TSTP Solution File: ITP387_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP387_1 : TPTP v8.1.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 04:18:55 EDT 2022
% Result : Theorem 1.05s 0.96s
% Output : Proof 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP387_1 : TPTP v8.1.0. Released v8.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.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 07:51:03 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.
% 1.05/0.96 % SZS status Theorem
% 1.05/0.96 % SZS output start Proof
% 1.05/0.96 tff(tptp_fun__fun_app_k__type, type, (
% 1.05/0.96 tptp_fun__fun_app_k_: ( 'A_c_prod_ell2_b_d_prod_ell2_fun$' * 'A_c_prod_ell2$' ) > 'B_d_prod_ell2$')).
% 1.05/0.96 tff(tptp_fun__fun_app_o__type, type, (
% 1.05/0.96 tptp_fun__fun_app_o_: ( 'A_c_prod_a_c_prod_ell2_fun$' * 'A_c_prod$' ) > 'A_c_prod_ell2$')).
% 1.05/0.96 tff(tptp_fun__fun_app_p__type, type, (
% 1.05/0.96 tptp_fun__fun_app_p_: ( 'C_a_c_prod_fun$' * 'C$' ) > 'A_c_prod$')).
% 1.05/0.96 tff(tptp_fun__j___type, type, (
% 1.05/0.96 tptp_fun__j__: 'C$')).
% 1.05/0.96 tff(tptp_fun__fun_app_q__type, type, (
% 1.05/0.96 tptp_fun__fun_app_q_: ( 'A_c_a_c_prod_fun_fun$' * 'A$' ) > 'C_a_c_prod_fun$')).
% 1.05/0.96 tff(tptp_fun__i___type, type, (
% 1.05/0.96 tptp_fun__i__: 'A$')).
% 1.05/0.96 tff(tptp_fun__pair___type, type, (
% 1.05/0.96 tptp_fun__pair__: 'A_c_a_c_prod_fun_fun$')).
% 1.05/0.96 tff(tptp_fun__ket___type, type, (
% 1.05/0.96 tptp_fun__ket__: 'A_c_prod_a_c_prod_ell2_fun$')).
% 1.05/0.96 tff(tptp_fun__fun_app_l__type, type, (
% 1.05/0.96 tptp_fun__fun_app_l_: ( 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_fun_fun$' * 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$' ) > 'A_c_prod_ell2_b_d_prod_ell2_fun$')).
% 1.05/0.96 tff(tptp_fun__fun_app_r__type, type, (
% 1.05/0.96 tptp_fun__fun_app_r_: ( 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_fun$' * 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$' ) > 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$')).
% 1.05/0.96 tff(tptp_fun__tensor_op___type, type, (
% 1.05/0.96 tptp_fun__tensor_op__: ( 'A_ell2_b_ell2_cblinfun$' * 'C_ell2_d_ell2_cblinfun$' ) > 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$')).
% 1.05/0.96 tff(tptp_fun__b2___type, type, (
% 1.05/0.96 tptp_fun__b2__: 'C_ell2_d_ell2_cblinfun$')).
% 1.05/0.96 tff(tptp_fun__a___type, type, (
% 1.05/0.96 tptp_fun__a__: 'A_ell2_b_ell2_cblinfun$')).
% 1.05/0.96 tff(tptp_fun__fun_app_s__type, type, (
% 1.05/0.96 tptp_fun__fun_app_s_: ( 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_fun_fun$' * 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$' ) > 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_fun$')).
% 1.05/0.96 tff(tptp_fun__b1___type, type, (
% 1.05/0.96 tptp_fun__b1__: 'C_ell2_d_ell2_cblinfun$')).
% 1.05/0.96 tff(tptp_fun__plus_b__type, type, (
% 1.05/0.96 tptp_fun__plus_b_: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_fun_fun$')).
% 1.05/0.96 tff(tptp_fun__cblinfun_apply___type, type, (
% 1.05/0.96 tptp_fun__cblinfun_apply__: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_fun_fun$')).
% 1.05/0.96 tff(tptp_fun__fun_app_m__type, type, (
% 1.05/0.96 tptp_fun__fun_app_m_: ( 'C_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_fun$' * 'C_ell2_d_ell2_cblinfun$' ) > 'C_ell2_d_ell2_cblinfun$')).
% 1.05/0.96 tff(tptp_fun__fun_app_n__type, type, (
% 1.05/0.96 tptp_fun__fun_app_n_: ( 'C_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_fun_fun$' * 'C_ell2_d_ell2_cblinfun$' ) > 'C_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_fun$')).
% 1.05/0.96 tff(tptp_fun__plus_a__type, type, (
% 1.05/0.96 tptp_fun__plus_a_: 'C_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_fun_fun$')).
% 1.05/0.96 tff(tptp_fun__plus_u__type, type, (
% 1.05/0.96 tptp_fun__plus_u_: ( 'B_d_prod_ell2$' * 'B_d_prod_ell2$' ) > 'B_d_prod_ell2$')).
% 1.05/0.96 tff(tptp_fun__tensor_ell2___type, type, (
% 1.05/0.96 tptp_fun__tensor_ell2__: ( 'B_ell2$' * 'D_ell2$' ) > 'B_d_prod_ell2$')).
% 1.05/0.96 tff(tptp_fun__fun_app_u__type, type, (
% 1.05/0.96 tptp_fun__fun_app_u_: ( 'C_ell2_d_ell2_fun$' * 'C_ell2$' ) > 'D_ell2$')).
% 1.05/0.96 tff(tptp_fun__ket_b__type, type, (
% 1.05/0.96 tptp_fun__ket_b_: 'C$' > 'C_ell2$')).
% 1.05/0.96 tff(tptp_fun__cblinfun_apply_b__type, type, (
% 1.05/0.96 tptp_fun__cblinfun_apply_b_: 'C_ell2_d_ell2_cblinfun$' > 'C_ell2_d_ell2_fun$')).
% 1.05/0.96 tff(tptp_fun__fun_app_t__type, type, (
% 1.05/0.96 tptp_fun__fun_app_t_: ( 'A_ell2_b_ell2_fun$' * 'A_ell2$' ) > 'B_ell2$')).
% 1.05/0.96 tff(tptp_fun__ket_a__type, type, (
% 1.05/0.96 tptp_fun__ket_a_: 'A$' > 'A_ell2$')).
% 1.05/0.96 tff(tptp_fun__cblinfun_apply_a__type, type, (
% 1.05/0.96 tptp_fun__cblinfun_apply_a_: 'A_ell2_b_ell2_cblinfun$' > 'A_ell2_b_ell2_fun$')).
% 1.05/0.96 tff(tptp_fun__plus_i__type, type, (
% 1.05/0.96 tptp_fun__plus_i_: ( 'D_ell2$' * 'D_ell2$' ) > 'D_ell2$')).
% 1.05/0.96 tff(1,plain,
% 1.05/0.96 (^[A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : refl((tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v1), A__questionmark_v0)) <=> (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v1), A__questionmark_v0)))),
% 1.05/0.96 inference(bind,[status(th)],[])).
% 1.05/0.96 tff(2,plain,
% 1.05/0.96 (![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v1), A__questionmark_v0)) <=> ![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v1), A__questionmark_v0))),
% 1.05/0.96 inference(quant_intro,[status(thm)],[1])).
% 1.05/0.96 tff(3,plain,
% 1.05/0.96 (![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v1), A__questionmark_v0)) <=> ![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v1), A__questionmark_v0))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(4,axiom,(![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v1), A__questionmark_v0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom156')).
% 1.05/0.96 tff(5,plain,
% 1.05/0.96 (![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v1), A__questionmark_v0))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.05/0.96 tff(6,plain,(
% 1.05/0.96 ![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v1), A__questionmark_v0))),
% 1.05/0.96 inference(skolemize,[status(sab)],[5])).
% 1.05/0.96 tff(7,plain,
% 1.05/0.96 (![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v1), A__questionmark_v0))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.05/0.96 tff(8,plain,
% 1.05/0.96 ((~![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v1), A__questionmark_v0))) | (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__tensor_op__(|'a$'|, |'b1$'|)) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__tensor_op__(|'a$'|, |'b2$'|)))),
% 1.05/0.96 inference(quant_inst,[status(thm)],[])).
% 1.05/0.96 tff(9,plain,
% 1.05/0.96 (tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__tensor_op__(|'a$'|, |'b1$'|)) = tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__tensor_op__(|'a$'|, |'b2$'|))),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.05/0.96 tff(10,plain,
% 1.05/0.96 (tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__tensor_op__(|'a$'|, |'b1$'|))) = tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__tensor_op__(|'a$'|, |'b2$'|)))),
% 1.05/0.96 inference(monotonicity,[status(thm)],[9])).
% 1.05/0.96 tff(11,plain,
% 1.05/0.96 (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__tensor_op__(|'a$'|, |'b1$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__tensor_op__(|'a$'|, |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|)))),
% 1.05/0.96 inference(monotonicity,[status(thm)],[10])).
% 1.05/0.96 tff(12,plain,
% 1.05/0.96 (^[A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v2: 'A_c_prod_ell2$'] : refl((tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v1), A__questionmark_v2))) <=> (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v1), A__questionmark_v2))))),
% 1.05/0.96 inference(bind,[status(th)],[])).
% 1.05/0.96 tff(13,plain,
% 1.05/0.96 (![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v2: 'A_c_prod_ell2$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v1), A__questionmark_v2))) <=> ![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v2: 'A_c_prod_ell2$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v1), A__questionmark_v2)))),
% 1.05/0.96 inference(quant_intro,[status(thm)],[12])).
% 1.05/0.96 tff(14,plain,
% 1.05/0.96 (![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v2: 'A_c_prod_ell2$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v1), A__questionmark_v2))) <=> ![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v2: 'A_c_prod_ell2$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v1), A__questionmark_v2)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(15,axiom,(![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v2: 'A_c_prod_ell2$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v1), A__questionmark_v2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom35')).
% 1.05/0.96 tff(16,plain,
% 1.05/0.96 (![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v2: 'A_c_prod_ell2$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v1), A__questionmark_v2)))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.05/0.96 tff(17,plain,(
% 1.05/0.96 ![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v2: 'A_c_prod_ell2$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v1), A__questionmark_v2)))),
% 1.05/0.96 inference(skolemize,[status(sab)],[16])).
% 1.05/0.96 tff(18,plain,
% 1.05/0.96 (![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v2: 'A_c_prod_ell2$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v1), A__questionmark_v2)))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.05/0.96 tff(19,plain,
% 1.05/0.96 ((~![A__questionmark_v0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$', A__questionmark_v2: 'A_c_prod_ell2$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, A__questionmark_v1), A__questionmark_v2)))) | (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__tensor_op__(|'a$'|, |'b1$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|)))))),
% 1.05/0.97 inference(quant_inst,[status(thm)],[])).
% 1.05/0.97 tff(20,plain,
% 1.05/0.97 (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__tensor_op__(|'a$'|, |'b1$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))))),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.05/0.97 tff(21,plain,
% 1.05/0.97 (tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|)))) = tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__tensor_op__(|'a$'|, |'b1$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|)))),
% 1.05/0.97 inference(symmetry,[status(thm)],[20])).
% 1.05/0.97 tff(22,plain,
% 1.05/0.97 (^[A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : refl((tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3)))) <=> (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3)))))),
% 1.05/0.97 inference(bind,[status(th)],[])).
% 1.05/0.97 tff(23,plain,
% 1.05/0.97 (![A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3)))) <=> ![A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3))))),
% 1.05/0.97 inference(quant_intro,[status(thm)],[22])).
% 1.05/0.97 tff(24,plain,
% 1.05/0.97 (![A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3)))) <=> ![A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3))))),
% 1.05/0.97 inference(rewrite,[status(thm)],[])).
% 1.05/0.97 tff(25,axiom,(![A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom20')).
% 1.05/0.97 tff(26,plain,
% 1.05/0.97 (![A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3))))),
% 1.05/0.97 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.05/0.97 tff(27,plain,(
% 1.05/0.97 ![A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3))))),
% 1.05/0.97 inference(skolemize,[status(sab)],[26])).
% 1.05/0.97 tff(28,plain,
% 1.05/0.97 (![A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3))))),
% 1.05/0.97 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.05/0.97 tff(29,plain,
% 1.05/0.97 ((~![A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3))))) | (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|))))),
% 1.05/0.97 inference(quant_inst,[status(thm)],[])).
% 1.05/0.97 tff(30,plain,
% 1.05/0.97 (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|)))),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[29, 28])).
% 1.05/0.97 tff(31,plain,
% 1.05/0.97 (tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|))) = tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|)))),
% 1.05/0.97 inference(symmetry,[status(thm)],[30])).
% 1.05/0.97 tff(32,plain,
% 1.05/0.97 ((~![A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3))))) | (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|))))),
% 1.05/0.97 inference(quant_inst,[status(thm)],[])).
% 1.05/0.97 tff(33,plain,
% 1.05/0.97 (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|)))),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[32, 28])).
% 1.05/0.97 tff(34,plain,
% 1.05/0.97 (tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|))) = tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|)))),
% 1.05/0.97 inference(symmetry,[status(thm)],[33])).
% 1.05/0.97 tff(35,plain,
% 1.05/0.97 (tptp_fun__plus_u_(tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|))), tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|)))) = tptp_fun__plus_u_(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b2$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))))),
% 1.05/0.97 inference(monotonicity,[status(thm)],[34, 31])).
% 1.05/0.97 tff(36,plain,
% 1.05/0.97 (^[A__questionmark_v0: 'B_ell2$', A__questionmark_v1: 'D_ell2$', A__questionmark_v2: 'D_ell2$'] : refl((tptp_fun__tensor_ell2__(A__questionmark_v0, tptp_fun__plus_i_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v1), tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v2))) <=> (tptp_fun__tensor_ell2__(A__questionmark_v0, tptp_fun__plus_i_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v1), tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v2))))),
% 1.05/0.97 inference(bind,[status(th)],[])).
% 1.05/0.97 tff(37,plain,
% 1.05/0.97 (![A__questionmark_v0: 'B_ell2$', A__questionmark_v1: 'D_ell2$', A__questionmark_v2: 'D_ell2$'] : (tptp_fun__tensor_ell2__(A__questionmark_v0, tptp_fun__plus_i_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v1), tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v2))) <=> ![A__questionmark_v0: 'B_ell2$', A__questionmark_v1: 'D_ell2$', A__questionmark_v2: 'D_ell2$'] : (tptp_fun__tensor_ell2__(A__questionmark_v0, tptp_fun__plus_i_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v1), tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v2)))),
% 1.05/0.97 inference(quant_intro,[status(thm)],[36])).
% 1.05/0.97 tff(38,plain,
% 1.05/0.97 (![A__questionmark_v0: 'B_ell2$', A__questionmark_v1: 'D_ell2$', A__questionmark_v2: 'D_ell2$'] : (tptp_fun__tensor_ell2__(A__questionmark_v0, tptp_fun__plus_i_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v1), tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v2))) <=> ![A__questionmark_v0: 'B_ell2$', A__questionmark_v1: 'D_ell2$', A__questionmark_v2: 'D_ell2$'] : (tptp_fun__tensor_ell2__(A__questionmark_v0, tptp_fun__plus_i_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v1), tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v2)))),
% 1.05/0.97 inference(rewrite,[status(thm)],[])).
% 1.05/0.97 tff(39,axiom,(![A__questionmark_v0: 'B_ell2$', A__questionmark_v1: 'D_ell2$', A__questionmark_v2: 'D_ell2$'] : (tptp_fun__tensor_ell2__(A__questionmark_v0, tptp_fun__plus_i_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v1), tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom95')).
% 1.05/0.97 tff(40,plain,
% 1.05/0.97 (![A__questionmark_v0: 'B_ell2$', A__questionmark_v1: 'D_ell2$', A__questionmark_v2: 'D_ell2$'] : (tptp_fun__tensor_ell2__(A__questionmark_v0, tptp_fun__plus_i_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v1), tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v2)))),
% 1.05/0.97 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.05/0.97 tff(41,plain,(
% 1.05/0.97 ![A__questionmark_v0: 'B_ell2$', A__questionmark_v1: 'D_ell2$', A__questionmark_v2: 'D_ell2$'] : (tptp_fun__tensor_ell2__(A__questionmark_v0, tptp_fun__plus_i_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v1), tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v2)))),
% 1.05/0.97 inference(skolemize,[status(sab)],[40])).
% 1.05/0.97 tff(42,plain,
% 1.05/0.97 (![A__questionmark_v0: 'B_ell2$', A__questionmark_v1: 'D_ell2$', A__questionmark_v2: 'D_ell2$'] : (tptp_fun__tensor_ell2__(A__questionmark_v0, tptp_fun__plus_i_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v1), tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v2)))),
% 1.05/0.97 inference(modus_ponens,[status(thm)],[41, 37])).
% 1.05/0.97 tff(43,plain,
% 1.05/0.97 ((~![A__questionmark_v0: 'B_ell2$', A__questionmark_v1: 'D_ell2$', A__questionmark_v2: 'D_ell2$'] : (tptp_fun__tensor_ell2__(A__questionmark_v0, tptp_fun__plus_i_(A__questionmark_v1, A__questionmark_v2)) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v1), tptp_fun__tensor_ell2__(A__questionmark_v0, A__questionmark_v2)))) | (tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|)))) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|))), tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|)))))),
% 1.05/0.97 inference(quant_inst,[status(thm)],[])).
% 1.05/0.97 tff(44,plain,
% 1.05/0.97 (tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|)))) = tptp_fun__plus_u_(tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|))), tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|))))),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[43, 42])).
% 1.05/0.97 tff(45,plain,
% 1.05/0.97 (^[A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'C_ell2$'] : refl((tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), A__questionmark_v2))) <=> (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), A__questionmark_v2))))),
% 1.05/0.97 inference(bind,[status(th)],[])).
% 1.05/0.97 tff(46,plain,
% 1.05/0.97 (![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'C_ell2$'] : (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), A__questionmark_v2))) <=> ![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'C_ell2$'] : (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), A__questionmark_v2)))),
% 1.05/0.97 inference(quant_intro,[status(thm)],[45])).
% 1.05/0.97 tff(47,plain,
% 1.05/0.97 (![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'C_ell2$'] : (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), A__questionmark_v2))) <=> ![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'C_ell2$'] : (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), A__questionmark_v2)))),
% 1.05/0.97 inference(rewrite,[status(thm)],[])).
% 1.05/0.97 tff(48,axiom,(![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'C_ell2$'] : (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), A__questionmark_v2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom34')).
% 1.05/0.97 tff(49,plain,
% 1.05/0.97 (![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'C_ell2$'] : (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), A__questionmark_v2)))),
% 1.05/0.97 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.05/0.97 tff(50,plain,(
% 1.05/0.97 ![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'C_ell2$'] : (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), A__questionmark_v2)))),
% 1.10/0.97 inference(skolemize,[status(sab)],[49])).
% 1.10/0.97 tff(51,plain,
% 1.10/0.97 (![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'C_ell2$'] : (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), A__questionmark_v2)))),
% 1.10/0.97 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.10/0.97 tff(52,plain,
% 1.10/0.97 ((~![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'C_ell2$'] : (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1)), A__questionmark_v2) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v0), A__questionmark_v2), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), A__questionmark_v2)))) | (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b2$'|), |'b1$'|)), tptp_fun__ket_b_(|'j$'|)) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|))))),
% 1.10/0.97 inference(quant_inst,[status(thm)],[])).
% 1.10/0.97 tff(53,plain,
% 1.10/0.97 (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b2$'|), |'b1$'|)), tptp_fun__ket_b_(|'j$'|)) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|)))),
% 1.10/0.97 inference(unit_resolution,[status(thm)],[52, 51])).
% 1.10/0.97 tff(54,plain,
% 1.10/0.97 (^[A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$'] : refl((tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v1), A__questionmark_v0)) <=> (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v1), A__questionmark_v0)))),
% 1.10/0.97 inference(bind,[status(th)],[])).
% 1.10/0.97 tff(55,plain,
% 1.10/0.97 (![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$'] : (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v1), A__questionmark_v0)) <=> ![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$'] : (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v1), A__questionmark_v0))),
% 1.10/0.97 inference(quant_intro,[status(thm)],[54])).
% 1.10/0.97 tff(56,plain,
% 1.10/0.97 (![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$'] : (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v1), A__questionmark_v0)) <=> ![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$'] : (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v1), A__questionmark_v0))),
% 1.10/0.97 inference(rewrite,[status(thm)],[])).
% 1.10/0.98 tff(57,axiom,(![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$'] : (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v1), A__questionmark_v0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom155')).
% 1.10/0.98 tff(58,plain,
% 1.10/0.98 (![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$'] : (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v1), A__questionmark_v0))),
% 1.10/0.98 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.10/0.98 tff(59,plain,(
% 1.10/0.98 ![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$'] : (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v1), A__questionmark_v0))),
% 1.10/0.98 inference(skolemize,[status(sab)],[58])).
% 1.10/0.98 tff(60,plain,
% 1.10/0.98 (![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$'] : (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v1), A__questionmark_v0))),
% 1.10/0.98 inference(modus_ponens,[status(thm)],[59, 55])).
% 1.10/0.98 tff(61,plain,
% 1.10/0.98 ((~![A__questionmark_v0: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$'] : (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v0), A__questionmark_v1) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, A__questionmark_v1), A__questionmark_v0))) | (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b2$'|), |'b1$'|) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|))),
% 1.10/0.98 inference(quant_inst,[status(thm)],[])).
% 1.10/0.98 tff(62,plain,
% 1.10/0.98 (tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b2$'|), |'b1$'|) = tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|)),
% 1.10/0.98 inference(unit_resolution,[status(thm)],[61, 60])).
% 1.10/0.98 tff(63,plain,
% 1.10/0.98 (tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b2$'|), |'b1$'|)) = tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|))),
% 1.10/0.98 inference(monotonicity,[status(thm)],[62])).
% 1.10/0.98 tff(64,plain,
% 1.10/0.98 (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b2$'|), |'b1$'|)), tptp_fun__ket_b_(|'j$'|)) = tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|)), tptp_fun__ket_b_(|'j$'|))),
% 1.10/0.98 inference(monotonicity,[status(thm)],[63])).
% 1.10/0.98 tff(65,plain,
% 1.10/0.98 (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|)), tptp_fun__ket_b_(|'j$'|)) = tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b2$'|), |'b1$'|)), tptp_fun__ket_b_(|'j$'|))),
% 1.10/0.98 inference(symmetry,[status(thm)],[64])).
% 1.10/0.98 tff(66,plain,
% 1.10/0.98 (tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|)), tptp_fun__ket_b_(|'j$'|)) = tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|)))),
% 1.10/0.98 inference(transitivity,[status(thm)],[65, 53])).
% 1.10/0.98 tff(67,plain,
% 1.10/0.98 (tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|)), tptp_fun__ket_b_(|'j$'|))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__plus_i_(tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b2$'|), tptp_fun__ket_b_(|'j$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(|'b1$'|), tptp_fun__ket_b_(|'j$'|))))),
% 1.10/0.98 inference(monotonicity,[status(thm)],[66])).
% 1.10/0.98 tff(68,plain,
% 1.10/0.98 ((~![A__questionmark_v0: 'A_ell2_b_ell2_cblinfun$', A__questionmark_v1: 'C_ell2_d_ell2_cblinfun$', A__questionmark_v2: 'A$', A__questionmark_v3: 'C$'] : (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, A__questionmark_v2), A__questionmark_v3))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(A__questionmark_v0), tptp_fun__ket_a_(A__questionmark_v2)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(A__questionmark_v1), tptp_fun__ket_b_(A__questionmark_v3))))) | (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|)), tptp_fun__ket_b_(|'j$'|))))),
% 1.10/0.98 inference(quant_inst,[status(thm)],[])).
% 1.10/0.98 tff(69,plain,
% 1.10/0.98 (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__tensor_ell2__(tptp_fun__fun_app_t_(tptp_fun__cblinfun_apply_a_(|'a$'|), tptp_fun__ket_a_(|'i$'|)), tptp_fun__fun_app_u_(tptp_fun__cblinfun_apply_b_(tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|)), tptp_fun__ket_b_(|'j$'|)))),
% 1.10/0.98 inference(unit_resolution,[status(thm)],[68, 28])).
% 1.10/0.98 tff(70,plain,
% 1.10/0.98 (tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__tensor_op__(|'a$'|, |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|)))),
% 1.10/0.98 inference(transitivity,[status(thm)],[69, 67, 44, 35, 21, 11])).
% 1.10/0.98 tff(71,plain,
% 1.10/0.98 ((~(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__tensor_op__(|'a$'|, |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))))) <=> (~(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__tensor_op__(|'a$'|, |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|)))))),
% 1.10/0.98 inference(rewrite,[status(thm)],[])).
% 1.10/0.98 tff(72,axiom,(~(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__tensor_op__(|'a$'|, |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture9')).
% 1.10/1.03 tff(73,plain,
% 1.10/1.03 (~(tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__tensor_op__(|'a$'|, tptp_fun__fun_app_m_(tptp_fun__fun_app_n_(|'plus$a'|, |'b1$'|), |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))) = tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'cblinfun_apply$'|, tptp_fun__fun_app_r_(tptp_fun__fun_app_s_(|'plus$b'|, tptp_fun__tensor_op__(|'a$'|, |'b1$'|)), tptp_fun__tensor_op__(|'a$'|, |'b2$'|))), tptp_fun__fun_app_o_(|'ket$'|, tptp_fun__fun_app_p_(tptp_fun__fun_app_q_(|'pair$'|, |'i$'|), |'j$'|))))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.10/1.03 tff(74,plain,
% 1.10/1.03 ($false),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[73, 70])).
% 1.10/1.03 % SZS output end Proof
%------------------------------------------------------------------------------