%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV166^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 09:40:27 AM UTC 2026
% Result : Theorem 1.51s 1.24s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 87 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 227 ( 40 ~; 36 |; 15 &; 130 @)
% ( 4 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 96 ( 96 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 84 ( 48 ^; 20 !; 16 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_7,type,
sK0: a ).
thf(func_def_8,type,
sK1: a ).
thf(func_def_9,type,
sK2: a ).
thf(func_def_10,type,
sK3: a ).
thf(func_def_11,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK5: a > a > a ).
thf(f49,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( sK5 @ sK1 @ sK0 )
!= ( sK5 @ sK1 @ sK0 ) ),
inference(forward_demodulation,[status(thm)],[f47,f41]) ).
thf(f41,plain,
sK0 = sK2,
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( sK0 = sK2 )
| ( sK0 != sK0 ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
( ( sK0 = sK2 )
| ( ( ^ [Y0: a,Y1: a] : Y1
@ sK1
@ sK0 )
!= sK0 ) ),
inference(equality_factoring,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: a > a > a] :
( ( ( X1 @ sK1 @ sK0 )
= ( X1 @ sK1 @ sK2 ) )
| ( sK0 = sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: a > a > a] :
( ( sK0 = sK2 )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK0 )
@ X1 )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK2 )
@ X1 ) ) ),
inference(argument_congruence,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK0 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK2 ) ) )
| ( sK0 = sK2 ) ),
inference(backward_demodulation,[status(thm)],[f12,f27]) ).
thf(f27,plain,
sK1 = sK3,
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( sK1 != sK1 )
| ( sK1 = sK3 ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( ( sK1
!= ( ^ [Y0: a,Y1: a] : Y0
@ sK1
@ sK0 ) )
| ( sK1 = sK3 ) ),
inference(equality_factoring,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: a > a > a] :
( ( ( X1 @ sK3 @ sK2 )
= ( X1 @ sK1 @ sK0 ) )
| ( sK1 = sK3 ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: a > a > a] :
( ( sK1 = sK3 )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ sK3 @ sK2 )
@ X1 )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK0 )
@ X1 ) ) ),
inference(argument_congruence,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK0 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK3 @ sK2 ) ) )
| ( sK1 = sK3 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( sK0 != sK2 )
| ( sK1 != sK3 )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK0 ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ sK3 @ sK2 ) ) ) )
& ( ( ( sK0 = sK2 )
& ( sK1 = sK3 ) )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK0 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK3 @ sK2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: a,X1: a,X2: a,X3: a] :
( ( ( X0 != X2 )
| ( X1 != X3 )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ X1 @ X0 ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ X3 @ X2 ) ) ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ X1 @ X0 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ X3 @ X2 ) ) ) ) )
=> ( ( ( sK0 != sK2 )
| ( sK1 != sK3 )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK0 ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ sK3 @ sK2 ) ) ) )
& ( ( ( sK0 = sK2 )
& ( sK1 = sK3 ) )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK0 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK3 @ sK2 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a,X1: a,X2: a,X3: a] :
( ( ( X0 != X2 )
| ( X1 != X3 )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ X1 @ X0 ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ X3 @ X2 ) ) ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ X1 @ X0 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ X3 @ X2 ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a,X1: a,X2: a,X3: a] :
( ( ( X0 != X2 )
| ( X1 != X3 )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ X1 @ X0 ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ X3 @ X2 ) ) ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ X1 @ X0 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ X3 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a,X1: a,X2: a,X3: a] :
( ( ( ^ [Y0: a > a > a] : ( Y0 @ X1 @ X0 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ X3 @ X2 ) ) )
<~> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a,X1: a,X2: a,X3: a] :
( ( ( ^ [Y0: a > a > a] : ( Y0 @ X1 @ X0 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ X3 @ X2 ) ) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: a,X3: a] :
( ( ( ^ [X4: a > a > a] : ( X4 @ X3 @ X2 ) )
= ( ^ [X5: a > a > a] : ( X5 @ X1 @ X0 ) ) )
<=> ( ( X1 = X3 )
& ( X0 = X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X2: a,X1: a,X0: a] :
( ( ( ^ [X4: a > a > a] : ( X4 @ X0 @ X1 ) )
= ( ^ [X4: a > a > a] : ( X4 @ X2 @ X3 ) ) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X3: a,X2: a,X1: a,X0: a] :
( ( ( ^ [X4: a > a > a] : ( X4 @ X0 @ X1 ) )
= ( ^ [X4: a > a > a] : ( X4 @ X2 @ X3 ) ) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SDwnP3VEmH/DTF2THF_13390.p',cTHM182_pme) ).
thf(f12,plain,
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK0 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK3 @ sK2 ) ) )
| ( sK0 = sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f47,plain,
( ( sK5 @ sK1 @ sK2 )
!= ( sK5 @ sK1 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( sK5 @ sK1 @ sK2 )
!= ( sK5 @ sK1 @ sK0 ) )
| ( sK0 != sK0 ) ),
inference(backward_demodulation,[status(thm)],[f32,f41]) ).
thf(f32,plain,
( ( sK0 != sK2 )
| ( ( sK5 @ sK1 @ sK2 )
!= ( sK5 @ sK1 @ sK0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f30,f27]) ).
thf(f30,plain,
( ( ( sK5 @ sK1 @ sK2 )
!= ( sK5 @ sK1 @ sK0 ) )
| ( sK1 != sK3 )
| ( sK0 != sK2 ) ),
inference(backward_demodulation,[status(thm)],[f15,f27]) ).
thf(f15,plain,
( ( ( sK5 @ sK3 @ sK2 )
!= ( sK5 @ sK1 @ sK0 ) )
| ( sK0 != sK2 )
| ( sK1 != sK3 ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK3 @ sK2 )
@ sK5 )
!= ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK0 )
@ sK5 ) )
| ( sK0 != sK2 )
| ( sK1 != sK3 ) ),
inference(negative_extensionality,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK0 ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ sK3 @ sK2 ) ) )
| ( sK1 != sK3 )
| ( sK0 != sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV166^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:41:15 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEV166^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : TPS problem THM182
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : Basic theorem about pairing.
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0458 [Bro09]
% 0.18/0.45 % : THM182 [TPS]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.18/0.45 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 3 ( 3 avg)
% 0.18/0.45 % Number of connectives : 6 ( 0 ~; 0 |; 1 &; 4 @)
% 0.18/0.45 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 7 ( 7 avg)
% 0.18/0.45 % Number of types : 1 ( 1 usr)
% 0.18/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.18/0.45 % Number of variables : 6 ( 2 ^; 4 !; 0 ?; 6 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 % : Polymorphic definitions expanded.
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(a_type,type,
% 0.18/0.45 a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(cTHM182_pme,conjecture,
% 0.18/0.45 ! [Xx: a,Xy: a,Xu: a,Xv: a] :
% 0.18/0.45 ( ( ( ^ [Xg: a > a > a] : ( Xg @ Xx @ Xy ) )
% 0.18/0.45 = ( ^ [Xg: a > a > a] : ( Xg @ Xu @ Xv ) ) )
% 0.18/0.45 <=> ( ( Xx = Xu )
% 0.18/0.45 & ( Xy = Xv ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.37/1.19 ---- Embedded in THF ---
% 1.37/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.19 %%% Generated on Tue Feb 24 12:41:16 EST 2026
% 1.37/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.19 %%% Logic specification used:
% 1.37/1.19 %%% thf(spec, logic, $$dhol).
% 1.37/1.19
% 1.37/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.SDwnP3VEmH/DTF2DTF13390.p
% See solution above
% 1.37/1.19 ------------------------
% 1.51/1.20 ---- Cleaned THF ---
% 1.51/1.20 thf(a_type,type,
% 1.51/1.20 a: $tType ).
% 1.51/1.20
% 1.51/1.20 thf(cTHM182_pme,conjecture,
% 1.51/1.20 ! [Xx: a,Xy: a,Xu: a,Xv: a] :
% 1.51/1.20 ( ( ( ^ [Xg: a > a > a] : ( Xg @ Xx @ Xy ) )
% 1.51/1.20 = ( ^ [Xg: a > a > a] : ( Xg @ Xu @ Xv ) ) )
% 1.51/1.20 <=> ( ( Xx = Xu )
% 1.51/1.20 & ( Xy = Xv ) ) ) ).
% 1.51/1.20 ------------------------
% 1.51/1.22 % (13608)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_13390 for (2999ds/275Mi)
% 1.51/1.22 % (13608)Refutation not found, incomplete strategy
% 1.51/1.22 % (13608)------------------------------
% 1.51/1.22 % (13608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.22 % (13608)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.22
% 1.51/1.22
% 1.51/1.22 % (13608)Memory used [KB]: 5500
% 1.51/1.22 % (13608)Time elapsed: 0.002 s
% 1.51/1.22 % (13608)Instructions burned: 2 (million)
% 1.51/1.22 % (13608)------------------------------
% 1.51/1.22 % (13608)------------------------------
% 1.51/1.22 % (13604)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_13390 for (2999ds/4Mi)
% 1.51/1.22 % (13603)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13390 for (2999ds/183Mi)
% 1.51/1.22 % (13605)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_13390 for (2999ds/27Mi)
% 1.51/1.22 % (13606)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13390 for (2999ds/2Mi)
% 1.51/1.22 % (13607)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_13390 for (2999ds/2Mi)
% 1.51/1.22 % (13609)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13390 for (2999ds/18Mi)
% 1.51/1.23 % (13607)Instruction limit reached!
% 1.51/1.23 % (13607)------------------------------
% 1.51/1.23 % (13607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.23 % (13607)Termination reason: Unknown
% 1.51/1.23 % (13607)Termination phase: Saturation
% 1.51/1.23
% 1.51/1.23 % (13607)Memory used [KB]: 895
% 1.51/1.23 % (13607)Time elapsed: 0.003 s
% 1.51/1.23 % (13607)Instructions burned: 2 (million)
% 1.51/1.23 % (13607)------------------------------
% 1.51/1.23 % (13607)------------------------------
% 1.51/1.23 % (13606)Instruction limit reached!
% 1.51/1.23 % (13606)------------------------------
% 1.51/1.23 % (13606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.23 % (13606)Termination reason: Unknown
% 1.51/1.23 % (13606)Termination phase: Saturation
% 1.51/1.23
% 1.51/1.23 % (13606)Memory used [KB]: 5500
% 1.51/1.23 % (13606)Time elapsed: 0.004 s
% 1.51/1.23 % (13606)Instructions burned: 2 (million)
% 1.51/1.23 % (13606)------------------------------
% 1.51/1.23 % (13606)------------------------------
% 1.51/1.23 % (13605)Refutation not found, incomplete strategy
% 1.51/1.23 % (13605)------------------------------
% 1.51/1.23 % (13605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.23 % (13605)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.23
% 1.51/1.23
% 1.51/1.23 % (13605)Memory used [KB]: 5500
% 1.51/1.23 % (13605)Time elapsed: 0.004 s
% 1.51/1.23 % (13605)Instructions burned: 2 (million)
% 1.51/1.23 % (13605)------------------------------
% 1.51/1.23 % (13605)------------------------------
% 1.51/1.23 % (13604)Instruction limit reached!
% 1.51/1.23 % (13604)------------------------------
% 1.51/1.23 % (13604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.23 % (13604)Termination reason: Unknown
% 1.51/1.23 % (13604)Termination phase: Saturation
% 1.51/1.23
% 1.51/1.23 % (13604)Memory used [KB]: 5500
% 1.51/1.23 % (13604)Time elapsed: 0.005 s
% 1.51/1.23 % (13604)Instructions burned: 4 (million)
% 1.51/1.23 % (13604)------------------------------
% 1.51/1.23 % (13604)------------------------------
% 1.51/1.23 % (13610)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13390 for (2999ds/3Mi)
% 1.51/1.23 % (13610)Instruction limit reached!
% 1.51/1.23 % (13610)------------------------------
% 1.51/1.23 % (13610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.23 % (13610)Termination reason: Unknown
% 1.51/1.23 % (13610)Termination phase: Saturation
% 1.51/1.23
% 1.51/1.23 % (13610)Memory used [KB]: 5500
% 1.51/1.23 % (13610)Time elapsed: 0.002 s
% 1.51/1.23 % (13610)Instructions burned: 3 (million)
% 1.51/1.23 % (13610)------------------------------
% 1.51/1.23 % (13610)------------------------------
% 1.51/1.24 % (13609)Instruction limit reached!
% 1.51/1.24 % (13609)------------------------------
% 1.51/1.24 % (13609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.24 % (13609)Termination reason: Unknown
% 1.51/1.24 % (13609)Termination phase: Saturation
% 1.51/1.24
% 1.51/1.24 % (13609)Memory used [KB]: 5500
% 1.51/1.24 % (13609)Time elapsed: 0.013 s
% 1.51/1.24 % (13609)Instructions burned: 19 (million)
% 1.51/1.24 % (13609)------------------------------
% 1.51/1.24 % (13609)------------------------------
% 1.51/1.24 % (13615)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13390 for (2999ds/7Mi)
% 1.51/1.24 % (13615)First to succeed.
% 1.51/1.24 % (13615)Refutation found. Thanks to Tanya!
% 1.51/1.24 % SZS status Theorem for DTF2THF_13390
% 1.51/1.24 % SZS output start Proof for DTF2THF_13390
% 1.51/1.24 thf(type_def_5, type, a: $tType).
% 1.51/1.24 thf(func_def_0, type, a: $tType).
% 1.51/1.24 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.51/1.24 thf(func_def_7, type, sK0: a).
% 1.51/1.24 thf(func_def_8, type, sK1: a).
% 1.51/1.24 thf(func_def_9, type, sK2: a).
% 1.51/1.24 thf(func_def_10, type, sK3: a).
% 1.51/1.24 thf(func_def_11, type, ph4: !>[X0: $tType]:(X0)).
% 1.51/1.24 thf(func_def_12, type, sK5: a > a > a).
% 1.51/1.24 thf(f49,plain,(
% 1.51/1.24 $false),
% 1.51/1.24 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.51/1.24 thf(f48,plain,(
% 1.51/1.24 ((sK5 @ sK1 @ sK0) != (sK5 @ sK1 @ sK0))),
% 1.51/1.24 inference(forward_demodulation,[status(thm)],[f47,f41])).
% 1.51/1.24 thf(f41,plain,(
% 1.51/1.24 (sK0 = sK2)),
% 1.51/1.24 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.51/1.24 thf(f40,plain,(
% 1.51/1.24 (sK0 = sK2) | (sK0 != sK0)),
% 1.51/1.24 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.51/1.24 thf(f37,plain,(
% 1.51/1.24 (sK0 = sK2) | (((^[Y0 : a]: ((^[Y1 : a]: (Y1)))) @ sK1 @ sK0) != sK0)),
% 1.51/1.24 inference(equality_factoring,[status(thm)],[f34])).
% 1.51/1.24 thf(f34,plain,(
% 1.51/1.24 ( ! [X1 : a > a > a] : (((X1 @ sK1 @ sK0) = (X1 @ sK1 @ sK2)) | (sK0 = sK2)) )),
% 1.51/1.24 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.51/1.24 thf(f33,plain,(
% 1.51/1.24 ( ! [X1 : a > a > a] : ((sK0 = sK2) | (((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK0)) @ X1) = ((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK2)) @ X1))) )),
% 1.51/1.24 inference(argument_congruence,[status(thm)],[f28])).
% 1.51/1.24 thf(f28,plain,(
% 1.51/1.24 ((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK0)) = (^[Y0 : a > a > a]: (Y0 @ sK1 @ sK2))) | (sK0 = sK2)),
% 1.51/1.24 inference(backward_demodulation,[status(thm)],[f12,f27])).
% 1.51/1.24 thf(f27,plain,(
% 1.51/1.24 (sK1 = sK3)),
% 1.51/1.24 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.51/1.24 thf(f26,plain,(
% 1.51/1.24 (sK1 != sK1) | (sK1 = sK3)),
% 1.51/1.24 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.51/1.24 thf(f21,plain,(
% 1.51/1.24 (sK1 != ((^[Y0 : a]: ((^[Y1 : a]: (Y0)))) @ sK1 @ sK0)) | (sK1 = sK3)),
% 1.51/1.24 inference(equality_factoring,[status(thm)],[f18])).
% 1.51/1.24 thf(f18,plain,(
% 1.51/1.24 ( ! [X1 : a > a > a] : (((X1 @ sK3 @ sK2) = (X1 @ sK1 @ sK0)) | (sK1 = sK3)) )),
% 1.51/1.24 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.51/1.24 thf(f16,plain,(
% 1.51/1.24 ( ! [X1 : a > a > a] : ((sK1 = sK3) | (((^[Y0 : a > a > a]: (Y0 @ sK3 @ sK2)) @ X1) = ((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK0)) @ X1))) )),
% 1.51/1.24 inference(argument_congruence,[status(thm)],[f11])).
% 1.51/1.24 thf(f11,plain,(
% 1.51/1.24 ((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK0)) = (^[Y0 : a > a > a]: (Y0 @ sK3 @ sK2))) | (sK1 = sK3)),
% 1.51/1.24 inference(cnf_transformation,[status(thm)],[f10])).
% 1.51/1.24 thf(f10,plain,(
% 1.51/1.24 ((sK0 != sK2) | (sK1 != sK3) | ((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK0)) != (^[Y0 : a > a > a]: (Y0 @ sK3 @ sK2)))) & (((sK0 = sK2) & (sK1 = sK3)) | ((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK0)) = (^[Y0 : a > a > a]: (Y0 @ sK3 @ sK2))))),
% 1.51/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f9])).
% 1.51/1.24 thf(f9,plain,(
% 1.51/1.24 ? [X0 : a,X1 : a,X2 : a,X3 : a] : (((X0 != X2) | (X1 != X3) | ((^[Y0 : a > a > a]: (Y0 @ X1 @ X0)) != (^[Y0 : a > a > a]: (Y0 @ X3 @ X2)))) & (((X0 = X2) & (X1 = X3)) | ((^[Y0 : a > a > a]: (Y0 @ X1 @ X0)) = (^[Y0 : a > a > a]: (Y0 @ X3 @ X2))))) => (((sK0 != sK2) | (sK1 != sK3) | ((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK0)) != (^[Y0 : a > a > a]: (Y0 @ sK3 @ sK2)))) & (((sK0 = sK2) & (sK1 = sK3)) | ((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK0)) = (^[Y0 : a > a > a]: (Y0 @ sK3 @ sK2)))))),
% 1.51/1.24 introduced(definition,[],[choice_axiom])).
% 1.51/1.24 thf(f8,plain,(
% 1.51/1.24 ? [X0 : a,X1 : a,X2 : a,X3 : a] : (((X0 != X2) | (X1 != X3) | ((^[Y0 : a > a > a]: (Y0 @ X1 @ X0)) != (^[Y0 : a > a > a]: (Y0 @ X3 @ X2)))) & (((X0 = X2) & (X1 = X3)) | ((^[Y0 : a > a > a]: (Y0 @ X1 @ X0)) = (^[Y0 : a > a > a]: (Y0 @ X3 @ X2)))))),
% 1.51/1.24 inference(flattening,[status(thm)],[f7])).
% 1.51/1.24 thf(f7,plain,(
% 1.51/1.24 ? [X0 : a,X1 : a,X2 : a,X3 : a] : ((((X0 != X2) | (X1 != X3)) | ((^[Y0 : a > a > a]: (Y0 @ X1 @ X0)) != (^[Y0 : a > a > a]: (Y0 @ X3 @ X2)))) & (((X0 = X2) & (X1 = X3)) | ((^[Y0 : a > a > a]: (Y0 @ X1 @ X0)) = (^[Y0 : a > a > a]: (Y0 @ X3 @ X2)))))),
% 1.51/1.24 inference(nnf_transformation,[status(thm)],[f6])).
% 1.51/1.24 thf(f6,plain,(
% 1.51/1.24 ? [X0 : a,X1 : a,X2 : a,X3 : a] : (((^[Y0 : a > a > a]: (Y0 @ X1 @ X0)) = (^[Y0 : a > a > a]: (Y0 @ X3 @ X2))) <~> ((X0 = X2) & (X1 = X3)))),
% 1.51/1.24 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.24 thf(f5,plain,(
% 1.51/1.24 ~! [X0 : a,X1 : a,X2 : a,X3 : a] : (((^[Y0 : a > a > a]: (Y0 @ X1 @ X0)) = (^[Y0 : a > a > a]: (Y0 @ X3 @ X2))) <=> ((X0 = X2) & (X1 = X3)))),
% 1.51/1.24 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.24 thf(f4,plain,(
% 1.51/1.24 ~! [X0 : a,X1 : a,X2 : a,X3 : a] : (((^[X4 : a > a > a] : (X4 @ X3 @ X2)) = (^[X5 : a > a > a] : (X5 @ X1 @ X0))) <=> ((X1 = X3) & (X0 = X2)))),
% 1.51/1.24 inference(rectify,[status(thm)],[f2])).
% 1.51/1.24 thf(f2,negated_conjecture,(
% 1.51/1.24 ~! [X3 : a,X2 : a,X1 : a,X0 : a] : (((^[X4 : a > a > a] : (X4 @ X0 @ X1)) = (^[X4 : a > a > a] : (X4 @ X2 @ X3))) <=> ((X0 = X2) & (X1 = X3)))),
% 1.51/1.24 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.24 thf(f1,conjecture,(
% 1.51/1.24 ! [X3 : a,X2 : a,X1 : a,X0 : a] : (((^[X4 : a > a > a] : (X4 @ X0 @ X1)) = (^[X4 : a > a > a] : (X4 @ X2 @ X3))) <=> ((X0 = X2) & (X1 = X3)))),
% 1.51/1.24 file('/export/starexec/sandbox2/tmp/tmp.SDwnP3VEmH/DTF2THF_13390.p',cTHM182_pme)).
% 1.51/1.24 thf(f12,plain,(
% 1.51/1.24 ((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK0)) = (^[Y0 : a > a > a]: (Y0 @ sK3 @ sK2))) | (sK0 = sK2)),
% 1.51/1.24 inference(cnf_transformation,[status(thm)],[f10])).
% 1.51/1.24 thf(f47,plain,(
% 1.51/1.24 ((sK5 @ sK1 @ sK2) != (sK5 @ sK1 @ sK0))),
% 1.51/1.24 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.51/1.24 thf(f45,plain,(
% 1.51/1.24 ((sK5 @ sK1 @ sK2) != (sK5 @ sK1 @ sK0)) | (sK0 != sK0)),
% 1.51/1.24 inference(backward_demodulation,[status(thm)],[f32,f41])).
% 1.51/1.24 thf(f32,plain,(
% 1.51/1.24 (sK0 != sK2) | ((sK5 @ sK1 @ sK2) != (sK5 @ sK1 @ sK0))),
% 1.51/1.24 inference(subsumption_resolution,[status(thm)],[f30,f27])).
% 1.51/1.24 thf(f30,plain,(
% 1.51/1.24 ((sK5 @ sK1 @ sK2) != (sK5 @ sK1 @ sK0)) | (sK1 != sK3) | (sK0 != sK2)),
% 1.51/1.24 inference(backward_demodulation,[status(thm)],[f15,f27])).
% 1.51/1.24 thf(f15,plain,(
% 1.51/1.24 ((sK5 @ sK3 @ sK2) != (sK5 @ sK1 @ sK0)) | (sK0 != sK2) | (sK1 != sK3)),
% 1.51/1.24 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.51/1.24 thf(f14,plain,(
% 1.51/1.24 (((^[Y0 : a > a > a]: (Y0 @ sK3 @ sK2)) @ sK5) != ((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK0)) @ sK5)) | (sK0 != sK2) | (sK1 != sK3)),
% 1.51/1.24 inference(negative_extensionality,[status(thm)],[f13])).
% 1.51/1.24 thf(f13,plain,(
% 1.51/1.24 ((^[Y0 : a > a > a]: (Y0 @ sK1 @ sK0)) != (^[Y0 : a > a > a]: (Y0 @ sK3 @ sK2))) | (sK1 != sK3) | (sK0 != sK2)),
% 1.51/1.24 inference(cnf_transformation,[status(thm)],[f10])).
% 1.51/1.24 % SZS output end Proof for DTF2THF_13390
% 1.51/1.24 % (13615)------------------------------
% 1.51/1.24 % (13615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.24 % (13615)Termination reason: Refutation
% 1.51/1.24
% 1.51/1.24 % (13615)Memory used [KB]: 1023
% 1.51/1.24 % (13615)Time elapsed: 0.003 s
% 1.51/1.24 % (13615)Instructions burned: 6 (million)
% 1.51/1.24 % (13615)------------------------------
% 1.51/1.24 % (13615)------------------------------
% 1.51/1.24 % (13602)Success in time 0.03 s
%------------------------------------------------------------------------------