%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ140^2 : TPTP v9.2.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 1.62s 1.32s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 79 ( 40 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 26 ~; 14 |; 11 &; 49 @)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 0 ^; 23 !; 10 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
beverage: $tType ).
thf(type_def_6,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,
mix: beverage > syrup > beverage ).
thf(func_def_4,type,
coffee_mixture: syrup > beverage ).
thf(func_def_5,type,
hot: beverage > $o ).
thf(func_def_9,type,
sK0: ( syrup > beverage ) > syrup ).
thf(func_def_11,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f32,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f29,f31]) ).
thf(f31,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
| ~ spl1_2 ),
inference(equality_resolution,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X0: syrup > beverage] :
( coffee
!= ( X0 @ ( sK0 @ X0 ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl1_2
<=> ! [X0: syrup > beverage] :
( coffee
!= ( X0 @ ( sK0 @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f29,plain,
spl1_1,
inference(avatar_split_clause,[status(thm)],[f28,f21]) ).
thf(f21,definition,
( spl1_1
<=> ( ( hot @ coffee )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f28,plain,
( ( hot @ coffee )
= $true ),
inference(forward_demodulation,[status(thm)],[f17,f18]) ).
thf(f18,plain,
! [X0: syrup] :
( coffee
= ( mix @ coffee @ X0 ) ),
inference(definition_unfolding,[status(thm)],[f15,f14]) ).
thf(f14,plain,
( coffee_mixture
= ( mix @ coffee ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
( coffee_mixture
= ( mix @ coffee ) ),
file('/export/starexec/sandbox2/tmp/tmp.2G1rDoiNrj/DTF2THF_27221.p',coffee_mixture_definition) ).
thf(f15,plain,
! [X0: syrup] :
( coffee
= ( coffee_mixture @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: syrup] :
( ( ( hot @ ( coffee_mixture @ X0 ) )
= $true )
& ( coffee
= ( coffee_mixture @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: syrup] :
( ( coffee
= ( coffee_mixture @ X0 ) )
& ( hot @ ( coffee_mixture @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: syrup] :
( ( coffee
= ( coffee_mixture @ X0 ) )
& ( hot @ ( coffee_mixture @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2G1rDoiNrj/DTF2THF_27221.p',coffee_and_syrup_is_hot_coffee) ).
thf(f17,plain,
! [X0: syrup] :
( ( hot @ ( mix @ coffee @ X0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f16,f14]) ).
thf(f16,plain,
! [X0: syrup] :
( ( hot @ ( coffee_mixture @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f27,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f25,f21]) ).
thf(f19,plain,
! [X0: syrup > beverage] :
( ( coffee
!= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( hot @ coffee )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: beverage,X0: syrup > beverage] :
( ( coffee != X2 )
| ( ( hot @ X2 )
!= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
!= X2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: syrup > beverage,X2: beverage] :
( ( coffee != X2 )
| ( ( hot @ X2 )
!= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
!= X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f11]) ).
thf(f11,plain,
! [X0: syrup > beverage] :
( ? [X1: syrup] :
! [X2: beverage] :
( ( coffee != X2 )
| ( ( hot @ X2 )
!= $true )
| ( ( X0 @ X1 )
!= X2 ) )
=> ! [X2: beverage] :
( ( coffee != X2 )
| ( ( hot @ X2 )
!= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
!= X2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: syrup > beverage] :
? [X1: syrup] :
! [X2: beverage] :
( ( coffee != X2 )
| ( ( hot @ X2 )
!= $true )
| ( ( X0 @ X1 )
!= X2 ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ? [X0: syrup > beverage] :
! [X1: syrup] :
? [X2: beverage] :
( ( coffee = X2 )
& ( ( hot @ X2 )
= $true )
& ( ( X0 @ X1 )
= X2 ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ? [X0: syrup > beverage] :
! [X1: syrup] :
? [X2: beverage] :
( ( ( X0 @ X1 )
= X2 )
& ( hot @ X2 )
& ( coffee = X2 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ? [X1: syrup > beverage] :
! [X0: syrup] :
? [X2: beverage] :
( ( ( X1 @ X0 )
= X2 )
& ( hot @ X2 )
& ( coffee = X2 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
? [X1: syrup > beverage] :
! [X0: syrup] :
? [X2: beverage] :
( ( ( X1 @ X0 )
= X2 )
& ( hot @ X2 )
& ( coffee = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2G1rDoiNrj/DTF2THF_27221.p',there_is_hot_coffee) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ140^2 : TPTP v9.2.1. Released v6.4.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n001.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 11:34:50 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.48 ---- Original DTF file ---
% 0.26/0.48 thf(spec,logic,$$dhol).
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 % File : PUZ140^2 : TPTP v9.2.1. Released v6.4.0.
% 0.26/0.48 % Domain : Puzzles
% 0.26/0.48 % Problem : A mixture of coffee and syrup that is hot
% 0.26/0.48 % Version : Especial.
% 0.26/0.48 % English :
% 0.26/0.48
% 0.26/0.48 % Refs :
% 0.26/0.48 % Source : [TPTP]
% 0.26/0.48 % Names :
% 0.26/0.48
% 0.26/0.48 % Status : Theorem
% 0.26/0.48 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.4.0
% 0.26/0.48 % Syntax : Number of formulae : 9 ( 1 unt; 6 typ; 1 def)
% 0.26/0.48 % Number of atoms : 6 ( 4 equ; 0 cnn)
% 0.26/0.48 % Maximal formula atoms : 3 ( 2 avg)
% 0.26/0.48 % Number of connectives : 9 ( 0 ~; 0 |; 3 &; 6 @)
% 0.26/0.48 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.26/0.48 % Maximal formula depth : 7 ( 4 avg)
% 0.26/0.48 % Number of types : 3 ( 2 usr)
% 0.26/0.48 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.26/0.48 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.26/0.48 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.26/0.48 % SPC : TH0_THM_EQU_NAR
% 0.26/0.48
% 0.26/0.48 % Comments : This version highlights partial application
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 thf(syrup_type,type,
% 0.26/0.48 syrup: $tType ).
% 0.26/0.48
% 0.26/0.48 thf(beverage_type,type,
% 0.26/0.48 beverage: $tType ).
% 0.26/0.48
% 0.26/0.48 thf(coffee_type,type,
% 0.26/0.48 coffee: beverage ).
% 0.26/0.48
% 0.26/0.48 thf(mix_type,type,
% 0.26/0.48 mix: beverage > syrup > beverage ).
% 0.26/0.48
% 0.26/0.48 thf(coffee_mixture_type,type,
% 0.26/0.48 coffee_mixture: syrup > beverage ).
% 0.26/0.48
% 0.26/0.48 thf(hot_type,type,
% 0.26/0.48 hot: beverage > $o ).
% 0.26/0.48
% 0.26/0.48 %----The mixture of coffee and something
% 0.26/0.48 thf(coffee_mixture_definition,definition,
% 0.26/0.48 ( coffee_mixture
% 0.26/0.48 = ( mix @ coffee ) ) ).
% 0.26/0.48
% 0.26/0.48 %----Any coffee mixture is hot coffee
% 0.26/0.48 thf(coffee_and_syrup_is_hot_coffee,axiom,
% 0.26/0.48 ! [S: syrup] :
% 0.26/0.48 ( ( ( coffee_mixture @ S )
% 0.26/0.48 = coffee )
% 0.26/0.48 & ( hot @ ( coffee_mixture @ S ) ) ) ).
% 0.26/0.48
% 0.26/0.48 %----There is some mixture of coffee and any syrup which is hot coffee
% 0.26/0.48 thf(there_is_hot_coffee,conjecture,
% 0.26/0.48 ? [SyrupMixer: syrup > beverage] :
% 0.26/0.48 ! [S: syrup] :
% 0.26/0.48 ? [B: beverage] :
% 0.26/0.48 ( ( B
% 0.26/0.48 = ( SyrupMixer @ S ) )
% 0.26/0.48 & ( B = coffee )
% 0.26/0.48 & ( hot @ B ) ) ).
% 0.26/0.48
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 ------------------------
% 1.42/1.29 ---- Embedded in THF ---
% 1.42/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.42/1.29 %%% Generated on Tue Feb 24 11:34:51 EST 2026
% 1.42/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.42/1.29 %%% Logic specification used:
% 1.42/1.29 %%% thf(spec, logic, $$dhol).
% 1.42/1.29
% 1.42/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2G1rDoiNrj/DTF2DTF27221.p
% See solution above
% 1.42/1.29 ------------------------
% 1.42/1.30 ---- Cleaned THF ---
% 1.62/1.30 thf(syrup_type,type,
% 1.62/1.30 syrup: $tType ).
% 1.62/1.30
% 1.62/1.30 thf(beverage_type,type,
% 1.62/1.30 beverage: $tType ).
% 1.62/1.30
% 1.62/1.30 thf(coffee_type,type,
% 1.62/1.30 coffee: beverage ).
% 1.62/1.30
% 1.62/1.30 thf(mix_type,type,
% 1.62/1.30 mix: beverage > syrup > beverage ).
% 1.62/1.30
% 1.62/1.30 thf(coffee_mixture_type,type,
% 1.62/1.30 coffee_mixture: syrup > beverage ).
% 1.62/1.30
% 1.62/1.30 thf(hot_type,type,
% 1.62/1.30 hot: beverage > $o ).
% 1.62/1.30
% 1.62/1.30 thf(coffee_mixture_definition,definition,
% 1.62/1.30 ( coffee_mixture
% 1.62/1.30 = ( mix @ coffee ) ) ).
% 1.62/1.30
% 1.62/1.30 thf(coffee_and_syrup_is_hot_coffee,axiom,
% 1.62/1.30 ! [S: syrup] :
% 1.62/1.30 ( ( ( coffee_mixture @ S )
% 1.62/1.30 = coffee )
% 1.62/1.30 & ( hot @ ( coffee_mixture @ S ) ) ) ).
% 1.62/1.30
% 1.62/1.30 thf(there_is_hot_coffee,conjecture,
% 1.62/1.30 ? [SyrupMixer: syrup > beverage] :
% 1.62/1.30 ! [S: syrup] :
% 1.62/1.30 ? [B: beverage] :
% 1.62/1.30 ( ( B
% 1.62/1.30 = ( SyrupMixer @ S ) )
% 1.62/1.30 & ( B = coffee )
% 1.62/1.30 & ( hot @ B ) ) ).
% 1.62/1.30 ------------------------
% 1.62/1.32 % (27435)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27221 for (3000ds/183Mi)
% 1.62/1.32 % (27436)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_27221 for (3000ds/4Mi)
% 1.62/1.32 % (27439)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_27221 for (3000ds/2Mi)
% 1.62/1.32 % (27438)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27221 for (3000ds/2Mi)
% 1.62/1.32 % (27437)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_27221 for (3000ds/27Mi)
% 1.62/1.32 % (27440)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_27221 for (3000ds/275Mi)
% 1.62/1.32 % (27441)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27221 for (3000ds/18Mi)
% 1.62/1.32 % (27439)Instruction limit reached!
% 1.62/1.32 % (27439)------------------------------
% 1.62/1.32 % (27439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (27439)Termination reason: Unknown
% 1.62/1.32 % (27439)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (27439)Memory used [KB]: 895
% 1.62/1.32 % (27439)Time elapsed: 0.003 s
% 1.62/1.32 % (27439)Instructions burned: 2 (million)
% 1.62/1.32 % (27439)------------------------------
% 1.62/1.32 % (27439)------------------------------
% 1.62/1.32 % (27440)Refutation not found, incomplete strategy
% 1.62/1.32 % (27440)------------------------------
% 1.62/1.32 % (27440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (27440)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.32
% 1.62/1.32
% 1.62/1.32 % (27440)Memory used [KB]: 5500
% 1.62/1.32 % (27440)Time elapsed: 0.003 s
% 1.62/1.32 % (27440)Instructions burned: 1 (million)
% 1.62/1.32 % (27440)------------------------------
% 1.62/1.32 % (27440)------------------------------
% 1.62/1.32 % (27438)Instruction limit reached!
% 1.62/1.32 % (27438)------------------------------
% 1.62/1.32 % (27438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (27438)Termination reason: Unknown
% 1.62/1.32 % (27438)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (27438)Memory used [KB]: 5500
% 1.62/1.32 % (27438)Time elapsed: 0.004 s
% 1.62/1.32 % (27438)Instructions burned: 2 (million)
% 1.62/1.32 % (27438)------------------------------
% 1.62/1.32 % (27438)------------------------------
% 1.62/1.32 % (27441)First to succeed.
% 1.62/1.32 % (27435)Also succeeded, but the first one will report.
% 1.62/1.32 % (27441)Refutation found. Thanks to Tanya!
% 1.62/1.32 % SZS status Theorem for DTF2THF_27221
% 1.62/1.32 % SZS output start Proof for DTF2THF_27221
% 1.62/1.32 thf(type_def_5, type, beverage: $tType).
% 1.62/1.32 thf(type_def_6, type, syrup: $tType).
% 1.62/1.32 thf(func_def_0, type, syrup: $tType).
% 1.62/1.32 thf(func_def_1, type, beverage: $tType).
% 1.62/1.32 thf(func_def_2, type, coffee: beverage).
% 1.62/1.32 thf(func_def_3, type, mix: beverage > syrup > beverage).
% 1.62/1.32 thf(func_def_4, type, coffee_mixture: syrup > beverage).
% 1.62/1.32 thf(func_def_5, type, hot: beverage > $o).
% 1.62/1.32 thf(func_def_9, type, sK0: (syrup > beverage) > syrup).
% 1.62/1.32 thf(func_def_11, type, ph2: !>[X0: $tType]:(X0)).
% 1.62/1.32 thf(f32,plain,(
% 1.62/1.32 $false),
% 1.62/1.32 inference(avatar_sat_refutation,[status(thm)],[f27,f29,f31])).
% 1.62/1.32 thf(f31,plain,(
% 1.62/1.32 ~spl1_2),
% 1.62/1.32 inference(avatar_contradiction_clause,[status(thm)],[f30])).
% 1.62/1.32 thf(f30,plain,(
% 1.62/1.32 $false | ~spl1_2),
% 1.62/1.32 inference(equality_resolution,[status(thm)],[f26])).
% 1.62/1.32 thf(f26,plain,(
% 1.62/1.32 ( ! [X0 : syrup > beverage] : ((coffee != (X0 @ (sK0 @ X0)))) ) | ~spl1_2),
% 1.62/1.32 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.62/1.32 thf(f25,definition,(
% 1.62/1.32 spl1_2 <=> ! [X0 : syrup > beverage] : (coffee != (X0 @ (sK0 @ X0)))),
% 1.62/1.32 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.62/1.32 thf(f29,plain,(
% 1.62/1.32 spl1_1),
% 1.62/1.32 inference(avatar_split_clause,[status(thm)],[f28,f21])).
% 1.62/1.32 thf(f21,definition,(
% 1.62/1.32 spl1_1 <=> ((hot @ coffee) = $true)),
% 1.62/1.32 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.62/1.32 thf(f28,plain,(
% 1.62/1.32 ((hot @ coffee) = $true)),
% 1.62/1.32 inference(forward_demodulation,[status(thm)],[f17,f18])).
% 1.62/1.32 thf(f18,plain,(
% 1.62/1.32 ( ! [X0 : syrup] : ((coffee = (mix @ coffee @ X0))) )),
% 1.62/1.32 inference(definition_unfolding,[status(thm)],[f15,f14])).
% 1.62/1.32 thf(f14,plain,(
% 1.62/1.32 (coffee_mixture = (mix @ coffee))),
% 1.62/1.32 inference(cnf_transformation,[status(thm)],[f1])).
% 1.62/1.32 thf(f1,axiom,(
% 1.62/1.32 (coffee_mixture = (mix @ coffee))),
% 1.62/1.32 file('/export/starexec/sandbox2/tmp/tmp.2G1rDoiNrj/DTF2THF_27221.p',coffee_mixture_definition)).
% 1.62/1.32 thf(f15,plain,(
% 1.62/1.32 ( ! [X0 : syrup] : ((coffee = (coffee_mixture @ X0))) )),
% 1.62/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.32 thf(f9,plain,(
% 1.62/1.32 ! [X0 : syrup] : (((hot @ (coffee_mixture @ X0)) = $true) & (coffee = (coffee_mixture @ X0)))),
% 1.62/1.32 inference(fool_elimination,[status(thm)],[f8])).
% 1.62/1.32 thf(f8,plain,(
% 1.62/1.32 ! [X0 : syrup] : ((coffee = (coffee_mixture @ X0)) & (hot @ (coffee_mixture @ X0)))),
% 1.62/1.32 inference(rectify,[status(thm)],[f2])).
% 1.62/1.32 thf(f2,axiom,(
% 1.62/1.32 ! [X0 : syrup] : ((coffee = (coffee_mixture @ X0)) & (hot @ (coffee_mixture @ X0)))),
% 1.62/1.32 file('/export/starexec/sandbox2/tmp/tmp.2G1rDoiNrj/DTF2THF_27221.p',coffee_and_syrup_is_hot_coffee)).
% 1.62/1.32 thf(f17,plain,(
% 1.62/1.32 ( ! [X0 : syrup] : (((hot @ (mix @ coffee @ X0)) = $true)) )),
% 1.62/1.32 inference(definition_unfolding,[status(thm)],[f16,f14])).
% 1.62/1.32 thf(f16,plain,(
% 1.62/1.32 ( ! [X0 : syrup] : (((hot @ (coffee_mixture @ X0)) = $true)) )),
% 1.62/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.32 thf(f27,plain,(
% 1.62/1.32 ~spl1_1 | spl1_2),
% 1.62/1.32 inference(avatar_split_clause,[status(thm)],[f19,f25,f21])).
% 1.62/1.32 thf(f19,plain,(
% 1.62/1.32 ( ! [X0 : syrup > beverage] : ((coffee != (X0 @ (sK0 @ X0))) | ((hot @ coffee) != $true)) )),
% 1.62/1.32 inference(equality_resolution,[status(thm)],[f13])).
% 1.62/1.32 thf(f13,plain,(
% 1.62/1.32 ( ! [X2 : beverage,X0 : syrup > beverage] : ((coffee != X2) | ((hot @ X2) != $true) | ((X0 @ (sK0 @ X0)) != X2)) )),
% 1.62/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.62/1.32 thf(f12,plain,(
% 1.62/1.32 ! [X0 : syrup > beverage] : ! [X2 : beverage] : ((coffee != X2) | ((hot @ X2) != $true) | ((X0 @ (sK0 @ X0)) != X2))),
% 1.62/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f11])).
% 1.62/1.32 thf(f11,plain,(
% 1.62/1.32 ! [X0 : syrup > beverage] : (? [X1 : syrup] : ! [X2 : beverage] : ((coffee != X2) | ((hot @ X2) != $true) | ((X0 @ X1) != X2)) => ! [X2 : beverage] : ((coffee != X2) | ((hot @ X2) != $true) | ((X0 @ (sK0 @ X0)) != X2)))),
% 1.62/1.32 introduced(definition,[],[choice_axiom])).
% 1.62/1.32 thf(f10,plain,(
% 1.62/1.32 ! [X0 : syrup > beverage] : ? [X1 : syrup] : ! [X2 : beverage] : ((coffee != X2) | ((hot @ X2) != $true) | ((X0 @ X1) != X2))),
% 1.62/1.32 inference(ennf_transformation,[status(thm)],[f7])).
% 1.62/1.32 thf(f7,plain,(
% 1.62/1.32 ~? [X0 : syrup > beverage] : ! [X1 : syrup] : ? [X2 : beverage] : ((coffee = X2) & ((hot @ X2) = $true) & ((X0 @ X1) = X2))),
% 1.62/1.32 inference(fool_elimination,[status(thm)],[f6])).
% 1.62/1.32 thf(f6,plain,(
% 1.62/1.32 ~? [X0 : syrup > beverage] : ! [X1 : syrup] : ? [X2 : beverage] : (((X0 @ X1) = X2) & (hot @ X2) & (coffee = X2))),
% 1.62/1.32 inference(rectify,[status(thm)],[f4])).
% 1.62/1.32 thf(f4,negated_conjecture,(
% 1.62/1.32 ~? [X1 : syrup > beverage] : ! [X0 : syrup] : ? [X2 : beverage] : (((X1 @ X0) = X2) & (hot @ X2) & (coffee = X2))),
% 1.62/1.32 inference(negated_conjecture,[status(cth)],[f3])).
% 1.62/1.32 thf(f3,conjecture,(
% 1.62/1.32 ? [X1 : syrup > beverage] : ! [X0 : syrup] : ? [X2 : beverage] : (((X1 @ X0) = X2) & (hot @ X2) & (coffee = X2))),
% 1.62/1.32 file('/export/starexec/sandbox2/tmp/tmp.2G1rDoiNrj/DTF2THF_27221.p',there_is_hot_coffee)).
% 1.62/1.32 % SZS output end Proof for DTF2THF_27221
% 1.62/1.32 % (27441)------------------------------
% 1.62/1.32 % (27441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (27441)Termination reason: Refutation
% 1.62/1.32
% 1.62/1.32 % (27441)Memory used [KB]: 5500
% 1.62/1.32 % (27441)Time elapsed: 0.004 s
% 1.62/1.32 % (27441)Instructions burned: 2 (million)
% 1.62/1.32 % (27441)------------------------------
% 1.62/1.32 % (27441)------------------------------
% 1.62/1.32 % (27434)Success in time 0.019 s
%------------------------------------------------------------------------------