%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV430^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 09:41:14 AM UTC 2026
% Result : Theorem 1.52s 1.30s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 57 ( 10 ~; 1 |; 0 &; 44 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 25 ( 4 ^; 14 !; 7 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $i > $i ).
thf(func_def_4,type,
sK0: ( $i > $i ) > $i ).
thf(func_def_5,type,
sK1: $i > $i ).
thf(func_def_7,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f18,plain,
$false,
inference(equality_resolution,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i > $i] :
( ( sK0
@ ^ [Y0: $i] : ( sK1 @ ( X0 @ Y0 ) ) )
!= ( X0
@ ( sK0
@ ^ [Y0: $i] : ( sK1 @ ( X0 @ Y0 ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i > $i,X1: $i] :
( ( ( sK0
@ ^ [Y0: $i] : ( sK1 @ ( X0 @ Y0 ) ) )
!= X1 )
| ( ( X0
@ ( sK0
@ ^ [Y0: $i] : ( sK1 @ ( X0 @ Y0 ) ) ) )
!= X1 ) ),
inference(constrained_superposition,[status(thm)],[f11,f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( f @ ( sK1 @ X0 ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i] :
( ( f @ ( sK1 @ X0 ) )
= X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f1,f9]) ).
thf(f9,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( f @ X1 )
= X0 )
=> ( ( f @ ( sK1 @ X0 ) )
= X0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1,axiom,
! [X0: $i] :
? [X1: $i] :
( ( f @ X1 )
= X0 ),
file('/export/starexec/sandbox/tmp/tmp.fyayGTrfTD/DTF2THF_30339.p',fsurj) ).
thf(f11,plain,
! [X0: $i > $i] :
( ( sK0 @ X0 )
!= ( f @ ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $i] :
( ( sK0 @ X0 )
!= ( f @ ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
! [X0: $i > $i] :
( ? [X1: $i] :
( ( f @ ( X0 @ X1 ) )
!= X1 )
=> ( ( sK0 @ X0 )
!= ( f @ ( X0 @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
! [X0: $i > $i] :
? [X1: $i] :
( ( f @ ( X0 @ X1 ) )
!= X1 ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i > $i] :
! [X1: $i] :
( ( f @ ( X0 @ X1 ) )
= X1 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ? [X2: $i > $i] :
! [X1: $i] :
( ( f @ ( X2 @ X1 ) )
= X1 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
? [X2: $i > $i] :
! [X1: $i] :
( ( f @ ( X2 @ X1 ) )
= X1 ),
file('/export/starexec/sandbox/tmp/tmp.fyayGTrfTD/DTF2THF_30339.p',invexists) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV430^1 : TPTP v9.2.1. Released v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n020.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 12:46:42 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
% 0.33/0.48 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SEV430^1 : TPTP v9.2.1. Released v5.2.0.
% 0.33/0.49 % Domain : Set Theory
% 0.33/0.49 % Problem : Surjective functions f:I->I have right inverses
% 0.33/0.49 % Version : Especial.
% 0.33/0.49 % English :
% 0.33/0.49
% 0.33/0.49 % Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% 0.33/0.49 % Source : [Bro11]
% 0.33/0.49 % Names : INVEXISTS2 [Bro11]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % 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, 0.11 v7.2.0, 0.12 v7.1.0, 0.00 v6.2.0, 0.43 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.3.0, 0.40 v5.2.0
% 0.33/0.49 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 0 def)
% 0.33/0.49 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 1 ( 1 avg)
% 0.33/0.49 % Number of connectives : 3 ( 0 ~; 0 |; 0 &; 3 @)
% 0.33/0.49 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 3 ( 3 avg)
% 0.33/0.49 % Number of types : 1 ( 0 usr)
% 0.33/0.49 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.33/0.49 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.33/0.49 % SPC : TH0_THM_EQU_NAR
% 0.33/0.49
% 0.33/0.49 % Comments :
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(f,type,
% 0.33/0.49 f: $i > $i ).
% 0.33/0.49
% 0.33/0.49 thf(fsurj,axiom,
% 0.33/0.49 ! [Y: $i] :
% 0.33/0.49 ? [X: $i] :
% 0.33/0.49 ( ( f @ X )
% 0.33/0.49 = Y ) ).
% 0.33/0.49
% 0.33/0.49 thf(invexists,conjecture,
% 0.33/0.49 ? [G: $i > $i] :
% 0.33/0.49 ! [X: $i] :
% 0.33/0.49 ( ( f @ ( G @ X ) )
% 0.33/0.49 = X ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.35/1.28 ---- Embedded in THF ---
% 1.35/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.35/1.28 %%% Generated on Tue Feb 24 12:46:43 EST 2026
% 1.35/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.35/1.28 %%% Logic specification used:
% 1.35/1.28 %%% thf(spec, logic, $$dhol).
% 1.35/1.28
% 1.35/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.fyayGTrfTD/DTF2DTF30339.p
% See solution above
% 1.35/1.28 ------------------------
% 1.35/1.29 ---- Cleaned THF ---
% 1.35/1.29 thf(f,type,
% 1.35/1.29 f: $i > $i ).
% 1.35/1.29
% 1.35/1.29 thf(fsurj,axiom,
% 1.35/1.29 ! [Y: $i] :
% 1.35/1.29 ? [X: $i] :
% 1.35/1.29 ( ( f @ X )
% 1.35/1.29 = Y ) ).
% 1.35/1.29
% 1.35/1.29 thf(invexists,conjecture,
% 1.35/1.29 ? [G: $i > $i] :
% 1.35/1.29 ! [X: $i] :
% 1.35/1.29 ( ( f @ ( G @ X ) )
% 1.35/1.29 = X ) ).
% 1.35/1.29 ------------------------
% 1.52/1.30 % (30437)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30339 for (3000ds/183Mi)
% 1.52/1.30 % (30437)First to succeed.
% 1.52/1.30 % (30437)Refutation found. Thanks to Tanya!
% 1.52/1.30 % SZS status Theorem for DTF2THF_30339
% 1.52/1.30 % SZS output start Proof for DTF2THF_30339
% 1.52/1.30 thf(func_def_0, type, f: $i > $i).
% 1.52/1.30 thf(func_def_4, type, sK0: ($i > $i) > $i).
% 1.52/1.30 thf(func_def_5, type, sK1: $i > $i).
% 1.52/1.30 thf(func_def_7, type, ph3: !>[X0: $tType]:(X0)).
% 1.52/1.30 thf(f18,plain,(
% 1.52/1.30 $false),
% 1.52/1.30 inference(equality_resolution,[status(thm)],[f16])).
% 1.52/1.30 thf(f16,plain,(
% 1.52/1.30 ( ! [X0 : $i > $i] : (((sK0 @ (^[Y0 : $i]: (sK1 @ (X0 @ Y0)))) != (X0 @ (sK0 @ (^[Y0 : $i]: (sK1 @ (X0 @ Y0))))))) )),
% 1.52/1.30 inference(equality_resolution,[status(thm)],[f14])).
% 1.52/1.30 thf(f14,plain,(
% 1.52/1.30 ( ! [X0 : $i > $i,X1 : $i] : (((sK0 @ (^[Y0 : $i]: (sK1 @ (X0 @ Y0)))) != X1) | ((X0 @ (sK0 @ (^[Y0 : $i]: (sK1 @ (X0 @ Y0))))) != X1)) )),
% 1.52/1.30 inference(constrained_superposition,[status(thm)],[f11,f12])).
% 1.52/1.30 thf(f12,plain,(
% 1.52/1.30 ( ! [X0 : $i] : (((f @ (sK1 @ X0)) = X0)) )),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.52/1.30 thf(f10,plain,(
% 1.52/1.30 ! [X0 : $i] : ((f @ (sK1 @ X0)) = X0)),
% 1.52/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f1,f9])).
% 1.52/1.30 thf(f9,plain,(
% 1.52/1.30 ! [X0 : $i] : (? [X1 : $i] : ((f @ X1) = X0) => ((f @ (sK1 @ X0)) = X0))),
% 1.52/1.30 introduced(definition,[],[choice_axiom])).
% 1.52/1.30 thf(f1,axiom,(
% 1.52/1.30 ! [X0 : $i] : ? [X1 : $i] : ((f @ X1) = X0)),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.fyayGTrfTD/DTF2THF_30339.p',fsurj)).
% 1.52/1.30 thf(f11,plain,(
% 1.52/1.30 ( ! [X0 : $i > $i] : (((sK0 @ X0) != (f @ (X0 @ (sK0 @ X0))))) )),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.52/1.30 thf(f8,plain,(
% 1.52/1.30 ! [X0 : $i > $i] : ((sK0 @ X0) != (f @ (X0 @ (sK0 @ X0))))),
% 1.52/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.52/1.30 thf(f7,plain,(
% 1.52/1.30 ! [X0 : $i > $i] : (? [X1 : $i] : ((f @ (X0 @ X1)) != X1) => ((sK0 @ X0) != (f @ (X0 @ (sK0 @ X0)))))),
% 1.52/1.30 introduced(definition,[],[choice_axiom])).
% 1.52/1.30 thf(f6,plain,(
% 1.52/1.30 ! [X0 : $i > $i] : ? [X1 : $i] : ((f @ (X0 @ X1)) != X1)),
% 1.52/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.52/1.30 thf(f5,plain,(
% 1.52/1.30 ~? [X0 : $i > $i] : ! [X1 : $i] : ((f @ (X0 @ X1)) = X1)),
% 1.52/1.30 inference(rectify,[status(thm)],[f3])).
% 1.52/1.30 thf(f3,negated_conjecture,(
% 1.52/1.30 ~? [X2 : $i > $i] : ! [X1 : $i] : ((f @ (X2 @ X1)) = X1)),
% 1.52/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.52/1.30 thf(f2,conjecture,(
% 1.52/1.30 ? [X2 : $i > $i] : ! [X1 : $i] : ((f @ (X2 @ X1)) = X1)),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.fyayGTrfTD/DTF2THF_30339.p',invexists)).
% 1.52/1.30 % SZS output end Proof for DTF2THF_30339
% 1.52/1.30 % (30437)------------------------------
% 1.52/1.30 % (30437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.30 % (30437)Termination reason: Refutation
% 1.52/1.30
% 1.52/1.30 % (30437)Memory used [KB]: 5500
% 1.52/1.30 % (30437)Time elapsed: 0.003 s
% 1.52/1.30 % (30437)Instructions burned: 1 (million)
% 1.52/1.30 % (30437)------------------------------
% 1.52/1.30 % (30437)------------------------------
% 1.52/1.30 % (30436)Success in time 0.012 s
%------------------------------------------------------------------------------