%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO037^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 09:53:11 AM UTC 2026
% Result : Theorem 1.58s 1.30s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 25 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 59 ( 15 ~; 6 |; 0 &; 32 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 35 ( 0 ^; 27 !; 8 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_5,type,
inv_sK0_2: $i > $i > $o ).
thf(func_def_6,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f18,plain,
$false,
inference(equality_resolution,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: $i,X1: $i > $o] :
( ( ~ ( inv_sK0_2 @ ( sK0 @ X1 ) @ X2 ) )
!= ( X1 @ X2 ) ),
inference(bool_equality_to_disequality,[status(thm)],[f14]) ).
thf(f14,plain,
! [X2: $i,X1: $i > $o] :
( ( inv_sK0_2 @ ( sK0 @ X1 ) @ X2 )
= ( X1 @ X2 ) ),
inference(argument_congruence,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $i > $o] :
( ( inv_sK0_2 @ ( sK0 @ X1 ) )
= X1 ),
inference(injectivity,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: $i > $o,X2: $i > $o] :
( ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) )
| ( X1 = X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
!= ( X0 @ X2 ) )
| ( X1 = X2 ) )
=> ! [X2: $i > $o,X1: $i > $o] :
( ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) )
| ( X1 = X2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
!= ( X0 @ X2 ) )
| ( X1 = X2 ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( $i > $o ) > $i] :
! [X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 )
!= ( X0 @ X2 ) )
| ( X1 = X2 ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: ( $i > $o ) > $i] :
! [X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ? [X0: ( $i > $o ) > $i] :
! [X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ? [X0: ( $i > $o ) > $i] :
! [X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ? [X0: ( $i > $o ) > $i] :
! [X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.QAJS5KQnq4/DTF2THF_19983.p',conj) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO037^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n016.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 14:22:21 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : SYO037^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.44 % Domain : Syntactic
% 0.19/0.44 % Problem : Injective Cantor theorem
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English :
% 0.19/0.44
% 0.19/0.44 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.19/0.44 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Ben09]
% 0.19/0.44 % Names : Example 32 [BB05]
% 0.19/0.44
% 0.19/0.44 % Status : ContradictoryAxioms
% 0.19/0.44 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.70 v8.2.0, 0.85 v8.1.0, 0.82 v7.5.0, 0.71 v7.4.0, 0.67 v7.3.0, 0.89 v7.2.0, 0.88 v7.1.0, 1.00 v3.7.0
% 0.19/0.44 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.19/0.44 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.44 % Number of connectives : 4 ( 1 ~; 0 |; 0 &; 2 @)
% 0.19/0.44 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 6 ( 6 avg)
% 0.19/0.44 % Number of types : 2 ( 0 usr)
% 0.19/0.44 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.44 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.19/0.44 % SPC : TH0_CAX_EQU_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : Requires set comprehension, and set instantiation
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 thf(conj,conjecture,
% 0.19/0.44 ~ ? [H: ( $i > $o ) > $i] :
% 0.19/0.44 ! [P: $i > $o,Q: $i > $o] :
% 0.19/0.44 ( ( ( H @ P )
% 0.19/0.44 = ( H @ Q ) )
% 0.19/0.44 => ( P = Q ) ) ).
% 0.19/0.44
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 ------------------------
% 1.46/1.26 ---- Embedded in THF ---
% 1.46/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.26 %%% Generated on Tue Feb 24 14:22:22 EST 2026
% 1.46/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.26 %%% Logic specification used:
% 1.46/1.26 %%% thf(spec, logic, $$dhol).
% 1.46/1.26
% 1.46/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QAJS5KQnq4/DTF2DTF19983.p
% See solution above
% 1.46/1.26 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.27 thf(conj,conjecture,
% 1.46/1.27 ~ ? [H: ( $i > $o ) > $i] :
% 1.46/1.27 ! [P: $i > $o,Q: $i > $o] :
% 1.46/1.27 ( ( ( H @ P )
% 1.46/1.27 = ( H @ Q ) )
% 1.46/1.27 => ( P = Q ) ) ).
% 1.46/1.27 ------------------------
% 1.46/1.29 % (20269)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_19983 for (3000ds/2Mi)
% 1.46/1.29 % (20269)Refutation not found, incomplete strategy
% 1.46/1.29 % (20269)------------------------------
% 1.46/1.29 % (20269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (20269)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.29
% 1.46/1.29
% 1.46/1.29 % (20269)Memory used [KB]: 5500
% 1.46/1.29 % (20269)Time elapsed: 0.002 s
% 1.46/1.29 % (20269)Instructions burned: 1 (million)
% 1.46/1.29 % (20269)------------------------------
% 1.46/1.29 % (20269)------------------------------
% 1.46/1.29 % (20268)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19983 for (3000ds/2Mi)
% 1.46/1.29 % (20265)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19983 for (3000ds/183Mi)
% 1.46/1.29 % (20266)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_19983 for (3000ds/4Mi)
% 1.46/1.29 % (20267)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_19983 for (3000ds/27Mi)
% 1.46/1.30 % (20270)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_19983 for (3000ds/275Mi)
% 1.46/1.30 % (20271)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19983 for (3000ds/18Mi)
% 1.46/1.30 % (20265)Refutation not found, incomplete strategy
% 1.46/1.30 % (20265)------------------------------
% 1.46/1.30 % (20265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (20265)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.30
% 1.46/1.30
% 1.46/1.30 % (20265)Memory used [KB]: 5373
% 1.46/1.30 % (20265)Time elapsed: 0.003 s
% 1.46/1.30 % (20265)Instructions burned: 1 (million)
% 1.46/1.30 % (20265)------------------------------
% 1.46/1.30 % (20265)------------------------------
% 1.46/1.30 % (20268)Instruction limit reached!
% 1.46/1.30 % (20268)------------------------------
% 1.46/1.30 % (20268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (20268)Termination reason: Unknown
% 1.46/1.30 % (20268)Termination phase: Saturation
% 1.46/1.30
% 1.46/1.30 % (20268)Memory used [KB]: 5500
% 1.46/1.30 % (20268)Time elapsed: 0.004 s
% 1.46/1.30 % (20268)Instructions burned: 3 (million)
% 1.46/1.30 % (20268)------------------------------
% 1.46/1.30 % (20268)------------------------------
% 1.46/1.30 % (20266)Refutation not found, incomplete strategy
% 1.46/1.30 % (20266)------------------------------
% 1.46/1.30 % (20266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (20266)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.30
% 1.46/1.30
% 1.46/1.30 % (20266)Memory used [KB]: 5373
% 1.46/1.30 % (20266)Time elapsed: 0.003 s
% 1.46/1.30 % (20266)Instructions burned: 1 (million)
% 1.46/1.30 % (20266)------------------------------
% 1.46/1.30 % (20266)------------------------------
% 1.46/1.30 % (20267)Refutation not found, incomplete strategy
% 1.46/1.30 % (20267)------------------------------
% 1.46/1.30 % (20267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (20267)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.30
% 1.46/1.30
% 1.46/1.30 % (20267)Memory used [KB]: 5373
% 1.46/1.30 % (20267)Time elapsed: 0.003 s
% 1.46/1.30 % (20267)Instructions burned: 1 (million)
% 1.46/1.30 % (20267)------------------------------
% 1.46/1.30 % (20267)------------------------------
% 1.46/1.30 % (20270)Refutation not found, incomplete strategy
% 1.46/1.30 % (20270)------------------------------
% 1.46/1.30 % (20270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (20270)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.30
% 1.46/1.30
% 1.46/1.30 % (20270)Memory used [KB]: 5373
% 1.46/1.30 % (20270)Time elapsed: 0.003 s
% 1.46/1.30 % (20270)Instructions burned: 1 (million)
% 1.46/1.30 % (20270)------------------------------
% 1.46/1.30 % (20270)------------------------------
% 1.58/1.30 % (20271)Refutation not found, incomplete strategy
% 1.58/1.30 % (20271)------------------------------
% 1.58/1.30 % (20271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.30 % (20271)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.30
% 1.58/1.30
% 1.58/1.30 % (20271)Memory used [KB]: 5373
% 1.58/1.30 % (20271)Time elapsed: 0.003 s
% 1.58/1.30 % (20271)Instructions burned: 1 (million)
% 1.58/1.30 % (20271)------------------------------
% 1.58/1.30 % (20271)------------------------------
% 1.58/1.30 % (20272)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19983 for (2999ds/3Mi)
% 1.58/1.30 % (20272)First to succeed.
% 1.58/1.30 % (20272)Refutation found. Thanks to Tanya!
% 1.58/1.30 % SZS status Theorem for DTF2THF_19983
% 1.58/1.30 % SZS output start Proof for DTF2THF_19983
% 1.58/1.30 thf(func_def_3, type, sK0: ($i > $o) > $i).
% 1.58/1.30 thf(func_def_5, type, inv_sK0_2: $i > $i > $o).
% 1.58/1.30 thf(func_def_6, type, ph3: !>[X0: $tType]:(X0)).
% 1.58/1.30 thf(f18,plain,(
% 1.58/1.30 $false),
% 1.58/1.30 inference(equality_resolution,[status(thm)],[f16])).
% 1.58/1.30 thf(f16,plain,(
% 1.58/1.30 ( ! [X2 : $i,X1 : $i > $o] : (((~ (inv_sK0_2 @ (sK0 @ X1) @ X2)) != (X1 @ X2))) )),
% 1.58/1.30 inference(bool_equality_to_disequality,[status(thm)],[f14])).
% 1.58/1.30 thf(f14,plain,(
% 1.58/1.30 ( ! [X2 : $i,X1 : $i > $o] : (((inv_sK0_2 @ (sK0 @ X1) @ X2) = (X1 @ X2))) )),
% 1.58/1.30 inference(argument_congruence,[status(thm)],[f12])).
% 1.58/1.30 thf(f12,plain,(
% 1.58/1.30 ( ! [X1 : $i > $o] : (((inv_sK0_2 @ (sK0 @ X1)) = X1)) )),
% 1.58/1.30 inference(injectivity,[status(thm)],[f11])).
% 1.58/1.30 thf(f11,plain,(
% 1.58/1.30 ( ! [X2 : $i > $o,X1 : $i > $o] : (((sK0 @ X1) != (sK0 @ X2)) | (X1 = X2)) )),
% 1.58/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.58/1.30 thf(f10,plain,(
% 1.58/1.30 ! [X1 : $i > $o,X2 : $i > $o] : (((sK0 @ X1) != (sK0 @ X2)) | (X1 = X2))),
% 1.58/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.58/1.30 thf(f9,plain,(
% 1.58/1.30 ? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1) != (X0 @ X2)) | (X1 = X2)) => ! [X2 : $i > $o,X1 : $i > $o] : (((sK0 @ X1) != (sK0 @ X2)) | (X1 = X2))),
% 1.58/1.30 introduced(definition,[],[choice_axiom])).
% 1.58/1.30 thf(f8,plain,(
% 1.58/1.30 ? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1) != (X0 @ X2)) | (X1 = X2))),
% 1.58/1.30 inference(rectify,[status(thm)],[f7])).
% 1.58/1.30 thf(f7,plain,(
% 1.58/1.30 ? [X0 : ($i > $o) > $i] : ! [X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1) != (X0 @ X2)) | (X1 = X2))),
% 1.58/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.58/1.30 thf(f6,plain,(
% 1.58/1.30 ? [X0 : ($i > $o) > $i] : ! [X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2))),
% 1.58/1.30 inference(flattening,[status(thm)],[f5])).
% 1.58/1.30 thf(f5,plain,(
% 1.58/1.30 ~~? [X0 : ($i > $o) > $i] : ! [X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2))),
% 1.58/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.58/1.30 thf(f4,plain,(
% 1.58/1.30 ~~? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2))),
% 1.58/1.30 inference(rectify,[status(thm)],[f2])).
% 1.58/1.30 thf(f2,negated_conjecture,(
% 1.58/1.30 ~~? [X0 : ($i > $o) > $i] : ! [X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2))),
% 1.58/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.58/1.30 thf(f1,conjecture,(
% 1.58/1.30 ~? [X0 : ($i > $o) > $i] : ! [X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2))),
% 1.58/1.30 file('/export/starexec/sandbox/tmp/tmp.QAJS5KQnq4/DTF2THF_19983.p',conj)).
% 1.58/1.30 % SZS output end Proof for DTF2THF_19983
% 1.58/1.30 % (20272)------------------------------
% 1.58/1.30 % (20272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.30 % (20272)Termination reason: Refutation
% 1.58/1.30
% 1.58/1.30 % (20272)Memory used [KB]: 5500
% 1.58/1.30 % (20272)Time elapsed: 0.002 s
% 1.58/1.30 % (20272)Instructions burned: 2 (million)
% 1.58/1.30 % (20272)------------------------------
% 1.58/1.30 % (20272)------------------------------
% 1.58/1.30 % (20264)Success in time 0.02 s
%------------------------------------------------------------------------------