%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV431^1 : 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 : n002.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 1.63s 1.30s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 49 ( 10 ~; 2 |; 0 &; 34 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 16 !; 5 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
f: a > b ).
thf(func_def_6,type,
sK0: ( b > a ) > a ).
thf(func_def_8,type,
inv_f_2: b > a ).
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f16,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK0 @ inv_f_2 )
!= ( sK0 @ inv_f_2 ) ),
inference(superposition,[status(thm)],[f11,f13]) ).
thf(f13,plain,
! [X0: a] :
( ( inv_f_2 @ ( f @ X0 ) )
= X0 ),
inference(injectivity,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: a,X1: a] :
( ( ( f @ X0 )
!= ( f @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: a,X1: a] :
( ( ( f @ X0 )
!= ( f @ X1 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X1: a,X0: a] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: a,X0: a] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.c1C87fwwyE/DTF2THF_24824.p',finj) ).
thf(f11,plain,
! [X0: b > a] :
( ( X0 @ ( f @ ( sK0 @ X0 ) ) )
!= ( sK0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: b > a] :
( ( X0 @ ( f @ ( sK0 @ X0 ) ) )
!= ( sK0 @ X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f9]) ).
thf(f9,plain,
! [X0: b > a] :
( ? [X1: a] :
( ( X0 @ ( f @ X1 ) )
!= X1 )
=> ( ( X0 @ ( f @ ( sK0 @ X0 ) ) )
!= ( sK0 @ X0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
! [X0: b > a] :
? [X1: a] :
( ( X0 @ ( f @ X1 ) )
!= X1 ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: b > a] :
! [X1: a] :
( ( X0 @ ( f @ X1 ) )
= X1 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ? [X2: b > a] :
! [X0: a] :
( ( X2 @ ( f @ X0 ) )
= X0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
? [X2: b > a] :
! [X0: a] :
( ( X2 @ ( f @ X0 ) )
= X0 ),
file('/export/starexec/sandbox/tmp/tmp.c1C87fwwyE/DTF2THF_24824.p',invexists) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV431^1 : 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 : n002.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 12:46:48 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEV431^1 : TPTP v9.2.1. Released v5.2.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Injective functions f:A->B have left inverses
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro11]
% 0.30/0.46 % Names : INVEXISTS4 [Bro11]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.29 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v5.2.0
% 0.30/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 0 def)
% 0.30/0.46 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.30/0.46 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 4 @)
% 0.30/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 4 ( 4 avg)
% 0.30/0.46 % Number of types : 2 ( 2 usr)
% 0.30/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.30/0.46 % Number of variables : 4 ( 0 ^; 3 !; 1 ?; 4 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments :
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(b,type,
% 0.30/0.46 b: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(f,type,
% 0.30/0.46 f: a > b ).
% 0.30/0.46
% 0.30/0.46 thf(finj,axiom,
% 0.30/0.46 ! [X: a,Y: a] :
% 0.30/0.46 ( ( ( f @ X )
% 0.30/0.46 = ( f @ Y ) )
% 0.30/0.46 => ( X = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(invexists,conjecture,
% 0.30/0.46 ? [G: b > a] :
% 0.30/0.46 ! [X: a] :
% 0.30/0.46 ( ( G @ ( f @ X ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.48/1.26 ---- Embedded in THF ---
% 1.48/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.26 %%% Generated on Tue Feb 24 12:46:49 EST 2026
% 1.48/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.26 %%% Logic specification used:
% 1.48/1.26 %%% thf(spec, logic, $$dhol).
% 1.48/1.26
% 1.48/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.c1C87fwwyE/DTF2DTF24824.p
% See solution above
% 1.48/1.26 ------------------------
% 1.48/1.27 ---- Cleaned THF ---
% 1.48/1.27 thf(a,type,
% 1.48/1.27 a: $tType ).
% 1.48/1.27
% 1.48/1.27 thf(b,type,
% 1.48/1.27 b: $tType ).
% 1.48/1.27
% 1.48/1.27 thf(f,type,
% 1.48/1.27 f: a > b ).
% 1.48/1.27
% 1.48/1.27 thf(finj,axiom,
% 1.48/1.27 ! [X: a,Y: a] :
% 1.48/1.27 ( ( ( f @ X )
% 1.48/1.27 = ( f @ Y ) )
% 1.48/1.27 => ( X = Y ) ) ).
% 1.48/1.27
% 1.48/1.27 thf(invexists,conjecture,
% 1.48/1.27 ? [G: b > a] :
% 1.48/1.27 ! [X: a] :
% 1.48/1.27 ( ( G @ ( f @ X ) )
% 1.48/1.27 = X ) ).
% 1.48/1.27 ------------------------
% 1.48/1.29 % (25152)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24824 for (3000ds/183Mi)
% 1.48/1.29 % (25153)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_24824 for (3000ds/4Mi)
% 1.48/1.29 % (25155)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24824 for (3000ds/2Mi)
% 1.48/1.29 % (25154)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_24824 for (3000ds/27Mi)
% 1.48/1.29 % (25156)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_24824 for (3000ds/2Mi)
% 1.48/1.29 % (25157)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_24824 for (3000ds/275Mi)
% 1.48/1.29 % (25158)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24824 for (3000ds/18Mi)
% 1.48/1.30 % (25157)Refutation not found, incomplete strategy
% 1.48/1.30 % (25157)------------------------------
% 1.48/1.30 % (25157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.30 % (25157)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.30
% 1.48/1.30
% 1.48/1.30 % (25157)Memory used [KB]: 5373
% 1.48/1.30 % (25157)Time elapsed: 0.003 s
% 1.48/1.30 % (25157)Instructions burned: 1 (million)
% 1.48/1.30 % (25157)------------------------------
% 1.48/1.30 % (25157)------------------------------
% 1.48/1.30 % (25154)Refutation not found, incomplete strategy
% 1.48/1.30 % (25154)------------------------------
% 1.48/1.30 % (25154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.30 % (25154)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.30
% 1.48/1.30
% 1.48/1.30 % (25154)Memory used [KB]: 5500
% 1.48/1.30 % (25154)Time elapsed: 0.003 s
% 1.48/1.30 % (25154)Instructions burned: 1 (million)
% 1.48/1.30 % (25154)------------------------------
% 1.48/1.30 % (25154)------------------------------
% 1.48/1.30 % (25155)First to succeed.
% 1.48/1.30 % (25156)Instruction limit reached!
% 1.48/1.30 % (25156)------------------------------
% 1.48/1.30 % (25156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.30 % (25156)Termination reason: Unknown
% 1.48/1.30 % (25156)Termination phase: Saturation
% 1.48/1.30
% 1.48/1.30 % (25156)Memory used [KB]: 5500
% 1.48/1.30 % (25156)Time elapsed: 0.004 s
% 1.48/1.30 % (25156)Instructions burned: 2 (million)
% 1.48/1.30 % (25156)------------------------------
% 1.48/1.30 % (25156)------------------------------
% 1.63/1.30 % (25153)Instruction limit reached!
% 1.63/1.30 % (25153)------------------------------
% 1.63/1.30 % (25153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (25153)Termination reason: Unknown
% 1.63/1.30 % (25153)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (25153)Memory used [KB]: 5500
% 1.63/1.30 % (25153)Time elapsed: 0.005 s
% 1.63/1.30 % (25153)Instructions burned: 4 (million)
% 1.63/1.30 % (25153)------------------------------
% 1.63/1.30 % (25153)------------------------------
% 1.63/1.30 % (25155)Refutation found. Thanks to Tanya!
% 1.63/1.30 % SZS status Theorem for DTF2THF_24824
% 1.63/1.30 % SZS output start Proof for DTF2THF_24824
% 1.63/1.30 thf(type_def_5, type, a: $tType).
% 1.63/1.30 thf(type_def_6, type, b: $tType).
% 1.63/1.30 thf(func_def_0, type, a: $tType).
% 1.63/1.30 thf(func_def_1, type, b: $tType).
% 1.63/1.30 thf(func_def_2, type, f: a > b).
% 1.63/1.30 thf(func_def_6, type, sK0: (b > a) > a).
% 1.63/1.30 thf(func_def_8, type, inv_f_2: b > a).
% 1.63/1.30 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 1.63/1.30 thf(f16,plain,(
% 1.63/1.30 $false),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.63/1.30 thf(f15,plain,(
% 1.63/1.30 ((sK0 @ inv_f_2) != (sK0 @ inv_f_2))),
% 1.63/1.30 inference(superposition,[status(thm)],[f11,f13])).
% 1.63/1.30 thf(f13,plain,(
% 1.63/1.30 ( ! [X0 : a] : (((inv_f_2 @ (f @ X0)) = X0)) )),
% 1.63/1.30 inference(injectivity,[status(thm)],[f12])).
% 1.63/1.30 thf(f12,plain,(
% 1.63/1.30 ( ! [X0 : a,X1 : a] : (((f @ X0) != (f @ X1)) | (X0 = X1)) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.30 thf(f8,plain,(
% 1.63/1.30 ! [X0 : a,X1 : a] : (((f @ X0) != (f @ X1)) | (X0 = X1))),
% 1.63/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.63/1.30 thf(f6,plain,(
% 1.63/1.30 ! [X1 : a,X0 : a] : (((f @ X0) = (f @ X1)) => (X0 = X1))),
% 1.63/1.30 inference(rectify,[status(thm)],[f1])).
% 1.63/1.30 thf(f1,axiom,(
% 1.63/1.30 ! [X1 : a,X0 : a] : (((f @ X0) = (f @ X1)) => (X0 = X1))),
% 1.63/1.30 file('/export/starexec/sandbox/tmp/tmp.c1C87fwwyE/DTF2THF_24824.p',finj)).
% 1.63/1.30 thf(f11,plain,(
% 1.63/1.30 ( ! [X0 : b > a] : (((X0 @ (f @ (sK0 @ X0))) != (sK0 @ X0))) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.30 thf(f10,plain,(
% 1.63/1.30 ! [X0 : b > a] : ((X0 @ (f @ (sK0 @ X0))) != (sK0 @ X0))),
% 1.63/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f9])).
% 1.63/1.30 thf(f9,plain,(
% 1.63/1.30 ! [X0 : b > a] : (? [X1 : a] : ((X0 @ (f @ X1)) != X1) => ((X0 @ (f @ (sK0 @ X0))) != (sK0 @ X0)))),
% 1.63/1.30 introduced(definition,[],[choice_axiom])).
% 1.63/1.30 thf(f7,plain,(
% 1.63/1.30 ! [X0 : b > a] : ? [X1 : a] : ((X0 @ (f @ X1)) != X1)),
% 1.63/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.30 thf(f5,plain,(
% 1.63/1.30 ~? [X0 : b > a] : ! [X1 : a] : ((X0 @ (f @ X1)) = X1)),
% 1.63/1.30 inference(rectify,[status(thm)],[f3])).
% 1.63/1.30 thf(f3,negated_conjecture,(
% 1.63/1.30 ~? [X2 : b > a] : ! [X0 : a] : ((X2 @ (f @ X0)) = X0)),
% 1.63/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.63/1.30 thf(f2,conjecture,(
% 1.63/1.30 ? [X2 : b > a] : ! [X0 : a] : ((X2 @ (f @ X0)) = X0)),
% 1.63/1.30 file('/export/starexec/sandbox/tmp/tmp.c1C87fwwyE/DTF2THF_24824.p',invexists)).
% 1.63/1.30 % SZS output end Proof for DTF2THF_24824
% 1.63/1.30 % (25155)------------------------------
% 1.63/1.30 % (25155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (25155)Termination reason: Refutation
% 1.63/1.30
% 1.63/1.30 % (25155)Memory used [KB]: 5500
% 1.63/1.30 % (25155)Time elapsed: 0.004 s
% 1.63/1.30 % (25155)Instructions burned: 1 (million)
% 1.63/1.30 % (25155)------------------------------
% 1.63/1.30 % (25155)------------------------------
% 1.63/1.30 % (25151)Success in time 0.019 s
%------------------------------------------------------------------------------