%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP341_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 Jun 21 05:12:44 AM UTC 2025
% Result : Theorem 0.18s 0.49s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP341_1 : TPTP v9.0.0. Released v8.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 18:45:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.49 % SZS status Theorem
% 0.18/0.49 % SZS output start Proof
% 0.18/0.49 tff(tptp_fun__matrix_matrix_mult___type, type, (
% 0.18/0.49 tptp_fun__matrix_matrix_mult__: ( |'A_n_vec_n_vec$'| * |'A_n_vec_n_vec$'| ) > |'A_n_vec_n_vec$'|)).
% 0.18/0.49 tff(tptp_fun__mat___type, type, (
% 0.18/0.49 tptp_fun__mat__: |'A$'| > |'A_n_vec_n_vec$'|)).
% 0.18/0.49 tff(tptp_fun__one___type, type, (
% 0.18/0.49 tptp_fun__one__: |'A$'|)).
% 0.18/0.49 tff(tptp_fun__matrix_inv___type, type, (
% 0.18/0.49 tptp_fun__matrix_inv__: |'A_n_vec_n_vec$'| > |'A_n_vec_n_vec$'|)).
% 0.18/0.49 tff(tptp_fun__p___type, type, (
% 0.18/0.49 tptp_fun__p__: |'A_n_vec_n_vec$'|)).
% 0.18/0.49 tff(1,plain,
% 0.18/0.49 (^[A__questionmark_v0: |'A_n_vec_n_vec$'|] : refl((tptp_fun__matrix_matrix_mult__(A__questionmark_v0, tptp_fun__mat__(|'one$'|)) = A__questionmark_v0) <=> (tptp_fun__matrix_matrix_mult__(A__questionmark_v0, tptp_fun__mat__(|'one$'|)) = A__questionmark_v0))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(2,plain,
% 0.18/0.49 (![A__questionmark_v0: |'A_n_vec_n_vec$'|] : (tptp_fun__matrix_matrix_mult__(A__questionmark_v0, tptp_fun__mat__(|'one$'|)) = A__questionmark_v0) <=> ![A__questionmark_v0: |'A_n_vec_n_vec$'|] : (tptp_fun__matrix_matrix_mult__(A__questionmark_v0, tptp_fun__mat__(|'one$'|)) = A__questionmark_v0)),
% 0.18/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.49 tff(3,plain,
% 0.18/0.49 (![A__questionmark_v0: |'A_n_vec_n_vec$'|] : (tptp_fun__matrix_matrix_mult__(A__questionmark_v0, tptp_fun__mat__(|'one$'|)) = A__questionmark_v0) <=> ![A__questionmark_v0: |'A_n_vec_n_vec$'|] : (tptp_fun__matrix_matrix_mult__(A__questionmark_v0, tptp_fun__mat__(|'one$'|)) = A__questionmark_v0)),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(4,axiom,(![A__questionmark_v0: |'A_n_vec_n_vec$'|] : (tptp_fun__matrix_matrix_mult__(A__questionmark_v0, tptp_fun__mat__(|'one$'|)) = A__questionmark_v0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom9')).
% 0.18/0.49 tff(5,plain,
% 0.18/0.49 (![A__questionmark_v0: |'A_n_vec_n_vec$'|] : (tptp_fun__matrix_matrix_mult__(A__questionmark_v0, tptp_fun__mat__(|'one$'|)) = A__questionmark_v0)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.49 tff(6,plain,(
% 0.18/0.49 ![A__questionmark_v0: |'A_n_vec_n_vec$'|] : (tptp_fun__matrix_matrix_mult__(A__questionmark_v0, tptp_fun__mat__(|'one$'|)) = A__questionmark_v0)),
% 0.18/0.49 inference(skolemize,[status(sab)],[5])).
% 0.18/0.49 tff(7,plain,
% 0.18/0.49 (![A__questionmark_v0: |'A_n_vec_n_vec$'|] : (tptp_fun__matrix_matrix_mult__(A__questionmark_v0, tptp_fun__mat__(|'one$'|)) = A__questionmark_v0)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.49 tff(8,plain,
% 0.18/0.49 ((~(tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_inv__(|'p$'|), tptp_fun__mat__(|'one$'|)) = tptp_fun__matrix_inv__(|'p$'|))) <=> (~(tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_inv__(|'p$'|), tptp_fun__mat__(|'one$'|)) = tptp_fun__matrix_inv__(|'p$'|)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(9,axiom,(~(tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_inv__(|'p$'|), tptp_fun__mat__(|'one$'|)) = tptp_fun__matrix_inv__(|'p$'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture3')).
% 0.18/0.49 tff(10,plain,
% 0.18/0.49 (~(tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_inv__(|'p$'|), tptp_fun__mat__(|'one$'|)) = tptp_fun__matrix_inv__(|'p$'|))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.49 tff(11,plain,
% 0.18/0.49 ((~![A__questionmark_v0: |'A_n_vec_n_vec$'|] : (tptp_fun__matrix_matrix_mult__(A__questionmark_v0, tptp_fun__mat__(|'one$'|)) = A__questionmark_v0)) | (tptp_fun__matrix_matrix_mult__(tptp_fun__matrix_inv__(|'p$'|), tptp_fun__mat__(|'one$'|)) = tptp_fun__matrix_inv__(|'p$'|))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(12,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[11, 10, 7])).
% 0.18/0.49 % SZS output end Proof
% 0.18/0.49 % E exiting
%------------------------------------------------------------------------------