%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP209^3 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 08:56:52 AM UTC 2026
% Result : Theorem 1.68s 1.33s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 11 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 85 ( 5 ~; 0 |; 0 &; 80 @)
% ( 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 : 13 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
syntax_ac_operator_a: ( a > a > a ) > $o ).
thf(func_def_2,type,
a2: a ).
thf(func_def_3,type,
b: a ).
thf(func_def_4,type,
c: a ).
thf(func_def_5,type,
f: a > a > a ).
thf(func_def_17,type,
sK0: ( a > a > a ) > a ).
thf(func_def_18,type,
sK1: ( a > a > a ) > a ).
thf(func_def_19,type,
sK2: ( a > a > a ) > a ).
thf(func_def_20,type,
sK3: ( a > a > a ) > a ).
thf(func_def_21,type,
sK4: ( a > a > a ) > a ).
thf(func_def_23,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f52,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f51,f43]) ).
thf(f43,plain,
! [X2: a,X0: a,X1: a] :
( ( f @ X1 @ ( f @ X0 @ X2 ) )
= ( f @ ( f @ X1 @ X0 ) @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: a,X1: a,X2: a] :
( ( f @ X1 @ ( f @ X0 @ X2 ) )
= ( f @ ( f @ X1 @ X0 ) @ X2 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: a,X0: a,X2: a] :
( ( f @ X0 @ ( f @ X1 @ X2 ) )
= ( f @ ( f @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.9jZzHO5U8A/DTF2THF_30761.p',fact_3_right__assoc) ).
thf(f51,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ a2 @ ( f @ b @ c ) ) ),
inference(forward_demodulation,[status(thm)],[f50,f48]) ).
thf(f48,plain,
! [X0: a,X1: a] :
( ( f @ X0 @ X1 )
= ( f @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: a,X1: a] :
( ( f @ X0 @ X1 )
= ( f @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.9jZzHO5U8A/DTF2THF_30761.p',fact_1_commute) ).
thf(f50,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ a2 @ ( f @ c @ b ) ) ),
inference(forward_demodulation,[status(thm)],[f40,f43]) ).
thf(f40,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,negated_conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f11,conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) ),
file('/export/starexec/sandbox2/tmp/tmp.9jZzHO5U8A/DTF2THF_30761.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP209^3 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n001.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 08:31:20 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.25/0.47 ---- Original DTF file ---
% 0.25/0.47 thf(spec,logic,$$dhol).
% 0.25/0.47 %------------------------------------------------------------------------------
% 0.25/0.47 % File : ITP209^3 : TPTP v9.2.1. Released v8.1.0.
% 0.25/0.47 % Domain : Interactive Theorem Proving
% 0.25/0.47 % Problem : Sledgehammer problem Syntax_Match 00088_002922
% 0.25/0.47 % Version : [Des22] axioms.
% 0.25/0.47 % English :
% 0.25/0.47
% 0.25/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.47 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.25/0.47 % Source : [Des22]
% 0.25/0.47 % Names : 0023_Syntax_Match_00088_002922 [Des22]
% 0.25/0.47
% 0.25/0.47 % Status : Theorem
% 0.25/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0
% 0.25/0.47 % Syntax : Number of formulae : 17 ( 6 unt; 6 typ; 0 def)
% 0.25/0.47 % Number of atoms : 20 ( 13 equ; 0 cnn)
% 0.25/0.47 % Maximal formula atoms : 3 ( 1 avg)
% 0.25/0.47 % Number of connectives : 93 ( 0 ~; 0 |; 1 &; 86 @)
% 0.25/0.47 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.25/0.47 % Maximal formula depth : 7 ( 4 avg)
% 0.25/0.47 % Number of types : 2 ( 1 usr)
% 0.25/0.47 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.25/0.47 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.25/0.47 % Number of variables : 35 ( 1 ^; 34 !; 0 ?; 35 :)
% 0.25/0.47 % SPC : TH0_THM_EQU_NAR
% 0.25/0.47
% 0.25/0.47 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.25/0.47 % from the van Emde Boas Trees session in the Archive of Formal
% 0.25/0.47 % proofs -
% 0.25/0.47 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.25/0.47 % 2022-02-17 14:22:46.652
% 0.25/0.47 %------------------------------------------------------------------------------
% 0.25/0.47 % Could-be-implicit typings (1)
% 0.25/0.47 thf(ty_n_tf__a,type,
% 0.25/0.47 a: $tType ).
% 0.25/0.47
% 0.25/0.47 % Explicit typings (5)
% 0.25/0.47 thf(sy_c_Syntax__Match_Oac__operator_001tf__a,type,
% 0.25/0.47 syntax_ac_operator_a: ( a > a > a ) > $o ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_a,type,
% 0.25/0.47 a2: a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_b,type,
% 0.25/0.47 b: a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_c,type,
% 0.25/0.47 c: a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_f,type,
% 0.25/0.47 f: a > a > a ).
% 0.25/0.47
% 0.25/0.47 % Relevant facts (10)
% 0.25/0.47 thf(fact_0_ac__operator__axioms,axiom,
% 0.25/0.47 syntax_ac_operator_a @ f ).
% 0.25/0.47
% 0.25/0.47 % ac_operator_axioms
% 0.25/0.47 thf(fact_1_commute,axiom,
% 0.25/0.47 ! [A: a,B: a] :
% 0.25/0.47 ( ( f @ A @ B )
% 0.25/0.47 = ( f @ B @ A ) ) ).
% 0.25/0.47
% 0.25/0.47 % commute
% 0.25/0.47 thf(fact_2_left__commute,axiom,
% 0.25/0.47 ! [A: a,B: a,C: a] :
% 0.25/0.47 ( ( f @ A @ ( f @ B @ C ) )
% 0.25/0.47 = ( f @ B @ ( f @ A @ C ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % left_commute
% 0.25/0.47 thf(fact_3_right__assoc,axiom,
% 0.25/0.47 ! [A: a,B: a,C: a] :
% 0.25/0.47 ( ( f @ ( f @ A @ B ) @ C )
% 0.25/0.47 = ( f @ A @ ( f @ B @ C ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % right_assoc
% 0.25/0.47 thf(fact_4_ac__operator_Ointro,axiom,
% 0.25/0.47 ! [F: a > a > a] :
% 0.25/0.47 ( ! [A2: a,B2: a,C2: a] :
% 0.25/0.47 ( ( F @ ( F @ A2 @ B2 ) @ C2 )
% 0.25/0.47 = ( F @ A2 @ ( F @ B2 @ C2 ) ) )
% 0.25/0.47 => ( ! [A2: a,B2: a] :
% 0.25/0.47 ( ( F @ A2 @ B2 )
% 0.25/0.47 = ( F @ B2 @ A2 ) )
% 0.25/0.47 => ( syntax_ac_operator_a @ F ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ac_operator.intro
% 0.25/0.47 thf(fact_5_ac__operator_Ocommute,axiom,
% 0.25/0.47 ! [F: a > a > a,A: a,B: a] :
% 0.25/0.47 ( ( syntax_ac_operator_a @ F )
% 0.25/0.47 => ( ( F @ A @ B )
% 0.25/0.47 = ( F @ B @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ac_operator.commute
% 0.25/0.47 thf(fact_6_ac__operator_Oleft__assoc,axiom,
% 0.25/0.47 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.25/0.47 ( ( syntax_ac_operator_a @ F )
% 0.25/0.47 => ( ( F @ A @ ( F @ B @ C ) )
% 0.25/0.47 = ( F @ ( F @ A @ B ) @ C ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ac_operator.left_assoc
% 0.25/0.47 thf(fact_7_ac__operator_Oright__assoc,axiom,
% 0.25/0.47 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.25/0.47 ( ( syntax_ac_operator_a @ F )
% 0.25/0.47 => ( ( F @ ( F @ A @ B ) @ C )
% 0.25/0.47 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ac_operator.right_assoc
% 0.25/0.47 thf(fact_8_ac__operator_Oleft__commute,axiom,
% 0.25/0.47 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.25/0.47 ( ( syntax_ac_operator_a @ F )
% 0.25/0.47 => ( ( F @ A @ ( F @ B @ C ) )
% 0.25/0.47 = ( F @ B @ ( F @ A @ C ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ac_operator.left_commute
% 0.25/0.47 thf(fact_9_ac__operator__def,axiom,
% 0.25/0.47 ( syntax_ac_operator_a
% 0.25/0.47 = ( ^ [F2: a > a > a] :
% 0.25/0.47 ( ! [A3: a,B3: a,C3: a] :
% 0.25/0.47 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 0.25/0.47 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) )
% 0.25/0.47 & ! [A3: a,B3: a] :
% 0.25/0.47 ( ( F2 @ A3 @ B3 )
% 0.25/0.47 = ( F2 @ B3 @ A3 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ac_operator_def
% 0.25/0.47
% 0.25/0.47 % Conjectures (1)
% 0.25/0.47 thf(conj_0,conjecture,
% 0.25/0.47 ( ( f @ ( f @ a2 @ b ) @ c )
% 0.25/0.47 = ( f @ ( f @ a2 @ c ) @ b ) ) ).
% 0.25/0.47
% 0.25/0.47 %------------------------------------------------------------------------------
% 0.25/0.47 ------------------------
% 1.49/1.29 ---- Embedded in THF ---
% 1.49/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.30 %%% Generated on Tue Feb 24 08:31:21 EST 2026
% 1.49/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.30 %%% Logic specification used:
% 1.49/1.30 %%% thf(spec, logic, $$dhol).
% 1.49/1.30
% 1.49/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.9jZzHO5U8A/DTF2DTF30761.p
% See solution above
% 1.49/1.30 ------------------------
% 1.68/1.31 ---- Cleaned THF ---
% 1.68/1.31 thf(ty_n_tf__a,type,
% 1.68/1.31 a: $tType ).
% 1.68/1.31
% 1.68/1.31 thf(sy_c_Syntax__Match_Oac__operator_001tf__a,type,
% 1.68/1.31 syntax_ac_operator_a: ( a > a > a ) > $o ).
% 1.68/1.31
% 1.68/1.31 thf(sy_v_a,type,
% 1.68/1.31 a2: a ).
% 1.68/1.31
% 1.68/1.31 thf(sy_v_b,type,
% 1.68/1.31 b: a ).
% 1.68/1.31
% 1.68/1.31 thf(sy_v_c,type,
% 1.68/1.31 c: a ).
% 1.68/1.31
% 1.68/1.31 thf(sy_v_f,type,
% 1.68/1.31 f: a > a > a ).
% 1.68/1.31
% 1.68/1.31 thf(fact_0_ac__operator__axioms,axiom,
% 1.68/1.31 syntax_ac_operator_a @ f ).
% 1.68/1.31
% 1.68/1.31 thf(fact_1_commute,axiom,
% 1.68/1.31 ! [A: a,B: a] :
% 1.68/1.31 ( ( f @ A @ B )
% 1.68/1.31 = ( f @ B @ A ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(fact_2_left__commute,axiom,
% 1.68/1.31 ! [A: a,B: a,C: a] :
% 1.68/1.31 ( ( f @ A @ ( f @ B @ C ) )
% 1.68/1.31 = ( f @ B @ ( f @ A @ C ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(fact_3_right__assoc,axiom,
% 1.68/1.31 ! [A: a,B: a,C: a] :
% 1.68/1.31 ( ( f @ ( f @ A @ B ) @ C )
% 1.68/1.31 = ( f @ A @ ( f @ B @ C ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(fact_4_ac__operator_Ointro,axiom,
% 1.68/1.31 ! [F: a > a > a] :
% 1.68/1.31 ( ! [A2: a,B2: a,C2: a] :
% 1.68/1.31 ( ( F @ ( F @ A2 @ B2 ) @ C2 )
% 1.68/1.31 = ( F @ A2 @ ( F @ B2 @ C2 ) ) )
% 1.68/1.31 => ( ! [A2: a,B2: a] :
% 1.68/1.31 ( ( F @ A2 @ B2 )
% 1.68/1.31 = ( F @ B2 @ A2 ) )
% 1.68/1.31 => ( syntax_ac_operator_a @ F ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(fact_5_ac__operator_Ocommute,axiom,
% 1.68/1.31 ! [F: a > a > a,A: a,B: a] :
% 1.68/1.31 ( ( syntax_ac_operator_a @ F )
% 1.68/1.31 => ( ( F @ A @ B )
% 1.68/1.31 = ( F @ B @ A ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(fact_6_ac__operator_Oleft__assoc,axiom,
% 1.68/1.31 ! [F: a > a > a,A: a,B: a,C: a] :
% 1.68/1.31 ( ( syntax_ac_operator_a @ F )
% 1.68/1.31 => ( ( F @ A @ ( F @ B @ C ) )
% 1.68/1.31 = ( F @ ( F @ A @ B ) @ C ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(fact_7_ac__operator_Oright__assoc,axiom,
% 1.68/1.31 ! [F: a > a > a,A: a,B: a,C: a] :
% 1.68/1.31 ( ( syntax_ac_operator_a @ F )
% 1.68/1.31 => ( ( F @ ( F @ A @ B ) @ C )
% 1.68/1.31 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(fact_8_ac__operator_Oleft__commute,axiom,
% 1.68/1.31 ! [F: a > a > a,A: a,B: a,C: a] :
% 1.68/1.31 ( ( syntax_ac_operator_a @ F )
% 1.68/1.31 => ( ( F @ A @ ( F @ B @ C ) )
% 1.68/1.31 = ( F @ B @ ( F @ A @ C ) ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(fact_9_ac__operator__def,axiom,
% 1.68/1.31 ( syntax_ac_operator_a
% 1.68/1.31 = ( ^ [F2: a > a > a] :
% 1.68/1.31 ( ! [A3: a,B3: a,C3: a] :
% 1.68/1.31 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 1.68/1.31 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) )
% 1.68/1.31 & ! [A3: a,B3: a] :
% 1.68/1.31 ( ( F2 @ A3 @ B3 )
% 1.68/1.31 = ( F2 @ B3 @ A3 ) ) ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf(conj_0,conjecture,
% 1.68/1.31 ( ( f @ ( f @ a2 @ b ) @ c )
% 1.68/1.31 = ( f @ ( f @ a2 @ c ) @ b ) ) ).
% 1.68/1.31 ------------------------
% 1.68/1.32 % (31038)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_30761 for (2999ds/2Mi)
% 1.68/1.32 % (31038)Instruction limit reached!
% 1.68/1.32 % (31038)------------------------------
% 1.68/1.32 % (31038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (31038)Termination reason: Unknown
% 1.68/1.32 % (31038)Termination phase: shuffling
% 1.68/1.32
% 1.68/1.32 % (31038)Memory used [KB]: 1023
% 1.68/1.32 % (31038)Time elapsed: 0.002 s
% 1.68/1.32 % (31038)Instructions burned: 2 (million)
% 1.68/1.32 % (31038)------------------------------
% 1.68/1.32 % (31038)------------------------------
% 1.68/1.32 % (31039)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_30761 for (2999ds/275Mi)
% 1.68/1.33 % (31039)First to succeed.
% 1.68/1.33 % (31039)Refutation found. Thanks to Tanya!
% 1.68/1.33 % SZS status Theorem for DTF2THF_30761
% 1.68/1.33 % SZS output start Proof for DTF2THF_30761
% 1.68/1.33 thf(type_def_5, type, a: $tType).
% 1.68/1.33 thf(func_def_0, type, a: $tType).
% 1.68/1.33 thf(func_def_1, type, syntax_ac_operator_a: (a > a > a) > $o).
% 1.68/1.33 thf(func_def_2, type, a2: a).
% 1.68/1.33 thf(func_def_3, type, b: a).
% 1.68/1.33 thf(func_def_4, type, c: a).
% 1.68/1.33 thf(func_def_5, type, f: a > a > a).
% 1.68/1.33 thf(func_def_17, type, sK0: (a > a > a) > a).
% 1.68/1.33 thf(func_def_18, type, sK1: (a > a > a) > a).
% 1.68/1.33 thf(func_def_19, type, sK2: (a > a > a) > a).
% 1.68/1.33 thf(func_def_20, type, sK3: (a > a > a) > a).
% 1.68/1.33 thf(func_def_21, type, sK4: (a > a > a) > a).
% 1.68/1.33 thf(func_def_23, type, ph6: !>[X0: $tType]:(X0)).
% 1.68/1.33 thf(f52,plain,(
% 1.68/1.33 $false),
% 1.68/1.33 inference(subsumption_resolution,[status(thm)],[f51,f43])).
% 1.68/1.33 thf(f43,plain,(
% 1.68/1.33 ( ! [X2 : a,X0 : a,X1 : a] : (((f @ X1 @ (f @ X0 @ X2)) = (f @ (f @ X1 @ X0) @ X2))) )),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f30])).
% 1.68/1.33 thf(f30,plain,(
% 1.68/1.33 ! [X0 : a,X1 : a,X2 : a] : ((f @ X1 @ (f @ X0 @ X2)) = (f @ (f @ X1 @ X0) @ X2))),
% 1.68/1.33 inference(rectify,[status(thm)],[f4])).
% 1.68/1.33 thf(f4,axiom,(
% 1.68/1.33 ! [X1 : a,X0 : a,X2 : a] : ((f @ X0 @ (f @ X1 @ X2)) = (f @ (f @ X0 @ X1) @ X2))),
% 1.68/1.33 file('/export/starexec/sandbox2/tmp/tmp.9jZzHO5U8A/DTF2THF_30761.p',fact_3_right__assoc)).
% 1.68/1.33 thf(f51,plain,(
% 1.68/1.33 ((f @ (f @ a2 @ b) @ c) != (f @ a2 @ (f @ b @ c)))),
% 1.68/1.33 inference(forward_demodulation,[status(thm)],[f50,f48])).
% 1.68/1.33 thf(f48,plain,(
% 1.68/1.33 ( ! [X0 : a,X1 : a] : (((f @ X0 @ X1) = (f @ X1 @ X0))) )),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f2])).
% 1.68/1.33 thf(f2,axiom,(
% 1.68/1.33 ! [X0 : a,X1 : a] : ((f @ X0 @ X1) = (f @ X1 @ X0))),
% 1.68/1.33 file('/export/starexec/sandbox2/tmp/tmp.9jZzHO5U8A/DTF2THF_30761.p',fact_1_commute)).
% 1.68/1.33 thf(f50,plain,(
% 1.68/1.33 ((f @ (f @ a2 @ b) @ c) != (f @ a2 @ (f @ c @ b)))),
% 1.68/1.33 inference(forward_demodulation,[status(thm)],[f40,f43])).
% 1.68/1.33 thf(f40,plain,(
% 1.68/1.33 ((f @ (f @ a2 @ b) @ c) != (f @ (f @ a2 @ c) @ b))),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f28])).
% 1.68/1.33 thf(f28,plain,(
% 1.68/1.33 ((f @ (f @ a2 @ b) @ c) != (f @ (f @ a2 @ c) @ b))),
% 1.68/1.33 inference(flattening,[status(thm)],[f12])).
% 1.68/1.33 thf(f12,negated_conjecture,(
% 1.68/1.33 ~((f @ (f @ a2 @ b) @ c) = (f @ (f @ a2 @ c) @ b))),
% 1.68/1.33 inference(negated_conjecture,[status(cth)],[f11])).
% 1.68/1.33 thf(f11,conjecture,(
% 1.68/1.33 ((f @ (f @ a2 @ b) @ c) = (f @ (f @ a2 @ c) @ b))),
% 1.68/1.33 file('/export/starexec/sandbox2/tmp/tmp.9jZzHO5U8A/DTF2THF_30761.p',conj_0)).
% 1.68/1.33 % SZS output end Proof for DTF2THF_30761
% 1.68/1.33 % (31039)------------------------------
% 1.68/1.33 % (31039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (31039)Termination reason: Refutation
% 1.68/1.33
% 1.68/1.33 % (31039)Memory used [KB]: 5500
% 1.68/1.33 % (31039)Time elapsed: 0.003 s
% 1.68/1.33 % (31039)Instructions burned: 3 (million)
% 1.68/1.33 % (31039)------------------------------
% 1.68/1.33 % (31039)------------------------------
% 1.68/1.33 % (31033)Success in time 0.013 s
%------------------------------------------------------------------------------