%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYP118^1 : 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 : n018.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 1.63s 1.31s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 300 ( 14 ~; 0 |; 0 &; 285 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-6 aty)
% Number of variables : 82 ( 15 ^; 53 !; 14 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(type_def_7,type,
sK1: $tType ).
thf(type_def_8,type,
sK2: $tType ).
thf(type_def_9,type,
sK3: $tType ).
thf(func_def_0,type,
o:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X2 ) > ( X1 > X0 ) > X1 > X2 ) ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_7,type,
sK4: sK1 > sK0 ).
thf(func_def_8,type,
sK5: sK3 > sK1 ).
thf(func_def_9,type,
sK6: sK2 > sK3 ).
thf(func_def_11,type,
ph8:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK9: sK2 ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( sK4 @ ( sK5 @ ( sK6 @ sK9 ) ) )
!= ( sK4 @ ( sK5 @ ( sK6 @ sK9 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f21,f14]) ).
thf(f14,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(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1,X5: X2] :
( ( ^ [Y0: X2] : ( X3 @ ( X4 @ Y0 ) )
@ X5 )
= ( o @ X1 @ X2 @ X0 @ X3 @ X4 @ X5 ) ),
inference(argument_congruence,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 )
= ( ^ [Y0: X2] : ( X3 @ ( X4 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 )
= ( ^ [Y0: X2] : ( X3 @ ( X4 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 )
= ( ^ [X5: X2] : ( X3 @ ( X4 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $tType,X0: $tType,X1: $tType,X3: X0 > X2,X4: X1 > X0] :
( ( o @ X0 @ X1 @ X2 @ X3 @ X4 )
= ( ^ [X5: X1] : ( X3 @ ( X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MqnCB3EcZJ/DTF2THF_10904.p','trivia/o_DEF_') ).
thf(f21,plain,
( ( sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ sK9 ) )
!= ( sK4 @ ( sK5 @ ( sK6 @ sK9 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [Y0: sK2] : ( sK4 @ ( sK5 @ ( sK6 @ Y0 ) ) )
@ sK9 )
!= ( ^ [Y0: sK2] : ( sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0 ) )
@ sK9 ) ),
inference(negative_extensionality,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: sK2] : ( sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0 ) ) )
!= ( ^ [Y0: sK2] : ( sK4 @ ( sK5 @ ( sK6 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: sK2] : ( sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0 ) ) )
!= ( ^ [Y0: sK2] :
( ^ [Y1: sK3] : ( sK4 @ ( sK5 @ Y1 ) )
@ ( sK6 @ Y0 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f17,f12]) ).
thf(f17,plain,
( ( o @ sK3 @ sK2 @ sK0
@ ^ [Y0: sK3] : ( sK4 @ ( sK5 @ Y0 ) )
@ sK6 )
!= ( ^ [Y0: sK2] : ( sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f16,f12]) ).
thf(f16,plain,
( ( ^ [Y0: sK2] : ( sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0 ) ) )
!= ( o @ sK3 @ sK2 @ sK0 @ ( o @ sK1 @ sK3 @ sK0 @ sK4 @ sK5 ) @ sK6 ) ),
inference(forward_demodulation,[status(thm)],[f11,f12]) ).
thf(f11,plain,
( ( o @ sK3 @ sK2 @ sK0 @ ( o @ sK1 @ sK3 @ sK0 @ sK4 @ sK5 ) @ sK6 )
!= ( o @ sK1 @ sK2 @ sK0 @ sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( o @ sK3 @ sK2 @ sK0 @ ( o @ sK1 @ sK3 @ sK0 @ sK4 @ sK5 ) @ sK6 )
!= ( o @ sK1 @ sK2 @ sK0 @ sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: X1 > X0,X5: X3 > X1,X6: X2 > X3] :
( ( o @ X1 @ X2 @ X0 @ X4 @ ( o @ X3 @ X2 @ X1 @ X5 @ X6 ) )
!= ( o @ X3 @ X2 @ X0 @ ( o @ X1 @ X3 @ X0 @ X4 @ X5 ) @ X6 ) )
=> ( ( o @ sK3 @ sK2 @ sK0 @ ( o @ sK1 @ sK3 @ sK0 @ sK4 @ sK5 ) @ sK6 )
!= ( o @ sK1 @ sK2 @ sK0 @ sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: X1 > X0,X5: X3 > X1,X6: X2 > X3] :
( ( o @ X1 @ X2 @ X0 @ X4 @ ( o @ X3 @ X2 @ X1 @ X5 @ X6 ) )
!= ( o @ X3 @ X2 @ X0 @ ( o @ X1 @ X3 @ X0 @ X4 @ X5 ) @ X6 ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: X1 > X0,X5: X3 > X1,X6: X2 > X3] :
( ( o @ X1 @ X2 @ X0 @ X4 @ ( o @ X3 @ X2 @ X1 @ X5 @ X6 ) )
= ( o @ X3 @ X2 @ X0 @ ( o @ X1 @ X3 @ X0 @ X4 @ X5 ) @ X6 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X6: $tType,X2: $tType,X1: $tType,X0: $tType,X3: X2 > X6,X4: X0 > X2,X7: X1 > X0] :
( ( o @ X2 @ X1 @ X6 @ X3 @ ( o @ X0 @ X1 @ X2 @ X4 @ X7 ) )
= ( o @ X0 @ X1 @ X6 @ ( o @ X2 @ X0 @ X6 @ X3 @ X4 ) @ X7 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X6: $tType,X2: $tType,X1: $tType,X0: $tType,X3: X2 > X6,X4: X0 > X2,X7: X1 > X0] :
( ( o @ X2 @ X1 @ X6 @ X3 @ ( o @ X0 @ X1 @ X2 @ X4 @ X7 ) )
= ( o @ X0 @ X1 @ X6 @ ( o @ X2 @ X0 @ X6 @ X3 @ X4 ) @ X7 ) ),
file('/export/starexec/sandbox2/tmp/tmp.MqnCB3EcZJ/DTF2THF_10904.p','trivia/o_ASSOC_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYP118^1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n018.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Mon May 4 17:52:17 EDT 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SYP118^1 : TPTP v9.3.0. Released v9.3.0.
% 0.30/0.47 % Domain : Syntactic
% 0.30/0.47 % Problem : Associativity of function composition
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs :
% 0.30/0.47 % Source : [TPTP]
% 0.30/0.47 % Names : 001 [TPTP]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : ? v9.3.0
% 0.30/0.47 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 0 def)
% 0.30/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.47 % Number of connectives : 27 ( 0 ~; 0 |; 0 &; 27 @)
% 0.30/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 8 ( 7 avg)
% 0.30/0.47 % Number of types : 0 ( 0 usr)
% 0.30/0.47 % Number of type decls : 1 ( 1 !>P; 0 !>D)
% 0.30/0.47 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 2 ( 1 usr; 0 con; 2-6 aty)
% 0.30/0.47 % Number of variables : 16 ( 1 ^; 12 !; 0 ?; 16 :)
% 0.30/0.47 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.47 % SPC : TH1_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : Originally from HOL Light
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(o,type,
% 0.30/0.47 o:
% 0.30/0.47 !>[B: $tType,A: $tType,C: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.30/0.47
% 0.30/0.47 thf('trivia/o_DEF_',axiom,
% 0.30/0.47 ! [C: $tType,B: $tType,A: $tType,F: B > C,G: A > B] :
% 0.30/0.47 ( ( o @ B @ A @ C @ F @ G )
% 0.30/0.47 = ( ^ [X: A] : ( F @ ( G @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf('trivia/o_ASSOC_',conjecture,
% 0.30/0.47 ! [D: $tType,C: $tType,A: $tType,B: $tType,F: C > D,G: B > C,H: A > B] :
% 0.30/0.47 ( ( o @ C @ A @ D @ F @ ( o @ B @ A @ C @ G @ H ) )
% 0.30/0.47 = ( o @ B @ A @ D @ ( o @ C @ B @ D @ F @ G ) @ H ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.28 %%% Generated on Mon May 04 17:52:17 EDT 2026
% 1.46/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.28 %%% Logic specification used:
% 1.46/1.28 %%% thf(spec, logic, $$dhol).
% 1.46/1.28
% 1.46/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.MqnCB3EcZJ/DTF2DTF10904.p
% See solution above
% 1.46/1.28 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.29 thf(o,type,
% 1.46/1.29 o:
% 1.46/1.29 !>[B: $tType,A: $tType,C: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 1.46/1.29
% 1.46/1.29 thf('trivia/o_DEF_',axiom,
% 1.46/1.29 ! [C: $tType,B: $tType,A: $tType,F: B > C,G: A > B] :
% 1.46/1.29 ( ( o @ B @ A @ C @ F @ G )
% 1.46/1.29 = ( ^ [X: A] : ( F @ ( G @ X ) ) ) ) ).
% 1.46/1.29
% 1.46/1.29 thf('trivia/o_ASSOC_',conjecture,
% 1.46/1.29 ! [D: $tType,C: $tType,A: $tType,B: $tType,F: C > D,G: B > C,H: A > B] :
% 1.46/1.29 ( ( o @ C @ A @ D @ F @ ( o @ B @ A @ C @ G @ H ) )
% 1.46/1.29 = ( o @ B @ A @ D @ ( o @ C @ B @ D @ F @ G ) @ H ) ) ).
% 1.46/1.29 ------------------------
% 1.63/1.30 % (11018)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_10904 for (2999ds/4Mi)
% 1.63/1.30 % (11017)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10904 for (2999ds/183Mi)
% 1.63/1.30 % (11018)Instruction limit reached!
% 1.63/1.30 % (11018)------------------------------
% 1.63/1.30 % (11018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (11018)Termination reason: Unknown
% 1.63/1.30 % (11018)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (11018)Memory used [KB]: 5500
% 1.63/1.30 % (11018)Time elapsed: 0.003 s
% 1.63/1.30 % (11018)Instructions burned: 5 (million)
% 1.63/1.30 % (11018)------------------------------
% 1.63/1.30 % (11018)------------------------------
% 1.63/1.31 % (11021)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_10904 for (2999ds/2Mi)
% 1.63/1.31 % (11022)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_10904 for (2999ds/275Mi)
% 1.63/1.31 % (11020)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10904 for (2999ds/2Mi)
% 1.63/1.31 % (11023)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10904 for (2999ds/18Mi)
% 1.63/1.31 % (11019)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_10904 for (2999ds/27Mi)
% 1.63/1.31 % Exception at run slice level
% 1.63/1.31 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.63/1.31 % (11022)Refutation not found, incomplete strategy
% 1.63/1.31 % (11022)------------------------------
% 1.63/1.31 % (11022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (11022)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.31
% 1.63/1.31
% 1.63/1.31 % (11022)Memory used [KB]: 5500
% 1.63/1.31 % (11022)Time elapsed: 0.003 s
% 1.63/1.31 % (11022)Instructions burned: 2 (million)
% 1.63/1.31 % (11022)------------------------------
% 1.63/1.31 % (11022)------------------------------
% 1.63/1.31 % (11020)Instruction limit reached!
% 1.63/1.31 % (11020)------------------------------
% 1.63/1.31 % (11020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (11020)Termination reason: Unknown
% 1.63/1.31 % (11020)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (11020)Memory used [KB]: 5500
% 1.63/1.31 % (11020)Time elapsed: 0.004 s
% 1.63/1.31 % (11020)Instructions burned: 2 (million)
% 1.63/1.31 % (11020)------------------------------
% 1.63/1.31 % (11020)------------------------------
% 1.63/1.31 % (11019)First to succeed.
% 1.63/1.31 % (11019)Refutation found. Thanks to Tanya!
% 1.63/1.31 % SZS status Theorem for DTF2THF_10904
% 1.63/1.31 % SZS output start Proof for DTF2THF_10904
% 1.63/1.31 thf(type_def_6, type, sK0: $tType).
% 1.63/1.31 thf(type_def_7, type, sK1: $tType).
% 1.63/1.31 thf(type_def_8, type, sK2: $tType).
% 1.63/1.31 thf(type_def_9, type, sK3: $tType).
% 1.63/1.31 thf(func_def_0, type, o: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X2) > (X1 > X0) > X1 > X2)).
% 1.63/1.31 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.31 thf(func_def_7, type, sK4: sK1 > sK0).
% 1.63/1.31 thf(func_def_8, type, sK5: sK3 > sK1).
% 1.63/1.31 thf(func_def_9, type, sK6: sK2 > sK3).
% 1.63/1.31 thf(func_def_11, type, ph8: !>[X0: $tType]:(X0)).
% 1.63/1.31 thf(func_def_12, type, sK9: sK2).
% 1.63/1.31 thf(f23,plain,(
% 1.63/1.31 $false),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.63/1.31 thf(f22,plain,(
% 1.63/1.31 ((sK4 @ (sK5 @ (sK6 @ sK9))) != (sK4 @ (sK5 @ (sK6 @ sK9))))),
% 1.63/1.31 inference(forward_demodulation,[status(thm)],[f21,f14])).
% 1.63/1.31 thf(f14,plain,(
% 1.63/1.31 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X1 > X0,X4 : X2 > X1,X5 : X2] : (((o @ X1 @ X2 @ X0 @ X3 @ X4 @ X5) = (X3 @ (X4 @ X5)))) )),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.63/1.31 thf(f13,plain,(
% 1.63/1.31 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X1 > X0,X4 : X2 > X1,X5 : X2] : ((((^[Y0 : X2]: (X3 @ (X4 @ Y0))) @ X5) = (o @ X1 @ X2 @ X0 @ X3 @ X4 @ X5))) )),
% 1.63/1.31 inference(argument_congruence,[status(thm)],[f12])).
% 1.63/1.31 thf(f12,plain,(
% 1.63/1.31 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X1 > X0,X4 : X2 > X1] : (((o @ X1 @ X2 @ X0 @ X3 @ X4) = (^[Y0 : X2]: (X3 @ (X4 @ Y0))))) )),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f6])).
% 1.63/1.31 thf(f6,plain,(
% 1.63/1.31 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1 > X0,X4 : X2 > X1] : ((o @ X1 @ X2 @ X0 @ X3 @ X4) = (^[Y0 : X2]: (X3 @ (X4 @ Y0))))),
% 1.63/1.31 inference(fool_elimination,[status(thm)],[f5])).
% 1.63/1.31 thf(f5,plain,(
% 1.63/1.31 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1 > X0,X4 : X2 > X1] : ((o @ X1 @ X2 @ X0 @ X3 @ X4) = (^[X5 : X2] : (X3 @ (X4 @ X5))))),
% 1.63/1.31 inference(rectify,[status(thm)],[f1])).
% 1.63/1.31 thf(f1,axiom,(
% 1.63/1.31 ! [X2 : $tType,X0 : $tType,X1 : $tType,X3 : X0 > X2,X4 : X1 > X0] : ((o @ X0 @ X1 @ X2 @ X3 @ X4) = (^[X5 : X1] : (X3 @ (X4 @ X5))))),
% 1.63/1.31 file('/export/starexec/sandbox2/tmp/tmp.MqnCB3EcZJ/DTF2THF_10904.p','trivia/o_DEF_')).
% 1.63/1.31 thf(f21,plain,(
% 1.63/1.31 ((sK4 @ (o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ sK9)) != (sK4 @ (sK5 @ (sK6 @ sK9))))),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.63/1.31 thf(f20,plain,(
% 1.63/1.31 (((^[Y0 : sK2]: (sK4 @ (sK5 @ (sK6 @ Y0)))) @ sK9) != ((^[Y0 : sK2]: (sK4 @ (o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0))) @ sK9))),
% 1.63/1.31 inference(negative_extensionality,[status(thm)],[f19])).
% 1.63/1.31 thf(f19,plain,(
% 1.63/1.31 ((^[Y0 : sK2]: (sK4 @ (o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0))) != (^[Y0 : sK2]: (sK4 @ (sK5 @ (sK6 @ Y0)))))),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.63/1.31 thf(f18,plain,(
% 1.63/1.31 ((^[Y0 : sK2]: (sK4 @ (o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0))) != (^[Y0 : sK2]: ((^[Y1 : sK3]: (sK4 @ (sK5 @ Y1))) @ (sK6 @ Y0))))),
% 1.63/1.31 inference(forward_demodulation,[status(thm)],[f17,f12])).
% 1.63/1.31 thf(f17,plain,(
% 1.63/1.31 ((o @ sK3 @ sK2 @ sK0 @ (^[Y0 : sK3]: (sK4 @ (sK5 @ Y0))) @ sK6) != (^[Y0 : sK2]: (sK4 @ (o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0))))),
% 1.63/1.31 inference(forward_demodulation,[status(thm)],[f16,f12])).
% 1.63/1.31 thf(f16,plain,(
% 1.63/1.31 ((^[Y0 : sK2]: (sK4 @ (o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0))) != (o @ sK3 @ sK2 @ sK0 @ (o @ sK1 @ sK3 @ sK0 @ sK4 @ sK5) @ sK6))),
% 1.63/1.31 inference(forward_demodulation,[status(thm)],[f11,f12])).
% 1.63/1.31 thf(f11,plain,(
% 1.63/1.31 ((o @ sK3 @ sK2 @ sK0 @ (o @ sK1 @ sK3 @ sK0 @ sK4 @ sK5) @ sK6) != (o @ sK1 @ sK2 @ sK0 @ sK4 @ (o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6)))),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.31 thf(f10,plain,(
% 1.63/1.31 ((o @ sK3 @ sK2 @ sK0 @ (o @ sK1 @ sK3 @ sK0 @ sK4 @ sK5) @ sK6) != (o @ sK1 @ sK2 @ sK0 @ sK4 @ (o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6)))),
% 1.63/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f9])).
% 1.63/1.31 thf(f9,plain,(
% 1.63/1.31 ? [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : X1 > X0,X5 : X3 > X1,X6 : X2 > X3] : ((o @ X1 @ X2 @ X0 @ X4 @ (o @ X3 @ X2 @ X1 @ X5 @ X6)) != (o @ X3 @ X2 @ X0 @ (o @ X1 @ X3 @ X0 @ X4 @ X5) @ X6)) => ((o @ sK3 @ sK2 @ sK0 @ (o @ sK1 @ sK3 @ sK0 @ sK4 @ sK5) @ sK6) != (o @ sK1 @ sK2 @ sK0 @ sK4 @ (o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6)))),
% 1.63/1.31 introduced(definition,[],[choice_axiom])).
% 1.63/1.31 thf(f8,plain,(
% 1.63/1.31 ? [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : X1 > X0,X5 : X3 > X1,X6 : X2 > X3] : ((o @ X1 @ X2 @ X0 @ X4 @ (o @ X3 @ X2 @ X1 @ X5 @ X6)) != (o @ X3 @ X2 @ X0 @ (o @ X1 @ X3 @ X0 @ X4 @ X5) @ X6))),
% 1.63/1.31 inference(ennf_transformation,[status(thm)],[f7])).
% 1.63/1.31 thf(f7,plain,(
% 1.63/1.31 ~! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : X1 > X0,X5 : X3 > X1,X6 : X2 > X3] : ((o @ X1 @ X2 @ X0 @ X4 @ (o @ X3 @ X2 @ X1 @ X5 @ X6)) = (o @ X3 @ X2 @ X0 @ (o @ X1 @ X3 @ X0 @ X4 @ X5) @ X6))),
% 1.63/1.31 inference(rectify,[status(thm)],[f3])).
% 1.63/1.31 thf(f3,negated_conjecture,(
% 1.63/1.31 ~! [X6 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X3 : X2 > X6,X4 : X0 > X2,X7 : X1 > X0] : ((o @ X2 @ X1 @ X6 @ X3 @ (o @ X0 @ X1 @ X2 @ X4 @ X7)) = (o @ X0 @ X1 @ X6 @ (o @ X2 @ X0 @ X6 @ X3 @ X4) @ X7))),
% 1.63/1.31 inference(negated_conjecture,[status(cth)],[f2])).
% 1.63/1.31 thf(f2,conjecture,(
% 1.63/1.31 ! [X6 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X3 : X2 > X6,X4 : X0 > X2,X7 : X1 > X0] : ((o @ X2 @ X1 @ X6 @ X3 @ (o @ X0 @ X1 @ X2 @ X4 @ X7)) = (o @ X0 @ X1 @ X6 @ (o @ X2 @ X0 @ X6 @ X3 @ X4) @ X7))),
% 1.63/1.31 file('/export/starexec/sandbox2/tmp/tmp.MqnCB3EcZJ/DTF2THF_10904.p','trivia/o_ASSOC_')).
% 1.63/1.31 % SZS output end Proof for DTF2THF_10904
% 1.63/1.31 % (11019)------------------------------
% 1.63/1.31 % (11019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (11019)Termination reason: Refutation
% 1.63/1.31
% 1.63/1.31 % (11019)Memory used [KB]: 5500
% 1.63/1.31 % (11019)Time elapsed: 0.006 s
% 1.63/1.31 % (11019)Instructions burned: 3 (million)
% 1.63/1.31 % (11019)------------------------------
% 1.63/1.31 % (11019)------------------------------
% 1.63/1.31 % (11016)Success in time 0.015 s
%------------------------------------------------------------------------------