%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYP119^1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 : Tue May 5 07:11:00 PM UTC 2026
% Result : Theorem 1.51s 1.25s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 57 ( 37 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 252 ( 23 ~; 17 |; 3 &; 206 @)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 7 con; 0-6 aty)
% Number of variables : 65 ( 6 ^; 53 !; 6 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(type_def_7,type,
sK1: $tType ).
thf(func_def_0,type,
i:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_1,type,
o:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X2 ) > ( X1 > X0 ) > X1 > X2 ) ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_10,type,
sK2: sK0 > sK1 ).
thf(func_def_12,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_13,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK6: sK0 ).
thf(func_def_15,type,
sK7: sK0 ).
thf(func_def_16,type,
sK8: sK0 ).
thf(func_def_17,type,
sK9: sK0 ).
thf(f98,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f41,f79,f97]) ).
thf(f97,plain,
spl3_2,
inference(avatar_contradiction_clause,[status(thm)],[f96]) ).
thf(f96,plain,
( $false
| spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ( sK2 @ sK9 )
!= ( sK2 @ sK9 ) )
| spl3_2 ),
inference(forward_demodulation,[status(thm)],[f94,f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0] :
( ( i @ X0 @ X1 )
= X1 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0] :
( ( i @ X0 @ X1 )
= X1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X3: X0] :
( ( i @ X0 @ X3 )
= X3 ),
file('/export/starexec/sandbox2/tmp/tmp.vLQFhCyWN6/DTF2THF_18797.p','trivia/I_THM_') ).
thf(f94,plain,
( ( ( sK2 @ ( i @ sK0 @ sK9 ) )
!= ( sK2 @ sK9 ) )
| spl3_2 ),
inference(beta_eta_normalization,[status(thm)],[f93]) ).
thf(f93,plain,
( ( ( ^ [Y0: sK0] : ( sK2 @ ( i @ sK0 @ Y0 ) )
@ sK9 )
!= ( sK2 @ sK9 ) )
| spl3_2 ),
inference(negative_extensionality,[status(thm)],[f88]) ).
thf(f88,plain,
( ( sK2
!= ( ^ [Y0: sK0] : ( sK2 @ ( i @ sK0 @ Y0 ) ) ) )
| spl3_2 ),
inference(superposition,[status(thm)],[f40,f22]) ).
thf(f22,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1] :
( ( ^ [Y0: X2] : ( X3 @ ( X4 @ Y0 ) ) )
= ( o @ X1 @ X2 @ X0 @ X3 @ X4 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1] :
( ( ^ [Y0: X2] : ( X3 @ ( X4 @ Y0 ) ) )
= ( o @ X1 @ X2 @ X0 @ X3 @ X4 ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1] :
( ( ^ [X5: X2] : ( X3 @ ( X4 @ X5 ) ) )
= ( o @ X1 @ X2 @ X0 @ X3 @ X4 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X4: X1 > X2,X5: X0 > X1] :
( ( ^ [X3: X0] : ( X4 @ ( X5 @ X3 ) ) )
= ( o @ X1 @ X0 @ X2 @ X4 @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vLQFhCyWN6/DTF2THF_18797.p','trivia/o_DEF_') ).
thf(f40,plain,
( ( ( o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0 )
!= sK2 )
| spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl3_2
<=> ( ( o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0 )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f79,plain,
spl3_1,
inference(avatar_contradiction_clause,[status(thm)],[f78]) ).
thf(f78,plain,
( $false
| spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ( sK2 @ sK6 )
!= ( sK2 @ sK6 ) )
| spl3_1 ),
inference(superposition,[status(thm)],[f60,f19]) ).
thf(f60,plain,
( ( ( sK2 @ sK6 )
!= ( i @ sK1 @ ( sK2 @ sK6 ) ) )
| spl3_1 ),
inference(superposition,[status(thm)],[f52,f18]) ).
thf(f18,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1,X5: X2] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 @ X5 )
= ( X3 @ ( X4 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1,X5: X2] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 @ X5 )
= ( X3 @ ( X4 @ X5 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X4: X1 > X2,X5: X0 > X1,X3: X0] :
( ( X4 @ ( X5 @ X3 ) )
= ( o @ X1 @ X0 @ X2 @ X4 @ X5 @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vLQFhCyWN6/DTF2THF_18797.p','trivia/o_THM_') ).
thf(f52,plain,
( ( ( sK2 @ sK6 )
!= ( o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2 @ sK6 ) )
| spl3_1 ),
inference(negative_extensionality,[status(thm)],[f36]) ).
thf(f36,plain,
( ( sK2
!= ( o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2 ) )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl3_1
<=> ( sK2
= ( o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f41,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f38,f34]) ).
thf(f21,plain,
( ( sK2
!= ( o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2 ) )
| ( ( o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0 )
!= sK2 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0 )
!= sK2 )
| ( sK2
!= ( o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: $tType,X1: $tType,X2: X0 > X1] :
( ( ( o @ X0 @ X0 @ X1 @ X2 @ i @ X0 )
!= X2 )
| ( ( o @ X1 @ X0 @ X1 @ i @ X1 @ X2 )
!= X2 ) )
=> ( ( ( o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0 )
!= sK2 )
| ( sK2
!= ( o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
? [X0: $tType,X1: $tType,X2: X0 > X1] :
( ( ( o @ X0 @ X0 @ X1 @ X2 @ i @ X0 )
!= X2 )
| ( ( o @ X1 @ X0 @ X1 @ i @ X1 @ X2 )
!= X2 ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > X1] :
( ( ( o @ X1 @ X0 @ X1 @ i @ X1 @ X2 )
= X2 )
& ( ( o @ X0 @ X0 @ X1 @ X2 @ i @ X0 )
= X2 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X1: $tType,X4: X0 > X1] :
( ( ( o @ X0 @ X0 @ X1 @ X4 @ i @ X0 )
= X4 )
& ( ( o @ X1 @ X0 @ X1 @ i @ X1 @ X4 )
= X4 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X0: $tType,X1: $tType,X4: X0 > X1] :
( ( ( o @ X0 @ X0 @ X1 @ X4 @ i @ X0 )
= X4 )
& ( ( o @ X1 @ X0 @ X1 @ i @ X1 @ X4 )
= X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vLQFhCyWN6/DTF2THF_18797.p','trivia/I_O_ID_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYP119^1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n013.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 : Mon May 4 17:53:25 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SYP119^1 : TPTP v9.3.0. Released v9.3.0.
% 0.20/0.45 % Domain : Syntactic
% 0.20/0.45 % Problem : Polymorphic identity - function composition idempotence
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English :
% 0.20/0.45
% 0.20/0.45 % Refs :
% 0.20/0.45 % Source : [TPTP]
% 0.20/0.45 % Names : 001 [TPTP]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : ? v9.3.0
% 0.20/0.45 % Syntax : Number of formulae : 7 ( 4 unt; 2 typ; 0 def)
% 0.20/0.45 % Number of atoms : 8 ( 8 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 2 ( 1 avg)
% 0.20/0.45 % Number of connectives : 32 ( 0 ~; 0 |; 1 &; 31 @)
% 0.20/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 7 ( 5 avg)
% 0.20/0.45 % Number of types : 0 ( 0 usr)
% 0.20/0.45 % Number of type decls : 2 ( 2 !>P; 0 !>D)
% 0.20/0.45 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 3 ( 2 usr; 0 con; 2-6 aty)
% 0.20/0.45 % Number of variables : 26 ( 1 ^; 21 !; 0 ?; 26 :)
% 0.20/0.45 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.45 % SPC : TH1_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : Originally from HOL Light
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(i,type,
% 0.20/0.45 i:
% 0.20/0.45 !>[A: $tType] : ( A > A ) ).
% 0.20/0.45
% 0.20/0.45 thf(o,type,
% 0.20/0.45 o:
% 0.20/0.45 !>[B: $tType,A: $tType,C: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.20/0.45
% 0.20/0.45 thf('trivia/I_THM_',axiom,
% 0.20/0.45 ! [A: $tType,X: A] :
% 0.20/0.45 ( ( i @ A @ X )
% 0.20/0.45 = X ) ).
% 0.20/0.45
% 0.20/0.45 thf('trivia/o_DEF_',axiom,
% 0.20/0.45 ! [C: $tType,B: $tType,A: $tType,F: B > C,G: A > B] :
% 0.20/0.45 ( ( o @ B @ A @ C @ F @ G )
% 0.20/0.45 = ( ^ [X: A] : ( F @ ( G @ X ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf('trivia/o_THM_',axiom,
% 0.20/0.45 ! [C: $tType,B: $tType,A: $tType,F: B > C,G: A > B,X: A] :
% 0.20/0.45 ( ( o @ B @ A @ C @ F @ G @ X )
% 0.20/0.45 = ( F @ ( G @ X ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf('class/FUN_EQ_THM_',axiom,
% 0.20/0.45 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.20/0.45 ( ( F = G )
% 0.20/0.45 = ( ! [X: A] :
% 0.20/0.45 ( ( F @ X )
% 0.20/0.45 = ( G @ X ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf('trivia/I_O_ID_',conjecture,
% 0.20/0.45 ! [A: $tType,B: $tType,F: A > B] :
% 0.20/0.45 ( ( ( o @ B @ A @ B @ ( i @ B ) @ F )
% 0.20/0.45 = F )
% 0.20/0.45 & ( ( o @ A @ A @ B @ F @ ( i @ A ) )
% 0.20/0.45 = F ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.51/1.22 ---- Embedded in THF ---
% 1.51/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.22 %%% Generated on Mon May 04 17:53:26 EDT 2026
% 1.51/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.22 %%% Logic specification used:
% 1.51/1.22 %%% thf(spec, logic, $$dhol).
% 1.51/1.22
% 1.51/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.vLQFhCyWN6/DTF2DTF18797.p
% See solution above
% 1.51/1.22 ------------------------
% 1.51/1.23 ---- Cleaned THF ---
% 1.51/1.23 thf(i,type,
% 1.51/1.23 i:
% 1.51/1.23 !>[A: $tType] : ( A > A ) ).
% 1.51/1.23
% 1.51/1.23 thf(o,type,
% 1.51/1.23 o:
% 1.51/1.23 !>[B: $tType,A: $tType,C: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 1.51/1.23
% 1.51/1.23 thf('trivia/I_THM_',axiom,
% 1.51/1.23 ! [A: $tType,X: A] :
% 1.51/1.23 ( ( i @ A @ X )
% 1.51/1.23 = X ) ).
% 1.51/1.23
% 1.51/1.23 thf('trivia/o_DEF_',axiom,
% 1.51/1.23 ! [C: $tType,B: $tType,A: $tType,F: B > C,G: A > B] :
% 1.51/1.23 ( ( o @ B @ A @ C @ F @ G )
% 1.51/1.23 = ( ^ [X: A] : ( F @ ( G @ X ) ) ) ) ).
% 1.51/1.23
% 1.51/1.23 thf('trivia/o_THM_',axiom,
% 1.51/1.23 ! [C: $tType,B: $tType,A: $tType,F: B > C,G: A > B,X: A] :
% 1.51/1.23 ( ( o @ B @ A @ C @ F @ G @ X )
% 1.51/1.23 = ( F @ ( G @ X ) ) ) ).
% 1.51/1.23
% 1.51/1.23 thf('class/FUN_EQ_THM_',axiom,
% 1.51/1.23 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 1.51/1.23 ( ( F = G )
% 1.51/1.23 = ( ! [X: A] :
% 1.51/1.23 ( ( F @ X )
% 1.51/1.23 = ( G @ X ) ) ) ) ).
% 1.51/1.23
% 1.51/1.23 thf('trivia/I_O_ID_',conjecture,
% 1.51/1.23 ! [A: $tType,B: $tType,F: A > B] :
% 1.51/1.23 ( ( ( o @ B @ A @ B @ ( i @ B ) @ F )
% 1.51/1.23 = F )
% 1.51/1.23 & ( ( o @ A @ A @ B @ F @ ( i @ A ) )
% 1.51/1.23 = F ) ) ).
% 1.51/1.23 ------------------------
% 1.51/1.24 % (18897)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_18797 for (2999ds/27Mi)
% 1.51/1.24 % (18896)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_18797 for (2999ds/4Mi)
% 1.51/1.25 % (18896)Instruction limit reached!
% 1.51/1.25 % (18896)------------------------------
% 1.51/1.25 % (18896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.25 % (18896)Termination reason: Unknown
% 1.51/1.25 % (18896)Termination phase: Saturation
% 1.51/1.25
% 1.51/1.25 % (18896)Memory used [KB]: 5500
% 1.51/1.25 % (18896)Time elapsed: 0.003 s
% 1.51/1.25 % (18896)Instructions burned: 5 (million)
% 1.51/1.25 % (18896)------------------------------
% 1.51/1.25 % (18896)------------------------------
% 1.51/1.25 % (18897)First to succeed.
% 1.51/1.25 % (18897)Refutation found. Thanks to Tanya!
% 1.51/1.25 % SZS status Theorem for DTF2THF_18797
% 1.51/1.25 % SZS output start Proof for DTF2THF_18797
% 1.51/1.25 thf(type_def_6, type, sK0: $tType).
% 1.51/1.25 thf(type_def_7, type, sK1: $tType).
% 1.51/1.25 thf(func_def_0, type, i: !>[X0: $tType]:(X0 > X0)).
% 1.51/1.25 thf(func_def_1, type, o: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X2) > (X1 > X0) > X1 > X2)).
% 1.51/1.25 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.51/1.25 thf(func_def_10, type, sK2: sK0 > sK1).
% 1.51/1.25 thf(func_def_12, type, sK4: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 1.51/1.25 thf(func_def_13, type, ph5: !>[X0: $tType]:(X0)).
% 1.51/1.25 thf(func_def_14, type, sK6: sK0).
% 1.51/1.25 thf(func_def_15, type, sK7: sK0).
% 1.51/1.25 thf(func_def_16, type, sK8: sK0).
% 1.51/1.25 thf(func_def_17, type, sK9: sK0).
% 1.51/1.25 thf(f98,plain,(
% 1.51/1.25 $false),
% 1.51/1.25 inference(avatar_sat_refutation,[status(thm)],[f41,f79,f97])).
% 1.51/1.25 thf(f97,plain,(
% 1.51/1.25 spl3_2),
% 1.51/1.25 inference(avatar_contradiction_clause,[status(thm)],[f96])).
% 1.51/1.25 thf(f96,plain,(
% 1.51/1.25 $false | spl3_2),
% 1.51/1.25 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.51/1.25 thf(f95,plain,(
% 1.51/1.25 ((sK2 @ sK9) != (sK2 @ sK9)) | spl3_2),
% 1.51/1.25 inference(forward_demodulation,[status(thm)],[f94,f19])).
% 1.51/1.25 thf(f19,plain,(
% 1.51/1.25 ( ! [X0 : $tType,X1 : X0] : (((i @ X0 @ X1) = X1)) )),
% 1.51/1.25 inference(cnf_transformation,[status(thm)],[f13])).
% 1.51/1.25 thf(f13,plain,(
% 1.51/1.25 ! [X0 : $tType,X1 : X0] : ((i @ X0 @ X1) = X1)),
% 1.51/1.25 inference(rectify,[status(thm)],[f1])).
% 1.51/1.25 thf(f1,axiom,(
% 1.51/1.25 ! [X0 : $tType,X3 : X0] : ((i @ X0 @ X3) = X3)),
% 1.51/1.25 file('/export/starexec/sandbox2/tmp/tmp.vLQFhCyWN6/DTF2THF_18797.p','trivia/I_THM_')).
% 1.51/1.25 thf(f94,plain,(
% 1.51/1.25 ((sK2 @ (i @ sK0 @ sK9)) != (sK2 @ sK9)) | spl3_2),
% 1.51/1.25 inference(beta_eta_normalization,[status(thm)],[f93])).
% 1.51/1.25 thf(f93,plain,(
% 1.51/1.25 (((^[Y0 : sK0]: (sK2 @ (i @ sK0 @ Y0))) @ sK9) != (sK2 @ sK9)) | spl3_2),
% 1.51/1.25 inference(negative_extensionality,[status(thm)],[f88])).
% 1.51/1.25 thf(f88,plain,(
% 1.51/1.25 (sK2 != (^[Y0 : sK0]: (sK2 @ (i @ sK0 @ Y0)))) | spl3_2),
% 1.51/1.25 inference(superposition,[status(thm)],[f40,f22])).
% 1.51/1.25 thf(f22,plain,(
% 1.51/1.25 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X1 > X0,X4 : X2 > X1] : (((^[Y0 : X2]: (X3 @ (X4 @ Y0))) = (o @ X1 @ X2 @ X0 @ X3 @ X4))) )),
% 1.51/1.25 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.25 thf(f9,plain,(
% 1.51/1.25 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1 > X0,X4 : X2 > X1] : ((^[Y0 : X2]: (X3 @ (X4 @ Y0))) = (o @ X1 @ X2 @ X0 @ X3 @ X4))),
% 1.51/1.25 inference(fool_elimination,[status(thm)],[f8])).
% 1.51/1.25 thf(f8,plain,(
% 1.51/1.25 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1 > X0,X4 : X2 > X1] : ((^[X5 : X2] : (X3 @ (X4 @ X5))) = (o @ X1 @ X2 @ X0 @ X3 @ X4))),
% 1.51/1.25 inference(rectify,[status(thm)],[f2])).
% 1.51/1.25 thf(f2,axiom,(
% 1.51/1.25 ! [X2 : $tType,X1 : $tType,X0 : $tType,X4 : X1 > X2,X5 : X0 > X1] : ((^[X3 : X0] : (X4 @ (X5 @ X3))) = (o @ X1 @ X0 @ X2 @ X4 @ X5))),
% 1.51/1.25 file('/export/starexec/sandbox2/tmp/tmp.vLQFhCyWN6/DTF2THF_18797.p','trivia/o_DEF_')).
% 1.51/1.25 thf(f40,plain,(
% 1.51/1.25 ((o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0) != sK2) | spl3_2),
% 1.51/1.25 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.51/1.25 thf(f38,definition,(
% 1.51/1.25 spl3_2 <=> ((o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0) = sK2)),
% 1.51/1.25 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.51/1.25 thf(f79,plain,(
% 1.51/1.25 spl3_1),
% 1.51/1.25 inference(avatar_contradiction_clause,[status(thm)],[f78])).
% 1.51/1.25 thf(f78,plain,(
% 1.51/1.25 $false | spl3_1),
% 1.51/1.25 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.51/1.25 thf(f77,plain,(
% 1.51/1.25 ((sK2 @ sK6) != (sK2 @ sK6)) | spl3_1),
% 1.51/1.25 inference(superposition,[status(thm)],[f60,f19])).
% 1.51/1.25 thf(f60,plain,(
% 1.51/1.25 ((sK2 @ sK6) != (i @ sK1 @ (sK2 @ sK6))) | spl3_1),
% 1.51/1.25 inference(superposition,[status(thm)],[f52,f18])).
% 1.51/1.25 thf(f18,plain,(
% 1.51/1.25 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X1 > X0,X4 : X2 > X1,X5 : X2] : (((o @ X1 @ X2 @ X0 @ X3 @ X4 @ X5) = (X3 @ (X4 @ X5)))) )),
% 1.51/1.25 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.25 thf(f12,plain,(
% 1.51/1.25 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1 > X0,X4 : X2 > X1,X5 : X2] : ((o @ X1 @ X2 @ X0 @ X3 @ X4 @ X5) = (X3 @ (X4 @ X5)))),
% 1.51/1.25 inference(rectify,[status(thm)],[f3])).
% 1.51/1.25 thf(f3,axiom,(
% 1.51/1.25 ! [X2 : $tType,X1 : $tType,X0 : $tType,X4 : X1 > X2,X5 : X0 > X1,X3 : X0] : ((X4 @ (X5 @ X3)) = (o @ X1 @ X0 @ X2 @ X4 @ X5 @ X3))),
% 1.51/1.25 file('/export/starexec/sandbox2/tmp/tmp.vLQFhCyWN6/DTF2THF_18797.p','trivia/o_THM_')).
% 1.51/1.25 thf(f52,plain,(
% 1.51/1.25 ((sK2 @ sK6) != (o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2 @ sK6)) | spl3_1),
% 1.51/1.25 inference(negative_extensionality,[status(thm)],[f36])).
% 1.51/1.25 thf(f36,plain,(
% 1.51/1.25 (sK2 != (o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2)) | spl3_1),
% 1.51/1.25 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.51/1.25 thf(f34,definition,(
% 1.51/1.25 spl3_1 <=> (sK2 = (o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2))),
% 1.51/1.25 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.51/1.25 thf(f41,plain,(
% 1.51/1.25 ~spl3_1 | ~spl3_2),
% 1.51/1.25 inference(avatar_split_clause,[status(thm)],[f21,f38,f34])).
% 1.51/1.25 thf(f21,plain,(
% 1.51/1.25 (sK2 != (o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2)) | ((o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0) != sK2)),
% 1.51/1.25 inference(cnf_transformation,[status(thm)],[f17])).
% 1.51/1.25 thf(f17,plain,(
% 1.51/1.25 ((o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0) != sK2) | (sK2 != (o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2))),
% 1.51/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16])).
% 1.51/1.25 thf(f16,plain,(
% 1.51/1.25 ? [X0 : $tType,X1 : $tType,X2 : X0 > X1] : (((o @ X0 @ X0 @ X1 @ X2 @ i @ X0) != X2) | ((o @ X1 @ X0 @ X1 @ i @ X1 @ X2) != X2)) => (((o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0) != sK2) | (sK2 != (o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2)))),
% 1.51/1.25 introduced(definition,[],[choice_axiom])).
% 1.51/1.25 thf(f15,plain,(
% 1.51/1.25 ? [X0 : $tType,X1 : $tType,X2 : X0 > X1] : (((o @ X0 @ X0 @ X1 @ X2 @ i @ X0) != X2) | ((o @ X1 @ X0 @ X1 @ i @ X1 @ X2) != X2))),
% 1.51/1.25 inference(ennf_transformation,[status(thm)],[f14])).
% 1.51/1.25 thf(f14,plain,(
% 1.51/1.25 ~! [X0 : $tType,X1 : $tType,X2 : X0 > X1] : (((o @ X1 @ X0 @ X1 @ i @ X1 @ X2) = X2) & ((o @ X0 @ X0 @ X1 @ X2 @ i @ X0) = X2))),
% 1.51/1.25 inference(rectify,[status(thm)],[f6])).
% 1.51/1.25 thf(f6,negated_conjecture,(
% 1.51/1.25 ~! [X0 : $tType,X1 : $tType,X4 : X0 > X1] : (((o @ X0 @ X0 @ X1 @ X4 @ i @ X0) = X4) & ((o @ X1 @ X0 @ X1 @ i @ X1 @ X4) = X4))),
% 1.51/1.25 inference(negated_conjecture,[status(cth)],[f5])).
% 1.51/1.25 thf(f5,conjecture,(
% 1.51/1.25 ! [X0 : $tType,X1 : $tType,X4 : X0 > X1] : (((o @ X0 @ X0 @ X1 @ X4 @ i @ X0) = X4) & ((o @ X1 @ X0 @ X1 @ i @ X1 @ X4) = X4))),
% 1.51/1.25 file('/export/starexec/sandbox2/tmp/tmp.vLQFhCyWN6/DTF2THF_18797.p','trivia/I_O_ID_')).
% 1.51/1.25 % SZS output end Proof for DTF2THF_18797
% 1.51/1.25 % (18897)------------------------------
% 1.51/1.25 % (18897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.25 % (18897)Termination reason: Refutation
% 1.51/1.25
% 1.51/1.25 % (18897)Memory used [KB]: 5628
% 1.51/1.25 % (18897)Time elapsed: 0.007 s
% 1.51/1.25 % (18897)Instructions burned: 11 (million)
% 1.51/1.25 % (18897)------------------------------
% 1.51/1.25 % (18897)------------------------------
% 1.51/1.25 % (18894)Success in time 0.005 s
%------------------------------------------------------------------------------