TSTP Solution File: ITP332_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 : n017.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 04:18:45 EDT 2022
% Result : Theorem 2.73s 2.07s
% Output : Proof 2.89s
% 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.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 06:47:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35 Usage: tptp [options] [-file:]file
% 0.19/0.35 -h, -? prints this message.
% 0.19/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.35 -m, -model generate model.
% 0.19/0.35 -p, -proof generate proof.
% 0.19/0.35 -c, -core generate unsat core of named formulas.
% 0.19/0.35 -st, -statistics display statistics.
% 0.19/0.35 -t:timeout set timeout (in second).
% 0.19/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35 -<param>:<value> configuration parameter and value.
% 0.19/0.35 -o:<output-file> file to place output in.
% 2.73/2.07 % SZS status Theorem
% 2.73/2.07 % SZS output start Proof
% 2.73/2.07 tff(tptp_fun__mat_a__type, type, (
% 2.73/2.07 tptp_fun__mat_a_: 'A$' > 'A_m_vec_m_vec$')).
% 2.73/2.07 tff(tptp_fun__one___type, type, (
% 2.73/2.07 tptp_fun__one__: 'A$')).
% 2.73/2.07 tff(tptp_fun__matrix_matrix_mult_b__type, type, (
% 2.73/2.07 tptp_fun__matrix_matrix_mult_b_: ( 'A_m_vec_m_vec$' * 'A_m_vec_m_vec$' ) > 'A_m_vec_m_vec$')).
% 2.73/2.07 tff(tptp_fun_A__questionmark_v2_6_type, type, (
% 2.73/2.07 tptp_fun_A__questionmark_v2_6: 'A_m_vec_m_vec$')).
% 2.73/2.07 tff(tptp_fun__mat___type, type, (
% 2.73/2.07 tptp_fun__mat__: 'A$' > 'A_n_vec_n_vec$')).
% 2.73/2.07 tff(tptp_fun__matrix_matrix_mult_f__type, type, (
% 2.73/2.07 tptp_fun__matrix_matrix_mult_f_: ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$')).
% 2.73/2.07 tff(tptp_fun_A__questionmark_v3_5_type, type, (
% 2.73/2.07 tptp_fun_A__questionmark_v3_5: 'A_n_vec_n_vec$')).
% 2.73/2.07 tff(tptp_fun_A__questionmark_v1_8_type, type, (
% 2.73/2.07 tptp_fun_A__questionmark_v1_8: 'A_n_vec_n_vec$')).
% 2.73/2.07 tff(tptp_fun__matrix_matrix_mult___type, type, (
% 2.73/2.07 tptp_fun__matrix_matrix_mult__: ( 'A_n_vec_m_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_m_vec$')).
% 2.73/2.07 tff(tptp_fun__matrix_matrix_mult_a__type, type, (
% 2.73/2.07 tptp_fun__matrix_matrix_mult_a_: ( 'A_m_vec_m_vec$' * 'A_n_vec_m_vec$' ) > 'A_n_vec_m_vec$')).
% 2.73/2.07 tff(tptp_fun__a___type, type, (
% 2.73/2.07 tptp_fun__a__: 'A_n_vec_m_vec$')).
% 2.73/2.07 tff(tptp_fun__matrix_inv___type, type, (
% 2.73/2.07 tptp_fun__matrix_inv__: 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$')).
% 2.73/2.07 tff(tptp_fun__b___type, type, (
% 2.73/2.07 tptp_fun__b__: 'A_n_vec_m_vec$')).
% 2.73/2.07 tff(tptp_fun_A__questionmark_v1_7_type, type, (
% 2.73/2.07 tptp_fun_A__questionmark_v1_7: 'A_m_vec_m_vec$')).
% 2.73/2.07 tff(tptp_fun__invertible_a__type, type, (
% 2.73/2.07 tptp_fun__invertible_a_: 'A_n_vec_n_vec$' > $o)).
% 2.73/2.07 tff(tptp_fun__invertible___type, type, (
% 2.73/2.07 tptp_fun__invertible__: 'A_m_vec_m_vec$' > $o)).
% 2.73/2.07 tff(tptp_fun__equivalent_matrices___type, type, (
% 2.73/2.07 tptp_fun__equivalent_matrices__: ( 'A_n_vec_m_vec$' * 'A_n_vec_m_vec$' ) > $o)).
% 2.73/2.07 tff(tptp_fun__thesis___type, type, (
% 2.73/2.07 tptp_fun__thesis__: $o)).
% 2.73/2.07 tff(1,assumption,(![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v3!5) = tptp_fun__mat__(|'one$'|)))), introduced(assumption)).
% 2.73/2.07 tff(2,plain,
% 2.73/2.07 (^[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : rewrite((tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), |'a$'|), A__questionmark_v3))) <=> (?[A__questionmark_v1: 'A_m_vec_m_vec$'] : (tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v2) = tptp_fun__mat_a_(|'one$'|)) & ?[A__questionmark_v1: 'A_n_vec_n_vec$'] : (tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v3) = tptp_fun__mat__(|'one$'|)) & (|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), |'a$'|), A__questionmark_v3))))),
% 2.73/2.07 inference(bind,[status(th)],[])).
% 2.73/2.07 tff(3,plain,
% 2.73/2.07 (?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), |'a$'|), A__questionmark_v3))) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (?[A__questionmark_v1: 'A_m_vec_m_vec$'] : (tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v2) = tptp_fun__mat_a_(|'one$'|)) & ?[A__questionmark_v1: 'A_n_vec_n_vec$'] : (tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v3) = tptp_fun__mat__(|'one$'|)) & (|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), |'a$'|), A__questionmark_v3)))),
% 2.73/2.07 inference(quant_intro,[status(thm)],[2])).
% 2.73/2.07 tff(4,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_n_vec_m_vec$', A__questionmark_v1: 'A_n_vec_m_vec$'] : (tptp_fun__equivalent_matrices__(A__questionmark_v0, A__questionmark_v1) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (A__questionmark_v1 = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))) <=> ![A__questionmark_v0: 'A_n_vec_m_vec$', A__questionmark_v1: 'A_n_vec_m_vec$'] : (tptp_fun__equivalent_matrices__(A__questionmark_v0, A__questionmark_v1) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (A__questionmark_v1 = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))))),
% 2.73/2.07 inference(rewrite,[status(thm)],[])).
% 2.73/2.07 tff(5,plain,
% 2.73/2.07 (^[A__questionmark_v0: 'A_n_vec_m_vec$', A__questionmark_v1: 'A_n_vec_m_vec$'] : rewrite((tptp_fun__equivalent_matrices__(A__questionmark_v0, A__questionmark_v1) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : ((tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3)) & (A__questionmark_v1 = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))) <=> (tptp_fun__equivalent_matrices__(A__questionmark_v0, A__questionmark_v1) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (A__questionmark_v1 = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))))),
% 2.73/2.07 inference(bind,[status(th)],[])).
% 2.73/2.07 tff(6,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_n_vec_m_vec$', A__questionmark_v1: 'A_n_vec_m_vec$'] : (tptp_fun__equivalent_matrices__(A__questionmark_v0, A__questionmark_v1) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : ((tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3)) & (A__questionmark_v1 = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))) <=> ![A__questionmark_v0: 'A_n_vec_m_vec$', A__questionmark_v1: 'A_n_vec_m_vec$'] : (tptp_fun__equivalent_matrices__(A__questionmark_v0, A__questionmark_v1) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (A__questionmark_v1 = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))))),
% 2.73/2.07 inference(quant_intro,[status(thm)],[5])).
% 2.73/2.07 tff(7,axiom,(![A__questionmark_v0: 'A_n_vec_m_vec$', A__questionmark_v1: 'A_n_vec_m_vec$'] : (tptp_fun__equivalent_matrices__(A__questionmark_v0, A__questionmark_v1) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : ((tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3)) & (A__questionmark_v1 = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom8')).
% 2.73/2.07 tff(8,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_n_vec_m_vec$', A__questionmark_v1: 'A_n_vec_m_vec$'] : (tptp_fun__equivalent_matrices__(A__questionmark_v0, A__questionmark_v1) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (A__questionmark_v1 = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))))),
% 2.73/2.07 inference(modus_ponens,[status(thm)],[7, 6])).
% 2.73/2.07 tff(9,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_n_vec_m_vec$', A__questionmark_v1: 'A_n_vec_m_vec$'] : (tptp_fun__equivalent_matrices__(A__questionmark_v0, A__questionmark_v1) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (A__questionmark_v1 = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))))),
% 2.73/2.07 inference(modus_ponens,[status(thm)],[8, 4])).
% 2.73/2.07 tff(10,plain,
% 2.73/2.07 ((~![A__questionmark_v0: 'A_n_vec_m_vec$', A__questionmark_v1: 'A_n_vec_m_vec$'] : (tptp_fun__equivalent_matrices__(A__questionmark_v0, A__questionmark_v1) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (A__questionmark_v1 = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))))) | (tptp_fun__equivalent_matrices__(|'a$'|, |'b$'|) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), |'a$'|), A__questionmark_v3))))),
% 2.73/2.07 inference(quant_inst,[status(thm)],[])).
% 2.73/2.07 tff(11,plain,
% 2.73/2.07 (tptp_fun__equivalent_matrices__(|'a$'|, |'b$'|) <=> ?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), |'a$'|), A__questionmark_v3)))),
% 2.73/2.07 inference(unit_resolution,[status(thm)],[10, 9])).
% 2.73/2.07 tff(12,plain,
% 2.73/2.07 (tptp_fun__equivalent_matrices__(|'a$'|, |'b$'|) <=> tptp_fun__equivalent_matrices__(|'a$'|, |'b$'|)),
% 2.73/2.07 inference(rewrite,[status(thm)],[])).
% 2.73/2.07 tff(13,axiom,(tptp_fun__equivalent_matrices__(|'a$'|, |'b$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom2')).
% 2.73/2.07 tff(14,plain,
% 2.73/2.07 (tptp_fun__equivalent_matrices__(|'a$'|, |'b$'|)),
% 2.73/2.07 inference(modus_ponens,[status(thm)],[13, 12])).
% 2.73/2.07 tff(15,plain,
% 2.73/2.07 (?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (tptp_fun__invertible__(A__questionmark_v2) & tptp_fun__invertible_a_(A__questionmark_v3) & (|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), |'a$'|), A__questionmark_v3)))),
% 2.73/2.07 inference(modus_ponens,[status(thm)],[14, 11])).
% 2.73/2.07 tff(16,plain,
% 2.73/2.07 (?[A__questionmark_v2: 'A_m_vec_m_vec$', A__questionmark_v3: 'A_n_vec_n_vec$'] : (?[A__questionmark_v1: 'A_m_vec_m_vec$'] : (tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v2) = tptp_fun__mat_a_(|'one$'|)) & ?[A__questionmark_v1: 'A_n_vec_n_vec$'] : (tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v3) = tptp_fun__mat__(|'one$'|)) & (|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2), |'a$'|), A__questionmark_v3)))),
% 2.73/2.07 inference(modus_ponens,[status(thm)],[15, 3])).
% 2.73/2.07 tff(17,plain,
% 2.73/2.07 (tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1!8, A__questionmark_v3!5) = tptp_fun__mat__(|'one$'|)),
% 2.73/2.07 inference(and_elim,[status(thm)],[16])).
% 2.73/2.07 tff(18,plain,
% 2.73/2.07 ((~![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v3!5) = tptp_fun__mat__(|'one$'|)))) | (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1!8, A__questionmark_v3!5) = tptp_fun__mat__(|'one$'|)))),
% 2.73/2.07 inference(quant_inst,[status(thm)],[])).
% 2.73/2.07 tff(19,plain,
% 2.73/2.07 ($false),
% 2.73/2.07 inference(unit_resolution,[status(thm)],[18, 17, 1])).
% 2.73/2.07 tff(20,plain,(~![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v3!5) = tptp_fun__mat__(|'one$'|)))), inference(lemma,lemma(discharge,[]))).
% 2.73/2.07 tff(21,plain,
% 2.73/2.07 (|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2!6), |'a$'|), A__questionmark_v3!5)),
% 2.73/2.07 inference(and_elim,[status(thm)],[16])).
% 2.73/2.07 tff(22,plain,
% 2.73/2.07 (^[A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : refl(((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|)))) <=> ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|)))))),
% 2.73/2.07 inference(bind,[status(th)],[])).
% 2.73/2.07 tff(23,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|)))) <=> ![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|))))),
% 2.73/2.07 inference(quant_intro,[status(thm)],[22])).
% 2.73/2.07 tff(24,plain,
% 2.73/2.07 (^[A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : rewrite(((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|)))) <=> ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|)))))),
% 2.73/2.07 inference(bind,[status(th)],[])).
% 2.73/2.07 tff(25,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|)))) <=> ![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|))))),
% 2.73/2.07 inference(quant_intro,[status(thm)],[24])).
% 2.73/2.07 tff(26,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|)))) <=> ![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|))))),
% 2.73/2.07 inference(transitivity,[status(thm)],[25, 23])).
% 2.73/2.07 tff(27,plain,
% 2.73/2.07 (^[A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : rewrite((~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1))) <=> (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & ?[A__questionmark_v1: 'A_m_vec_m_vec$'] : (tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|)) & ?[A__questionmark_v1: 'A_n_vec_n_vec$'] : (tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|)))))),
% 2.73/2.07 inference(bind,[status(th)],[])).
% 2.73/2.07 tff(28,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1))) <=> ![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & ?[A__questionmark_v1: 'A_m_vec_m_vec$'] : (tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|)) & ?[A__questionmark_v1: 'A_n_vec_n_vec$'] : (tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|))))),
% 2.73/2.07 inference(quant_intro,[status(thm)],[27])).
% 2.73/2.07 tff(29,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1))) <=> ![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)))),
% 2.73/2.07 inference(rewrite,[status(thm)],[])).
% 2.73/2.07 tff(30,plain,
% 2.73/2.07 (^[A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : trans(monotonicity(iff_false(asserted(~|'thesis$'|), (|'thesis$'| <=> $false)), ((|'thesis$'| | (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)))) <=> ($false | (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)))))), rewrite(($false | (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)))) <=> (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)))), ((|'thesis$'| | (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)))) <=> (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)))))),
% 2.73/2.07 inference(bind,[status(th)],[])).
% 2.73/2.07 tff(31,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : (|'thesis$'| | (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)))) <=> ![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)))),
% 2.73/2.07 inference(quant_intro,[status(thm)],[30])).
% 2.73/2.07 tff(32,plain,
% 2.73/2.07 (^[A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : trans(monotonicity(rewrite((((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0)) & tptp_fun__invertible_a_(A__questionmark_v1)) <=> ((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1))), (((((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0)) & tptp_fun__invertible_a_(A__questionmark_v1)) => |'thesis$'|) <=> (((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)) => |'thesis$'|))), rewrite((((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)) => |'thesis$'|) <=> (|'thesis$'| | (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1))))), (((((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0)) & tptp_fun__invertible_a_(A__questionmark_v1)) => |'thesis$'|) <=> (|'thesis$'| | (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1))))))),
% 2.73/2.07 inference(bind,[status(th)],[])).
% 2.73/2.07 tff(33,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0)) & tptp_fun__invertible_a_(A__questionmark_v1)) => |'thesis$'|) <=> ![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : (|'thesis$'| | (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1))))),
% 2.73/2.07 inference(quant_intro,[status(thm)],[32])).
% 2.73/2.07 tff(34,axiom,(![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0)) & tptp_fun__invertible_a_(A__questionmark_v1)) => |'thesis$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis1')).
% 2.73/2.07 tff(35,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : (|'thesis$'| | (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1))))),
% 2.73/2.07 inference(modus_ponens,[status(thm)],[34, 33])).
% 2.73/2.07 tff(36,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)))),
% 2.73/2.07 inference(modus_ponens,[status(thm)],[35, 31])).
% 2.73/2.07 tff(37,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & tptp_fun__invertible__(A__questionmark_v0) & tptp_fun__invertible_a_(A__questionmark_v1)))),
% 2.73/2.07 inference(modus_ponens,[status(thm)],[36, 29])).
% 2.73/2.07 tff(38,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : (~((|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1)) & ?[A__questionmark_v1: 'A_m_vec_m_vec$'] : (tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|)) & ?[A__questionmark_v1: 'A_n_vec_n_vec$'] : (tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|))))),
% 2.73/2.07 inference(modus_ponens,[status(thm)],[37, 28])).
% 2.73/2.07 tff(39,plain,(
% 2.73/2.07 ![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|))))),
% 2.73/2.07 inference(skolemize,[status(sab)],[38])).
% 2.73/2.07 tff(40,plain,
% 2.73/2.07 (![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|))))),
% 2.73/2.07 inference(modus_ponens,[status(thm)],[39, 26])).
% 2.73/2.07 tff(41,plain,
% 2.73/2.07 (((~![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|))))) | ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2!6), |'a$'|), A__questionmark_v3!5))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v2!6) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v3!5) = tptp_fun__mat__(|'one$'|))))) <=> ((~![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|))))) | (~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2!6), |'a$'|), A__questionmark_v3!5))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v2!6) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v3!5) = tptp_fun__mat__(|'one$'|))))),
% 2.73/2.07 inference(rewrite,[status(thm)],[])).
% 2.73/2.07 tff(42,plain,
% 2.73/2.07 ((~![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|))))) | ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2!6), |'a$'|), A__questionmark_v3!5))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v2!6) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v3!5) = tptp_fun__mat__(|'one$'|))))),
% 2.73/2.07 inference(quant_inst,[status(thm)],[])).
% 2.73/2.07 tff(43,plain,
% 2.73/2.07 ((~![A__questionmark_v0: 'A_m_vec_m_vec$', A__questionmark_v1: 'A_n_vec_n_vec$'] : ((~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v0), |'a$'|), A__questionmark_v1))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v0) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v1) = tptp_fun__mat__(|'one$'|))))) | (~(|'b$'| = tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_matrix_mult_a_(tptp_fun__matrix_inv__(A__questionmark_v2!6), |'a$'|), A__questionmark_v3!5))) | ![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v2!6) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v3!5) = tptp_fun__mat__(|'one$'|)))),
% 2.89/2.10 inference(modus_ponens,[status(thm)],[42, 41])).
% 2.89/2.10 tff(44,plain,
% 2.89/2.10 (![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v2!6) = tptp_fun__mat_a_(|'one$'|))) | ![A__questionmark_v1: 'A_n_vec_n_vec$'] : (~(tptp_fun__matrix_matrix_mult_f_(A__questionmark_v1, A__questionmark_v3!5) = tptp_fun__mat__(|'one$'|)))),
% 2.89/2.10 inference(unit_resolution,[status(thm)],[43, 40, 21])).
% 2.89/2.10 tff(45,plain,
% 2.89/2.10 (![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v2!6) = tptp_fun__mat_a_(|'one$'|)))),
% 2.89/2.10 inference(unit_resolution,[status(thm)],[44, 20])).
% 2.89/2.10 tff(46,plain,
% 2.89/2.10 (tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1!7, A__questionmark_v2!6) = tptp_fun__mat_a_(|'one$'|)),
% 2.89/2.10 inference(and_elim,[status(thm)],[16])).
% 2.89/2.10 tff(47,plain,
% 2.89/2.10 ((~![A__questionmark_v1: 'A_m_vec_m_vec$'] : (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1, A__questionmark_v2!6) = tptp_fun__mat_a_(|'one$'|)))) | (~(tptp_fun__matrix_matrix_mult_b_(A__questionmark_v1!7, A__questionmark_v2!6) = tptp_fun__mat_a_(|'one$'|)))),
% 2.89/2.10 inference(quant_inst,[status(thm)],[])).
% 2.89/2.10 tff(48,plain,
% 2.89/2.10 ($false),
% 2.89/2.10 inference(unit_resolution,[status(thm)],[47, 46, 45])).
% 2.89/2.10 % SZS output end Proof
%------------------------------------------------------------------------------