%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU920^5 : 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 : n031.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 09:37:45 AM UTC 2026
% Result : Theorem 1.26s 1.18s
% Output : Refutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 23 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 11 ~; 0 |; 5 &; 36 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 0 ^; 28 !; 22 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_8,type,
c: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
c: $tType ).
thf(func_def_6,type,
sK0: b > c ).
thf(func_def_7,type,
sK1: a > b ).
thf(func_def_8,type,
sK2: c ).
thf(func_def_9,type,
sK3: c > a ).
thf(f14,plain,
$false,
inference(equality_resolution,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: c] : ( sK2 != X0 ),
inference(superposition,[status(thm)],[f12,f11]) ).
thf(f11,plain,
! [X4: c] :
( ( sK0 @ ( sK1 @ ( sK3 @ X4 ) ) )
= X4 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X3: b] :
( ( sK0 @ X3 )
!= sK2 )
& ! [X4: c] :
( ( sK0 @ ( sK1 @ ( sK3 @ X4 ) ) )
= X4 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f9,f8,f7]) ).
thf(f7,plain,
( ? [X0: b > c,X1: a > b] :
( ? [X2: c] :
! [X3: b] :
( ( X0 @ X3 )
!= X2 )
& ! [X4: c] :
? [X5: a] :
( ( X0 @ ( X1 @ X5 ) )
= X4 ) )
=> ( ? [X2: c] :
! [X3: b] :
( ( sK0 @ X3 )
!= X2 )
& ! [X4: c] :
? [X5: a] :
( ( sK0 @ ( sK1 @ X5 ) )
= X4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X2: c] :
! [X3: b] :
( ( sK0 @ X3 )
!= X2 )
=> ! [X3: b] :
( ( sK0 @ X3 )
!= sK2 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X4: c] :
( ? [X5: a] :
( ( sK0 @ ( sK1 @ X5 ) )
= X4 )
=> ( ( sK0 @ ( sK1 @ ( sK3 @ X4 ) ) )
= X4 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: b > c,X1: a > b] :
( ? [X2: c] :
! [X3: b] :
( ( X0 @ X3 )
!= X2 )
& ! [X4: c] :
? [X5: a] :
( ( X0 @ ( X1 @ X5 ) )
= X4 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
? [X0: b > c,X1: a > b] :
( ? [X4: c] :
! [X5: b] :
( ( X0 @ X5 )
!= X4 )
& ! [X2: c] :
? [X3: a] :
( ( X0 @ ( X1 @ X3 ) )
= X2 ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X1: a > b,X0: b > c] :
( ! [X2: c] :
? [X3: a] :
( ( X0 @ ( X1 @ X3 ) )
= X2 )
=> ! [X4: c] :
? [X5: b] :
( ( X0 @ X5 )
= X4 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: b > c,X0: a > b] :
( ! [X2: c] :
? [X3: a] :
( ( X1 @ ( X0 @ X3 ) )
= X2 )
=> ! [X2: c] :
? [X3: b] :
( ( X1 @ X3 )
= X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: b > c,X0: a > b] :
( ! [X2: c] :
? [X3: a] :
( ( X1 @ ( X0 @ X3 ) )
= X2 )
=> ! [X2: c] :
? [X3: b] :
( ( X1 @ X3 )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.zxhEmD158A/DTF2THF_16331.p',cFN_THM_4_pme) ).
thf(f12,plain,
! [X3: b] :
( ( sK0 @ X3 )
!= sK2 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU920^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.33 % Computer : n031.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Feb 24 12:38:03 EST 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.43 ---- Original DTF file ---
% 0.16/0.43 thf(spec,logic,$$dhol).
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 % File : SEU920^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.43 % Domain : Set Theory (Functions)
% 0.16/0.43 % Problem : TPS problem FN-THM-4
% 0.16/0.43 % Version : Especial.
% 0.16/0.43 % English :
% 0.16/0.43
% 0.16/0.43 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.43 % Source : [Bro09]
% 0.16/0.43 % Names : tps_0114 [Bro09]
% 0.16/0.43 % : FN-THM-4 [TPS]
% 0.16/0.43
% 0.16/0.43 % Status : Theorem
% 0.16/0.43 % Rating : 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.16/0.43 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.43 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.16/0.43 % Maximal formula atoms : 2 ( 2 avg)
% 0.16/0.43 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 3 @)
% 0.16/0.43 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.43 % Maximal formula depth : 6 ( 6 avg)
% 0.16/0.43 % Number of types : 3 ( 3 usr)
% 0.16/0.43 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.16/0.43 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.43 % Number of variables : 6 ( 0 ^; 4 !; 2 ?; 6 :)
% 0.16/0.43 % SPC : TH0_THM_EQU_NAR
% 0.16/0.43
% 0.16/0.43 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.43 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.43 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.43 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.43 % : Polymorphic definitions expanded.
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 thf(a_type,type,
% 0.16/0.43 a: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(b_type,type,
% 0.16/0.43 b: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(c_type,type,
% 0.16/0.43 c: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(cFN_THM_4_pme,conjecture,
% 0.16/0.43 ! [F: a > b,G: b > c] :
% 0.16/0.43 ( ! [Y: c] :
% 0.16/0.43 ? [X: a] :
% 0.16/0.43 ( ( G @ ( F @ X ) )
% 0.16/0.43 = Y )
% 0.16/0.43 => ! [Y: c] :
% 0.16/0.43 ? [X: b] :
% 0.16/0.43 ( ( G @ X )
% 0.16/0.43 = Y ) ) ).
% 0.16/0.43
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 ------------------------
% 1.26/1.16 ---- Embedded in THF ---
% 1.26/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.26/1.16 %%% Generated on Tue Feb 24 12:38:04 EST 2026
% 1.26/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.26/1.16 %%% Logic specification used:
% 1.26/1.16 %%% thf(spec, logic, $$dhol).
% 1.26/1.16
% 1.26/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zxhEmD158A/DTF2DTF16331.p
% See solution above
% 1.26/1.16 ------------------------
% 1.26/1.17 ---- Cleaned THF ---
% 1.26/1.17 thf(a_type,type,
% 1.26/1.17 a: $tType ).
% 1.26/1.17
% 1.26/1.17 thf(b_type,type,
% 1.26/1.17 b: $tType ).
% 1.26/1.17
% 1.26/1.17 thf(c_type,type,
% 1.26/1.17 c: $tType ).
% 1.26/1.17
% 1.26/1.17 thf(cFN_THM_4_pme,conjecture,
% 1.26/1.17 ! [F: a > b,G: b > c] :
% 1.26/1.17 ( ! [Y: c] :
% 1.26/1.17 ? [X: a] :
% 1.26/1.17 ( ( G @ ( F @ X ) )
% 1.26/1.17 = Y )
% 1.26/1.17 => ! [Y: c] :
% 1.26/1.17 ? [X: b] :
% 1.26/1.17 ( ( G @ X )
% 1.26/1.17 = Y ) ) ).
% 1.26/1.17 ------------------------
% 1.26/1.18 % (16428)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16331 for (3000ds/183Mi)
% 1.26/1.18 % (16428)First to succeed.
% 1.26/1.18 % (16428)Refutation found. Thanks to Tanya!
% 1.26/1.18 % SZS status Theorem for DTF2THF_16331
% 1.26/1.18 % SZS output start Proof for DTF2THF_16331
% 1.26/1.18 thf(type_def_5, type, a: $tType).
% 1.26/1.18 thf(type_def_6, type, b: $tType).
% 1.26/1.18 thf(type_def_8, type, c: $tType).
% 1.26/1.18 thf(func_def_0, type, a: $tType).
% 1.26/1.18 thf(func_def_1, type, b: $tType).
% 1.26/1.18 thf(func_def_2, type, c: $tType).
% 1.26/1.18 thf(func_def_6, type, sK0: b > c).
% 1.26/1.18 thf(func_def_7, type, sK1: a > b).
% 1.26/1.18 thf(func_def_8, type, sK2: c).
% 1.26/1.18 thf(func_def_9, type, sK3: c > a).
% 1.26/1.18 thf(f14,plain,(
% 1.26/1.18 $false),
% 1.26/1.18 inference(equality_resolution,[status(thm)],[f13])).
% 1.26/1.18 thf(f13,plain,(
% 1.26/1.18 ( ! [X0 : c] : ((sK2 != X0)) )),
% 1.26/1.18 inference(superposition,[status(thm)],[f12,f11])).
% 1.26/1.18 thf(f11,plain,(
% 1.26/1.18 ( ! [X4 : c] : (((sK0 @ (sK1 @ (sK3 @ X4))) = X4)) )),
% 1.26/1.18 inference(cnf_transformation,[status(thm)],[f10])).
% 1.26/1.18 thf(f10,plain,(
% 1.26/1.18 ! [X3 : b] : ((sK0 @ X3) != sK2) & ! [X4 : c] : ((sK0 @ (sK1 @ (sK3 @ X4))) = X4)),
% 1.26/1.18 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f9,f8,f7])).
% 1.26/1.18 thf(f7,plain,(
% 1.26/1.18 ? [X0 : b > c,X1 : a > b] : (? [X2 : c] : ! [X3 : b] : ((X0 @ X3) != X2) & ! [X4 : c] : ? [X5 : a] : ((X0 @ (X1 @ X5)) = X4)) => (? [X2 : c] : ! [X3 : b] : ((sK0 @ X3) != X2) & ! [X4 : c] : ? [X5 : a] : ((sK0 @ (sK1 @ X5)) = X4))),
% 1.26/1.18 introduced(definition,[],[choice_axiom])).
% 1.26/1.18 thf(f8,plain,(
% 1.26/1.18 ? [X2 : c] : ! [X3 : b] : ((sK0 @ X3) != X2) => ! [X3 : b] : ((sK0 @ X3) != sK2)),
% 1.26/1.18 introduced(definition,[],[choice_axiom])).
% 1.26/1.18 thf(f9,plain,(
% 1.26/1.18 ! [X4 : c] : (? [X5 : a] : ((sK0 @ (sK1 @ X5)) = X4) => ((sK0 @ (sK1 @ (sK3 @ X4))) = X4))),
% 1.26/1.18 introduced(definition,[],[choice_axiom])).
% 1.26/1.18 thf(f6,plain,(
% 1.26/1.18 ? [X0 : b > c,X1 : a > b] : (? [X2 : c] : ! [X3 : b] : ((X0 @ X3) != X2) & ! [X4 : c] : ? [X5 : a] : ((X0 @ (X1 @ X5)) = X4))),
% 1.26/1.18 inference(rectify,[status(thm)],[f5])).
% 1.26/1.18 thf(f5,plain,(
% 1.26/1.18 ? [X0 : b > c,X1 : a > b] : (? [X4 : c] : ! [X5 : b] : ((X0 @ X5) != X4) & ! [X2 : c] : ? [X3 : a] : ((X0 @ (X1 @ X3)) = X2))),
% 1.26/1.18 inference(ennf_transformation,[status(thm)],[f4])).
% 1.26/1.18 thf(f4,plain,(
% 1.26/1.18 ~! [X1 : a > b,X0 : b > c] : (! [X2 : c] : ? [X3 : a] : ((X0 @ (X1 @ X3)) = X2) => ! [X4 : c] : ? [X5 : b] : ((X0 @ X5) = X4))),
% 1.26/1.18 inference(rectify,[status(thm)],[f2])).
% 1.26/1.18 thf(f2,negated_conjecture,(
% 1.26/1.18 ~! [X1 : b > c,X0 : a > b] : (! [X2 : c] : ? [X3 : a] : ((X1 @ (X0 @ X3)) = X2) => ! [X2 : c] : ? [X3 : b] : ((X1 @ X3) = X2))),
% 1.26/1.18 inference(negated_conjecture,[status(cth)],[f1])).
% 1.26/1.18 thf(f1,conjecture,(
% 1.26/1.18 ! [X1 : b > c,X0 : a > b] : (! [X2 : c] : ? [X3 : a] : ((X1 @ (X0 @ X3)) = X2) => ! [X2 : c] : ? [X3 : b] : ((X1 @ X3) = X2))),
% 1.26/1.18 file('/export/starexec/sandbox/tmp/tmp.zxhEmD158A/DTF2THF_16331.p',cFN_THM_4_pme)).
% 1.26/1.18 thf(f12,plain,(
% 1.26/1.18 ( ! [X3 : b] : (((sK0 @ X3) != sK2)) )),
% 1.26/1.18 inference(cnf_transformation,[status(thm)],[f10])).
% 1.26/1.18 % SZS output end Proof for DTF2THF_16331
% 1.26/1.18 % (16428)------------------------------
% 1.26/1.18 % (16428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.18 % (16428)Termination reason: Refutation
% 1.26/1.18
% 1.26/1.18 % (16428)Memory used [KB]: 5500
% 1.26/1.18 % (16428)Time elapsed: 0.002 s
% 1.26/1.18 % (16428)Instructions burned: 1 (million)
% 1.26/1.18 % (16428)------------------------------
% 1.26/1.18 % (16428)------------------------------
% 1.26/1.18 % (16427)Success in time 0.011 s
%------------------------------------------------------------------------------