%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU957^5 : 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 : n019.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 09:37:50 AM UTC 2026
% Result : Theorem 1.63s 1.42s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 52 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 145 ( 17 ~; 6 |; 14 &; 88 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 85 ( 0 ^; 43 !; 42 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_6,type,
sK0: ( b > a ) > b ).
thf(func_def_7,type,
sK1: ( b > a ) > b ).
thf(func_def_8,type,
sK2: a > b ).
thf(func_def_9,type,
sK3: b > a ).
thf(func_def_10,type,
sK4: ( a > $o ) > a ).
thf(func_def_12,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f21,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( sK0 @ sK3 )
!= ( sK0 @ sK3 ) ),
inference(superposition,[status(thm)],[f17,f19]) ).
thf(f19,plain,
( ( sK1 @ sK3 )
= ( sK0 @ sK3 ) ),
inference(forward_demodulation,[status(thm)],[f18,f15]) ).
thf(f15,plain,
! [X4: b] :
( ( sK2 @ ( sK3 @ X4 ) )
= X4 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: b > a] :
( ( ( sK1 @ X0 )
!= ( sK0 @ X0 ) )
& ( ( X0 @ ( sK0 @ X0 ) )
= ( X0 @ ( sK1 @ X0 ) ) ) )
& ! [X4: b] :
( ( sK2 @ ( sK3 @ X4 ) )
= X4 )
& ! [X7: a > $o] :
( ( $true
= ( X7 @ ( sK4 @ X7 ) ) )
| ! [X8: a] :
( $true
!= ( X7 @ X8 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
! [X0: b > a] :
( ? [X1: b,X2: b] :
( ( X1 != X2 )
& ( ( X0 @ X1 )
= ( X0 @ X2 ) ) )
=> ( ( ( sK1 @ X0 )
!= ( sK0 @ X0 ) )
& ( ( X0 @ ( sK0 @ X0 ) )
= ( X0 @ ( sK1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: a > b] :
! [X4: b] :
? [X5: a] :
( ( X3 @ X5 )
= X4 )
=> ! [X4: b] :
? [X5: a] :
( ( sK2 @ X5 )
= X4 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X4: b] :
( ? [X5: a] :
( ( sK2 @ X5 )
= X4 )
=> ( ( sK2 @ ( sK3 @ X4 ) )
= X4 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X6: ( a > $o ) > a] :
! [X7: a > $o] :
( ( $true
= ( X7 @ ( X6 @ X7 ) ) )
| ! [X8: a] :
( $true
!= ( X7 @ X8 ) ) )
=> ! [X7: a > $o] :
( ( $true
= ( X7 @ ( sK4 @ X7 ) ) )
| ! [X8: a] :
( $true
!= ( X7 @ X8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: b > a] :
? [X1: b,X2: b] :
( ( X1 != X2 )
& ( ( X0 @ X1 )
= ( X0 @ X2 ) ) )
& ? [X3: a > b] :
! [X4: b] :
? [X5: a] :
( ( X3 @ X5 )
= X4 )
& ? [X6: ( a > $o ) > a] :
! [X7: a > $o] :
( ( $true
= ( X7 @ ( X6 @ X7 ) ) )
| ! [X8: a] :
( $true
!= ( X7 @ X8 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X6: b > a] :
? [X8: b,X7: b] :
( ( X7 != X8 )
& ( ( X6 @ X7 )
= ( X6 @ X8 ) ) )
& ? [X3: a > b] :
! [X4: b] :
? [X5: a] :
( ( X3 @ X5 )
= X4 )
& ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ! [X2: a] :
( ( X1 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X6: b > a] :
? [X8: b,X7: b] :
( ( X7 != X8 )
& ( ( X6 @ X7 )
= ( X6 @ X8 ) ) )
& ? [X3: a > b] :
! [X4: b] :
? [X5: a] :
( ( X3 @ X5 )
= X4 )
& ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ! [X2: a] :
( ( X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ? [X2: a] :
( ( X1 @ X2 )
= $true )
=> ( ( X1 @ ( X0 @ X1 ) )
= $true ) )
=> ( ? [X3: a > b] :
! [X4: b] :
? [X5: a] :
( ( X3 @ X5 )
= X4 )
=> ? [X6: b > a] :
! [X8: b,X7: b] :
( ( ( X6 @ X7 )
= ( X6 @ X8 ) )
=> ( X7 = X8 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ? [X2: a] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ( ? [X3: a > b] :
! [X4: b] :
? [X5: a] :
( ( X3 @ X5 )
= X4 )
=> ? [X6: b > a] :
! [X7: b,X8: b] :
( ( ( X6 @ X7 )
= ( X6 @ X8 ) )
=> ( X7 = X8 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ? [X2: a] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ( ? [X3: a > b] :
! [X4: b] :
? [X1: a] :
( ( X3 @ X1 )
= X4 )
=> ? [X5: b > a] :
! [X7: b,X6: b] :
( ( ( X5 @ X6 )
= ( X5 @ X7 ) )
=> ( X6 = X7 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ? [X2: a] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ( ? [X3: a > b] :
! [X4: b] :
? [X1: a] :
( ( X3 @ X1 )
= X4 )
=> ? [X5: b > a] :
! [X7: b,X6: b] :
( ( ( X5 @ X6 )
= ( X5 @ X7 ) )
=> ( X6 = X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ELpP3mvBp8/DTF2THF_10513.p',cTHM607_pme) ).
thf(f18,plain,
( ( sK1 @ sK3 )
= ( sK2 @ ( sK3 @ ( sK0 @ sK3 ) ) ) ),
inference(superposition,[status(thm)],[f15,f16]) ).
thf(f16,plain,
! [X0: b > a] :
( ( X0 @ ( sK0 @ X0 ) )
= ( X0 @ ( sK1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f17,plain,
! [X0: b > a] :
( ( sK1 @ X0 )
!= ( sK0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU957^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:37:39 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.49 ---- Original DTF file ---
% 0.27/0.50 thf(spec,logic,$$dhol).
% 0.27/0.50 %------------------------------------------------------------------------------
% 0.27/0.50 % File : SEU957^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.50 % Domain : Set Theory (Functions)
% 0.27/0.50 % Problem : TPS problem from FUNCTION-THMS
% 0.27/0.50 % Version : Especial.
% 0.27/0.50 % English :
% 0.27/0.50
% 0.27/0.50 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.50 % Source : [Bro09]
% 0.27/0.50 % Names : tps_0895 [Bro09]
% 0.27/0.50
% 0.27/0.50 % Status : Theorem
% 0.27/0.50 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.44 v7.3.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.86 v6.1.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.27/0.50 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.27/0.50 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.27/0.50 % Maximal formula atoms : 3 ( 3 avg)
% 0.27/0.50 % Number of connectives : 10 ( 0 ~; 0 |; 0 &; 6 @)
% 0.27/0.50 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.27/0.50 % Maximal formula depth : 7 ( 7 avg)
% 0.27/0.50 % Number of types : 3 ( 2 usr)
% 0.27/0.50 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.27/0.50 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.27/0.50 % Number of variables : 9 ( 0 ^; 4 !; 5 ?; 9 :)
% 0.27/0.50 % SPC : TH0_THM_EQU_NAR
% 0.27/0.50
% 0.27/0.50 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.50 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.50 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.50 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.50 %------------------------------------------------------------------------------
% 0.27/0.50 thf(a_type,type,
% 0.27/0.50 a: $tType ).
% 0.27/0.50
% 0.27/0.50 thf(b_type,type,
% 0.27/0.50 b: $tType ).
% 0.27/0.50
% 0.27/0.50 thf(cTHM607_pme,conjecture,
% 0.27/0.50 ( ? [Xc: ( a > $o ) > a] :
% 0.27/0.50 ! [X: a > $o] :
% 0.27/0.50 ( ? [Xt: a] : ( X @ Xt )
% 0.27/0.50 => ( X @ ( Xc @ X ) ) )
% 0.27/0.50 => ( ? [Xg: a > b] :
% 0.27/0.50 ! [Y: b] :
% 0.27/0.50 ? [X: a] :
% 0.27/0.50 ( ( Xg @ X )
% 0.27/0.50 = Y )
% 0.27/0.50 => ? [Xf: b > a] :
% 0.27/0.50 ! [Xx: b,Xy: b] :
% 0.27/0.50 ( ( ( Xf @ Xx )
% 0.27/0.50 = ( Xf @ Xy ) )
% 0.27/0.50 => ( Xx = Xy ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 %------------------------------------------------------------------------------
% 0.27/0.50 ------------------------
% 1.46/1.39 ---- Embedded in THF ---
% 1.46/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.39 %%% Generated on Tue Feb 24 12:37:40 EST 2026
% 1.46/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.39 %%% Logic specification used:
% 1.46/1.39 %%% thf(spec, logic, $$dhol).
% 1.46/1.39
% 1.46/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ELpP3mvBp8/DTF2DTF10513.p
% See solution above
% 1.46/1.39 ------------------------
% 1.63/1.40 ---- Cleaned THF ---
% 1.63/1.40 thf(a_type,type,
% 1.63/1.40 a: $tType ).
% 1.63/1.40
% 1.63/1.40 thf(b_type,type,
% 1.63/1.40 b: $tType ).
% 1.63/1.40
% 1.63/1.40 thf(cTHM607_pme,conjecture,
% 1.63/1.40 ( ? [Xc: ( a > $o ) > a] :
% 1.63/1.40 ! [X: a > $o] :
% 1.63/1.40 ( ? [Xt: a] : ( X @ Xt )
% 1.63/1.40 => ( X @ ( Xc @ X ) ) )
% 1.63/1.40 => ( ? [Xg: a > b] :
% 1.63/1.40 ! [Y: b] :
% 1.63/1.40 ? [X: a] :
% 1.63/1.40 ( ( Xg @ X )
% 1.63/1.40 = Y )
% 1.63/1.40 => ? [Xf: b > a] :
% 1.63/1.40 ! [Xx: b,Xy: b] :
% 1.63/1.40 ( ( ( Xf @ Xx )
% 1.63/1.40 = ( Xf @ Xy ) )
% 1.63/1.40 => ( Xx = Xy ) ) ) ) ).
% 1.63/1.40 ------------------------
% 1.63/1.41 % (10640)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10513 for (2999ds/183Mi)
% 1.63/1.42 % (10644)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_10513 for (2999ds/2Mi)
% 1.63/1.42 % (10642)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_10513 for (2999ds/27Mi)
% 1.63/1.42 % (10643)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10513 for (2999ds/2Mi)
% 1.63/1.42 % (10646)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10513 for (2999ds/18Mi)
% 1.63/1.42 % (10645)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_10513 for (2999ds/275Mi)
% 1.63/1.42 % (10643)Instruction limit reached!
% 1.63/1.42 % (10643)------------------------------
% 1.63/1.42 % (10643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.42 % (10643)Termination reason: Unknown
% 1.63/1.42 % (10643)Termination phase: Saturation
% 1.63/1.42 % (10644)Instruction limit reached!
% 1.63/1.42 % (10644)------------------------------
% 1.63/1.42 % (10644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.42 % (10644)Termination reason: Unknown
% 1.63/1.42 % (10644)Termination phase: Saturation
% 1.63/1.42
% 1.63/1.42 % (10644)Memory used [KB]: 5500
% 1.63/1.42 % (10644)Time elapsed: 0.003 s
% 1.63/1.42 % (10644)Instructions burned: 3 (million)
% 1.63/1.42 % (10644)------------------------------
% 1.63/1.42 % (10644)------------------------------
% 1.63/1.42
% 1.63/1.42 % (10643)Memory used [KB]: 5500
% 1.63/1.42 % (10643)Time elapsed: 0.003 s
% 1.63/1.42 % (10643)Instructions burned: 2 (million)
% 1.63/1.42 % (10643)------------------------------
% 1.63/1.42 % (10643)------------------------------
% 1.63/1.42 % (10642)First to succeed.
% 1.63/1.42 % (10645)Also succeeded, but the first one will report.
% 1.63/1.42 % (10642)Refutation found. Thanks to Tanya!
% 1.63/1.42 % SZS status Theorem for DTF2THF_10513
% 1.63/1.42 % SZS output start Proof for DTF2THF_10513
% 1.63/1.42 thf(type_def_5, type, a: $tType).
% 1.63/1.42 thf(type_def_7, type, b: $tType).
% 1.63/1.42 thf(func_def_0, type, a: $tType).
% 1.63/1.42 thf(func_def_1, type, b: $tType).
% 1.63/1.42 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.42 thf(func_def_6, type, sK0: (b > a) > b).
% 1.63/1.42 thf(func_def_7, type, sK1: (b > a) > b).
% 1.63/1.42 thf(func_def_8, type, sK2: a > b).
% 1.63/1.42 thf(func_def_9, type, sK3: b > a).
% 1.63/1.42 thf(func_def_10, type, sK4: (a > $o) > a).
% 1.63/1.42 thf(func_def_12, type, ph6: !>[X0: $tType]:(X0)).
% 1.63/1.42 thf(f21,plain,(
% 1.63/1.42 $false),
% 1.63/1.42 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.63/1.42 thf(f20,plain,(
% 1.63/1.42 ((sK0 @ sK3) != (sK0 @ sK3))),
% 1.63/1.42 inference(superposition,[status(thm)],[f17,f19])).
% 1.63/1.42 thf(f19,plain,(
% 1.63/1.42 ((sK1 @ sK3) = (sK0 @ sK3))),
% 1.63/1.42 inference(forward_demodulation,[status(thm)],[f18,f15])).
% 1.63/1.42 thf(f15,plain,(
% 1.63/1.42 ( ! [X4 : b] : (((sK2 @ (sK3 @ X4)) = X4)) )),
% 1.63/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.42 thf(f13,plain,(
% 1.63/1.42 ! [X0 : b > a] : (((sK1 @ X0) != (sK0 @ X0)) & ((X0 @ (sK0 @ X0)) = (X0 @ (sK1 @ X0)))) & ! [X4 : b] : ((sK2 @ (sK3 @ X4)) = X4) & ! [X7 : a > $o] : (($true = (X7 @ (sK4 @ X7))) | ! [X8 : a] : ($true != (X7 @ X8)))),
% 1.63/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f12,f11,f10,f9])).
% 1.63/1.42 thf(f9,plain,(
% 1.63/1.42 ! [X0 : b > a] : (? [X1 : b,X2 : b] : ((X1 != X2) & ((X0 @ X1) = (X0 @ X2))) => (((sK1 @ X0) != (sK0 @ X0)) & ((X0 @ (sK0 @ X0)) = (X0 @ (sK1 @ X0)))))),
% 1.63/1.42 introduced(definition,[],[choice_axiom])).
% 1.63/1.42 thf(f10,plain,(
% 1.63/1.42 ? [X3 : a > b] : ! [X4 : b] : ? [X5 : a] : ((X3 @ X5) = X4) => ! [X4 : b] : ? [X5 : a] : ((sK2 @ X5) = X4)),
% 1.63/1.42 introduced(definition,[],[choice_axiom])).
% 1.63/1.42 thf(f11,plain,(
% 1.63/1.42 ! [X4 : b] : (? [X5 : a] : ((sK2 @ X5) = X4) => ((sK2 @ (sK3 @ X4)) = X4))),
% 1.63/1.42 introduced(definition,[],[choice_axiom])).
% 1.63/1.42 thf(f12,plain,(
% 1.63/1.42 ? [X6 : (a > $o) > a] : ! [X7 : a > $o] : (($true = (X7 @ (X6 @ X7))) | ! [X8 : a] : ($true != (X7 @ X8))) => ! [X7 : a > $o] : (($true = (X7 @ (sK4 @ X7))) | ! [X8 : a] : ($true != (X7 @ X8)))),
% 1.63/1.42 introduced(definition,[],[choice_axiom])).
% 1.63/1.42 thf(f8,plain,(
% 1.63/1.42 ! [X0 : b > a] : ? [X1 : b,X2 : b] : ((X1 != X2) & ((X0 @ X1) = (X0 @ X2))) & ? [X3 : a > b] : ! [X4 : b] : ? [X5 : a] : ((X3 @ X5) = X4) & ? [X6 : (a > $o) > a] : ! [X7 : a > $o] : (($true = (X7 @ (X6 @ X7))) | ! [X8 : a] : ($true != (X7 @ X8)))),
% 1.63/1.42 inference(rectify,[status(thm)],[f7])).
% 1.63/1.42 thf(f7,plain,(
% 1.63/1.42 ! [X6 : b > a] : ? [X8 : b,X7 : b] : ((X7 != X8) & ((X6 @ X7) = (X6 @ X8))) & ? [X3 : a > b] : ! [X4 : b] : ? [X5 : a] : ((X3 @ X5) = X4) & ? [X0 : (a > $o) > a] : ! [X1 : a > $o] : (((X1 @ (X0 @ X1)) = $true) | ! [X2 : a] : ((X1 @ X2) != $true))),
% 1.63/1.42 inference(flattening,[status(thm)],[f6])).
% 1.63/1.42 thf(f6,plain,(
% 1.63/1.42 (! [X6 : b > a] : ? [X8 : b,X7 : b] : ((X7 != X8) & ((X6 @ X7) = (X6 @ X8))) & ? [X3 : a > b] : ! [X4 : b] : ? [X5 : a] : ((X3 @ X5) = X4)) & ? [X0 : (a > $o) > a] : ! [X1 : a > $o] : (((X1 @ (X0 @ X1)) = $true) | ! [X2 : a] : ((X1 @ X2) != $true))),
% 1.63/1.42 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.42 thf(f5,plain,(
% 1.63/1.42 ~(? [X0 : (a > $o) > a] : ! [X1 : a > $o] : (? [X2 : a] : ((X1 @ X2) = $true) => ((X1 @ (X0 @ X1)) = $true)) => (? [X3 : a > b] : ! [X4 : b] : ? [X5 : a] : ((X3 @ X5) = X4) => ? [X6 : b > a] : ! [X8 : b,X7 : b] : (((X6 @ X7) = (X6 @ X8)) => (X7 = X8))))),
% 1.63/1.42 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.42 thf(f4,plain,(
% 1.63/1.42 ~(? [X0 : (a > $o) > a] : ! [X1 : a > $o] : (? [X2 : a] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (? [X3 : a > b] : ! [X4 : b] : ? [X5 : a] : ((X3 @ X5) = X4) => ? [X6 : b > a] : ! [X7 : b,X8 : b] : (((X6 @ X7) = (X6 @ X8)) => (X7 = X8))))),
% 1.63/1.42 inference(rectify,[status(thm)],[f2])).
% 1.63/1.42 thf(f2,negated_conjecture,(
% 1.63/1.42 ~(? [X0 : (a > $o) > a] : ! [X1 : a > $o] : (? [X2 : a] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (? [X3 : a > b] : ! [X4 : b] : ? [X1 : a] : ((X3 @ X1) = X4) => ? [X5 : b > a] : ! [X7 : b,X6 : b] : (((X5 @ X6) = (X5 @ X7)) => (X6 = X7))))),
% 1.63/1.42 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.42 thf(f1,conjecture,(
% 1.63/1.42 ? [X0 : (a > $o) > a] : ! [X1 : a > $o] : (? [X2 : a] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (? [X3 : a > b] : ! [X4 : b] : ? [X1 : a] : ((X3 @ X1) = X4) => ? [X5 : b > a] : ! [X7 : b,X6 : b] : (((X5 @ X6) = (X5 @ X7)) => (X6 = X7)))),
% 1.63/1.42 file('/export/starexec/sandbox/tmp/tmp.ELpP3mvBp8/DTF2THF_10513.p',cTHM607_pme)).
% 1.63/1.42 thf(f18,plain,(
% 1.63/1.42 ((sK1 @ sK3) = (sK2 @ (sK3 @ (sK0 @ sK3))))),
% 1.63/1.42 inference(superposition,[status(thm)],[f15,f16])).
% 1.63/1.42 thf(f16,plain,(
% 1.63/1.42 ( ! [X0 : b > a] : (((X0 @ (sK0 @ X0)) = (X0 @ (sK1 @ X0)))) )),
% 1.63/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.42 thf(f17,plain,(
% 1.63/1.42 ( ! [X0 : b > a] : (((sK1 @ X0) != (sK0 @ X0))) )),
% 1.63/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.63/1.42 % SZS output end Proof for DTF2THF_10513
% 1.63/1.42 % (10642)------------------------------
% 1.63/1.42 % (10642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.42 % (10642)Termination reason: Refutation
% 1.63/1.42
% 1.63/1.42 % (10642)Memory used [KB]: 5500
% 1.63/1.42 % (10642)Time elapsed: 0.004 s
% 1.63/1.42 % (10642)Instructions burned: 2 (million)
% 1.63/1.42 % (10642)------------------------------
% 1.63/1.42 % (10642)------------------------------
% 1.63/1.42 % (10639)Success in time 0.015 s
%------------------------------------------------------------------------------