TSTP Solution File: ITP392_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 04:18:56 EDT 2022
% Result : Theorem 0.42s 0.62s
% Output : Proof 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 07:33:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.42/0.62 % SZS status Theorem
% 0.42/0.62 % SZS output start Proof
% 0.42/0.62 tff(tptp_fun__comp_a__type, type, (
% 0.42/0.62 tptp_fun__comp_a_: ( 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$' * 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$' ) > 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$')).
% 0.42/0.62 tff(tptp_fun__assoc___type, type, (
% 0.42/0.62 tptp_fun__assoc__: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$')).
% 0.42/0.62 tff(tptp_fun__inv_into_a__type, type, (
% 0.42/0.62 tptp_fun__inv_into_a_: ( 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_set$' * 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$' ) > 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$')).
% 0.42/0.62 tff(tptp_fun__collect_c__type, type, (
% 0.42/0.62 tptp_fun__collect_c_: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_bool_fun$' > 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_set$')).
% 0.42/0.62 tff(tptp_fun__top_h__type, type, (
% 0.42/0.62 tptp_fun__top_h_: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_bool_fun$')).
% 0.42/0.62 tff(tptp_fun__comp_b__type, type, (
% 0.42/0.62 tptp_fun__comp_b_: ( 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$' * 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$' ) > 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$')).
% 0.42/0.62 tff(tptp_fun__bij_betw___type, type, (
% 0.42/0.62 tptp_fun__bij_betw__: ( 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$' * 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_set$' * 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_set$' ) > $o)).
% 0.42/0.62 tff(tptp_fun__collect_d__type, type, (
% 0.42/0.62 tptp_fun__collect_d_: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$' > 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_set$')).
% 0.42/0.62 tff(tptp_fun__top_f__type, type, (
% 0.42/0.62 tptp_fun__top_f_: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$')).
% 0.42/0.62 tff(tptp_fun__top_a__type, type, (
% 0.42/0.62 tptp_fun__top_a_: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_set$')).
% 0.42/0.62 tff(tptp_fun__top___type, type, (
% 0.42/0.62 tptp_fun__top__: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_set$')).
% 0.42/0.62 tff(tptp_fun__id_a__type, type, (
% 0.42/0.62 tptp_fun__id_a_: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$')).
% 0.42/0.62 tff(tptp_fun__id___type, type, (
% 0.42/0.62 tptp_fun__id__: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$')).
% 0.42/0.62 tff(1,plain,
% 0.42/0.62 (^[A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : refl((tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)))) <=> (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)))))),
% 0.42/0.62 inference(bind,[status(th)],[])).
% 0.42/0.62 tff(2,plain,
% 0.42/0.62 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)))) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))),
% 0.42/0.62 inference(quant_intro,[status(thm)],[1])).
% 0.42/0.62 tff(3,plain,
% 0.42/0.62 (^[A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) <=> (~((~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))))), ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))) <=> (~(~((~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))))))), rewrite((~(~((~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))))) <=> ((~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))))), ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))) <=> ((~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))))), (((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))) | tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|))) <=> (((~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))) | tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|))))), rewrite((((~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))) | tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|))) <=> (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))), (((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))) | tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|))) <=> (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))))),
% 0.42/0.62 inference(bind,[status(th)],[])).
% 0.42/0.62 tff(4,plain,
% 0.42/0.62 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))) | tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|))) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))),
% 0.42/0.62 inference(quant_intro,[status(thm)],[3])).
% 0.42/0.62 tff(5,plain,
% 0.42/0.62 (^[A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : rewrite(((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = |'id$a'|))) | tptp_fun__bij_betw__(A__questionmark_v1, |'top$'|, |'top$a'|)) <=> ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))) | tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|))))),
% 0.42/0.62 inference(bind,[status(th)],[])).
% 0.42/0.62 tff(6,plain,
% 0.42/0.62 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = |'id$a'|))) | tptp_fun__bij_betw__(A__questionmark_v1, |'top$'|, |'top$a'|)) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))) | tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)))),
% 0.42/0.62 inference(quant_intro,[status(thm)],[5])).
% 0.42/0.62 tff(7,plain,
% 0.42/0.62 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = |'id$a'|))) | tptp_fun__bij_betw__(A__questionmark_v1, |'top$'|, |'top$a'|)) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = |'id$a'|))) | tptp_fun__bij_betw__(A__questionmark_v1, |'top$'|, |'top$a'|))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(8,plain,
% 0.42/0.62 (^[A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : rewrite((((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = |'id$a'|)) => tptp_fun__bij_betw__(A__questionmark_v1, |'top$'|, |'top$a'|)) <=> ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = |'id$a'|))) | tptp_fun__bij_betw__(A__questionmark_v1, |'top$'|, |'top$a'|)))),
% 0.42/0.62 inference(bind,[status(th)],[])).
% 0.42/0.62 tff(9,plain,
% 0.42/0.62 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = |'id$a'|)) => tptp_fun__bij_betw__(A__questionmark_v1, |'top$'|, |'top$a'|)) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = |'id$a'|))) | tptp_fun__bij_betw__(A__questionmark_v1, |'top$'|, |'top$a'|))),
% 0.42/0.62 inference(quant_intro,[status(thm)],[8])).
% 0.42/0.62 tff(10,axiom,(![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = |'id$a'|)) => tptp_fun__bij_betw__(A__questionmark_v1, |'top$'|, |'top$a'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom5')).
% 0.42/0.62 tff(11,plain,
% 0.42/0.62 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = |'id$a'|))) | tptp_fun__bij_betw__(A__questionmark_v1, |'top$'|, |'top$a'|))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.42/0.62 tff(12,plain,
% 0.42/0.62 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = |'id$'|) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = |'id$a'|))) | tptp_fun__bij_betw__(A__questionmark_v1, |'top$'|, |'top$a'|))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.42/0.62 tff(13,plain,
% 0.42/0.62 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))) | tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.42/0.62 tff(14,plain,(
% 0.42/0.62 ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : ((~((tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)) & (tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))))) | tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)))),
% 0.42/0.62 inference(skolemize,[status(sab)],[13])).
% 0.42/0.62 tff(15,plain,
% 0.42/0.62 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.42/0.62 tff(16,plain,
% 0.42/0.62 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.42/0.62 tff(17,plain,
% 0.42/0.62 ((~tptp_fun__bij_betw__(|'assoc$'|, |'top$'|, |'top$a'|)) <=> (~tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(18,plain,
% 0.42/0.62 ((~tptp_fun__bij_betw__(|'assoc$'|, |'top$'|, |'top$a'|)) <=> (~tptp_fun__bij_betw__(|'assoc$'|, |'top$'|, |'top$a'|))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(19,axiom,(~tptp_fun__bij_betw__(|'assoc$'|, |'top$'|, |'top$a'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture3')).
% 0.42/0.62 tff(20,plain,
% 0.42/0.62 (~tptp_fun__bij_betw__(|'assoc$'|, |'top$'|, |'top$a'|)),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.42/0.62 tff(21,plain,
% 0.42/0.62 (~tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.42/0.62 tff(22,plain,
% 0.42/0.62 (((~![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))) | tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|))) <=> ((~![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))) | tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)))),
% 0.42/0.63 inference(rewrite,[status(thm)],[])).
% 0.42/0.63 tff(23,plain,
% 0.42/0.63 ((tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | $false | $false) <=> tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|))),
% 0.42/0.63 inference(rewrite,[status(thm)],[])).
% 0.42/0.63 tff(24,plain,
% 0.42/0.63 ((~$true) <=> $false),
% 0.42/0.63 inference(rewrite,[status(thm)],[])).
% 0.42/0.63 tff(25,plain,
% 0.42/0.63 ((tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)) <=> $true),
% 0.42/0.63 inference(rewrite,[status(thm)],[])).
% 0.42/0.63 tff(26,plain,
% 0.42/0.63 ((~(tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))) <=> (~$true)),
% 0.42/0.63 inference(monotonicity,[status(thm)],[25])).
% 0.42/0.63 tff(27,plain,
% 0.42/0.63 ((~(tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))) <=> $false),
% 0.42/0.63 inference(transitivity,[status(thm)],[26, 24])).
% 0.42/0.63 tff(28,plain,
% 0.42/0.63 ((tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|))) <=> $true),
% 0.42/0.63 inference(rewrite,[status(thm)],[])).
% 0.42/0.63 tff(29,plain,
% 0.42/0.63 ((~(tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) <=> (~$true)),
% 0.42/0.63 inference(monotonicity,[status(thm)],[28])).
% 0.42/0.63 tff(30,plain,
% 0.42/0.63 ((~(tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) <=> $false),
% 0.42/0.63 inference(transitivity,[status(thm)],[29, 24])).
% 0.42/0.63 tff(31,plain,
% 0.42/0.63 ((tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)))) <=> (tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | $false | $false)),
% 0.42/0.63 inference(monotonicity,[status(thm)],[30, 27])).
% 0.42/0.63 tff(32,plain,
% 0.42/0.63 ((tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|)))) <=> tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|))),
% 0.42/0.63 inference(transitivity,[status(thm)],[31, 23])).
% 0.42/0.63 tff(33,plain,
% 0.42/0.63 (((~![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))) | (tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))) <=> ((~![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))) | tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)))),
% 0.42/0.63 inference(monotonicity,[status(thm)],[32])).
% 0.42/0.63 tff(34,plain,
% 0.42/0.63 (((~![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))) | (tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))) <=> ((~![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))) | tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)))),
% 0.42/0.63 inference(transitivity,[status(thm)],[33, 22])).
% 0.42/0.63 tff(35,plain,
% 0.42/0.63 ((~![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))) | (tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))),
% 0.54/0.67 inference(quant_inst,[status(thm)],[])).
% 0.54/0.67 tff(36,plain,
% 0.54/0.67 ((~![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_a_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_fun$', A__questionmark_v1: 'A_b_c_prod_prod_ell2_a_b_c_prod_prod_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$'] : (tptp_fun__bij_betw__(A__questionmark_v1, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|)) | (~(tptp_fun__comp_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__comp_b_(|'assoc$'|, tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|)))) | (~(tptp_fun__comp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__comp_a_(tptp_fun__inv_into_a_(tptp_fun__collect_c_(|'top$h'|), |'assoc$'|), |'assoc$'|))))) | tptp_fun__bij_betw__(|'assoc$'|, tptp_fun__collect_c_(|'top$h'|), tptp_fun__collect_d_(|'top$f'|))),
% 0.54/0.67 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.54/0.67 tff(37,plain,
% 0.54/0.67 ($false),
% 0.54/0.67 inference(unit_resolution,[status(thm)],[36, 21, 16])).
% 0.54/0.67 % SZS output end Proof
%------------------------------------------------------------------------------