TSTP Solution File: ITP390_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 0.56s 0.65s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % 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 07:32:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.56/0.65 % SZS status Theorem
% 0.56/0.65 % SZS output start Proof
% 0.56/0.65 tff(tptp_fun__fun_app_s__type, type, (
% 0.56/0.65 tptp_fun__fun_app_s_: ( 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_d_ell2_d_ell2_cblinfun_fun$' * 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$' ) > 'D_ell2_d_ell2_cblinfun$')).
% 0.56/0.65 tff(tptp_fun__x___type, type, (
% 0.56/0.65 tptp_fun__x__: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$')).
% 0.56/0.65 tff(tptp_fun__g___type, type, (
% 0.56/0.65 tptp_fun__g__: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_d_ell2_d_ell2_cblinfun_fun$')).
% 0.56/0.65 tff(tptp_fun__f___type, type, (
% 0.56/0.65 tptp_fun__f__: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_d_ell2_d_ell2_cblinfun_fun$')).
% 0.56/0.65 tff(tptp_fun__fun_app_c__type, type, (
% 0.56/0.65 tptp_fun__fun_app_c_: ( 'C_ell2_c_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun$' ) > 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$')).
% 0.56/0.65 tff(tptp_fun_A__questionmark_v3_11_type, type, (
% 0.56/0.65 tptp_fun_A__questionmark_v3_11: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$' > 'C_ell2_c_ell2_cblinfun$')).
% 0.56/0.65 tff(tptp_fun__fun_app_d__type, type, (
% 0.56/0.65 tptp_fun__fun_app_d_: ( 'A_b_prod_ell2_a_b_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun_fun$' * 'A_b_prod_ell2_a_b_prod_ell2_cblinfun$' ) > 'C_ell2_c_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun$')).
% 0.56/0.65 tff(tptp_fun__fun_app_h__type, type, (
% 0.56/0.65 tptp_fun__fun_app_h_: ( 'B_ell2_b_ell2_cblinfun_a_b_prod_ell2_a_b_prod_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'A_b_prod_ell2_a_b_prod_ell2_cblinfun$')).
% 0.56/0.65 tff(tptp_fun_A__questionmark_v2_12_type, type, (
% 0.56/0.65 tptp_fun_A__questionmark_v2_12: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$')).
% 0.56/0.65 tff(tptp_fun__fun_app_i__type, type, (
% 0.56/0.65 tptp_fun__fun_app_i_: ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_a_b_prod_ell2_a_b_prod_ell2_cblinfun_fun_fun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'B_ell2_b_ell2_cblinfun_a_b_prod_ell2_a_b_prod_ell2_cblinfun_fun$')).
% 0.56/0.65 tff(tptp_fun_A__questionmark_v1_13_type, type, (
% 0.56/0.65 tptp_fun_A__questionmark_v1_13: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun$')).
% 0.56/0.65 tff(tptp_fun__tensor_op_c__type, type, (
% 0.56/0.65 tptp_fun__tensor_op_c_: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_a_b_prod_ell2_a_b_prod_ell2_cblinfun_fun_fun$')).
% 0.56/0.65 tff(tptp_fun__tensor_op_a__type, type, (
% 0.56/0.65 tptp_fun__tensor_op_a_: 'A_b_prod_ell2_a_b_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_a_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_fun_fun$')).
% 0.56/0.65 tff(tptp_fun__fun_app_k__type, type, (
% 0.56/0.65 tptp_fun__fun_app_k_: ( 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$' * 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$' ) > $o)).
% 0.56/0.65 tff(tptp_fun__uu___type, type, (
% 0.56/0.65 tptp_fun__uu__: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$')).
% 0.56/0.65 tff(tptp_fun__member_a__type, type, (
% 0.56/0.65 tptp_fun__member_a_: ( 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$' * 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_set$' ) > $o)).
% 0.56/0.65 tff(tptp_fun__collect___type, type, (
% 0.56/0.65 tptp_fun__collect__: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$' > 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_set$')).
% 0.56/0.65 tff(1,plain,
% 0.56/0.65 (^[A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : refl((~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))))) <=> (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))))))),
% 0.56/0.65 inference(bind,[status(th)],[])).
% 0.56/0.65 tff(2,plain,
% 0.56/0.65 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))))) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))))),
% 0.56/0.65 inference(quant_intro,[status(thm)],[1])).
% 0.56/0.65 tff(3,plain,
% 0.56/0.65 (^[A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : rewrite((~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))))) <=> (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))))))),
% 0.56/0.65 inference(bind,[status(th)],[])).
% 0.56/0.65 tff(4,plain,
% 0.56/0.65 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))))) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))))),
% 0.56/0.65 inference(quant_intro,[status(thm)],[3])).
% 0.56/0.65 tff(5,plain,
% 0.56/0.65 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))))) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))))),
% 0.56/0.65 inference(transitivity,[status(thm)],[4, 2])).
% 0.56/0.65 tff(6,plain,
% 0.56/0.65 (^[A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : trans(monotonicity(rewrite((tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))) <=> (tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))), ((((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0)))) & (tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))) <=> (((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0)))) & (tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))))), rewrite((((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0)))) & (tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))) <=> (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))))), ((((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0)))) & (tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))) <=> (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))))))),
% 0.56/0.66 inference(bind,[status(th)],[])).
% 0.56/0.66 tff(7,plain,
% 0.56/0.66 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0)))) & (tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))))),
% 0.56/0.66 inference(quant_intro,[status(thm)],[6])).
% 0.56/0.66 tff(8,plain,
% 0.56/0.66 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) <=> ?[A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) <=> ?[A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))),
% 0.56/0.66 inference(rewrite,[status(thm)],[])).
% 0.56/0.66 tff(9,axiom,(![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) <=> ?[A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom9')).
% 0.56/0.66 tff(10,plain,
% 0.56/0.66 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) <=> ?[A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.56/0.66 tff(11,plain,(
% 0.56/0.66 ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0)))) & (tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))),
% 0.56/0.66 inference(skolemize,[status(sab)],[10])).
% 0.56/0.66 tff(12,plain,
% 0.56/0.66 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.56/0.66 tff(13,plain,
% 0.56/0.66 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.56/0.66 tff(14,plain,
% 0.56/0.66 ((~![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] : (~((~((~tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0)) | (A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(A__questionmark_v0)), tptp_fun_A__questionmark_v2_12(A__questionmark_v0))), tptp_fun_A__questionmark_v3_11(A__questionmark_v0))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, A__questionmark_v0) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(A__questionmark_v0 = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))))) | (~((~((~tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)) | (|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, |'x$'|) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))))),
% 0.56/0.66 inference(quant_inst,[status(thm)],[])).
% 0.56/0.66 tff(15,plain,
% 0.56/0.66 (~((~((~tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)) | (|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, |'x$'|) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3))))))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.56/0.66 tff(16,plain,
% 0.56/0.66 (((~((~tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)) | (|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|))))) | (~(tptp_fun__fun_app_k_(|'uu$'|, |'x$'|) | ![A__questionmark_v1: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v2: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v3: 'C_ell2_c_ell2_cblinfun$'] : (~(|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v1), A__questionmark_v2)), A__questionmark_v3)))))) | ((~tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)) | (|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|))))),
% 0.56/0.66 inference(tautology,[status(thm)],[])).
% 0.56/0.66 tff(17,plain,
% 0.56/0.66 ((~tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)) | (|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|)))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.56/0.66 tff(18,plain,
% 0.56/0.66 (^[A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$', A__questionmark_v1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] : refl((tptp_fun__member_a_(A__questionmark_v0, tptp_fun__collect__(A__questionmark_v1)) <=> tptp_fun__fun_app_k_(A__questionmark_v1, A__questionmark_v0)) <=> (tptp_fun__member_a_(A__questionmark_v0, tptp_fun__collect__(A__questionmark_v1)) <=> tptp_fun__fun_app_k_(A__questionmark_v1, A__questionmark_v0)))),
% 0.56/0.66 inference(bind,[status(th)],[])).
% 0.56/0.66 tff(19,plain,
% 0.56/0.66 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$', A__questionmark_v1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] : (tptp_fun__member_a_(A__questionmark_v0, tptp_fun__collect__(A__questionmark_v1)) <=> tptp_fun__fun_app_k_(A__questionmark_v1, A__questionmark_v0)) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$', A__questionmark_v1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] : (tptp_fun__member_a_(A__questionmark_v0, tptp_fun__collect__(A__questionmark_v1)) <=> tptp_fun__fun_app_k_(A__questionmark_v1, A__questionmark_v0))),
% 0.56/0.66 inference(quant_intro,[status(thm)],[18])).
% 0.56/0.66 tff(20,plain,
% 0.56/0.66 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$', A__questionmark_v1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] : (tptp_fun__member_a_(A__questionmark_v0, tptp_fun__collect__(A__questionmark_v1)) <=> tptp_fun__fun_app_k_(A__questionmark_v1, A__questionmark_v0)) <=> ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$', A__questionmark_v1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] : (tptp_fun__member_a_(A__questionmark_v0, tptp_fun__collect__(A__questionmark_v1)) <=> tptp_fun__fun_app_k_(A__questionmark_v1, A__questionmark_v0))),
% 0.56/0.66 inference(rewrite,[status(thm)],[])).
% 0.56/0.66 tff(21,axiom,(![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$', A__questionmark_v1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] : (tptp_fun__member_a_(A__questionmark_v0, tptp_fun__collect__(A__questionmark_v1)) <=> tptp_fun__fun_app_k_(A__questionmark_v1, A__questionmark_v0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom260')).
% 0.56/0.66 tff(22,plain,
% 0.56/0.66 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$', A__questionmark_v1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] : (tptp_fun__member_a_(A__questionmark_v0, tptp_fun__collect__(A__questionmark_v1)) <=> tptp_fun__fun_app_k_(A__questionmark_v1, A__questionmark_v0))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.56/0.66 tff(23,plain,(
% 0.56/0.66 ![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$', A__questionmark_v1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] : (tptp_fun__member_a_(A__questionmark_v0, tptp_fun__collect__(A__questionmark_v1)) <=> tptp_fun__fun_app_k_(A__questionmark_v1, A__questionmark_v0))),
% 0.56/0.66 inference(skolemize,[status(sab)],[22])).
% 0.56/0.66 tff(24,plain,
% 0.56/0.66 (![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$', A__questionmark_v1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] : (tptp_fun__member_a_(A__questionmark_v0, tptp_fun__collect__(A__questionmark_v1)) <=> tptp_fun__fun_app_k_(A__questionmark_v1, A__questionmark_v0))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.56/0.66 tff(25,plain,
% 0.56/0.66 ((~![A__questionmark_v0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$', A__questionmark_v1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] : (tptp_fun__member_a_(A__questionmark_v0, tptp_fun__collect__(A__questionmark_v1)) <=> tptp_fun__fun_app_k_(A__questionmark_v1, A__questionmark_v0))) | (tptp_fun__member_a_(|'x$'|, tptp_fun__collect__(|'uu$'|)) <=> tptp_fun__fun_app_k_(|'uu$'|, |'x$'|))),
% 0.56/0.66 inference(quant_inst,[status(thm)],[])).
% 0.56/0.66 tff(26,plain,
% 0.56/0.66 (tptp_fun__member_a_(|'x$'|, tptp_fun__collect__(|'uu$'|)) <=> tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.56/0.66 tff(27,plain,
% 0.56/0.66 (tptp_fun__member_a_(|'x$'|, tptp_fun__collect__(|'uu$'|)) <=> tptp_fun__member_a_(|'x$'|, tptp_fun__collect__(|'uu$'|))),
% 0.56/0.66 inference(rewrite,[status(thm)],[])).
% 0.56/0.66 tff(28,axiom,(tptp_fun__member_a_(|'x$'|, tptp_fun__collect__(|'uu$'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis100')).
% 0.56/0.66 tff(29,plain,
% 0.56/0.66 (tptp_fun__member_a_(|'x$'|, tptp_fun__collect__(|'uu$'|))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.56/0.66 tff(30,plain,
% 0.56/0.66 ((~(tptp_fun__member_a_(|'x$'|, tptp_fun__collect__(|'uu$'|)) <=> tptp_fun__fun_app_k_(|'uu$'|, |'x$'|))) | (~tptp_fun__member_a_(|'x$'|, tptp_fun__collect__(|'uu$'|))) | tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)),
% 0.56/0.66 inference(tautology,[status(thm)],[])).
% 0.56/0.66 tff(31,plain,
% 0.56/0.66 ((~(tptp_fun__member_a_(|'x$'|, tptp_fun__collect__(|'uu$'|)) <=> tptp_fun__fun_app_k_(|'uu$'|, |'x$'|))) | tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.56/0.66 tff(32,plain,
% 0.56/0.66 (tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[31, 26])).
% 0.56/0.66 tff(33,plain,
% 0.56/0.66 ((~((~tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)) | (|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|))))) | (~tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)) | (|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|)))),
% 0.56/0.66 inference(tautology,[status(thm)],[])).
% 0.56/0.66 tff(34,plain,
% 0.56/0.66 ((~((~tptp_fun__fun_app_k_(|'uu$'|, |'x$'|)) | (|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|))))) | (|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|)))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.56/0.66 tff(35,plain,
% 0.56/0.66 (|'x$'| = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[34, 17])).
% 0.56/0.66 tff(36,plain,
% 0.56/0.66 (tptp_fun__fun_app_s_(|'g$'|, |'x$'|) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|)))),
% 0.56/0.66 inference(monotonicity,[status(thm)],[35])).
% 0.56/0.66 tff(37,plain,
% 0.56/0.66 (tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|))) = tptp_fun__fun_app_s_(|'g$'|, |'x$'|)),
% 0.56/0.66 inference(symmetry,[status(thm)],[36])).
% 0.56/0.66 tff(38,plain,
% 0.56/0.66 (^[A__questionmark_v0: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v2: 'C_ell2_c_ell2_cblinfun$'] : refl((tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2))) <=> (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2))))),
% 0.56/0.66 inference(bind,[status(th)],[])).
% 0.56/0.66 tff(39,plain,
% 0.56/0.66 (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v2: 'C_ell2_c_ell2_cblinfun$'] : (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v2: 'C_ell2_c_ell2_cblinfun$'] : (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[38])).
% 0.60/0.66 tff(40,plain,
% 0.60/0.66 (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v2: 'C_ell2_c_ell2_cblinfun$'] : (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2))) <=> ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v2: 'C_ell2_c_ell2_cblinfun$'] : (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(41,axiom,(![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v2: 'C_ell2_c_ell2_cblinfun$'] : (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom101')).
% 0.60/0.66 tff(42,plain,
% 0.60/0.66 (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v2: 'C_ell2_c_ell2_cblinfun$'] : (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.60/0.66 tff(43,plain,(
% 0.60/0.66 ![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v2: 'C_ell2_c_ell2_cblinfun$'] : (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)))),
% 0.60/0.70 inference(skolemize,[status(sab)],[42])).
% 0.60/0.70 tff(44,plain,
% 0.60/0.70 (![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v2: 'C_ell2_c_ell2_cblinfun$'] : (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)))),
% 0.60/0.70 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.60/0.70 tff(45,plain,
% 0.60/0.70 ((~![A__questionmark_v0: 'A_ell2_a_ell2_cblinfun$', A__questionmark_v1: 'B_ell2_b_ell2_cblinfun$', A__questionmark_v2: 'C_ell2_c_ell2_cblinfun$'] : (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2)))) | (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|))) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|))))),
% 0.60/0.70 inference(quant_inst,[status(thm)],[])).
% 0.60/0.70 tff(46,plain,
% 0.60/0.70 (tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|))) = tptp_fun__fun_app_s_(|'g$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|)))),
% 0.60/0.70 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.60/0.70 tff(47,plain,
% 0.60/0.70 (tptp_fun__fun_app_s_(|'f$'|, |'x$'|) = tptp_fun__fun_app_s_(|'f$'|, tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'tensor_op$a'|, tptp_fun__fun_app_h_(tptp_fun__fun_app_i_(|'tensor_op$c'|, tptp_fun_A__questionmark_v1_13(|'x$'|)), tptp_fun_A__questionmark_v2_12(|'x$'|))), tptp_fun_A__questionmark_v3_11(|'x$'|)))),
% 0.60/0.70 inference(monotonicity,[status(thm)],[35])).
% 0.60/0.70 tff(48,plain,
% 0.60/0.70 (tptp_fun__fun_app_s_(|'f$'|, |'x$'|) = tptp_fun__fun_app_s_(|'g$'|, |'x$'|)),
% 0.60/0.70 inference(transitivity,[status(thm)],[47, 46, 37])).
% 0.60/0.70 tff(49,plain,
% 0.60/0.70 ((~(tptp_fun__fun_app_s_(|'f$'|, |'x$'|) = tptp_fun__fun_app_s_(|'g$'|, |'x$'|))) <=> (~(tptp_fun__fun_app_s_(|'f$'|, |'x$'|) = tptp_fun__fun_app_s_(|'g$'|, |'x$'|)))),
% 0.60/0.70 inference(rewrite,[status(thm)],[])).
% 0.60/0.70 tff(50,axiom,(~(tptp_fun__fun_app_s_(|'f$'|, |'x$'|) = tptp_fun__fun_app_s_(|'g$'|, |'x$'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture99')).
% 0.60/0.70 tff(51,plain,
% 0.60/0.70 (~(tptp_fun__fun_app_s_(|'f$'|, |'x$'|) = tptp_fun__fun_app_s_(|'g$'|, |'x$'|))),
% 0.60/0.70 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.60/0.70 tff(52,plain,
% 0.60/0.70 ($false),
% 0.60/0.70 inference(unit_resolution,[status(thm)],[51, 48])).
% 0.60/0.70 % SZS output end Proof
%------------------------------------------------------------------------------