%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ140^1 : TPTP v9.2.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 09:28:35 AM UTC 2026
% Result : Theorem 1.58s 1.31s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 21 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 82 ( 17 ~; 6 |; 4 &; 54 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 4 ^; 22 !; 10 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
beverage: $tType ).
thf(type_def_7,type,
syrup: $tType ).
thf(func_def_0,type,
syrup: $tType ).
thf(func_def_1,type,
beverage: $tType ).
thf(func_def_2,type,
coffee: beverage ).
thf(func_def_3,type,
heat: beverage > beverage ).
thf(func_def_4,type,
hot: beverage > $o ).
thf(func_def_5,type,
mix: beverage > syrup > beverage ).
thf(func_def_6,type,
hot_mixture: beverage > syrup > beverage ).
thf(func_def_7,type,
cold_mixture: beverage > syrup > beverage ).
thf(func_def_14,type,
sK0: ( beverage > syrup > beverage ) > syrup ).
thf(func_def_16,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f23,plain,
$false,
inference(flex-flex_simplify,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: beverage > syrup > beverage,X1: beverage] :
( ( X0 @ coffee
@ ( sK0
@ ^ [Y0: beverage,Y1: syrup] : ( heat @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: beverage > syrup > beverage,X1: beverage] :
( ( $true != $true )
| ( ( X0 @ coffee
@ ( sK0
@ ^ [Y0: beverage,Y1: syrup] : ( heat @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 ) ),
inference(constrained_superposition,[status(thm)],[f20,f17]) ).
thf(f17,plain,
! [X0: beverage] :
( ( hot @ ( heat @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: beverage] :
( ( hot @ ( heat @ X0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: beverage] : ( hot @ ( heat @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: beverage] : ( hot @ ( heat @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.23s70ZWxmj/DTF2THF_31138.p',its_hot) ).
thf(f20,plain,
! [X0: beverage > syrup > beverage] :
( ( hot @ ( X0 @ coffee @ ( sK0 @ X0 ) ) )
!= $true ),
inference(equality_resolution,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: beverage,X0: beverage > syrup > beverage] :
( ( $true
!= ( hot @ X2 ) )
| ( ( X0 @ coffee @ ( sK0 @ X0 ) )
!= X2 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: beverage > syrup > beverage,X2: beverage] :
( ( $true
!= ( hot @ X2 ) )
| ( ( X0 @ coffee @ ( sK0 @ X0 ) )
!= X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).
thf(f14,plain,
! [X0: beverage > syrup > beverage] :
( ? [X1: syrup] :
! [X2: beverage] :
( ( $true
!= ( hot @ X2 ) )
| ( ( X0 @ coffee @ X1 )
!= X2 ) )
=> ! [X2: beverage] :
( ( $true
!= ( hot @ X2 ) )
| ( ( X0 @ coffee @ ( sK0 @ X0 ) )
!= X2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: beverage > syrup > beverage] :
? [X1: syrup] :
! [X2: beverage] :
( ( $true
!= ( hot @ X2 ) )
| ( ( X0 @ coffee @ X1 )
!= X2 ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ? [X0: beverage > syrup > beverage] :
! [X1: syrup] :
? [X2: beverage] :
( ( ( X0 @ coffee @ X1 )
= X2 )
& ( $true
= ( hot @ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ? [X0: beverage > syrup > beverage] :
! [X1: syrup] :
? [X2: beverage] :
( ( ( X0 @ coffee @ X1 )
= X2 )
& ( hot @ X2 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ? [X2: beverage > syrup > beverage] :
! [X1: syrup] :
? [X0: beverage] :
( ( ( X2 @ coffee @ X1 )
= X0 )
& ( hot @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
? [X2: beverage > syrup > beverage] :
! [X1: syrup] :
? [X0: beverage] :
( ( ( X2 @ coffee @ X1 )
= X0 )
& ( hot @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.23s70ZWxmj/DTF2THF_31138.p',hot_coffee) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : PUZ140^1 : TPTP v9.2.1. Released v6.1.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n025.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 11:34:12 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.39 ---- Original DTF file ---
% 0.18/0.39 thf(spec,logic,$$dhol).
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 % File : PUZ140^1 : TPTP v9.2.1. Released v6.1.0.
% 0.18/0.39 % Domain : Puzzles
% 0.18/0.39 % Problem : A mixture of coffee and syrup that is hot
% 0.18/0.39 % Version : Especial.
% 0.18/0.39 % English :
% 0.18/0.39
% 0.18/0.39 % Refs : [Arh14] Arhami (2010), Email to Geoff Sutcliffe
% 0.18/0.39 % Source : [Arh14]
% 0.18/0.39 % Names :
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.43 v6.1.0
% 0.18/0.39 % Syntax : Number of formulae : 12 ( 3 unt; 8 typ; 2 def)
% 0.18/0.39 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 2 ( 1 avg)
% 0.18/0.39 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 10 @)
% 0.18/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 6 ( 3 avg)
% 0.18/0.39 % Number of types : 3 ( 2 usr)
% 0.18/0.39 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 7 ( 6 usr; 1 con; 0-2 aty)
% 0.18/0.39 % Number of variables : 8 ( 4 ^; 2 !; 2 ?; 8 :)
% 0.18/0.39 % SPC : TH0_THM_EQU_NAR
% 0.18/0.39
% 0.18/0.39 % Comments :
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 thf(syrup_type,type,
% 0.18/0.39 syrup: $tType ).
% 0.18/0.39
% 0.18/0.39 thf(beverage_type,type,
% 0.18/0.39 beverage: $tType ).
% 0.18/0.39
% 0.18/0.39 %----Coffee is a beverage
% 0.18/0.39 thf(coffee_type,type,
% 0.18/0.39 coffee: beverage ).
% 0.18/0.39
% 0.18/0.39 thf(heat_type,type,
% 0.18/0.39 heat: beverage > beverage ).
% 0.18/0.39
% 0.18/0.39 thf(hot_type,type,
% 0.18/0.39 hot: beverage > $o ).
% 0.18/0.39
% 0.18/0.39 thf(mix_type,type,
% 0.18/0.39 mix: beverage > syrup > beverage ).
% 0.18/0.39
% 0.18/0.39 %----The mixture of a beverage and a syrup is a beverage
% 0.18/0.39 thf(hot_mixture_type,type,
% 0.18/0.39 hot_mixture: beverage > syrup > beverage ).
% 0.18/0.39
% 0.18/0.39 thf(cold_mixture_type,type,
% 0.18/0.39 cold_mixture: beverage > syrup > beverage ).
% 0.18/0.39
% 0.18/0.39 %----Heating a beverage makes the beverage hot
% 0.18/0.39 thf(its_hot,axiom,
% 0.18/0.39 ! [B: beverage] : ( hot @ ( heat @ B ) ) ).
% 0.18/0.39
% 0.18/0.39 %----The cold mixture of a beverage and a syrup is a mixture of the beverage
% 0.18/0.39 %----and the syrup
% 0.18/0.39 thf(cold_mixture_definition,definition,
% 0.18/0.39 ( cold_mixture
% 0.18/0.39 = ( ^ [B: beverage,S: syrup] : ( mix @ B @ S ) ) ) ).
% 0.18/0.39
% 0.18/0.39 %----The hot mixture of a beverage and a syrup is a mixture of the beverage
% 0.18/0.39 %----and the syrup, which is heated
% 0.18/0.39 thf(hot_mixture_definition,definition,
% 0.18/0.39 ( hot_mixture
% 0.18/0.39 = ( ^ [B: beverage,S: syrup] : ( heat @ ( mix @ B @ S ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 %----There is some mixture of coffee and any syrup which is hot
% 0.18/0.39 thf(hot_coffee,conjecture,
% 0.18/0.39 ? [Mixture: beverage > syrup > beverage] :
% 0.18/0.39 ! [S: syrup] :
% 0.18/0.39 ? [B: beverage] :
% 0.18/0.39 ( ( ( Mixture @ coffee @ S )
% 0.18/0.39 = B )
% 0.18/0.39 & ( hot @ B ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 1.39/1.28 ---- Embedded in THF ---
% 1.39/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.28 %%% Generated on Tue Feb 24 11:34:13 EST 2026
% 1.39/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.28 %%% Logic specification used:
% 1.39/1.28 %%% thf(spec, logic, $$dhol).
% 1.39/1.28
% 1.39/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.23s70ZWxmj/DTF2DTF31138.p
% See solution above
% 1.39/1.28 ------------------------
% 1.39/1.29 ---- Cleaned THF ---
% 1.39/1.29 thf(syrup_type,type,
% 1.39/1.29 syrup: $tType ).
% 1.39/1.29
% 1.39/1.29 thf(beverage_type,type,
% 1.39/1.29 beverage: $tType ).
% 1.39/1.29
% 1.39/1.29 thf(coffee_type,type,
% 1.39/1.29 coffee: beverage ).
% 1.39/1.29
% 1.39/1.29 thf(heat_type,type,
% 1.39/1.29 heat: beverage > beverage ).
% 1.39/1.29
% 1.39/1.29 thf(hot_type,type,
% 1.39/1.29 hot: beverage > $o ).
% 1.39/1.29
% 1.39/1.29 thf(mix_type,type,
% 1.39/1.29 mix: beverage > syrup > beverage ).
% 1.39/1.29
% 1.39/1.29 thf(hot_mixture_type,type,
% 1.39/1.29 hot_mixture: beverage > syrup > beverage ).
% 1.39/1.29
% 1.39/1.29 thf(cold_mixture_type,type,
% 1.39/1.29 cold_mixture: beverage > syrup > beverage ).
% 1.39/1.29
% 1.39/1.29 thf(its_hot,axiom,
% 1.39/1.29 ! [B: beverage] : ( hot @ ( heat @ B ) ) ).
% 1.39/1.29
% 1.39/1.29 thf(cold_mixture_definition,definition,
% 1.39/1.29 ( cold_mixture
% 1.39/1.29 = ( ^ [B: beverage,S: syrup] : ( mix @ B @ S ) ) ) ).
% 1.39/1.29
% 1.39/1.29 thf(hot_mixture_definition,definition,
% 1.39/1.29 ( hot_mixture
% 1.39/1.29 = ( ^ [B: beverage,S: syrup] : ( heat @ ( mix @ B @ S ) ) ) ) ).
% 1.39/1.29
% 1.39/1.29 thf(hot_coffee,conjecture,
% 1.39/1.29 ? [Mixture: beverage > syrup > beverage] :
% 1.39/1.29 ! [S: syrup] :
% 1.39/1.29 ? [B: beverage] :
% 1.39/1.29 ( ( ( Mixture @ coffee @ S )
% 1.39/1.29 = B )
% 1.39/1.29 & ( hot @ B ) ) ).
% 1.39/1.29 ------------------------
% 1.58/1.31 % (31240)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_31138 for (2999ds/275Mi)
% 1.58/1.31 % (31235)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31138 for (2999ds/183Mi)
% 1.58/1.31 % (31238)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31138 for (2999ds/2Mi)
% 1.58/1.31 % (31237)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_31138 for (2999ds/27Mi)
% 1.58/1.31 % (31236)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_31138 for (2999ds/4Mi)
% 1.58/1.31 % (31239)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_31138 for (2999ds/2Mi)
% 1.58/1.31 % (31241)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31138 for (2999ds/18Mi)
% 1.58/1.31 % (31240)Refutation not found, incomplete strategy
% 1.58/1.31 % (31240)------------------------------
% 1.58/1.31 % (31240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (31240)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.31
% 1.58/1.31
% 1.58/1.31 % (31240)Memory used [KB]: 5500
% 1.58/1.31 % (31240)Time elapsed: 0.002 s
% 1.58/1.31 % (31240)Instructions burned: 1 (million)
% 1.58/1.31 % (31240)------------------------------
% 1.58/1.31 % (31240)------------------------------
% 1.58/1.31 % (31238)Refutation not found, incomplete strategy
% 1.58/1.31 % (31238)------------------------------
% 1.58/1.31 % (31238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (31238)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.31
% 1.58/1.31
% 1.58/1.31 % (31238)Memory used [KB]: 5500
% 1.58/1.31 % (31238)Time elapsed: 0.002 s
% 1.58/1.31 % (31238)Instructions burned: 1 (million)
% 1.58/1.31 % (31238)------------------------------
% 1.58/1.31 % (31238)------------------------------
% 1.58/1.31 % (31237)Refutation not found, incomplete strategy
% 1.58/1.31 % (31237)------------------------------
% 1.58/1.31 % (31237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (31237)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.31
% 1.58/1.31
% 1.58/1.31 % (31237)Memory used [KB]: 5500
% 1.58/1.31 % (31237)Time elapsed: 0.003 s
% 1.58/1.31 % (31237)Instructions burned: 2 (million)
% 1.58/1.31 % (31237)------------------------------
% 1.58/1.31 % (31237)------------------------------
% 1.58/1.31 % (31239)Instruction limit reached!
% 1.58/1.31 % (31239)------------------------------
% 1.58/1.31 % (31239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (31239)Termination reason: Unknown
% 1.58/1.31 % (31235)First to succeed.
% 1.58/1.31 % (31239)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (31239)Memory used [KB]: 5500
% 1.58/1.31 % (31239)Time elapsed: 0.003 s
% 1.58/1.31 % (31239)Instructions burned: 2 (million)
% 1.58/1.31 % (31239)------------------------------
% 1.58/1.31 % (31239)------------------------------
% 1.58/1.31 % (31236)Also succeeded, but the first one will report.
% 1.58/1.31 % (31235)Refutation found. Thanks to Tanya!
% 1.58/1.31 % SZS status Theorem for DTF2THF_31138
% 1.58/1.31 % SZS output start Proof for DTF2THF_31138
% 1.58/1.31 thf(type_def_5, type, beverage: $tType).
% 1.58/1.31 thf(type_def_7, type, syrup: $tType).
% 1.58/1.31 thf(func_def_0, type, syrup: $tType).
% 1.58/1.31 thf(func_def_1, type, beverage: $tType).
% 1.58/1.31 thf(func_def_2, type, coffee: beverage).
% 1.58/1.31 thf(func_def_3, type, heat: beverage > beverage).
% 1.58/1.31 thf(func_def_4, type, hot: beverage > $o).
% 1.58/1.31 thf(func_def_5, type, mix: beverage > syrup > beverage).
% 1.58/1.31 thf(func_def_6, type, hot_mixture: beverage > syrup > beverage).
% 1.58/1.31 thf(func_def_7, type, cold_mixture: beverage > syrup > beverage).
% 1.58/1.31 thf(func_def_14, type, sK0: (beverage > syrup > beverage) > syrup).
% 1.58/1.31 thf(func_def_16, type, ph2: !>[X0: $tType]:(X0)).
% 1.58/1.31 thf(f23,plain,(
% 1.58/1.31 $false),
% 1.58/1.31 inference(flex-flex_simplify,[status(thm)],[f22])).
% 1.58/1.31 thf(f22,plain,(
% 1.58/1.31 ( ! [X0 : beverage > syrup > beverage,X1 : beverage] : (((X0 @ coffee @ (sK0 @ (^[Y0 : beverage]: ((^[Y1 : syrup]: (heat @ (X0 @ Y0 @ Y1))))))) != X1)) )),
% 1.58/1.31 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.58/1.31 thf(f21,plain,(
% 1.58/1.31 ( ! [X0 : beverage > syrup > beverage,X1 : beverage] : (($true != $true) | ((X0 @ coffee @ (sK0 @ (^[Y0 : beverage]: ((^[Y1 : syrup]: (heat @ (X0 @ Y0 @ Y1))))))) != X1)) )),
% 1.58/1.31 inference(constrained_superposition,[status(thm)],[f20,f17])).
% 1.58/1.31 thf(f17,plain,(
% 1.58/1.31 ( ! [X0 : beverage] : (((hot @ (heat @ X0)) = $true)) )),
% 1.58/1.31 inference(cnf_transformation,[status(thm)],[f9])).
% 1.58/1.31 thf(f9,plain,(
% 1.58/1.31 ! [X0 : beverage] : ((hot @ (heat @ X0)) = $true)),
% 1.58/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.58/1.31 thf(f8,plain,(
% 1.58/1.31 ! [X0 : beverage] : (hot @ (heat @ X0))),
% 1.58/1.31 inference(rectify,[status(thm)],[f1])).
% 1.58/1.31 thf(f1,axiom,(
% 1.58/1.31 ! [X0 : beverage] : (hot @ (heat @ X0))),
% 1.58/1.31 file('/export/starexec/sandbox/tmp/tmp.23s70ZWxmj/DTF2THF_31138.p',its_hot)).
% 1.58/1.31 thf(f20,plain,(
% 1.58/1.31 ( ! [X0 : beverage > syrup > beverage] : (((hot @ (X0 @ coffee @ (sK0 @ X0))) != $true)) )),
% 1.58/1.31 inference(equality_resolution,[status(thm)],[f19])).
% 1.58/1.31 thf(f19,plain,(
% 1.58/1.31 ( ! [X2 : beverage,X0 : beverage > syrup > beverage] : (($true != (hot @ X2)) | ((X0 @ coffee @ (sK0 @ X0)) != X2)) )),
% 1.58/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.58/1.31 thf(f15,plain,(
% 1.58/1.31 ! [X0 : beverage > syrup > beverage] : ! [X2 : beverage] : (($true != (hot @ X2)) | ((X0 @ coffee @ (sK0 @ X0)) != X2))),
% 1.58/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14])).
% 1.58/1.31 thf(f14,plain,(
% 1.58/1.31 ! [X0 : beverage > syrup > beverage] : (? [X1 : syrup] : ! [X2 : beverage] : (($true != (hot @ X2)) | ((X0 @ coffee @ X1) != X2)) => ! [X2 : beverage] : (($true != (hot @ X2)) | ((X0 @ coffee @ (sK0 @ X0)) != X2)))),
% 1.58/1.31 introduced(definition,[],[choice_axiom])).
% 1.58/1.31 thf(f13,plain,(
% 1.58/1.31 ! [X0 : beverage > syrup > beverage] : ? [X1 : syrup] : ! [X2 : beverage] : (($true != (hot @ X2)) | ((X0 @ coffee @ X1) != X2))),
% 1.58/1.31 inference(ennf_transformation,[status(thm)],[f11])).
% 1.58/1.31 thf(f11,plain,(
% 1.58/1.31 ~? [X0 : beverage > syrup > beverage] : ! [X1 : syrup] : ? [X2 : beverage] : (((X0 @ coffee @ X1) = X2) & ($true = (hot @ X2)))),
% 1.58/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.58/1.31 thf(f10,plain,(
% 1.58/1.31 ~? [X0 : beverage > syrup > beverage] : ! [X1 : syrup] : ? [X2 : beverage] : (((X0 @ coffee @ X1) = X2) & (hot @ X2))),
% 1.58/1.31 inference(rectify,[status(thm)],[f5])).
% 1.58/1.31 thf(f5,negated_conjecture,(
% 1.58/1.31 ~? [X2 : beverage > syrup > beverage] : ! [X1 : syrup] : ? [X0 : beverage] : (((X2 @ coffee @ X1) = X0) & (hot @ X0))),
% 1.58/1.31 inference(negated_conjecture,[status(cth)],[f4])).
% 1.58/1.31 thf(f4,conjecture,(
% 1.58/1.31 ? [X2 : beverage > syrup > beverage] : ! [X1 : syrup] : ? [X0 : beverage] : (((X2 @ coffee @ X1) = X0) & (hot @ X0))),
% 1.58/1.31 file('/export/starexec/sandbox/tmp/tmp.23s70ZWxmj/DTF2THF_31138.p',hot_coffee)).
% 1.58/1.31 % SZS output end Proof for DTF2THF_31138
% 1.58/1.31 % (31235)------------------------------
% 1.58/1.31 % (31235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (31235)Termination reason: Refutation
% 1.58/1.31
% 1.58/1.31 % (31235)Memory used [KB]: 5500
% 1.58/1.31 % (31235)Time elapsed: 0.003 s
% 1.58/1.31 % (31235)Instructions burned: 2 (million)
% 1.58/1.31 % (31235)------------------------------
% 1.58/1.31 % (31235)------------------------------
% 1.58/1.31 % (31234)Success in time 0.018 s
%------------------------------------------------------------------------------