%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP209^4 : TPTP v9.2.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.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 : Wed Feb 25 08:56:53 AM UTC 2026
% Result : Theorem 1.56s 1.27s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 89 ( 5 ~; 0 |; 0 &; 84 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 4 con; 0-4 aty)
% Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
syntax_ac_operator:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_2,type,
syntax7388354845996824322omatch:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > $o ) ).
thf(func_def_3,type,
syntax2379306206330768139omatch:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > $o ) ).
thf(func_def_4,type,
a2: a ).
thf(func_def_5,type,
b: a ).
thf(func_def_6,type,
c: a ).
thf(func_def_7,type,
f: a > a > a ).
thf(func_def_19,type,
sK0:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_20,type,
sK1:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_21,type,
sK2:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_22,type,
sK3:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_23,type,
sK4:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_25,type,
sK6:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_26,type,
sK7:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_27,type,
sK8:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_28,type,
sK9:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_29,type,
sK10:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_30,type,
sK11:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_31,type,
sK12:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_32,type,
sK13:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_33,type,
sK14:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_34,type,
sK15:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_35,type,
sK16:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_36,type,
sK17:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_37,type,
sK18:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_38,type,
sK19:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_39,type,
sK20:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_40,type,
sK21:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_41,type,
sK22:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_42,type,
sK23:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_43,type,
sK24:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_44,type,
sK25:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(f155,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f154,f54]) ).
thf(f54,plain,
! [X2: a,X0: a,X1: a] :
( ( f @ ( f @ X0 @ X1 ) @ X2 )
= ( f @ X0 @ ( f @ X1 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: a,X1: a,X2: a] :
( ( f @ ( f @ X0 @ X1 ) @ X2 )
= ( f @ X0 @ ( f @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: a,X3: a,X4: a] :
( ( f @ X2 @ ( f @ X3 @ X4 ) )
= ( f @ ( f @ X2 @ X3 ) @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.d1DeUUJVeW/DTF2THF_27653.p',fact_3_right__assoc) ).
thf(f154,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ a2 @ ( f @ b @ c ) ) ),
inference(forward_demodulation,[status(thm)],[f153,f51]) ).
thf(f51,plain,
! [X0: a,X1: a] :
( ( f @ X1 @ X0 )
= ( f @ X0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: a,X1: a] :
( ( f @ X1 @ X0 )
= ( f @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: a,X3: a] :
( ( f @ X2 @ X3 )
= ( f @ X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.d1DeUUJVeW/DTF2THF_27653.p',fact_1_commute) ).
thf(f153,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ a2 @ ( f @ c @ b ) ) ),
inference(forward_demodulation,[status(thm)],[f57,f54]) ).
thf(f57,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,negated_conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
thf(f13,conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) ),
file('/export/starexec/sandbox2/tmp/tmp.d1DeUUJVeW/DTF2THF_27653.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP209^4 : TPTP v9.2.1. Released v8.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:30:44 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : ITP209^4 : TPTP v9.2.1. Released v8.0.0.
% 0.30/0.45 % Domain : Interactive Theorem Proving
% 0.30/0.45 % Problem : Sledgehammer problem Syntax_Match 00088_002922
% 0.30/0.45 % Version : [Des22] axioms.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.45 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Des22]
% 0.30/0.45 % Names : 0023_Syntax_Match_00088_002922 [Des22]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.00 v8.1.0
% 0.30/0.45 % Syntax : Number of formulae : 21 ( 8 unt; 8 typ; 0 def)
% 0.30/0.45 % Number of atoms : 26 ( 15 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 3 ( 2 avg)
% 0.30/0.45 % Number of connectives : 104 ( 0 ~; 0 |; 1 &; 97 @)
% 0.30/0.45 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 9 ( 5 avg)
% 0.30/0.45 % Number of types : 2 ( 1 usr)
% 0.30/0.45 % Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 9 ( 7 usr; 4 con; 0-4 aty)
% 0.30/0.45 % Number of variables : 54 ( 5 ^; 44 !; 0 ?; 54 :)
% 0.30/0.45 % ( 5 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.45 % SPC : TH1_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.30/0.45 % from the van Emde Boas Trees session in the Archive of Formal
% 0.30/0.45 % proofs -
% 0.30/0.45 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.30/0.45 % 2022-02-17 14:22:46.767
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % Could-be-implicit typings (1)
% 0.30/0.45 thf(ty_tf_a,type,
% 0.30/0.45 a: $tType ).
% 0.30/0.45
% 0.30/0.45 % Explicit typings (7)
% 0.30/0.45 thf(sy_c_Syntax__Match_Oac__operator,type,
% 0.30/0.45 syntax_ac_operator:
% 0.30/0.45 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax__Match_Osyntax__fo__nomatch,type,
% 0.30/0.45 syntax7388354845996824322omatch:
% 0.30/0.45 !>[A: $tType,B: $tType] : ( A > B > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Syntax__Match_Osyntax__nomatch,type,
% 0.30/0.45 syntax2379306206330768139omatch:
% 0.30/0.45 !>[A: $tType,B: $tType] : ( A > B > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_a,type,
% 0.30/0.45 a2: a ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_b,type,
% 0.30/0.45 b: a ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_c,type,
% 0.30/0.45 c: a ).
% 0.30/0.45
% 0.30/0.45 thf(sy_v_f,type,
% 0.30/0.45 f: a > a > a ).
% 0.30/0.45
% 0.30/0.45 % Relevant facts (12)
% 0.30/0.45 thf(fact_0_ac__operator__axioms,axiom,
% 0.30/0.45 syntax_ac_operator @ a @ f ).
% 0.30/0.45
% 0.30/0.45 % ac_operator_axioms
% 0.30/0.45 thf(fact_1_commute,axiom,
% 0.30/0.45 ! [A2: a,B2: a] :
% 0.30/0.45 ( ( f @ A2 @ B2 )
% 0.30/0.45 = ( f @ B2 @ A2 ) ) ).
% 0.30/0.45
% 0.30/0.45 % commute
% 0.30/0.45 thf(fact_2_left__commute,axiom,
% 0.30/0.45 ! [A2: a,B2: a,C: a] :
% 0.30/0.45 ( ( f @ A2 @ ( f @ B2 @ C ) )
% 0.30/0.45 = ( f @ B2 @ ( f @ A2 @ C ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % left_commute
% 0.30/0.45 thf(fact_3_right__assoc,axiom,
% 0.30/0.45 ! [A2: a,B2: a,C: a] :
% 0.30/0.45 ( ( f @ ( f @ A2 @ B2 ) @ C )
% 0.30/0.45 = ( f @ A2 @ ( f @ B2 @ C ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % right_assoc
% 0.30/0.45 thf(fact_4_syntax__nomatch__def,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType] :
% 0.30/0.45 ( ( syntax2379306206330768139omatch @ A @ B )
% 0.30/0.45 = ( ^ [Pat: A,Obj: B] : $true ) ) ).
% 0.30/0.45
% 0.30/0.45 % syntax_nomatch_def
% 0.30/0.45 thf(fact_5_syntax__fo__nomatch__def,axiom,
% 0.30/0.45 ! [B: $tType,A: $tType] :
% 0.30/0.45 ( ( syntax7388354845996824322omatch @ A @ B )
% 0.30/0.45 = ( ^ [Pat: A,Obj: B] : $true ) ) ).
% 0.30/0.45
% 0.30/0.45 % syntax_fo_nomatch_def
% 0.30/0.45 thf(fact_6_ac__operator_Ointro,axiom,
% 0.30/0.45 ! [A: $tType,F: A > A > A] :
% 0.30/0.45 ( ! [A3: A,B3: A,C2: A] :
% 0.30/0.45 ( ( F @ ( F @ A3 @ B3 ) @ C2 )
% 0.30/0.45 = ( F @ A3 @ ( F @ B3 @ C2 ) ) )
% 0.30/0.45 => ( ! [A3: A,B3: A] :
% 0.30/0.45 ( ( F @ A3 @ B3 )
% 0.30/0.45 = ( F @ B3 @ A3 ) )
% 0.30/0.45 => ( syntax_ac_operator @ A @ F ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ac_operator.intro
% 0.30/0.45 thf(fact_7_ac__operator_Ocommute,axiom,
% 0.30/0.45 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 0.30/0.45 ( ( syntax_ac_operator @ A @ F )
% 0.30/0.45 => ( ( F @ A2 @ B2 )
% 0.30/0.45 = ( F @ B2 @ A2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ac_operator.commute
% 0.30/0.45 thf(fact_8_ac__operator_Oleft__assoc,axiom,
% 0.30/0.45 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 0.30/0.45 ( ( syntax_ac_operator @ A @ F )
% 0.30/0.45 => ( ( F @ A2 @ ( F @ B2 @ C ) )
% 0.30/0.45 = ( F @ ( F @ A2 @ B2 ) @ C ) ) ) ).
% 0.30/0.45
% 0.30/0.45 % ac_operator.left_assoc
% 0.30/0.45 thf(fact_9_ac__operator_Oright__assoc,axiom,
% 0.30/0.45 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( syntax_ac_operator @ A @ F )
% 0.30/0.46 => ( ( F @ ( F @ A2 @ B2 ) @ C )
% 0.30/0.46 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ac_operator.right_assoc
% 0.30/0.46 thf(fact_10_ac__operator_Oleft__commute,axiom,
% 0.30/0.46 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( syntax_ac_operator @ A @ F )
% 0.30/0.46 => ( ( F @ A2 @ ( F @ B2 @ C ) )
% 0.30/0.46 = ( F @ B2 @ ( F @ A2 @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ac_operator.left_commute
% 0.30/0.46 thf(fact_11_ac__operator__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( syntax_ac_operator @ A )
% 0.30/0.46 = ( ^ [F2: A > A > A] :
% 0.30/0.46 ( ! [A4: A,B4: A,C3: A] :
% 0.30/0.46 ( ( F2 @ ( F2 @ A4 @ B4 ) @ C3 )
% 0.30/0.46 = ( F2 @ A4 @ ( F2 @ B4 @ C3 ) ) )
% 0.30/0.46 & ! [A4: A,B4: A] :
% 0.30/0.46 ( ( F2 @ A4 @ B4 )
% 0.30/0.46 = ( F2 @ B4 @ A4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ac_operator_def
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 ( ( f @ ( f @ a2 @ b ) @ c )
% 0.30/0.46 = ( f @ ( f @ a2 @ c ) @ b ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.56/1.24 ---- Embedded in THF ---
% 1.56/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.24 %%% Generated on Tue Feb 24 08:30:45 EST 2026
% 1.56/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.24 %%% Logic specification used:
% 1.56/1.24 %%% thf(spec, logic, $$dhol).
% 1.56/1.24
% 1.56/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.d1DeUUJVeW/DTF2DTF27653.p
% See solution above
% 1.56/1.24 ------------------------
% 1.56/1.25 ---- Cleaned THF ---
% 1.56/1.25 thf(ty_tf_a,type,
% 1.56/1.25 a: $tType ).
% 1.56/1.25
% 1.56/1.25 thf(sy_c_Syntax__Match_Oac__operator,type,
% 1.56/1.25 syntax_ac_operator:
% 1.56/1.25 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 1.56/1.25
% 1.56/1.25 thf(sy_c_Syntax__Match_Osyntax__fo__nomatch,type,
% 1.56/1.25 syntax7388354845996824322omatch:
% 1.56/1.25 !>[A: $tType,B: $tType] : ( A > B > $o ) ).
% 1.56/1.25
% 1.56/1.25 thf(sy_c_Syntax__Match_Osyntax__nomatch,type,
% 1.56/1.25 syntax2379306206330768139omatch:
% 1.56/1.25 !>[A: $tType,B: $tType] : ( A > B > $o ) ).
% 1.56/1.25
% 1.56/1.25 thf(sy_v_a,type,
% 1.56/1.25 a2: a ).
% 1.56/1.25
% 1.56/1.25 thf(sy_v_b,type,
% 1.56/1.25 b: a ).
% 1.56/1.25
% 1.56/1.25 thf(sy_v_c,type,
% 1.56/1.25 c: a ).
% 1.56/1.25
% 1.56/1.25 thf(sy_v_f,type,
% 1.56/1.25 f: a > a > a ).
% 1.56/1.25
% 1.56/1.25 thf(fact_0_ac__operator__axioms,axiom,
% 1.56/1.25 syntax_ac_operator @ a @ f ).
% 1.56/1.25
% 1.56/1.25 thf(fact_1_commute,axiom,
% 1.56/1.25 ! [A2: a,B2: a] :
% 1.56/1.25 ( ( f @ A2 @ B2 )
% 1.56/1.25 = ( f @ B2 @ A2 ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(fact_2_left__commute,axiom,
% 1.56/1.25 ! [A2: a,B2: a,C: a] :
% 1.56/1.25 ( ( f @ A2 @ ( f @ B2 @ C ) )
% 1.56/1.25 = ( f @ B2 @ ( f @ A2 @ C ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(fact_3_right__assoc,axiom,
% 1.56/1.25 ! [A2: a,B2: a,C: a] :
% 1.56/1.25 ( ( f @ ( f @ A2 @ B2 ) @ C )
% 1.56/1.25 = ( f @ A2 @ ( f @ B2 @ C ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(fact_4_syntax__nomatch__def,axiom,
% 1.56/1.25 ! [B: $tType,A: $tType] :
% 1.56/1.25 ( ( syntax2379306206330768139omatch @ A @ B )
% 1.56/1.25 = ( ^ [Pat: A,Obj: B] : $true ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(fact_5_syntax__fo__nomatch__def,axiom,
% 1.56/1.25 ! [B: $tType,A: $tType] :
% 1.56/1.25 ( ( syntax7388354845996824322omatch @ A @ B )
% 1.56/1.25 = ( ^ [Pat: A,Obj: B] : $true ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(fact_6_ac__operator_Ointro,axiom,
% 1.56/1.25 ! [A: $tType,F: A > A > A] :
% 1.56/1.25 ( ! [A3: A,B3: A,C2: A] :
% 1.56/1.25 ( ( F @ ( F @ A3 @ B3 ) @ C2 )
% 1.56/1.25 = ( F @ A3 @ ( F @ B3 @ C2 ) ) )
% 1.56/1.25 => ( ! [A3: A,B3: A] :
% 1.56/1.25 ( ( F @ A3 @ B3 )
% 1.56/1.25 = ( F @ B3 @ A3 ) )
% 1.56/1.25 => ( syntax_ac_operator @ A @ F ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(fact_7_ac__operator_Ocommute,axiom,
% 1.56/1.25 ! [A: $tType,F: A > A > A,A2: A,B2: A] :
% 1.56/1.25 ( ( syntax_ac_operator @ A @ F )
% 1.56/1.25 => ( ( F @ A2 @ B2 )
% 1.56/1.25 = ( F @ B2 @ A2 ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(fact_8_ac__operator_Oleft__assoc,axiom,
% 1.56/1.25 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 1.56/1.25 ( ( syntax_ac_operator @ A @ F )
% 1.56/1.25 => ( ( F @ A2 @ ( F @ B2 @ C ) )
% 1.56/1.25 = ( F @ ( F @ A2 @ B2 ) @ C ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(fact_9_ac__operator_Oright__assoc,axiom,
% 1.56/1.25 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 1.56/1.25 ( ( syntax_ac_operator @ A @ F )
% 1.56/1.25 => ( ( F @ ( F @ A2 @ B2 ) @ C )
% 1.56/1.25 = ( F @ A2 @ ( F @ B2 @ C ) ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(fact_10_ac__operator_Oleft__commute,axiom,
% 1.56/1.25 ! [A: $tType,F: A > A > A,A2: A,B2: A,C: A] :
% 1.56/1.25 ( ( syntax_ac_operator @ A @ F )
% 1.56/1.25 => ( ( F @ A2 @ ( F @ B2 @ C ) )
% 1.56/1.25 = ( F @ B2 @ ( F @ A2 @ C ) ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(fact_11_ac__operator__def,axiom,
% 1.56/1.25 ! [A: $tType] :
% 1.56/1.25 ( ( syntax_ac_operator @ A )
% 1.56/1.25 = ( ^ [F2: A > A > A] :
% 1.56/1.25 ( ! [A4: A,B4: A,C3: A] :
% 1.56/1.25 ( ( F2 @ ( F2 @ A4 @ B4 ) @ C3 )
% 1.56/1.25 = ( F2 @ A4 @ ( F2 @ B4 @ C3 ) ) )
% 1.56/1.25 & ! [A4: A,B4: A] :
% 1.56/1.25 ( ( F2 @ A4 @ B4 )
% 1.56/1.25 = ( F2 @ B4 @ A4 ) ) ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(conj_0,conjecture,
% 1.56/1.25 ( ( f @ ( f @ a2 @ b ) @ c )
% 1.56/1.25 = ( f @ ( f @ a2 @ c ) @ b ) ) ).
% 1.56/1.25 ------------------------
% 1.56/1.26 % (27757)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27653 for (3000ds/18Mi)
% 1.56/1.27 % (27754)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27653 for (3000ds/2Mi)
% 1.56/1.27 % (27754)Instruction limit reached!
% 1.56/1.27 % (27754)------------------------------
% 1.56/1.27 % (27754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.27 % (27754)Termination reason: Unknown
% 1.56/1.27 % (27754)Termination phase: Property scanning
% 1.56/1.27
% 1.56/1.27 % (27754)Memory used [KB]: 1023
% 1.56/1.27 % (27754)Time elapsed: 0.003 s
% 1.56/1.27 % (27754)Instructions burned: 3 (million)
% 1.56/1.27 % (27754)------------------------------
% 1.56/1.27 % (27754)------------------------------
% 1.56/1.27 % (27757)First to succeed.
% 1.56/1.27 % (27757)Refutation found. Thanks to Tanya!
% 1.56/1.27 % SZS status Theorem for DTF2THF_27653
% 1.56/1.27 % SZS output start Proof for DTF2THF_27653
% 1.56/1.27 thf(type_def_6, type, a: $tType).
% 1.56/1.27 thf(func_def_0, type, a: $tType).
% 1.56/1.27 thf(func_def_1, type, syntax_ac_operator: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 1.56/1.27 thf(func_def_2, type, syntax7388354845996824322omatch: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 1.56/1.27 thf(func_def_3, type, syntax2379306206330768139omatch: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 1.56/1.27 thf(func_def_4, type, a2: a).
% 1.56/1.27 thf(func_def_5, type, b: a).
% 1.56/1.27 thf(func_def_6, type, c: a).
% 1.56/1.27 thf(func_def_7, type, f: a > a > a).
% 1.56/1.27 thf(func_def_19, type, sK0: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_20, type, sK1: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_21, type, sK2: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_22, type, sK3: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_23, type, sK4: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_25, type, sK6: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_26, type, sK7: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_27, type, sK8: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_28, type, sK9: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_29, type, sK10: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_30, type, sK11: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_31, type, sK12: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_32, type, sK13: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_33, type, sK14: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_34, type, sK15: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_35, type, sK16: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_36, type, sK17: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_37, type, sK18: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_38, type, sK19: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_39, type, sK20: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_40, type, sK21: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_41, type, sK22: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_42, type, sK23: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_43, type, sK24: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(func_def_44, type, sK25: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.56/1.27 thf(f155,plain,(
% 1.56/1.27 $false),
% 1.56/1.27 inference(subsumption_resolution,[status(thm)],[f154,f54])).
% 1.56/1.27 thf(f54,plain,(
% 1.56/1.27 ( ! [X2 : a,X0 : a,X1 : a] : (((f @ (f @ X0 @ X1) @ X2) = (f @ X0 @ (f @ X1 @ X2)))) )),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f34])).
% 1.56/1.27 thf(f34,plain,(
% 1.56/1.27 ! [X0 : a,X1 : a,X2 : a] : ((f @ (f @ X0 @ X1) @ X2) = (f @ X0 @ (f @ X1 @ X2)))),
% 1.56/1.27 inference(rectify,[status(thm)],[f4])).
% 1.56/1.27 thf(f4,axiom,(
% 1.56/1.27 ! [X2 : a,X3 : a,X4 : a] : ((f @ X2 @ (f @ X3 @ X4)) = (f @ (f @ X2 @ X3) @ X4))),
% 1.56/1.27 file('/export/starexec/sandbox2/tmp/tmp.d1DeUUJVeW/DTF2THF_27653.p',fact_3_right__assoc)).
% 1.56/1.27 thf(f154,plain,(
% 1.56/1.27 ((f @ (f @ a2 @ b) @ c) != (f @ a2 @ (f @ b @ c)))),
% 1.56/1.27 inference(forward_demodulation,[status(thm)],[f153,f51])).
% 1.56/1.27 thf(f51,plain,(
% 1.56/1.27 ( ! [X0 : a,X1 : a] : (((f @ X1 @ X0) = (f @ X0 @ X1))) )),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f36])).
% 1.56/1.27 thf(f36,plain,(
% 1.56/1.27 ! [X0 : a,X1 : a] : ((f @ X1 @ X0) = (f @ X0 @ X1))),
% 1.56/1.27 inference(rectify,[status(thm)],[f2])).
% 1.56/1.27 thf(f2,axiom,(
% 1.56/1.27 ! [X2 : a,X3 : a] : ((f @ X2 @ X3) = (f @ X3 @ X2))),
% 1.56/1.27 file('/export/starexec/sandbox2/tmp/tmp.d1DeUUJVeW/DTF2THF_27653.p',fact_1_commute)).
% 1.56/1.27 thf(f153,plain,(
% 1.56/1.27 ((f @ (f @ a2 @ b) @ c) != (f @ a2 @ (f @ c @ b)))),
% 1.56/1.27 inference(forward_demodulation,[status(thm)],[f57,f54])).
% 1.56/1.27 thf(f57,plain,(
% 1.56/1.27 ((f @ (f @ a2 @ b) @ c) != (f @ (f @ a2 @ c) @ b))),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f37])).
% 1.56/1.27 thf(f37,plain,(
% 1.56/1.27 ((f @ (f @ a2 @ b) @ c) != (f @ (f @ a2 @ c) @ b))),
% 1.56/1.27 inference(flattening,[status(thm)],[f14])).
% 1.56/1.27 thf(f14,negated_conjecture,(
% 1.56/1.27 ~((f @ (f @ a2 @ b) @ c) = (f @ (f @ a2 @ c) @ b))),
% 1.56/1.27 inference(negated_conjecture,[status(cth)],[f13])).
% 1.56/1.27 thf(f13,conjecture,(
% 1.56/1.27 ((f @ (f @ a2 @ b) @ c) = (f @ (f @ a2 @ c) @ b))),
% 1.56/1.27 file('/export/starexec/sandbox2/tmp/tmp.d1DeUUJVeW/DTF2THF_27653.p',conj_0)).
% 1.56/1.27 % SZS output end Proof for DTF2THF_27653
% 1.56/1.27 % (27757)------------------------------
% 1.56/1.27 % (27757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.27 % (27757)Termination reason: Refutation
% 1.56/1.27
% 1.56/1.27 % (27757)Memory used [KB]: 5628
% 1.56/1.27 % (27757)Time elapsed: 0.007 s
% 1.56/1.27 % (27757)Instructions burned: 15 (million)
% 1.56/1.27 % (27757)------------------------------
% 1.56/1.27 % (27757)------------------------------
% 1.56/1.27 % (27750)Success in time 0.005 s
%------------------------------------------------------------------------------