%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU936^5 : 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 : n010.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 09:37:47 AM UTC 2026
% Result : Theorem 1.38s 1.20s
% Output : Refutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 43 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 109 ( 17 ~; 7 |; 12 &; 62 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 0 ^; 31 !; 16 ?; 47 :)
% 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: a ).
thf(func_def_9,type,
sK3: a ).
thf(f18,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f17,f11]) ).
thf(f11,plain,
sK2 != sK3,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X2: a,X3: a] :
( ( ( sK0 @ ( sK1 @ X2 ) )
!= ( sK0 @ ( sK1 @ X3 ) ) )
| ( X2 = X3 ) )
& ( sK2 != sK3 )
& ( ( sK1 @ sK2 )
= ( sK1 @ sK3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f8,f7]) ).
thf(f7,plain,
( ? [X0: b > c,X1: a > b] :
( ! [X2: a,X3: a] :
( ( ( X0 @ ( X1 @ X2 ) )
!= ( X0 @ ( X1 @ X3 ) ) )
| ( X2 = X3 ) )
& ? [X4: a,X5: a] :
( ( X4 != X5 )
& ( ( X1 @ X5 )
= ( X1 @ X4 ) ) ) )
=> ( ! [X3: a,X2: a] :
( ( ( sK0 @ ( sK1 @ X2 ) )
!= ( sK0 @ ( sK1 @ X3 ) ) )
| ( X2 = X3 ) )
& ? [X5: a,X4: a] :
( ( X4 != X5 )
& ( ( sK1 @ X5 )
= ( sK1 @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X5: a,X4: a] :
( ( X4 != X5 )
& ( ( sK1 @ X5 )
= ( sK1 @ X4 ) ) )
=> ( ( sK2 != sK3 )
& ( ( sK1 @ sK2 )
= ( sK1 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: b > c,X1: a > b] :
( ! [X2: a,X3: a] :
( ( ( X0 @ ( X1 @ X2 ) )
!= ( X0 @ ( X1 @ X3 ) ) )
| ( X2 = X3 ) )
& ? [X4: a,X5: a] :
( ( X4 != X5 )
& ( ( X1 @ X5 )
= ( X1 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
? [X0: b > c,X1: a > b] :
( ! [X3: a,X2: a] :
( ( ( X0 @ ( X1 @ X2 ) )
!= ( X0 @ ( X1 @ X3 ) ) )
| ( X2 = X3 ) )
& ? [X5: a,X4: a] :
( ( X4 != X5 )
& ( ( X1 @ X5 )
= ( X1 @ X4 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X1: a > b,X0: b > c] :
( ! [X3: a,X2: a] :
( ( ( X0 @ ( X1 @ X2 ) )
= ( X0 @ ( X1 @ X3 ) ) )
=> ( X2 = X3 ) )
=> ! [X5: a,X4: a] :
( ( ( X1 @ X5 )
= ( X1 @ X4 ) )
=> ( X4 = X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: b > c,X0: a > b] :
( ! [X3: a,X2: a] :
( ( ( X1 @ ( X0 @ X2 ) )
= ( X1 @ ( X0 @ X3 ) ) )
=> ( X2 = X3 ) )
=> ! [X2: a,X3: a] :
( ( ( X0 @ X2 )
= ( X0 @ X3 ) )
=> ( X2 = X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: b > c,X0: a > b] :
( ! [X3: a,X2: a] :
( ( ( X1 @ ( X0 @ X2 ) )
= ( X1 @ ( X0 @ X3 ) ) )
=> ( X2 = X3 ) )
=> ! [X2: a,X3: a] :
( ( ( X0 @ X2 )
= ( X0 @ X3 ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cRHrG7vzXr/DTF2THF_29863.p',cFN_THM_3_pme) ).
thf(f17,plain,
sK2 = sK3,
inference(equality_resolution,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: a] :
( ( ( sK0 @ ( sK1 @ X0 ) )
!= ( sK0 @ ( sK1 @ sK2 ) ) )
| ( sK3 = X0 ) ),
inference(superposition,[status(thm)],[f12,f10]) ).
thf(f10,plain,
( ( sK1 @ sK2 )
= ( sK1 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f12,plain,
! [X2: a,X3: a] :
( ( ( sK0 @ ( sK1 @ X2 ) )
!= ( sK0 @ ( sK1 @ X3 ) ) )
| ( X2 = X3 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU936^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n010.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 12:36:18 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : SEU936^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.40 % Domain : Set Theory (Functions)
% 0.17/0.40 % Problem : TPS problem FN-THM-3
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English :
% 0.17/0.40
% 0.17/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.40 % Source : [Bro09]
% 0.17/0.40 % Names : tps_0311 [Bro09]
% 0.17/0.40 % : FN-THM-3 [TPS]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % Rating : 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 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
% 0.17/0.40 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.17/0.40 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 4 ( 4 avg)
% 0.17/0.40 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 6 @)
% 0.17/0.40 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 7 ( 7 avg)
% 0.17/0.40 % Number of types : 3 ( 3 usr)
% 0.17/0.40 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.17/0.40 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.17/0.40 % SPC : TH0_THM_EQU_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.40 % : Polymorphic definitions expanded.
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(a_type,type,
% 0.17/0.40 a: $tType ).
% 0.17/0.40
% 0.17/0.40 thf(b_type,type,
% 0.17/0.40 b: $tType ).
% 0.17/0.40
% 0.17/0.40 thf(c_type,type,
% 0.17/0.40 c: $tType ).
% 0.17/0.40
% 0.17/0.40 thf(cFN_THM_3_pme,conjecture,
% 0.17/0.40 ! [F: a > b,G: b > c] :
% 0.17/0.40 ( ! [Xx: a,Xy: a] :
% 0.17/0.40 ( ( ( G @ ( F @ Xx ) )
% 0.17/0.40 = ( G @ ( F @ Xy ) ) )
% 0.17/0.40 => ( Xx = Xy ) )
% 0.17/0.40 => ! [Xx: a,Xy: a] :
% 0.17/0.40 ( ( ( F @ Xx )
% 0.17/0.40 = ( F @ Xy ) )
% 0.17/0.40 => ( Xx = Xy ) ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.26/1.17 ---- Embedded in THF ---
% 1.26/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.26/1.17 %%% Generated on Tue Feb 24 12:36:19 EST 2026
% 1.26/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.26/1.17 %%% Logic specification used:
% 1.26/1.17 %%% thf(spec, logic, $$dhol).
% 1.26/1.17
% 1.26/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cRHrG7vzXr/DTF2DTF29863.p
% See solution above
% 1.26/1.17 ------------------------
% 1.26/1.18 ---- Cleaned THF ---
% 1.26/1.18 thf(a_type,type,
% 1.26/1.18 a: $tType ).
% 1.26/1.18
% 1.26/1.18 thf(b_type,type,
% 1.26/1.18 b: $tType ).
% 1.26/1.18
% 1.26/1.18 thf(c_type,type,
% 1.26/1.18 c: $tType ).
% 1.26/1.18
% 1.26/1.18 thf(cFN_THM_3_pme,conjecture,
% 1.26/1.18 ! [F: a > b,G: b > c] :
% 1.26/1.18 ( ! [Xx: a,Xy: a] :
% 1.26/1.18 ( ( ( G @ ( F @ Xx ) )
% 1.26/1.18 = ( G @ ( F @ Xy ) ) )
% 1.26/1.18 => ( Xx = Xy ) )
% 1.26/1.18 => ! [Xx: a,Xy: a] :
% 1.26/1.18 ( ( ( F @ Xx )
% 1.26/1.18 = ( F @ Xy ) )
% 1.26/1.18 => ( Xx = Xy ) ) ) ).
% 1.26/1.18 ------------------------
% 1.26/1.19 % (30024)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29863 for (3000ds/18Mi)
% 1.26/1.19 % (30021)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29863 for (3000ds/2Mi)
% 1.26/1.19 % (30023)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_29863 for (3000ds/275Mi)
% 1.26/1.19 % (30020)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_29863 for (3000ds/27Mi)
% 1.26/1.19 % (30019)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_29863 for (3000ds/4Mi)
% 1.26/1.19 % (30018)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29863 for (3000ds/183Mi)
% 1.26/1.20 % (30023)First to succeed.
% 1.26/1.20 % (30018)Also succeeded, but the first one will report.
% 1.38/1.20 % (30024)Also succeeded, but the first one will report.
% 1.38/1.20 % (30023)Refutation found. Thanks to Tanya!
% 1.38/1.20 % SZS status Theorem for DTF2THF_29863
% 1.38/1.20 % SZS output start Proof for DTF2THF_29863
% 1.38/1.20 thf(type_def_5, type, a: $tType).
% 1.38/1.20 thf(type_def_6, type, b: $tType).
% 1.38/1.20 thf(type_def_8, type, c: $tType).
% 1.38/1.20 thf(func_def_0, type, a: $tType).
% 1.38/1.20 thf(func_def_1, type, b: $tType).
% 1.38/1.20 thf(func_def_2, type, c: $tType).
% 1.38/1.20 thf(func_def_6, type, sK0: b > c).
% 1.38/1.20 thf(func_def_7, type, sK1: a > b).
% 1.38/1.20 thf(func_def_8, type, sK2: a).
% 1.38/1.20 thf(func_def_9, type, sK3: a).
% 1.38/1.20 thf(f18,plain,(
% 1.38/1.20 $false),
% 1.38/1.20 inference(subsumption_resolution,[status(thm)],[f17,f11])).
% 1.38/1.20 thf(f11,plain,(
% 1.38/1.20 (sK2 != sK3)),
% 1.38/1.20 inference(cnf_transformation,[status(thm)],[f9])).
% 1.38/1.20 thf(f9,plain,(
% 1.38/1.20 ! [X2 : a,X3 : a] : (((sK0 @ (sK1 @ X2)) != (sK0 @ (sK1 @ X3))) | (X2 = X3)) & ((sK2 != sK3) & ((sK1 @ sK2) = (sK1 @ sK3)))),
% 1.38/1.20 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f8,f7])).
% 1.38/1.20 thf(f7,plain,(
% 1.38/1.20 ? [X0 : b > c,X1 : a > b] : (! [X2 : a,X3 : a] : (((X0 @ (X1 @ X2)) != (X0 @ (X1 @ X3))) | (X2 = X3)) & ? [X4 : a,X5 : a] : ((X4 != X5) & ((X1 @ X5) = (X1 @ X4)))) => (! [X3 : a,X2 : a] : (((sK0 @ (sK1 @ X2)) != (sK0 @ (sK1 @ X3))) | (X2 = X3)) & ? [X5 : a,X4 : a] : ((X4 != X5) & ((sK1 @ X5) = (sK1 @ X4))))),
% 1.38/1.20 introduced(definition,[],[choice_axiom])).
% 1.38/1.20 thf(f8,plain,(
% 1.38/1.20 ? [X5 : a,X4 : a] : ((X4 != X5) & ((sK1 @ X5) = (sK1 @ X4))) => ((sK2 != sK3) & ((sK1 @ sK2) = (sK1 @ sK3)))),
% 1.38/1.20 introduced(definition,[],[choice_axiom])).
% 1.38/1.20 thf(f6,plain,(
% 1.38/1.20 ? [X0 : b > c,X1 : a > b] : (! [X2 : a,X3 : a] : (((X0 @ (X1 @ X2)) != (X0 @ (X1 @ X3))) | (X2 = X3)) & ? [X4 : a,X5 : a] : ((X4 != X5) & ((X1 @ X5) = (X1 @ X4))))),
% 1.38/1.20 inference(rectify,[status(thm)],[f5])).
% 1.38/1.20 thf(f5,plain,(
% 1.38/1.20 ? [X0 : b > c,X1 : a > b] : (! [X3 : a,X2 : a] : (((X0 @ (X1 @ X2)) != (X0 @ (X1 @ X3))) | (X2 = X3)) & ? [X5 : a,X4 : a] : ((X4 != X5) & ((X1 @ X5) = (X1 @ X4))))),
% 1.38/1.20 inference(ennf_transformation,[status(thm)],[f4])).
% 1.38/1.20 thf(f4,plain,(
% 1.38/1.20 ~! [X1 : a > b,X0 : b > c] : (! [X3 : a,X2 : a] : (((X0 @ (X1 @ X2)) = (X0 @ (X1 @ X3))) => (X2 = X3)) => ! [X5 : a,X4 : a] : (((X1 @ X5) = (X1 @ X4)) => (X4 = X5)))),
% 1.38/1.20 inference(rectify,[status(thm)],[f2])).
% 1.38/1.20 thf(f2,negated_conjecture,(
% 1.38/1.20 ~! [X1 : b > c,X0 : a > b] : (! [X3 : a,X2 : a] : (((X1 @ (X0 @ X2)) = (X1 @ (X0 @ X3))) => (X2 = X3)) => ! [X2 : a,X3 : a] : (((X0 @ X2) = (X0 @ X3)) => (X2 = X3)))),
% 1.38/1.20 inference(negated_conjecture,[status(cth)],[f1])).
% 1.38/1.20 thf(f1,conjecture,(
% 1.38/1.20 ! [X1 : b > c,X0 : a > b] : (! [X3 : a,X2 : a] : (((X1 @ (X0 @ X2)) = (X1 @ (X0 @ X3))) => (X2 = X3)) => ! [X2 : a,X3 : a] : (((X0 @ X2) = (X0 @ X3)) => (X2 = X3)))),
% 1.38/1.20 file('/export/starexec/sandbox/tmp/tmp.cRHrG7vzXr/DTF2THF_29863.p',cFN_THM_3_pme)).
% 1.38/1.20 thf(f17,plain,(
% 1.38/1.20 (sK2 = sK3)),
% 1.38/1.20 inference(equality_resolution,[status(thm)],[f13])).
% 1.38/1.20 thf(f13,plain,(
% 1.38/1.20 ( ! [X0 : a] : (((sK0 @ (sK1 @ X0)) != (sK0 @ (sK1 @ sK2))) | (sK3 = X0)) )),
% 1.38/1.20 inference(superposition,[status(thm)],[f12,f10])).
% 1.38/1.20 thf(f10,plain,(
% 1.38/1.20 ((sK1 @ sK2) = (sK1 @ sK3))),
% 1.38/1.20 inference(cnf_transformation,[status(thm)],[f9])).
% 1.38/1.20 thf(f12,plain,(
% 1.38/1.20 ( ! [X2 : a,X3 : a] : (((sK0 @ (sK1 @ X2)) != (sK0 @ (sK1 @ X3))) | (X2 = X3)) )),
% 1.38/1.20 inference(cnf_transformation,[status(thm)],[f9])).
% 1.38/1.20 % SZS output end Proof for DTF2THF_29863
% 1.38/1.20 % (30023)------------------------------
% 1.38/1.20 % (30023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.20 % (30023)Termination reason: Refutation
% 1.38/1.20
% 1.38/1.20 % (30023)Memory used [KB]: 5500
% 1.38/1.20 % (30023)Time elapsed: 0.003 s
% 1.38/1.20 % (30023)Instructions burned: 1 (million)
% 1.38/1.20 % (30023)------------------------------
% 1.38/1.20 % (30023)------------------------------
% 1.38/1.20 % (30017)Success in time 0.012 s
%------------------------------------------------------------------------------