%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV195^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n023.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 09:40:31 AM UTC 2026
% Result : Theorem 1.50s 1.29s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 149 ( 111 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 320 ( 56 ~; 24 |; 54 &; 168 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 127 ( 9 ^; 98 !; 20 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cP: a > a > a ).
thf(func_def_2,type,
cZ: a ).
thf(func_def_6,type,
sK0: a ).
thf(func_def_7,type,
sK1: ( a > $o ) > a ).
thf(func_def_8,type,
sK2: ( a > $o ) > a ).
thf(func_def_11,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f272,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f245]) ).
thf(f245,plain,
( ( sK0 != sK0 )
| ( cZ != cZ ) ),
inference(superposition,[status(thm)],[f18,f207]) ).
thf(f207,plain,
! [X0: a] :
( ( cZ = X0 )
| ( sK0 != X0 ) ),
inference(superposition,[status(thm)],[f17,f98]) ).
thf(f98,plain,
! [X0: a] :
( ( ( cP
@ ( sK2
@ ^ [Y0: a] : ( X0 != Y0 ) )
@ ( sK1
@ ^ [Y0: a] : ( X0 != Y0 ) ) )
= X0 )
| ( cZ = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X0: a] :
( ( $true
= ( X0 = cZ ) )
| ( ( cP
@ ( sK2
@ ^ [Y0: a] : ( X0 != Y0 ) )
@ ( sK1
@ ^ [Y0: a] : ( X0 != Y0 ) ) )
= X0 ) ),
inference(not_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X0: a] :
( ( ( cP
@ ( sK2
@ ^ [Y0: a] : ( X0 != Y0 ) )
@ ( sK1
@ ^ [Y0: a] : ( X0 != Y0 ) ) )
= X0 )
| ( $true
!= ( X0 != cZ ) ) ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: a] :
( ( ( ^ [Y0: a] : ( X0 != Y0 )
@ cZ )
!= $true )
| ( ( cP
@ ( sK2
@ ^ [Y0: a] : ( X0 != Y0 ) )
@ ( sK1
@ ^ [Y0: a] : ( X0 != Y0 ) ) )
= X0 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X8: a,X5: a > $o] :
( ( ( X5 @ ( cP @ ( sK2 @ X5 ) @ ( sK1 @ X5 ) ) )
!= $true )
| ( ( X5 @ X8 )
= $true )
| ( ( X5 @ cZ )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: a,X1: a] :
( cZ
!= ( cP @ X1 @ X0 ) )
& ( cZ != sK0 )
& ! [X3: a,X4: a] :
( ( cP @ X3 @ X4 )
!= sK0 )
& ! [X5: a > $o] :
( ( ( $true
= ( X5 @ ( sK1 @ X5 ) ) )
& ( ( X5 @ ( sK2 @ X5 ) )
= $true )
& ( ( X5 @ ( cP @ ( sK2 @ X5 ) @ ( sK1 @ X5 ) ) )
!= $true ) )
| ! [X8: a] :
( ( X5 @ X8 )
= $true )
| ( ( X5 @ cZ )
!= $true ) )
& ! [X9: a,X10: a,X11: a,X12: a] :
( ( ( X9 = X11 )
& ( X10 = X12 ) )
| ( ( cP @ X12 @ X11 )
!= ( cP @ X10 @ X9 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X2: a] :
( ( cZ != X2 )
& ! [X3: a,X4: a] :
( ( cP @ X3 @ X4 )
!= X2 ) )
=> ( ( cZ != sK0 )
& ! [X4: a,X3: a] :
( ( cP @ X3 @ X4 )
!= sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X5: a > $o] :
( ? [X6: a,X7: a] :
( ( ( X5 @ X6 )
= $true )
& ( ( X5 @ X7 )
= $true )
& ( $true
!= ( X5 @ ( cP @ X7 @ X6 ) ) ) )
=> ( ( $true
= ( X5 @ ( sK1 @ X5 ) ) )
& ( ( X5 @ ( sK2 @ X5 ) )
= $true )
& ( ( X5 @ ( cP @ ( sK2 @ X5 ) @ ( sK1 @ X5 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: a,X1: a] :
( cZ
!= ( cP @ X1 @ X0 ) )
& ? [X2: a] :
( ( cZ != X2 )
& ! [X3: a,X4: a] :
( ( cP @ X3 @ X4 )
!= X2 ) )
& ! [X5: a > $o] :
( ? [X6: a,X7: a] :
( ( ( X5 @ X6 )
= $true )
& ( ( X5 @ X7 )
= $true )
& ( $true
!= ( X5 @ ( cP @ X7 @ X6 ) ) ) )
| ! [X8: a] :
( ( X5 @ X8 )
= $true )
| ( ( X5 @ cZ )
!= $true ) )
& ! [X9: a,X10: a,X11: a,X12: a] :
( ( ( X9 = X11 )
& ( X10 = X12 ) )
| ( ( cP @ X12 @ X11 )
!= ( cP @ X10 @ X9 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X1: a,X0: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ? [X10: a] :
( ( cZ != X10 )
& ! [X11: a,X12: a] :
( ( cP @ X11 @ X12 )
!= X10 ) )
& ! [X6: a > $o] :
( ? [X8: a,X7: a] :
( ( ( X6 @ X8 )
= $true )
& ( ( X6 @ X7 )
= $true )
& ( ( X6 @ ( cP @ X7 @ X8 ) )
!= $true ) )
| ! [X9: a] :
( ( X6 @ X9 )
= $true )
| ( ( X6 @ cZ )
!= $true ) )
& ! [X4: a,X3: a,X5: a,X2: a] :
( ( ( X4 = X5 )
& ( X2 = X3 ) )
| ( ( cP @ X3 @ X4 )
!= ( cP @ X2 @ X5 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X10: a] :
( ( cZ != X10 )
& ! [X11: a,X12: a] :
( ( cP @ X11 @ X12 )
!= X10 ) )
& ! [X6: a > $o] :
( ! [X9: a] :
( ( X6 @ X9 )
= $true )
| ? [X8: a,X7: a] :
( ( ( X6 @ ( cP @ X7 @ X8 ) )
!= $true )
& ( ( X6 @ X7 )
= $true )
& ( ( X6 @ X8 )
= $true ) )
| ( ( X6 @ cZ )
!= $true ) )
& ! [X4: a,X3: a,X5: a,X2: a] :
( ( ( X4 = X5 )
& ( X2 = X3 ) )
| ( ( cP @ X3 @ X4 )
!= ( cP @ X2 @ X5 ) ) )
& ! [X1: a,X0: a] :
( ( cP @ X0 @ X1 )
!= cZ ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X6: a > $o] :
( ( ! [X8: a,X7: a] :
( ( ( ( X6 @ X7 )
= $true )
& ( ( X6 @ X8 )
= $true ) )
=> ( ( X6 @ ( cP @ X7 @ X8 ) )
= $true ) )
& ( ( X6 @ cZ )
= $true ) )
=> ! [X9: a] :
( ( X6 @ X9 )
= $true ) )
& ! [X5: a,X3: a,X2: a,X4: a] :
( ( ( cP @ X3 @ X4 )
= ( cP @ X2 @ X5 ) )
=> ( ( X4 = X5 )
& ( X2 = X3 ) ) )
& ! [X1: a,X0: a] :
( ( cP @ X0 @ X1 )
!= cZ ) )
=> ! [X10: a] :
( ( cZ = X10 )
| ? [X11: a,X12: a] :
( ( cP @ X11 @ X12 )
= X10 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X2: a,X3: a,X4: a,X5: a] :
( ( ( cP @ X3 @ X4 )
= ( cP @ X2 @ X5 ) )
=> ( ( X2 = X3 )
& ( X4 = X5 ) ) )
& ! [X6: a > $o] :
( ( ! [X7: a,X8: a] :
( ( ( X6 @ X8 )
& ( X6 @ X7 ) )
=> ( X6 @ ( cP @ X7 @ X8 ) ) )
& ( X6 @ cZ ) )
=> ! [X9: a] : ( X6 @ X9 ) ) )
=> ! [X10: a] :
( ( cZ = X10 )
| ? [X11: a,X12: a] :
( ( cP @ X11 @ X12 )
= X10 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X1: a,X0: a,X2: a,X3: a] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X0 = X1 )
& ( X2 = X3 ) ) )
& ! [X4: a > $o] :
( ( ! [X0: a,X1: a] :
( ( ( X4 @ X1 )
& ( X4 @ X0 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) )
& ( X4 @ cZ ) )
=> ! [X0: a] : ( X4 @ X0 ) ) )
=> ! [X0: a] :
( ( cZ = X0 )
| ? [X1: a,X5: a] :
( ( cP @ X1 @ X5 )
= X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
!= cZ )
& ! [X1: a,X0: a,X2: a,X3: a] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X0 = X1 )
& ( X2 = X3 ) ) )
& ! [X4: a > $o] :
( ( ! [X0: a,X1: a] :
( ( ( X4 @ X1 )
& ( X4 @ X0 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) )
& ( X4 @ cZ ) )
=> ! [X0: a] : ( X4 @ X0 ) ) )
=> ! [X0: a] :
( ( cZ = X0 )
| ? [X1: a,X5: a] :
( ( cP @ X1 @ X5 )
= X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c8VKnJbKCs/DTF2THF_9129.p',cS_LEM1D_pme) ).
thf(f17,plain,
! [X3: a,X4: a] :
( ( cP @ X3 @ X4 )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f18,plain,
cZ != sK0,
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV195^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n023.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:42:34 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEV195^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Set Theory (Sets of sets)
% 0.19/0.46 % Problem : TPS problem from S-THMS
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_1034 [Bro09]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.71 v6.1.0, 0.57 v5.5.0, 1.00 v5.3.0, 0.80 v5.2.0, 1.00 v5.1.0, 0.80 v4.1.0, 0.67 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.46 % Number of atoms : 6 ( 6 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 6 ( 6 avg)
% 0.19/0.46 % Number of connectives : 26 ( 1 ~; 1 |; 5 &; 15 @)
% 0.19/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 13 ( 13 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 13 ( 0 ^; 11 !; 2 ?; 13 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(a_type,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(cP,type,
% 0.19/0.46 cP: a > a > a ).
% 0.19/0.46
% 0.19/0.46 thf(cZ,type,
% 0.19/0.46 cZ: a ).
% 0.19/0.46
% 0.19/0.46 thf(cS_LEM1D_pme,conjecture,
% 0.19/0.46 ( ( ! [Xx: a,Xy: a] :
% 0.19/0.46 ( ( cP @ Xx @ Xy )
% 0.19/0.46 != cZ )
% 0.19/0.46 & ! [Xx: a,Xy: a,Xu: a,Xv: a] :
% 0.19/0.46 ( ( ( cP @ Xx @ Xu )
% 0.19/0.46 = ( cP @ Xy @ Xv ) )
% 0.19/0.46 => ( ( Xx = Xy )
% 0.19/0.46 & ( Xu = Xv ) ) )
% 0.19/0.46 & ! [X: a > $o] :
% 0.19/0.46 ( ( ( X @ cZ )
% 0.19/0.46 & ! [Xx: a,Xy: a] :
% 0.19/0.46 ( ( ( X @ Xx )
% 0.19/0.46 & ( X @ Xy ) )
% 0.19/0.46 => ( X @ ( cP @ Xx @ Xy ) ) ) )
% 0.19/0.46 => ! [Xx: a] : ( X @ Xx ) ) )
% 0.19/0.46 => ! [Xx: a] :
% 0.19/0.46 ( ( Xx = cZ )
% 0.19/0.46 | ? [Xy: a,Xz: a] :
% 0.19/0.46 ( Xx
% 0.19/0.46 = ( cP @ Xy @ Xz ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.50/1.25 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 12:42:35 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.c8VKnJbKCs/DTF2DTF9129.p
% See solution above
% 1.50/1.25 ------------------------
% 1.50/1.26 ---- Cleaned THF ---
% 1.50/1.26 thf(a_type,type,
% 1.50/1.26 a: $tType ).
% 1.50/1.26
% 1.50/1.26 thf(cP,type,
% 1.50/1.26 cP: a > a > a ).
% 1.50/1.26
% 1.50/1.26 thf(cZ,type,
% 1.50/1.26 cZ: a ).
% 1.50/1.26
% 1.50/1.26 thf(cS_LEM1D_pme,conjecture,
% 1.50/1.26 ( ( ! [Xx: a,Xy: a] :
% 1.50/1.26 ( ( cP @ Xx @ Xy )
% 1.50/1.26 != cZ )
% 1.50/1.26 & ! [Xx: a,Xy: a,Xu: a,Xv: a] :
% 1.50/1.26 ( ( ( cP @ Xx @ Xu )
% 1.50/1.26 = ( cP @ Xy @ Xv ) )
% 1.50/1.26 => ( ( Xx = Xy )
% 1.50/1.26 & ( Xu = Xv ) ) )
% 1.50/1.26 & ! [X: a > $o] :
% 1.50/1.26 ( ( ( X @ cZ )
% 1.50/1.26 & ! [Xx: a,Xy: a] :
% 1.50/1.26 ( ( ( X @ Xx )
% 1.50/1.26 & ( X @ Xy ) )
% 1.50/1.26 => ( X @ ( cP @ Xx @ Xy ) ) ) )
% 1.50/1.26 => ! [Xx: a] : ( X @ Xx ) ) )
% 1.50/1.26 => ! [Xx: a] :
% 1.50/1.26 ( ( Xx = cZ )
% 1.50/1.26 | ? [Xy: a,Xz: a] :
% 1.50/1.26 ( Xx
% 1.50/1.26 = ( cP @ Xy @ Xz ) ) ) ) ).
% 1.50/1.26 ------------------------
% 1.50/1.28 % (9322)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_9129 for (3000ds/275Mi)
% 1.50/1.28 % (9318)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_9129 for (3000ds/4Mi)
% 1.50/1.28 % (9318)Instruction limit reached!
% 1.50/1.28 % (9318)------------------------------
% 1.50/1.28 % (9318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (9318)Termination reason: Unknown
% 1.50/1.28 % (9318)Termination phase: Saturation
% 1.50/1.28
% 1.50/1.28 % (9318)Memory used [KB]: 5500
% 1.50/1.28 % (9318)Time elapsed: 0.003 s
% 1.50/1.28 % (9318)Instructions burned: 4 (million)
% 1.50/1.28 % (9318)------------------------------
% 1.50/1.28 % (9318)------------------------------
% 1.50/1.28 % (9323)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9129 for (3000ds/18Mi)
% 1.50/1.28 % (9322)First to succeed.
% 1.50/1.28 % (9319)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_9129 for (3000ds/27Mi)
% 1.50/1.28 % (9321)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_9129 for (3000ds/2Mi)
% 1.50/1.29 % (9320)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9129 for (3000ds/2Mi)
% 1.50/1.29 % (9321)Instruction limit reached!
% 1.50/1.29 % (9321)------------------------------
% 1.50/1.29 % (9321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (9321)Termination reason: Unknown
% 1.50/1.29 % (9321)Termination phase: Property scanning
% 1.50/1.29
% 1.50/1.29 % (9321)Memory used [KB]: 895
% 1.50/1.29 % (9321)Time elapsed: 0.003 s
% 1.50/1.29 % (9321)Instructions burned: 2 (million)
% 1.50/1.29 % (9321)------------------------------
% 1.50/1.29 % (9321)------------------------------
% 1.50/1.29 % (9322)Refutation found. Thanks to Tanya!
% 1.50/1.29 % SZS status Theorem for DTF2THF_9129
% 1.50/1.29 % SZS output start Proof for DTF2THF_9129
% 1.50/1.29 thf(type_def_5, type, a: $tType).
% 1.50/1.29 thf(func_def_0, type, a: $tType).
% 1.50/1.29 thf(func_def_1, type, cP: a > a > a).
% 1.50/1.29 thf(func_def_2, type, cZ: a).
% 1.50/1.29 thf(func_def_6, type, sK0: a).
% 1.50/1.29 thf(func_def_7, type, sK1: (a > $o) > a).
% 1.50/1.29 thf(func_def_8, type, sK2: (a > $o) > a).
% 1.50/1.29 thf(func_def_11, type, ph4: !>[X0: $tType]:(X0)).
% 1.50/1.29 thf(f272,plain,(
% 1.50/1.29 $false),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f245])).
% 1.50/1.29 thf(f245,plain,(
% 1.50/1.29 (sK0 != sK0) | (cZ != cZ)),
% 1.50/1.29 inference(superposition,[status(thm)],[f18,f207])).
% 1.50/1.29 thf(f207,plain,(
% 1.50/1.29 ( ! [X0 : a] : ((cZ = X0) | (sK0 != X0)) )),
% 1.50/1.29 inference(superposition,[status(thm)],[f17,f98])).
% 1.50/1.29 thf(f98,plain,(
% 1.50/1.29 ( ! [X0 : a] : (((cP @ (sK2 @ (^[Y0 : a]: (~ (X0 = Y0)))) @ (sK1 @ (^[Y0 : a]: (~ (X0 = Y0))))) = X0) | (cZ = X0)) )),
% 1.50/1.29 inference(equality_proxy_clausification,[status(thm)],[f97])).
% 1.50/1.29 thf(f97,plain,(
% 1.50/1.29 ( ! [X0 : a] : (($true = (X0 = cZ)) | ((cP @ (sK2 @ (^[Y0 : a]: (~ (X0 = Y0)))) @ (sK1 @ (^[Y0 : a]: (~ (X0 = Y0))))) = X0)) )),
% 1.50/1.29 inference(not_proxy_clausification,[status(thm)],[f96])).
% 1.50/1.29 thf(f96,plain,(
% 1.50/1.29 ( ! [X0 : a] : (((cP @ (sK2 @ (^[Y0 : a]: (~ (X0 = Y0)))) @ (sK1 @ (^[Y0 : a]: (~ (X0 = Y0))))) = X0) | ($true != (~ (X0 = cZ)))) )),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.50/1.29 thf(f81,plain,(
% 1.50/1.29 ( ! [X0 : a] : ((((^[Y0 : a]: (~ (X0 = Y0))) @ cZ) != $true) | ((cP @ (sK2 @ (^[Y0 : a]: (~ (X0 = Y0)))) @ (sK1 @ (^[Y0 : a]: (~ (X0 = Y0))))) = X0)) )),
% 1.50/1.29 inference(leibniz_equality_elimination,[status(thm)],[f14])).
% 1.50/1.29 thf(f14,plain,(
% 1.50/1.29 ( ! [X8 : a,X5 : a > $o] : (((X5 @ (cP @ (sK2 @ X5) @ (sK1 @ X5))) != $true) | ((X5 @ X8) = $true) | ((X5 @ cZ) != $true)) )),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.29 thf(f11,plain,(
% 1.50/1.29 ! [X0 : a,X1 : a] : (cZ != (cP @ X1 @ X0)) & ((cZ != sK0) & ! [X3 : a,X4 : a] : ((cP @ X3 @ X4) != sK0)) & ! [X5 : a > $o] : ((($true = (X5 @ (sK1 @ X5))) & ((X5 @ (sK2 @ X5)) = $true) & ((X5 @ (cP @ (sK2 @ X5) @ (sK1 @ X5))) != $true)) | ! [X8 : a] : ((X5 @ X8) = $true) | ((X5 @ cZ) != $true)) & ! [X9 : a,X10 : a,X11 : a,X12 : a] : (((X9 = X11) & (X10 = X12)) | ((cP @ X12 @ X11) != (cP @ X10 @ X9)))),
% 1.50/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9])).
% 1.50/1.29 thf(f9,plain,(
% 1.50/1.29 ? [X2 : a] : ((cZ != X2) & ! [X3 : a,X4 : a] : ((cP @ X3 @ X4) != X2)) => ((cZ != sK0) & ! [X4 : a,X3 : a] : ((cP @ X3 @ X4) != sK0))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f10,plain,(
% 1.50/1.29 ! [X5 : a > $o] : (? [X6 : a,X7 : a] : (((X5 @ X6) = $true) & ((X5 @ X7) = $true) & ($true != (X5 @ (cP @ X7 @ X6)))) => (($true = (X5 @ (sK1 @ X5))) & ((X5 @ (sK2 @ X5)) = $true) & ((X5 @ (cP @ (sK2 @ X5) @ (sK1 @ X5))) != $true)))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f8,plain,(
% 1.50/1.29 ! [X0 : a,X1 : a] : (cZ != (cP @ X1 @ X0)) & ? [X2 : a] : ((cZ != X2) & ! [X3 : a,X4 : a] : ((cP @ X3 @ X4) != X2)) & ! [X5 : a > $o] : (? [X6 : a,X7 : a] : (((X5 @ X6) = $true) & ((X5 @ X7) = $true) & ($true != (X5 @ (cP @ X7 @ X6)))) | ! [X8 : a] : ((X5 @ X8) = $true) | ((X5 @ cZ) != $true)) & ! [X9 : a,X10 : a,X11 : a,X12 : a] : (((X9 = X11) & (X10 = X12)) | ((cP @ X12 @ X11) != (cP @ X10 @ X9)))),
% 1.50/1.29 inference(rectify,[status(thm)],[f7])).
% 1.50/1.29 thf(f7,plain,(
% 1.50/1.29 ! [X1 : a,X0 : a] : ((cP @ X0 @ X1) != cZ) & ? [X10 : a] : ((cZ != X10) & ! [X11 : a,X12 : a] : ((cP @ X11 @ X12) != X10)) & ! [X6 : a > $o] : (? [X8 : a,X7 : a] : (((X6 @ X8) = $true) & ((X6 @ X7) = $true) & ((X6 @ (cP @ X7 @ X8)) != $true)) | ! [X9 : a] : ((X6 @ X9) = $true) | ((X6 @ cZ) != $true)) & ! [X4 : a,X3 : a,X5 : a,X2 : a] : (((X4 = X5) & (X2 = X3)) | ((cP @ X3 @ X4) != (cP @ X2 @ X5)))),
% 1.50/1.29 inference(flattening,[status(thm)],[f6])).
% 1.50/1.29 thf(f6,plain,(
% 1.50/1.29 ? [X10 : a] : ((cZ != X10) & ! [X11 : a,X12 : a] : ((cP @ X11 @ X12) != X10)) & (! [X6 : a > $o] : (! [X9 : a] : ((X6 @ X9) = $true) | (? [X8 : a,X7 : a] : (((X6 @ (cP @ X7 @ X8)) != $true) & (((X6 @ X7) = $true) & ((X6 @ X8) = $true))) | ((X6 @ cZ) != $true))) & ! [X4 : a,X3 : a,X5 : a,X2 : a] : (((X4 = X5) & (X2 = X3)) | ((cP @ X3 @ X4) != (cP @ X2 @ X5))) & ! [X1 : a,X0 : a] : ((cP @ X0 @ X1) != cZ))),
% 1.50/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.29 thf(f5,plain,(
% 1.50/1.29 ~((! [X6 : a > $o] : ((! [X8 : a,X7 : a] : ((((X6 @ X7) = $true) & ((X6 @ X8) = $true)) => ((X6 @ (cP @ X7 @ X8)) = $true)) & ((X6 @ cZ) = $true)) => ! [X9 : a] : ((X6 @ X9) = $true)) & ! [X5 : a,X3 : a,X2 : a,X4 : a] : (((cP @ X3 @ X4) = (cP @ X2 @ X5)) => ((X4 = X5) & (X2 = X3))) & ! [X1 : a,X0 : a] : ((cP @ X0 @ X1) != cZ)) => ! [X10 : a] : ((cZ = X10) | ? [X11 : a,X12 : a] : ((cP @ X11 @ X12) = X10)))),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.29 thf(f4,plain,(
% 1.50/1.29 ~((! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X2 : a,X3 : a,X4 : a,X5 : a] : (((cP @ X3 @ X4) = (cP @ X2 @ X5)) => ((X2 = X3) & (X4 = X5))) & ! [X6 : a > $o] : ((! [X7 : a,X8 : a] : (((X6 @ X8) & (X6 @ X7)) => (X6 @ (cP @ X7 @ X8))) & (X6 @ cZ)) => ! [X9 : a] : (X6 @ X9))) => ! [X10 : a] : ((cZ = X10) | ? [X11 : a,X12 : a] : ((cP @ X11 @ X12) = X10)))),
% 1.50/1.29 inference(rectify,[status(thm)],[f2])).
% 1.50/1.29 thf(f2,negated_conjecture,(
% 1.50/1.29 ~((! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X1 : a,X0 : a,X2 : a,X3 : a] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X0 = X1) & (X2 = X3))) & ! [X4 : a > $o] : ((! [X0 : a,X1 : a] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ cZ)) => ! [X0 : a] : (X4 @ X0))) => ! [X0 : a] : ((cZ = X0) | ? [X1 : a,X5 : a] : ((cP @ X1 @ X5) = X0)))),
% 1.50/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.29 thf(f1,conjecture,(
% 1.50/1.29 (! [X0 : a,X1 : a] : ((cP @ X0 @ X1) != cZ) & ! [X1 : a,X0 : a,X2 : a,X3 : a] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X0 = X1) & (X2 = X3))) & ! [X4 : a > $o] : ((! [X0 : a,X1 : a] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ cZ)) => ! [X0 : a] : (X4 @ X0))) => ! [X0 : a] : ((cZ = X0) | ? [X1 : a,X5 : a] : ((cP @ X1 @ X5) = X0))),
% 1.50/1.29 file('/export/starexec/sandbox/tmp/tmp.c8VKnJbKCs/DTF2THF_9129.p',cS_LEM1D_pme)).
% 1.50/1.29 thf(f17,plain,(
% 1.50/1.29 ( ! [X3 : a,X4 : a] : (((cP @ X3 @ X4) != sK0)) )),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.29 thf(f18,plain,(
% 1.50/1.29 (cZ != sK0)),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.29 % SZS output end Proof for DTF2THF_9129
% 1.50/1.29 % (9322)------------------------------
% 1.50/1.29 % (9322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (9322)Termination reason: Refutation
% 1.50/1.29
% 1.50/1.29 % (9322)Memory used [KB]: 5628
% 1.50/1.29 % (9322)Time elapsed: 0.009 s
% 1.50/1.29 % (9322)Instructions burned: 19 (million)
% 1.50/1.29 % (9322)------------------------------
% 1.50/1.29 % (9322)------------------------------
% 1.50/1.29 % (9316)Success in time 0.002 s
%------------------------------------------------------------------------------