/0.45 ((~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))) | ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))),
% 0.15/0.45 inference(quant_inst,[status(thm)],[])).
% 0.15/0.45 tff(168,plain,
% 0.15/0.45 ((~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))) | (~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15))))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.15/0.45 tff(169,plain,
% 0.15/0.45 (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15)))))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[168, 91, 165])).
% 0.15/0.45 tff(170,plain,
% 0.15/0.45 (((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15))))) | (h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15)))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(171,plain,
% 0.15/0.45 (h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.15/0.45 tff(172,plain,
% 0.15/0.45 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(173,plain,
% 0.15/0.45 ((~((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15)))))) <=> (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))))),
% 0.15/0.45 inference(rewrite,[status(thm)],[])).
% 0.15/0.45 tff(174,plain,
% 0.15/0.45 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))))),
% 0.15/0.45 inference(monotonicity,[status(thm)],[173])).
% 0.15/0.45 tff(175,plain,
% 0.15/0.45 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))))),
% 0.15/0.45 inference(transitivity,[status(thm)],[174, 172])).
% 0.15/0.45 tff(176,plain,
% 0.15/0.45 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~h_false_only(A!15, tptp_fun_B_5(A!15))) | (~g_both(A!15, B!14)) | g_true_only(A!15, tptp_fun_B_6(A!15))))))),
% 0.15/0.45 inference(quant_inst,[status(thm)],[])).
% 0.15/0.45 tff(177,plain,
% 0.15/0.45 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))))),
% 0.15/0.45 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.15/0.45 tff(178,plain,
% 0.15/0.45 (~((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[177, 1])).
% 0.15/0.45 tff(179,plain,
% 0.15/0.45 (((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))) | g_true_only(A!15, tptp_fun_B_6(A!15)))) | (~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))))) | ((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(180,plain,
% 0.15/0.45 ((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.15/0.45 tff(181,plain,
% 0.15/0.45 ((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(182,plain,
% 0.15/0.45 ((~((~g_true_only(A!15, B!14)) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))))) | (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15))))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[181, 125])).
% 0.15/0.45 tff(183,plain,
% 0.15/0.45 (~((~((~h_both(A!15, B!1)) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_false_only(A!15, tptp_fun_B_5(A!15)))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[182, 180])).
% 0.15/0.45 tff(184,plain,
% 0.15/0.45 (~h_false_only(A!15, tptp_fun_B_5(A!15))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[85, 183])).
% 0.15/0.45 tff(185,plain,
% 0.15/0.45 ((~(h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15)))) | h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(186,plain,
% 0.15/0.45 ((~(h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15)))) | h_both(A!15, tptp_fun_B_5(A!15))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.15/0.45 tff(187,plain,
% 0.15/0.45 (h_both(A!15, tptp_fun_B_5(A!15))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[186, 171])).
% 0.15/0.45 tff(188,plain,
% 0.15/0.45 ((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | (~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(189,plain,
% 0.15/0.45 ((~((~h_both(A!15, tptp_fun_B_5(A!15))) | h_true_only(A!15, tptp_fun_B_4(A!15)))) | h_true_only(A!15, tptp_fun_B_4(A!15))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.15/0.45 tff(190,plain,
% 0.15/0.45 (h_true_only(A!15, tptp_fun_B_4(A!15))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[189, 130])).
% 0.15/0.45 tff(191,plain,
% 0.15/0.45 ((~(h_true_only(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_true(A!15, tptp_fun_B_4(A!15))) | h_false(A!15, tptp_fun_B_4(A!15)))))) | (~h_true_only(A!15, tptp_fun_B_4(A!15))) | (~((~h_true(A!15, tptp_fun_B_4(A!15))) | h_false(A!15, tptp_fun_B_4(A!15))))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(192,plain,
% 0.15/0.45 ((~(h_true_only(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_true(A!15, tptp_fun_B_4(A!15))) | h_false(A!15, tptp_fun_B_4(A!15)))))) | (~((~h_true(A!15, tptp_fun_B_4(A!15))) | h_false(A!15, tptp_fun_B_4(A!15))))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.15/0.45 tff(193,plain,
% 0.15/0.45 (~((~h_true(A!15, tptp_fun_B_4(A!15))) | h_false(A!15, tptp_fun_B_4(A!15)))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[192, 115])).
% 0.15/0.45 tff(194,plain,
% 0.15/0.45 (((~h_true(A!15, tptp_fun_B_4(A!15))) | h_false(A!15, tptp_fun_B_4(A!15))) | (~h_false(A!15, tptp_fun_B_4(A!15)))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(195,plain,
% 0.15/0.45 (~h_false(A!15, tptp_fun_B_4(A!15))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.15/0.45 tff(196,plain,
% 0.15/0.45 (((~h_false(A!15, tptp_fun_B_4(A!15))) | (~h_true(A!15, tptp_fun_B_4(A!15)))) | h_false(A!15, tptp_fun_B_4(A!15))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(197,plain,
% 0.15/0.45 ((~h_false(A!15, tptp_fun_B_4(A!15))) | (~h_true(A!15, tptp_fun_B_4(A!15)))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.15/0.45 tff(198,plain,
% 0.15/0.45 ((~(h_both(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_false(A!15, tptp_fun_B_4(A!15))) | (~h_true(A!15, tptp_fun_B_4(A!15))))))) | (~h_both(A!15, tptp_fun_B_4(A!15))) | (~((~h_false(A!15, tptp_fun_B_4(A!15))) | (~h_true(A!15, tptp_fun_B_4(A!15)))))),
% 0.15/0.45 inference(tautology,[status(thm)],[])).
% 0.15/0.45 tff(199,plain,
% 0.15/0.45 ((~(h_both(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_false(A!15, tptp_fun_B_4(A!15))) | (~h_true(A!15, tptp_fun_B_4(A!15))))))) | (~h_both(A!15, tptp_fun_B_4(A!15)))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.15/0.45 tff(200,plain,
% 0.15/0.45 (~h_both(A!15, tptp_fun_B_4(A!15))),
% 0.15/0.45 inference(unit_resolution,[status(thm)],[199, 103])).
% 0.15/0.45 tff(201,plain,
% 0.15/0.45 (^[X_2: $i, X_1: $i] : refl((h_false_only(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | h_true(X_2, X_1)))) <=> (h_false_only(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | h_true(X_2, X_1)))))),
% 0.15/0.45 inference(bind,[status(th)],[])).
% 0.15/0.45 tff(202,plain,
% 0.15/0.46 (![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | h_true(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | h_true(X_2, X_1))))),
% 0.15/0.46 inference(quant_intro,[status(thm)],[201])).
% 0.15/0.46 tff(203,plain,
% 0.15/0.46 (^[X_2: $i, X_1: $i] : rewrite((h_false_only(X_2, X_1) <=> (h_false(X_2, X_1) & (~h_true(X_2, X_1)))) <=> (h_false_only(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | h_true(X_2, X_1)))))),
% 0.15/0.46 inference(bind,[status(th)],[])).
% 0.15/0.46 tff(204,plain,
% 0.15/0.46 (![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (h_false(X_2, X_1) & (~h_true(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | h_true(X_2, X_1))))),
% 0.15/0.46 inference(quant_intro,[status(thm)],[203])).
% 0.15/0.46 tff(205,plain,
% 0.15/0.46 (![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (h_false(X_2, X_1) & (~h_true(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (h_false(X_2, X_1) & (~h_true(X_2, X_1))))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(206,axiom,(![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (h_false(X_2, X_1) & (~h_true(X_2, X_1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','false_only_h')).
% 0.15/0.46 tff(207,plain,
% 0.15/0.46 (![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (h_false(X_2, X_1) & (~h_true(X_2, X_1))))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.15/0.46 tff(208,plain,(
% 0.15/0.46 ![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (h_false(X_2, X_1) & (~h_true(X_2, X_1))))),
% 0.15/0.46 inference(skolemize,[status(sab)],[207])).
% 0.15/0.46 tff(209,plain,
% 0.15/0.46 (![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | h_true(X_2, X_1))))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.15/0.46 tff(210,plain,
% 0.15/0.46 (![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | h_true(X_2, X_1))))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.15/0.46 tff(211,plain,
% 0.15/0.46 ((~![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) <=> (~((~h_false(X_2, X_1)) | h_true(X_2, X_1))))) | (h_false_only(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_false(A!15, tptp_fun_B_4(A!15))) | h_true(A!15, tptp_fun_B_4(A!15)))))),
% 0.15/0.46 inference(quant_inst,[status(thm)],[])).
% 0.15/0.46 tff(212,plain,
% 0.15/0.46 (h_false_only(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_false(A!15, tptp_fun_B_4(A!15))) | h_true(A!15, tptp_fun_B_4(A!15))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.15/0.46 tff(213,plain,
% 0.15/0.46 (((~h_false(A!15, tptp_fun_B_4(A!15))) | h_true(A!15, tptp_fun_B_4(A!15))) | h_false(A!15, tptp_fun_B_4(A!15))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(214,plain,
% 0.15/0.46 ((~h_false(A!15, tptp_fun_B_4(A!15))) | h_true(A!15, tptp_fun_B_4(A!15))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[213, 195])).
% 0.15/0.46 tff(215,plain,
% 0.15/0.46 ((~(h_false_only(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_false(A!15, tptp_fun_B_4(A!15))) | h_true(A!15, tptp_fun_B_4(A!15)))))) | (~h_false_only(A!15, tptp_fun_B_4(A!15))) | (~((~h_false(A!15, tptp_fun_B_4(A!15))) | h_true(A!15, tptp_fun_B_4(A!15))))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(216,plain,
% 0.15/0.46 ((~(h_false_only(A!15, tptp_fun_B_4(A!15)) <=> (~((~h_false(A!15, tptp_fun_B_4(A!15))) | h_true(A!15, tptp_fun_B_4(A!15)))))) | (~h_false_only(A!15, tptp_fun_B_4(A!15)))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.15/0.46 tff(217,plain,
% 0.15/0.46 (~h_false_only(A!15, tptp_fun_B_4(A!15))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[216, 212])).
% 0.15/0.46 tff(218,plain,
% 0.15/0.46 ((~(h_both(A!15, tptp_fun_B_4(A!15)) | h_false_only(A!15, tptp_fun_B_4(A!15)))) | h_both(A!15, tptp_fun_B_4(A!15)) | h_false_only(A!15, tptp_fun_B_4(A!15))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(219,plain,
% 0.15/0.46 (~(h_both(A!15, tptp_fun_B_4(A!15)) | h_false_only(A!15, tptp_fun_B_4(A!15)))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[218, 217, 200])).
% 0.15/0.46 tff(220,plain,
% 0.15/0.46 (((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_4(A!15)) | h_false_only(A!15, tptp_fun_B_4(A!15))))) | (h_both(A!15, tptp_fun_B_4(A!15)) | h_false_only(A!15, tptp_fun_B_4(A!15)))),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(221,plain,
% 0.15/0.46 ((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_4(A!15)) | h_false_only(A!15, tptp_fun_B_4(A!15))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.15/0.46 tff(222,plain,
% 0.15/0.46 (((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_4(A!15)))) | g_both(A!15, B!14)),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(223,plain,
% 0.15/0.46 ((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_4(A!15)))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[222, 164])).
% 0.15/0.46 tff(224,plain,
% 0.15/0.46 (((~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))) | ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_4(A!15))))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_4(A!15)) | h_false_only(A!15, tptp_fun_B_4(A!15)))))))) <=> ((~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))) | (~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_4(A!15))))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_4(A!15)) | h_false_only(A!15, tptp_fun_B_4(A!15)))))))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(225,plain,
% 0.15/0.46 ((~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))) | ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_4(A!15))))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_4(A!15)) | h_false_only(A!15, tptp_fun_B_4(A!15)))))))),
% 0.15/0.46 inference(quant_inst,[status(thm)],[])).
% 0.15/0.46 tff(226,plain,
% 0.15/0.46 ((~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))) | (~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_4(A!15))))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_4(A!15)) | h_false_only(A!15, tptp_fun_B_4(A!15))))))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.15/0.46 tff(227,plain,
% 0.15/0.46 ($false),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[226, 91, 223, 221])).
% 0.15/0.46 tff(228,plain,((~g_true_only(A!15, B!14)) | (~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))) | (~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.46 tff(229,plain,
% 0.15/0.46 (~g_true_only(A!15, B!14)),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[228, 91, 1])).
% 0.15/0.46 tff(230,assumption,(~g_true_only(A!15, B!14)), introduced(assumption)).
% 0.15/0.46 tff(231,plain,
% 0.15/0.46 (((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15))))) | g_true_only(A!15, B!14)),
% 0.15/0.46 inference(tautology,[status(thm)],[])).
% 0.15/0.46 tff(232,plain,
% 0.15/0.46 ((~g_true_only(A!15, B!14)) | (~(h_both(A!15, tptp_fun_B_5(A!15)) | h_false_only(A!15, tptp_fun_B_5(A!15))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.15/0.46 tff(233,assumption,((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15)))), introduced(assumption)).
% 0.15/0.46 tff(234,plain,
% 0.15/0.46 ($false),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[168, 91, 233, 232])).
% 0.15/0.46 tff(235,plain,((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, tptp_fun_B_5(A!15))))) | (~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))) | g_true_only(A!15, B!14)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.46 tff(236,plain,
% 0.15/0.46 ($false),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[235, 229, 91, 90])).
% 0.15/0.46 tff(237,plain,((~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))) | (~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.46 tff(238,plain,
% 0.15/0.46 (~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[237, 1])).
% 0.15/0.46 tff(239,assumption,((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)))) | (~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))))))), introduced(assumption)).
% 0.15/0.46 tff(240,plain,
% 0.15/0.46 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)))) | (~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)))) | (~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))))))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(241,plain,
% 0.15/0.46 ((~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | (~g_both(A!8, B!11)) | g_true_only(A!8, tptp_fun_B_6(A!8)))))) <=> (~((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)))) | (~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))))))))),
% 0.15/0.46 inference(rewrite,[status(thm)],[])).
% 0.15/0.46 tff(242,plain,
% 0.15/0.46 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | (~g_both(A!8, B!11)) | g_true_only(A!8, tptp_fun_B_6(A!8))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)))) | (~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))))))),
% 0.15/0.46 inference(monotonicity,[status(thm)],[241])).
% 0.15/0.46 tff(243,plain,
% 0.15/0.46 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | (~g_both(A!8, B!11)) | g_true_only(A!8, tptp_fun_B_6(A!8))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)))) | (~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))))))),
% 0.15/0.46 inference(transitivity,[status(thm)],[242, 240])).
% 0.15/0.46 tff(244,plain,
% 0.15/0.46 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | (~g_both(A!8, B!11)) | g_true_only(A!8, tptp_fun_B_6(A!8))))))),
% 0.15/0.46 inference(quant_inst,[status(thm)],[])).
% 0.15/0.46 tff(245,plain,
% 0.15/0.46 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)))) | (~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))))))))),
% 0.15/0.46 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.15/0.46 tff(246,plain,
% 0.15/0.46 ($false),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[245, 1, 239])).
% 0.15/0.46 tff(247,plain,((~((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)))) | (~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))))) | (~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.46 tff(248,plain,
% 0.15/0.46 (~((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)))) | (~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))))),
% 0.15/0.46 inference(unit_resolution,[status(thm)],[247, 1])).
% 0.15/0.46 tff(249,plain,
% 0.15/0.46 (((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)))) | (~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))))))) | ((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(250,plain,
% 0.15/0.47 ((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.15/0.47 tff(251,assumption,(~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))) | ![B: $i] : h_false_only(A!8, B))))), introduced(assumption)).
% 0.15/0.47 tff(252,plain,
% 0.15/0.47 (((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))) | ![B: $i] : h_false_only(A!8, B)))) | g_true_only(A!8, B!9)),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(253,plain,
% 0.15/0.47 (g_true_only(A!8, B!9)),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.15/0.47 tff(254,plain,
% 0.15/0.47 ((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))))),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(255,plain,
% 0.15/0.47 (~((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[254, 253, 250])).
% 0.15/0.47 tff(256,plain,
% 0.15/0.47 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)) | (~g_both(A!8, B!9))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)) | (~g_both(A!8, B!9)))))))),
% 0.15/0.47 inference(rewrite,[status(thm)],[])).
% 0.15/0.47 tff(257,plain,
% 0.15/0.47 ((~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | (~g_both(A!8, B!9)) | g_true_only(A!8, tptp_fun_B_6(A!8)))))) <=> (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)) | (~g_both(A!8, B!9))))))),
% 0.15/0.47 inference(rewrite,[status(thm)],[])).
% 0.15/0.47 tff(258,plain,
% 0.15/0.47 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | (~g_both(A!8, B!9)) | g_true_only(A!8, tptp_fun_B_6(A!8))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)) | (~g_both(A!8, B!9)))))))),
% 0.15/0.47 inference(monotonicity,[status(thm)],[257])).
% 0.15/0.47 tff(259,plain,
% 0.15/0.47 (((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | (~g_both(A!8, B!9)) | g_true_only(A!8, tptp_fun_B_6(A!8))))))) <=> ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)) | (~g_both(A!8, B!9)))))))),
% 0.15/0.47 inference(transitivity,[status(thm)],[258, 256])).
% 0.15/0.47 tff(260,plain,
% 0.15/0.47 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | (~g_both(A!8, B!9)) | g_true_only(A!8, tptp_fun_B_6(A!8))))))),
% 0.15/0.47 inference(quant_inst,[status(thm)],[])).
% 0.15/0.47 tff(261,plain,
% 0.15/0.47 ((~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)) | (~g_both(A!8, B!9))))))),
% 0.15/0.47 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.15/0.47 tff(262,plain,
% 0.15/0.47 (~((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)) | (~g_both(A!8, B!9)))))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[261, 1])).
% 0.15/0.47 tff(263,plain,
% 0.15/0.47 (((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~h_false_only(A!8, tptp_fun_B_5(A!8))) | g_true_only(A!8, tptp_fun_B_6(A!8)) | (~g_both(A!8, B!9))))) | ((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(264,plain,
% 0.15/0.47 ((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.15/0.47 tff(265,plain,
% 0.15/0.47 ((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))))),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(266,plain,
% 0.15/0.47 ((~((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))))) | (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[265, 253])).
% 0.15/0.47 tff(267,plain,
% 0.15/0.47 (~((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8)))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[266, 264])).
% 0.15/0.47 tff(268,plain,
% 0.15/0.47 (((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))) | ((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(269,plain,
% 0.15/0.47 ((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.15/0.47 tff(270,assumption,(~![B: $i] : h_false_only(A!8, B)), introduced(assumption)).
% 0.15/0.47 tff(271,plain,
% 0.15/0.47 (((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))) | ![B: $i] : h_false_only(A!8, B)))) | ((~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))) | ![B: $i] : h_false_only(A!8, B))),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(272,plain,
% 0.15/0.47 ((~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))) | ![B: $i] : h_false_only(A!8, B)),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[271, 251])).
% 0.15/0.47 tff(273,plain,
% 0.15/0.47 ((~((~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))) | ![B: $i] : h_false_only(A!8, B))) | (~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))) | ![B: $i] : h_false_only(A!8, B)),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(274,plain,
% 0.15/0.47 (~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[273, 272, 270])).
% 0.15/0.47 tff(275,plain,
% 0.15/0.47 (((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B)))) | h_both(A!8, B!10)),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(276,plain,
% 0.15/0.47 (h_both(A!8, B!10)),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[275, 274])).
% 0.15/0.47 tff(277,plain,
% 0.15/0.47 ((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | (~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8))),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(278,plain,
% 0.15/0.47 ((~((~h_both(A!8, B!10)) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_true_only(A!8, tptp_fun_B_4(A!8))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[277, 276])).
% 0.15/0.47 tff(279,plain,
% 0.15/0.47 (h_true_only(A!8, tptp_fun_B_4(A!8))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[278, 269])).
% 0.15/0.47 tff(280,plain,
% 0.15/0.47 (((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B)))) | ![B: $i] : (~h_true_only(A!8, B))),
% 0.15/0.47 inference(tautology,[status(thm)],[])).
% 0.15/0.47 tff(281,plain,
% 0.15/0.47 (![B: $i] : (~h_true_only(A!8, B))),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[280, 274])).
% 0.15/0.47 tff(282,plain,
% 0.15/0.47 ((~![B: $i] : (~h_true_only(A!8, B))) | (~h_true_only(A!8, tptp_fun_B_4(A!8)))),
% 0.15/0.47 inference(quant_inst,[status(thm)],[])).
% 0.15/0.47 tff(283,plain,
% 0.15/0.47 ($false),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[282, 281, 279])).
% 0.15/0.47 tff(284,plain,(((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))) | ![B: $i] : h_false_only(A!8, B)))) | (~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A))))))) | ![B: $i] : h_false_only(A!8, B)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.47 tff(285,plain,
% 0.15/0.47 (![B: $i] : h_false_only(A!8, B)),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[284, 251, 1])).
% 0.15/0.47 tff(286,assumption,(~h_false_only(A!8, tptp_fun_B_5(A!8))), introduced(assumption)).
% 0.15/0.47 tff(287,assumption,(![B: $i] : h_false_only(A!8, B)), introduced(assumption)).
% 0.15/0.47 tff(288,plain,
% 0.15/0.47 ((~![B: $i] : h_false_only(A!8, B)) | h_false_only(A!8, tptp_fun_B_5(A!8))),
% 0.15/0.47 inference(quant_inst,[status(thm)],[])).
% 0.15/0.47 tff(289,plain,
% 0.15/0.47 ($false),
% 0.15/0.47 inference(unit_resolution,[status(thm)],[288, 287, 286])).
% 0.15/0.48 tff(290,plain,(h_false_only(A!8, tptp_fun_B_5(A!8)) | (~![B: $i] : h_false_only(A!8, B))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.48 tff(291,plain,
% 0.15/0.48 (h_false_only(A!8, tptp_fun_B_5(A!8))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[290, 285])).
% 0.15/0.48 tff(292,plain,
% 0.15/0.48 (((~((~h_both(A!8, tptp_fun_C_7(B!9, A!0))) | h_true_only(A!8, tptp_fun_B_4(A!8)))) | h_false_only(A!8, tptp_fun_B_5(A!8))) | (~h_false_only(A!8, tptp_fun_B_5(A!8)))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(293,plain,
% 0.15/0.48 ($false),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[292, 291, 255])).
% 0.15/0.48 tff(294,plain,(((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))) | ![B: $i] : h_false_only(A!8, B)))) | (~![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.48 tff(295,plain,
% 0.15/0.48 ((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))) | ![B: $i] : h_false_only(A!8, B)))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[294, 1])).
% 0.15/0.48 tff(296,assumption,(~![C: $i] : ((~((~g_both(A!15, B!14)) | (~h_false_only(A!15, C)))) | (~((~g_true_only(A!15, B!14)) | (~(h_both(A!15, C) | h_false_only(A!15, C))))))), introduced(assumption)).
% 0.15/0.48 tff(297,assumption,((~g_true_only(A!8, B!9)) | (~((~((~h_both(A!8, B!10)) | (~![B: $i] : (~h_true_only(A!8, B))))) | ![B: $i] : h_false_only(A!8, B)))), introduced(assumption)).
% 0.15/0.48 tff(298,assumption,(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3)))), introduced(assumption)).
% 0.15/0.48 tff(299,assumption,((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))), introduced(assumption)).
% 0.15/0.48 tff(300,assumption,((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))), introduced(assumption)).
% 0.15/0.48 tff(301,assumption,(![C: $i] : (~(g_false_only(A!3, B!2) | h_true_only(A!3, C)))), introduced(assumption)).
% 0.15/0.48 tff(302,assumption,(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_B_4(A!3))), introduced(assumption)).
% 0.15/0.48 tff(303,plain,
% 0.15/0.48 ((~![C: $i] : (~(g_false_only(A!3, B!2) | h_true_only(A!3, C)))) | (~(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_B_4(A!3))))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(304,plain,
% 0.15/0.48 ($false),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[303, 301, 302])).
% 0.15/0.48 tff(305,plain,((~(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | (~![C: $i] : (~(g_false_only(A!3, B!2) | h_true_only(A!3, C))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.48 tff(306,plain,
% 0.15/0.48 (~(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_B_4(A!3)))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[305, 301])).
% 0.15/0.48 tff(307,plain,
% 0.15/0.48 ((g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_B_4(A!3))) | (~h_true_only(A!3, tptp_fun_B_4(A!3)))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(308,plain,
% 0.15/0.48 (~h_true_only(A!3, tptp_fun_B_4(A!3))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[307, 306])).
% 0.15/0.48 tff(309,assumption,(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_B_5(A!3))), introduced(assumption)).
% 0.15/0.48 tff(310,plain,
% 0.15/0.48 ((~![C: $i] : (~(g_false_only(A!3, B!2) | h_true_only(A!3, C)))) | (~(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(311,plain,
% 0.15/0.48 ($false),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[310, 301, 309])).
% 0.15/0.48 tff(312,plain,((~(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_B_5(A!3)))) | (~![C: $i] : (~(g_false_only(A!3, B!2) | h_true_only(A!3, C))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.48 tff(313,plain,
% 0.15/0.48 (~(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_B_5(A!3)))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[312, 301])).
% 0.15/0.48 tff(314,plain,
% 0.15/0.48 ((g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_B_5(A!3))) | (~h_true_only(A!3, tptp_fun_B_5(A!3)))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(315,plain,
% 0.15/0.48 (~h_true_only(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[314, 313])).
% 0.15/0.48 tff(316,assumption,(~h_true_only(A!3, tptp_fun_B_4(A!3))), introduced(assumption)).
% 0.15/0.48 tff(317,assumption,(~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))), introduced(assumption)).
% 0.15/0.48 tff(318,plain,
% 0.15/0.48 (((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))) | ((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(319,plain,
% 0.15/0.48 ((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[318, 317])).
% 0.15/0.48 tff(320,plain,
% 0.15/0.48 ((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | (~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(321,plain,
% 0.15/0.48 (~h_both(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[320, 319, 316])).
% 0.15/0.48 tff(322,plain,
% 0.15/0.48 (((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3)))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(323,plain,
% 0.15/0.48 (~h_false_only(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[322, 317])).
% 0.15/0.48 tff(324,assumption,(~h_true_only(A!3, tptp_fun_B_5(A!3))), introduced(assumption)).
% 0.15/0.48 tff(325,plain,
% 0.15/0.48 (^[X_2: $i, X_1: $i] : refl((h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1)) <=> (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1)))),
% 0.15/0.48 inference(bind,[status(th)],[])).
% 0.15/0.48 tff(326,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))),
% 0.15/0.48 inference(quant_intro,[status(thm)],[325])).
% 0.15/0.48 tff(327,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))),
% 0.15/0.48 inference(rewrite,[status(thm)],[])).
% 0.15/0.48 tff(328,plain,
% 0.15/0.48 (^[X_2: $i, X_1: $i] : trans(monotonicity(rewrite((h_true_only(X_2, X_1) | h_both(X_2, X_1)) <=> (h_true_only(X_2, X_1) | h_both(X_2, X_1))), (((h_true_only(X_2, X_1) | h_both(X_2, X_1)) | h_false_only(X_2, X_1)) <=> ((h_true_only(X_2, X_1) | h_both(X_2, X_1)) | h_false_only(X_2, X_1)))), rewrite(((h_true_only(X_2, X_1) | h_both(X_2, X_1)) | h_false_only(X_2, X_1)) <=> (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))), (((h_true_only(X_2, X_1) | h_both(X_2, X_1)) | h_false_only(X_2, X_1)) <=> (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))))),
% 0.15/0.48 inference(bind,[status(th)],[])).
% 0.15/0.48 tff(329,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : ((h_true_only(X_2, X_1) | h_both(X_2, X_1)) | h_false_only(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))),
% 0.15/0.48 inference(quant_intro,[status(thm)],[328])).
% 0.15/0.48 tff(330,axiom,(![X_2: $i, X_1: $i] : ((h_true_only(X_2, X_1) | h_both(X_2, X_1)) | h_false_only(X_2, X_1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','exhaustion_h')).
% 0.15/0.48 tff(331,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.15/0.48 tff(332,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[331, 327])).
% 0.15/0.48 tff(333,plain,(
% 0.15/0.48 ![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))),
% 0.15/0.48 inference(skolemize,[status(sab)],[332])).
% 0.15/0.48 tff(334,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[333, 326])).
% 0.15/0.48 tff(335,plain,
% 0.15/0.48 (((~![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))) | (h_false_only(A!3, tptp_fun_B_5(A!3)) | h_true_only(A!3, tptp_fun_B_5(A!3)) | h_both(A!3, tptp_fun_B_5(A!3)))) <=> ((~![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))) | h_false_only(A!3, tptp_fun_B_5(A!3)) | h_true_only(A!3, tptp_fun_B_5(A!3)) | h_both(A!3, tptp_fun_B_5(A!3)))),
% 0.15/0.48 inference(rewrite,[status(thm)],[])).
% 0.15/0.48 tff(336,plain,
% 0.15/0.48 ((~![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))) | (h_false_only(A!3, tptp_fun_B_5(A!3)) | h_true_only(A!3, tptp_fun_B_5(A!3)) | h_both(A!3, tptp_fun_B_5(A!3)))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(337,plain,
% 0.15/0.48 ((~![X_2: $i, X_1: $i] : (h_false_only(X_2, X_1) | h_true_only(X_2, X_1) | h_both(X_2, X_1))) | h_false_only(A!3, tptp_fun_B_5(A!3)) | h_true_only(A!3, tptp_fun_B_5(A!3)) | h_both(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.15/0.48 tff(338,plain,
% 0.15/0.48 ($false),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[337, 334, 324, 323, 321])).
% 0.15/0.48 tff(339,plain,(((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_5(A!3)) | h_true_only(A!3, tptp_fun_B_4(A!3))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.48 tff(340,plain,
% 0.15/0.48 ((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[339, 315, 308])).
% 0.15/0.48 tff(341,plain,
% 0.15/0.48 ((~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(342,plain,
% 0.15/0.48 (~g_true_only(A!3, B!2)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[341, 340, 300])).
% 0.15/0.48 tff(343,plain,
% 0.15/0.48 ((~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(344,plain,
% 0.15/0.48 (~g_true_only(A!3, tptp_fun_B_6(A!3))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[343, 340, 299])).
% 0.15/0.48 tff(345,assumption,((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3))), introduced(assumption)).
% 0.15/0.48 tff(346,plain,
% 0.15/0.48 ((~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))) | (~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(347,plain,
% 0.15/0.48 (h_false_only(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[346, 340, 345])).
% 0.15/0.48 tff(348,plain,
% 0.15/0.48 ((~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3)))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(349,plain,
% 0.15/0.48 (~g_both(A!3, B!2)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[348, 347, 344, 298])).
% 0.15/0.48 tff(350,plain,
% 0.15/0.48 ((~![C: $i] : (~(g_false_only(A!3, B!2) | h_true_only(A!3, C)))) | (~(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_7(B!9, A!0))))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(351,plain,
% 0.15/0.48 (~(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_7(B!9, A!0)))),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[350, 301])).
% 0.15/0.48 tff(352,plain,
% 0.15/0.48 ((g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_7(B!9, A!0))) | (~g_false_only(A!3, B!2))),
% 0.15/0.48 inference(tautology,[status(thm)],[])).
% 0.15/0.48 tff(353,plain,
% 0.15/0.48 (~g_false_only(A!3, B!2)),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[352, 351])).
% 0.15/0.48 tff(354,plain,
% 0.15/0.48 (^[X_2: $i, X_1: $i] : refl((g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1)) <=> (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1)))),
% 0.15/0.48 inference(bind,[status(th)],[])).
% 0.15/0.48 tff(355,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.15/0.48 inference(quant_intro,[status(thm)],[354])).
% 0.15/0.48 tff(356,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.15/0.48 inference(rewrite,[status(thm)],[])).
% 0.15/0.48 tff(357,plain,
% 0.15/0.48 (^[X_2: $i, X_1: $i] : trans(monotonicity(rewrite((g_true_only(X_2, X_1) | g_both(X_2, X_1)) <=> (g_true_only(X_2, X_1) | g_both(X_2, X_1))), (((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> ((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)))), rewrite(((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))), (((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))))),
% 0.15/0.48 inference(bind,[status(th)],[])).
% 0.15/0.48 tff(358,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : ((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.15/0.48 inference(quant_intro,[status(thm)],[357])).
% 0.15/0.48 tff(359,axiom,(![X_2: $i, X_1: $i] : ((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','exhaustion_g')).
% 0.15/0.48 tff(360,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.15/0.48 tff(361,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[360, 356])).
% 0.15/0.48 tff(362,plain,(
% 0.15/0.48 ![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.15/0.48 inference(skolemize,[status(sab)],[361])).
% 0.15/0.48 tff(363,plain,
% 0.15/0.48 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[362, 355])).
% 0.15/0.48 tff(364,plain,
% 0.15/0.48 (((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(A!3, B!2) | g_true_only(A!3, B!2) | g_both(A!3, B!2))) <=> ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(A!3, B!2) | g_true_only(A!3, B!2) | g_both(A!3, B!2))),
% 0.15/0.48 inference(rewrite,[status(thm)],[])).
% 0.15/0.48 tff(365,plain,
% 0.15/0.48 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(A!3, B!2) | g_true_only(A!3, B!2) | g_both(A!3, B!2))),
% 0.15/0.48 inference(quant_inst,[status(thm)],[])).
% 0.15/0.48 tff(366,plain,
% 0.15/0.48 ((~![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) | g_true_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(A!3, B!2) | g_true_only(A!3, B!2) | g_both(A!3, B!2)),
% 0.15/0.48 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.15/0.48 tff(367,plain,
% 0.15/0.48 ($false),
% 0.15/0.48 inference(unit_resolution,[status(thm)],[366, 363, 353, 349, 342])).
% 0.15/0.48 tff(368,plain,((~![C: $i] : (~(g_false_only(A!3, B!2) | h_true_only(A!3, C)))) | (~(g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | (~((~g_true_only(A!3, tptp_fun_B_6(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~((~g_true_only(A!3, B!2)) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.49 tff(369,plain,
% 0.15/0.49 (~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[368, 301, 298, 299, 300])).
% 0.15/0.49 tff(370,plain,
% 0.15/0.49 ((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[318, 369])).
% 0.15/0.49 tff(371,plain,
% 0.15/0.49 (~g_true_only(A!3, tptp_fun_B_6(A!3))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[343, 370, 299])).
% 0.15/0.49 tff(372,plain,
% 0.15/0.49 (~g_true_only(A!3, B!2)),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[341, 370, 300])).
% 0.15/0.49 tff(373,plain,
% 0.15/0.49 (g_both(A!3, B!2)),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[366, 363, 353, 372])).
% 0.15/0.49 tff(374,plain,
% 0.15/0.49 (~h_false_only(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[348, 373, 371, 298])).
% 0.15/0.49 tff(375,assumption,((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))), introduced(assumption)).
% 0.15/0.49 tff(376,plain,
% 0.15/0.49 ((~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~((~((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(377,plain,
% 0.15/0.49 (~g_true_only(A!3, tptp_fun_B_13(A!3))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[376, 370, 375])).
% 0.15/0.49 tff(378,plain,
% 0.15/0.49 (((~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3))) | h_both(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(379,plain,
% 0.15/0.49 (h_both(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[378, 369])).
% 0.15/0.49 tff(380,assumption,(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3))), introduced(assumption)).
% 0.15/0.49 tff(381,plain,
% 0.15/0.49 ((~![C: $i] : (~(g_false_only(A!3, B!2) | h_true_only(A!3, C)))) | (~(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3))))),
% 0.15/0.49 inference(quant_inst,[status(thm)],[])).
% 0.15/0.49 tff(382,plain,
% 0.15/0.49 ($false),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[381, 301, 380])).
% 0.15/0.49 tff(383,plain,((~(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3)))) | (~![C: $i] : (~(g_false_only(A!3, B!2) | h_true_only(A!3, C))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.49 tff(384,plain,
% 0.15/0.49 (~(g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[383, 301])).
% 0.15/0.49 tff(385,plain,
% 0.15/0.49 ((g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3))) | (~h_true_only(A!3, tptp_fun_C_12(B!2, A!3)))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(386,plain,
% 0.15/0.49 (~h_true_only(A!3, tptp_fun_C_12(B!2, A!3))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[385, 384])).
% 0.15/0.49 tff(387,assumption,(~g_true_only(A!3, tptp_fun_B_13(A!3))), introduced(assumption)).
% 0.15/0.49 tff(388,plain,
% 0.15/0.49 (((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3))))) | g_true_only(A!3, tptp_fun_B_13(A!3))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(389,plain,
% 0.15/0.49 ((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[388, 387])).
% 0.15/0.49 tff(390,assumption,(~h_false_only(A!3, tptp_fun_B_5(A!3))), introduced(assumption)).
% 0.15/0.49 tff(391,plain,
% 0.15/0.49 (((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3)))) | h_false_only(A!3, tptp_fun_B_5(A!3))),
% 0.15/0.49 inference(tautology,[status(thm)],[])).
% 0.15/0.49 tff(392,plain,
% 0.15/0.49 ((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3)))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[391, 390])).
% 0.15/0.49 tff(393,assumption,(h_both(A!3, tptp_fun_B_5(A!3))), introduced(assumption)).
% 0.15/0.49 tff(394,assumption,(g_both(A!3, B!2)), introduced(assumption)).
% 0.15/0.49 tff(395,assumption,(~h_true_only(A!3, tptp_fun_C_12(B!2, A!3))), introduced(assumption)).
% 0.15/0.49 tff(396,assumption,(~g_false_only(A!3, B!2)), introduced(assumption)).
% 0.15/0.49 tff(397,assumption,(![A: $i, C_19: $i, B: $i, C: $i] : (h_true_only(A, tptp_fun_C_12(B, A)) | g_false_only(A, B) | (~g_both(A, B)) | (~h_both(A, C)) | (~((~g_both(A, tptp_fun_B_13(A))) | (~h_false_only(A, C_19)))) | (~((~g_true_only(A, tptp_fun_B_13(A))) | (~(h_both(A, C_19) | h_false_only(A, C_19))))))), introduced(assumption)).
% 0.15/0.49 tff(398,plain,
% 0.15/0.49 (((~![A: $i, C_19: $i, B: $i, C: $i] : (h_true_only(A, tptp_fun_C_12(B, A)) | g_false_only(A, B) | (~g_both(A, B)) | (~h_both(A, C)) | (~((~g_both(A, tptp_fun_B_13(A))) | (~h_false_only(A, C_19)))) | (~((~g_true_only(A, tptp_fun_B_13(A))) | (~(h_both(A, C_19) | h_false_only(A, C_19))))))) | (g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3)) | (~g_both(A!3, B!2)) | (~((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~h_both(A!3, tptp_fun_B_5(A!3))))) <=> ((~![A: $i, C_19: $i, B: $i, C: $i] : (h_true_only(A, tptp_fun_C_12(B, A)) | g_false_only(A, B) | (~g_both(A, B)) | (~h_both(A, C)) | (~((~g_both(A, tptp_fun_B_13(A))) | (~h_false_only(A, C_19)))) | (~((~g_true_only(A, tptp_fun_B_13(A))) | (~(h_both(A, C_19) | h_false_only(A, C_19))))))) | g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3)) | (~g_both(A!3, B!2)) | (~((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~h_both(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.49 inference(rewrite,[status(thm)],[])).
% 0.15/0.49 tff(399,plain,
% 0.15/0.49 ((h_true_only(A!3, tptp_fun_C_12(B!2, A!3)) | g_false_only(A!3, B!2) | (~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))) | (~((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3))))))) <=> (g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3)) | (~g_both(A!3, B!2)) | (~((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~h_both(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.49 inference(rewrite,[status(thm)],[])).
% 0.15/0.49 tff(400,plain,
% 0.15/0.49 (((~![A: $i, C_19: $i, B: $i, C: $i] : (h_true_only(A, tptp_fun_C_12(B, A)) | g_false_only(A, B) | (~g_both(A, B)) | (~h_both(A, C)) | (~((~g_both(A, tptp_fun_B_13(A))) | (~h_false_only(A, C_19)))) | (~((~g_true_only(A, tptp_fun_B_13(A))) | (~(h_both(A, C_19) | h_false_only(A, C_19))))))) | (h_true_only(A!3, tptp_fun_C_12(B!2, A!3)) | g_false_only(A!3, B!2) | (~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))) | (~((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))) <=> ((~![A: $i, C_19: $i, B: $i, C: $i] : (h_true_only(A, tptp_fun_C_12(B, A)) | g_false_only(A, B) | (~g_both(A, B)) | (~h_both(A, C)) | (~((~g_both(A, tptp_fun_B_13(A))) | (~h_false_only(A, C_19)))) | (~((~g_true_only(A, tptp_fun_B_13(A))) | (~(h_both(A, C_19) | h_false_only(A, C_19))))))) | (g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3)) | (~g_both(A!3, B!2)) | (~((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~h_both(A!3, tptp_fun_B_5(A!3)))))),
% 0.15/0.49 inference(monotonicity,[status(thm)],[399])).
% 0.15/0.49 tff(401,plain,
% 0.15/0.49 (((~![A: $i, C_19: $i, B: $i, C: $i] : (h_true_only(A, tptp_fun_C_12(B, A)) | g_false_only(A, B) | (~g_both(A, B)) | (~h_both(A, C)) | (~((~g_both(A, tptp_fun_B_13(A))) | (~h_false_only(A, C_19)))) | (~((~g_true_only(A, tptp_fun_B_13(A))) | (~(h_both(A, C_19) | h_false_only(A, C_19))))))) | (h_true_only(A!3, tptp_fun_C_12(B!2, A!3)) | g_false_only(A!3, B!2) | (~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))) | (~((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))) <=> ((~![A: $i, C_19: $i, B: $i, C: $i] : (h_true_only(A, tptp_fun_C_12(B, A)) | g_false_only(A, B) | (~g_both(A, B)) | (~h_both(A, C)) | (~((~g_both(A, tptp_fun_B_13(A))) | (~h_false_only(A, C_19)))) | (~((~g_true_only(A, tptp_fun_B_13(A))) | (~(h_both(A, C_19) | h_false_only(A, C_19))))))) | g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3)) | (~g_both(A!3, B!2)) | (~((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~h_both(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.49 inference(transitivity,[status(thm)],[400, 398])).
% 0.15/0.49 tff(402,plain,
% 0.15/0.49 ((~![A: $i, C_19: $i, B: $i, C: $i] : (h_true_only(A, tptp_fun_C_12(B, A)) | g_false_only(A, B) | (~g_both(A, B)) | (~h_both(A, C)) | (~((~g_both(A, tptp_fun_B_13(A))) | (~h_false_only(A, C_19)))) | (~((~g_true_only(A, tptp_fun_B_13(A))) | (~(h_both(A, C_19) | h_false_only(A, C_19))))))) | (h_true_only(A!3, tptp_fun_C_12(B!2, A!3)) | g_false_only(A!3, B!2) | (~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))) | (~((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3)))))))),
% 0.15/0.49 inference(quant_inst,[status(thm)],[])).
% 0.15/0.49 tff(403,plain,
% 0.15/0.49 ((~![A: $i, C_19: $i, B: $i, C: $i] : (h_true_only(A, tptp_fun_C_12(B, A)) | g_false_only(A, B) | (~g_both(A, B)) | (~h_both(A, C)) | (~((~g_both(A, tptp_fun_B_13(A))) | (~h_false_only(A, C_19)))) | (~((~g_true_only(A, tptp_fun_B_13(A))) | (~(h_both(A, C_19) | h_false_only(A, C_19))))))) | g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3)) | (~g_both(A!3, B!2)) | (~((~g_both(A!3, tptp_fun_B_13(A!3))) | (~h_false_only(A!3, tptp_fun_B_5(A!3))))) | (~((~g_true_only(A!3, tptp_fun_B_13(A!3))) | (~(h_both(A!3, tptp_fun_B_5(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3)))))) | (~h_both(A!3, tptp_fun_B_5(A!3)))),
% 0.15/0.49 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.15/0.49 tff(404,plain,
% 0.15/0.49 ($false),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[403, 397, 396, 395, 394, 393, 392, 389])).
% 0.15/0.49 tff(405,plain,((~![A: $i, C_19: $i, B: $i, C: $i] : (h_true_only(A, tptp_fun_C_12(B, A)) | g_false_only(A, B) | (~g_both(A, B)) | (~h_both(A, C)) | (~((~g_both(A, tptp_fun_B_13(A))) | (~h_false_only(A, C_19)))) | (~((~g_true_only(A, tptp_fun_B_13(A))) | (~(h_both(A, C_19) | h_false_only(A, C_19))))))) | g_false_only(A!3, B!2) | h_true_only(A!3, tptp_fun_C_12(B!2, A!3)) | (~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))) | g_true_only(A!3, tptp_fun_B_13(A!3)) | h_false_only(A!3, tptp_fun_B_5(A!3))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.49 tff(406,plain,
% 0.15/0.49 (~![A: $i, C_19: $i, B: $i, C: $i] : (h_true_only(A, tptp_fun_C_12(B, A)) | g_false_only(A, B) | (~g_both(A, B)) | (~h_both(A, C)) | (~((~g_both(A, tptp_fun_B_13(A))) | (~h_false_only(A, C_19)))) | (~((~g_true_only(A, tptp_fun_B_13(A))) | (~(h_both(A, C_19) | h_false_only(A, C_19))))))),
% 0.15/0.49 inference(unit_resolution,[status(thm)],[405, 373, 386, 353, 379, 377, 374])).
% 0.15/0.49 tff(407,assumption,(~g_true_only(A!3, tptp_fun_B_6(A!3))), introduced(assumption)).
% 0.15/0.49 tff(408,assumption,(![A: $i, B_18: $i, B: $i] : ((~g_both(A, B_18)) | (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)) | g_true_only(A, tptp_fun_B_6(A)))), introduced(assumption)).
% 0.15/0.49 tff(409,plain,
% 0.15/0.49 (((~![A: $i, B_18: $i, B: $i] : ((~g_both(A, B_18)) | (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)) | g_true_only(A, tptp_fun_B_6(A)))) | (h_true_only(A!3, tptp_fun_B_4(A!3)) | g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))))) <=> ((~![A: $i, B_18: $i, B: $i] : ((~g_both(A, B_18)) | (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)) | g_true_only(A, tptp_fun_B_6(A)))) | h_true_only(A!3, tptp_fun_B_4(A!3)) | g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(410,plain,
% 0.15/0.50 (((~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)) | g_true_only(A!3, tptp_fun_B_6(A!3))) <=> (h_true_only(A!3, tptp_fun_B_4(A!3)) | g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(411,plain,
% 0.15/0.50 (((~![A: $i, B_18: $i, B: $i] : ((~g_both(A, B_18)) | (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)) | g_true_only(A, tptp_fun_B_6(A)))) | ((~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)) | g_true_only(A!3, tptp_fun_B_6(A!3)))) <=> ((~![A: $i, B_18: $i, B: $i] : ((~g_both(A, B_18)) | (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)) | g_true_only(A, tptp_fun_B_6(A)))) | (h_true_only(A!3, tptp_fun_B_4(A!3)) | g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3)))))),
% 0.15/0.50 inference(monotonicity,[status(thm)],[410])).
% 0.15/0.50 tff(412,plain,
% 0.15/0.50 (((~![A: $i, B_18: $i, B: $i] : ((~g_both(A, B_18)) | (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)) | g_true_only(A, tptp_fun_B_6(A)))) | ((~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)) | g_true_only(A!3, tptp_fun_B_6(A!3)))) <=> ((~![A: $i, B_18: $i, B: $i] : ((~g_both(A, B_18)) | (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)) | g_true_only(A, tptp_fun_B_6(A)))) | h_true_only(A!3, tptp_fun_B_4(A!3)) | g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))))),
% 0.15/0.50 inference(transitivity,[status(thm)],[411, 409])).
% 0.15/0.50 tff(413,plain,
% 0.15/0.50 ((~![A: $i, B_18: $i, B: $i] : ((~g_both(A, B_18)) | (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)) | g_true_only(A, tptp_fun_B_6(A)))) | ((~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3))) | h_true_only(A!3, tptp_fun_B_4(A!3)) | g_true_only(A!3, tptp_fun_B_6(A!3)))),
% 0.15/0.50 inference(quant_inst,[status(thm)],[])).
% 0.15/0.50 tff(414,plain,
% 0.15/0.50 ((~![A: $i, B_18: $i, B: $i] : ((~g_both(A, B_18)) | (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)) | g_true_only(A, tptp_fun_B_6(A)))) | h_true_only(A!3, tptp_fun_B_4(A!3)) | g_true_only(A!3, tptp_fun_B_6(A!3)) | (~g_both(A!3, B!2)) | (~h_both(A!3, tptp_fun_B_5(A!3)))),
% 0.15/0.50 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.15/0.50 tff(415,plain,
% 0.15/0.50 ($false),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[414, 408, 394, 316, 407, 393])).
% 0.15/0.50 tff(416,plain,((~![A: $i, B_18: $i, B: $i] : ((~g_both(A, B_18)) | (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)) | g_true_only(A, tptp_fun_B_6(A)))) | (~g_both(A!3, B!2)) | h_true_only(A!3, tptp_fun_B_4(A!3)) | g_true_only(A!3, tptp_fun_B_6(A!3)) | (~h_both(A!3, tptp_fun_B_5(A!3)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.50 tff(417,plain,
% 0.15/0.50 (~![A: $i, B_18: $i, B: $i] : ((~g_both(A, B_18)) | (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)) | g_true_only(A, tptp_fun_B_6(A)))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[416, 373, 308, 379, 371])).
% 0.15/0.50 tff(418,assumption,(~((~g_both(A!8, B!11)) | (~![B: $i] : (~g_true_only(A!8, B))) | (~![B: $i] : h_false_only(A!8, B)))), introduced(assumption)).
% 0.15/0.50 tff(419,plain,
% 0.15/0.50 (((~g_both(A!8, B!11)) | (~![B: $i] : (~g_true_only(A!8, B))) | (~![B: $i] : h_false_only(A!8, B))) | ![B: $i] : h_false_only(A!8, B)),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(420,plain,
% 0.15/0.50 (![B: $i] : h_false_only(A!8, B)),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[419, 418])).
% 0.15/0.50 tff(421,assumption,(~h_false_only(A!8, tptp_fun_C_7(B!11, A!8))), introduced(assumption)).
% 0.15/0.50 tff(422,plain,
% 0.15/0.50 ((~![B: $i] : h_false_only(A!8, B)) | h_false_only(A!8, tptp_fun_C_7(B!11, A!8))),
% 0.15/0.50 inference(quant_inst,[status(thm)],[])).
% 0.15/0.50 tff(423,plain,
% 0.15/0.50 ($false),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[422, 287, 421])).
% 0.15/0.50 tff(424,plain,(h_false_only(A!8, tptp_fun_C_7(B!11, A!8)) | (~![B: $i] : h_false_only(A!8, B))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.50 tff(425,plain,
% 0.15/0.50 (h_false_only(A!8, tptp_fun_C_7(B!11, A!8))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[424, 420])).
% 0.15/0.50 tff(426,plain,
% 0.15/0.50 (((~g_both(A!8, B!11)) | (~![B: $i] : (~g_true_only(A!8, B))) | (~![B: $i] : h_false_only(A!8, B))) | g_both(A!8, B!11)),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(427,plain,
% 0.15/0.50 (g_both(A!8, B!11)),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[426, 418])).
% 0.15/0.50 tff(428,assumption,(h_false_only(A!8, tptp_fun_C_7(B!11, A!8))), introduced(assumption)).
% 0.15/0.50 tff(429,assumption,(g_both(A!8, B!11)), introduced(assumption)).
% 0.15/0.50 tff(430,plain,
% 0.15/0.50 ((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_C_7(B!11, A!8))))) | (~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_C_7(B!11, A!8)))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(431,plain,
% 0.15/0.50 (~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_C_7(B!11, A!8))))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[430, 429, 428])).
% 0.15/0.50 tff(432,plain,
% 0.15/0.50 (((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_C_7(B!11, A!8))))) | (~((~g_true_only(A!8, B!11)) | (~(h_both(A!8, tptp_fun_C_7(B!11, A!8)) | h_false_only(A!8, tptp_fun_C_7(B!11, A!8))))))) | ((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_C_7(B!11, A!8))))),
% 0.15/0.50 inference(tautology,[status(thm)],[])).
% 0.15/0.50 tff(433,plain,
% 0.15/0.50 ((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_C_7(B!11, A!8))))) | (~((~g_true_only(A!8, B!11)) | (~(h_both(A!8, tptp_fun_C_7(B!11, A!8)) | h_false_only(A!8, tptp_fun_C_7(B!11, A!8))))))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[432, 431])).
% 0.15/0.50 tff(434,assumption,(![A: $i, B: $i] : (~((~((~g_both(A, B)) | (~h_false_only(A, tptp_fun_C_7(B, A))))) | (~((~g_true_only(A, B)) | (~(h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A))))))))), introduced(assumption)).
% 0.15/0.50 tff(435,plain,
% 0.15/0.50 ((~![A: $i, B: $i] : (~((~((~g_both(A, B)) | (~h_false_only(A, tptp_fun_C_7(B, A))))) | (~((~g_true_only(A, B)) | (~(h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A))))))))) | (~((~((~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_C_7(B!11, A!8))))) | (~((~g_true_only(A!8, B!11)) | (~(h_both(A!8, tptp_fun_C_7(B!11, A!8)) | h_false_only(A!8, tptp_fun_C_7(B!11, A!8))))))))),
% 0.15/0.50 inference(quant_inst,[status(thm)],[])).
% 0.15/0.50 tff(436,plain,
% 0.15/0.50 ($false),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[435, 434, 433])).
% 0.15/0.50 tff(437,plain,((~![A: $i, B: $i] : (~((~((~g_both(A, B)) | (~h_false_only(A, tptp_fun_C_7(B, A))))) | (~((~g_true_only(A, B)) | (~(h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A))))))))) | (~g_both(A!8, B!11)) | (~h_false_only(A!8, tptp_fun_C_7(B!11, A!8)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.50 tff(438,plain,
% 0.15/0.50 (~![A: $i, B: $i] : (~((~((~g_both(A, B)) | (~h_false_only(A, tptp_fun_C_7(B, A))))) | (~((~g_true_only(A, B)) | (~(h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A))))))))),
% 0.15/0.50 inference(unit_resolution,[status(thm)],[437, 427, 425])).
% 0.15/0.50 tff(439,plain,
% 0.15/0.50 ((![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))) | ![A: $i, B: $i] : (~((~((~g_both(A, B)) | (~h_false_only(A, tptp_fun_C_7(B, A))))) | (~((~g_true_only(A, B)) | (~(h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A))))))))) <=> (![A: $i, B: $i] : (~((~((~g_both(A, B)) | (~h_false_only(A, tptp_fun_C_7(B, A))))) | (~((~g_true_only(A, B)) | (~(h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A)))))))) | ![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(440,plain,
% 0.15/0.50 ((![A: $i] : (~((~(![B: $i] : (~g_true_only(A, B)) | (~((~(![B: $i] : (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | ![B: $i] : (~g_both(A, B)) | g_true_only(A, tptp_fun_B_6(A)))))) | ![A: $i, B: $i] : (~((~((~g_both(A, B)) | (~h_false_only(A, tptp_fun_C_7(B, A))))) | (~((~g_true_only(A, B)) | (~(h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A))))))))) <=> (![A: $i, B_17: $i, B_16: $i, B: $i] : (~((~((~g_true_only(A, B)) | (~((~((~h_both(A, B_16)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | (~g_both(A, B_17)) | g_true_only(A, tptp_fun_B_6(A)))))) | ![A: $i, B: $i] : (~((~((~g_both(A, B)) | (~h_false_only(A, tptp_fun_C_7(B, A))))) | (~((~g_true_only(A, B)) | (~(h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A)))))))))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(441,plain,
% 0.15/0.50 ((![A: $i] : ((![B: $i] : (~g_true_only(A, B)) | ((![B: $i] : (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A))) & (~h_false_only(A, tptp_fun_B_5(A))))) & ((~h_false_only(A, tptp_fun_B_5(A))) | ![B: $i] : (~g_both(A, B)) | g_true_only(A, tptp_fun_B_6(A)))) | ![A: $i, B: $i] : (~((g_both(A, B) & h_false_only(A, tptp_fun_C_7(B, A))) | (g_true_only(A, B) & (h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A))))))) <=> (![A: $i] : (~((~(![B: $i] : (~g_true_only(A, B)) | (~((~(![B: $i] : (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A)))) | h_false_only(A, tptp_fun_B_5(A)))))) | (~((~h_false_only(A, tptp_fun_B_5(A))) | ![B: $i] : (~g_both(A, B)) | g_true_only(A, tptp_fun_B_6(A)))))) | ![A: $i, B: $i] : (~((~((~g_both(A, B)) | (~h_false_only(A, tptp_fun_C_7(B, A))))) | (~((~g_true_only(A, B)) | (~(h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A)))))))))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(442,plain,
% 0.15/0.50 ((![A: $i] : ((![B: $i] : (~g_true_only(A, B)) | ((![B: $i] : (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A))) & (~h_false_only(A, tptp_fun_B_5(A))))) & (![B: $i] : (~g_both(A, B)) | g_true_only(A, tptp_fun_B_6(A)) | (~h_false_only(A, tptp_fun_B_5(A))))) | ![A: $i, B: $i] : (~((g_both(A, B) & h_false_only(A, tptp_fun_C_7(B, A))) | (g_true_only(A, B) & (h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A))))))) <=> (![A: $i] : ((![B: $i] : (~g_true_only(A, B)) | ((![B: $i] : (~h_both(A, B)) | h_true_only(A, tptp_fun_B_4(A))) & (~h_false_only(A, tptp_fun_B_5(A))))) & ((~h_false_only(A, tptp_fun_B_5(A))) | ![B: $i] : (~g_both(A, B)) | g_true_only(A, tptp_fun_B_6(A)))) | ![A: $i, B: $i] : (~((g_both(A, B) & h_false_only(A, tptp_fun_C_7(B, A))) | (g_true_only(A, B) & (h_both(A, tptp_fun_C_7(B, A)) | h_false_only(A, tptp_fun_C_7(B, A)))))))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(443,plain,
% 0.15/0.50 ((?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C))))) <=> (?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C)))))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(444,plain,
% 0.15/0.50 ((~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C)))))) <=> (~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C))))))),
% 0.15/0.50 inference(monotonicity,[status(thm)],[443])).
% 0.15/0.50 tff(445,plain,
% 0.15/0.50 ((~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C)))))) <=> (~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C))))))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(446,plain,
% 0.15/0.50 ((~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | ((?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B))) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C))) | (g_both(A, B) & h_false_only(A, C))))) <=> (~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C))))))),
% 0.15/0.50 inference(rewrite,[status(thm)],[])).
% 0.15/0.50 tff(447,axiom,(~(((![A: $i] : (![B: $i] : g_false_only(A, B) | ?[B: $i] : h_true_only(A, B)) & ![A: $i, B: $i] : ?[C: $i] : (g_false_only(A, B) | h_true_only(A, C))) | (?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | ((?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B))) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C))) | (g_both(A, B) & h_false_only(A, C))))) | (((?[A: $i] : (((?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B))) & ?[B: $i] : h_both(A, B)) & (~?[B: $i] : h_true_only(A, B))) & (~?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | ((?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B))) & ![B: $i] : h_false_only(A, B))))) & ?[A: $i] : (?[B: $i] : (?[C: $i] : (g_both(A, B) & h_both(A, C)) & (~?[C: $i] : (g_false_only(A, B) | h_true_only(A, C)))) & (~?[B: $i] : ![C: $i] : ((g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C))) | (g_both(A, B) & h_false_only(A, C)))))) & (~?[A: $i, B: $i] : ![C: $i] : ((g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C))) | (g_both(A, B) & h_false_only(A, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nc5')).
% 0.15/0.50 tff(448,plain,
% 0.15/0.50 (~((![A: $i] : (![B: $i] : g_false_only(A, B) | ?[B: $i] : h_true_only(A, B)) & ![A: $i, B: $i] : ?[C: $i] : (g_false_only(A, B) | h_true_only(A, C))) | (?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | ((?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B))) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C))) | (g_both(A, B) & h_false_only(A, C)))))),
% 0.15/0.50 inference(or_elim,[status(thm)],[447])).
% 0.15/0.50 tff(449,plain,
% 0.15/0.50 (~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | ((?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B))) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C))) | (g_both(A, B) & h_false_only(A, C))))),
% 0.15/0.52 inference(or_elim,[status(thm)],[448])).
% 0.15/0.52 tff(450,plain,
% 0.15/0.52 (~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C)))))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[449, 446])).
% 0.15/0.52 tff(451,plain,
% 0.15/0.52 (~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C)))))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[450, 444])).
% 0.15/0.52 tff(452,plain,
% 0.15/0.52 (~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C)))))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[451, 445])).
% 0.15/0.52 tff(453,plain,
% 0.15/0.52 (~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C)))))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[452, 444])).
% 0.15/0.52 tff(454,plain,
% 0.15/0.52 (~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C)))))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[453, 444])).
% 0.15/0.52 tff(455,plain,
% 0.15/0.52 (~(?[A: $i] : ((?[B: $i] : g_true_only(A, B) & ((?[B: $i] : h_both(A, B) & (~?[B: $i] : h_true_only(A, B))) | ![B: $i] : h_false_only(A, B))) | (?[B: $i] : g_both(A, B) & (~?[B: $i] : g_true_only(A, B)) & ![B: $i] : h_false_only(A, B))) & ?[A: $i, B: $i] : ![C: $i] : ((g_both(A, B) & h_false_only(A, C)) | (g_true_only(A, B) & (h_both(A, C) | h_false_only(A, C)))))),
% 0.15/0.52 inference(modus_ponens,[status(thm)],[454, 444])).
% 0.15/0.52 unexpected number of arguments: (let ((a!1 (lambda ((A $i))
% 0.15/0.52 (let ((a!1 (lambda ((B $i))
% 0.15/0.52 (refl (~ (not (g_true_only A B))
% 0.15/0.52 (not (g_true_only A B))))))
% 0.15/0.52 (a!2 (exists ((B $i)) (g_true_only A B)))
% 0.15/0.52 (a!3 (forall ((B $i)) (not (g_true_only A B))))
% 0.15/0.52 (a!4 (lambda ((B $i))
% 0.15/0.52 (refl (~ (not (h_both A B)) (not (h_both A B))))))
% 0.15/0.52 (a!5 (exists ((B $i)) (h_both A B)))
% 0.15/0.52 (a!6 (forall ((B $i)) (not (h_both A B))))
% 0.15/0.52 (a!7 (exists ((B $i)) (h_true_only A B)))
% 0.15/0.52 (a!12 (forall ((B $i)) (h_false_only A B)))
% 0.15/0.52 (a!18 (lambda ((B $i))
% 0.15/0.52 (refl (~ (not (g_both A B)) (not (g_both A B))))))
% 0.15/0.52 (a!19 (exists ((B $i)) (g_both A B)))
% 0.15/0.52 (a!20 (forall ((B $i)) (not (g_both A B)))))
% 0.15/0.52 (let ((a!8 (sk (~ a!7 (h_true_only A (B!4 A)))))
% 0.15/0.52 (a!10 (~ (not (and a!5 (not a!7)))
% 0.15/0.52 (or a!6 (h_true_only A (B!4 A)))))
% 0.15/0.52 (a!13 (~ (not a!12) (not (h_false_only A (B!5 A)))))
% 0.15/0.52 (a!14 (not (or (and a!5 (not a!7)) a!12)))
% 0.15/0.52 (a!15 (and (or a!6 (h_true_only A (B!4 A)))
% 0.15/0.52 (not (h_false_only A (B!5 A)))))
% 0.15/0.52 (a!16 (and a!2 (or (and a!5 (not a!7)) a!12)))
% 0.15/0.52 (a!21 (sk (~ a!2 (g_true_only A (B!6 A)))))
% 0.15/0.52 (a!23 (or a!20
% 0.15/0.52 (g_true_only A (B!6 A))
% 0.15/0.52 (not (h_false_only A (B!5 A))))))
% 0.15/0.52 (let ((a!9 (nnf-neg a!8
% 0.15/0.52 (~ (not (not a!7)) (h_true_only A (B!4 A)))))
% 0.15/0.52 (a!22 (nnf-neg a!21
% 0.15/0.52 (~ (not (not a!2)) (g_true_only A (B!6 A)))))
% 0.15/0.52 (a!24 (~ (not (and a!19 (not a!2) a!12)) a!23))
% 0.15/0.52 (a!26 (not (or a!16 (and a!19 (not a!2) a!12)))))
% 0.15/0.52 (let ((a!11 (nnf-neg (nnf-neg (proof-bind a!4) (~ (not a!5) a!6))
% 0.15/0.52 a!9
% 0.15/0.52 a!10))
% 0.15/0.52 (a!25 (nnf-neg (nnf-neg (proof-bind a!18)
% 0.15/0.52 (~ (not a!19) a!20))
% 0.15/0.52 a!22
% 0.15/0.52 (sk a!13)
% 0.15/0.52 a!24)))
% 0.15/0.52 (let ((a!17 (nnf-neg (nnf-neg (proof-bind a!1) (~ (not a!2) a!3))
% 0.15/0.52 (nnf-neg a!11 (sk a!13) (~ a!14 a!15))
% 0.15/0.52 (~ (not a!16) (or a!3 a!15)))))
% 0.15/0.52 (nnf-neg a!17 a!25 (~ a!26 (and (or a!3 a!15) a!23))))))))))
% 0.15/0.52 (a!2 (exists ((A $i))
% 0.15/0.52 (let ((a!1 (exists ((B $i)) (g_true_only A B)))
% 0.15/0.52 (a!2 (exists ((B $i)) (h_both A B)))
% 0.15/0.52 (a!3 (exists ((B $i)) (h_true_only A B)))
% 0.15/0.52 (a!4 (forall ((B $i)) (h_false_only A B)))
% 0.15/0.52 (a!6 (exists ((B $i)) (g_both A B))))
% 0.15/0.52 (let ((a!5 (and a!1 (or (and a!2 (not a!3)) a!4))))
% 0.15/0.52 (or a!5 (and a!6 (not a!1) a!4))))))
% 0.15/0.52 (a!3 (forall ((A $i))
% 0.15/0.52 (let ((a!1 (forall ((B $i)) (not (g_true_only A B))))
% 0.15/0.52 (a!2 (forall ((B $i)) (not (h_both A B))))
% 0.15/0.52 (a!4 (forall ((B $i)) (not (g_both A B)))))
% 0.15/0.52 (let ((a!3 (and (or a!2 (h_true_only A (B!4 A)))
% 0.15/0.52 (not (h_false_only A (B!5 A)))))
% 0.15/0.52 (a!5 (or a!4
% 0.15/0.52 (g_true_only A (B!6 A))
% 0.15/0.52 (not (h_false_only A (B!5 A))))))
% 0.15/0.52 (and (or a!1 a!3) a!5)))))
% 0.15/0.52 (a!4 (lambda ((A $i) (B $i))
% 0.15/0.52 (let ((a!1 (forall ((C $i))
% 0.15/0.52 (or (and (g_both A B) (h_false_only A C))
% 0.15/0.52 (and (g_true_only A B)
% 0.15/0.52 (or (h_both A C) (h_false_only A C))))))
% 0.15/0.52 (a!2 (and (g_true_only A B)
% 0.15/0.52 (or (h_both A (C!7 B A))
% 0.15/0.52 (h_false_only A (C!7 B A))))))
% 0.15/0.52 (let ((a!3 (or (and (g_both A B) (h_false_only A (C!7 B A))) a!2)))
% 0.15/0.52 (sk (~ (not a!1) (not a!3)))))))
% 0.15/0.52 (a!5 (exists ((A $i) (B $i))
% 0.15/0.52 (forall ((C $i))
% 0.15/0.52 (or (and (g_both A B) (h_false_only A C))
% 0.15/0.52 (and (g_true_only A B) (or (h_both A C) (h_false_only A C)))))))
% 0.15/0.52 (a!6 (forall ((A $i) (B $i))
% 0.15/0.52 (let ((a!1 (and (g_true_only A B)
% 0.15/0.52 (or (h_both A (C!7 B A))
% 0.15/0.52 (h_false_only A (C!7 B A))))))
% 0.15/0.52 (let ((a!2 (or (and (g_both A B) (h_false_only A (C!7 B A))) a!1)))
% 0.15/0.52 (not a!2))))))
% 0.15/0.52 (nnf-neg (nnf-neg (proof-bind a!1) (~ (not a!2) a!3))
% 0.15/0.52 (nnf-neg (proof-bind a!4) (~ (not a!5) a!6))
% 0.15/0.52 (~ (not (and a!2 a!5)) (or a!3 a!6))))
% 0.15/0.52 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------