%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PUZ140^1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:37:01 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 19 unt; 0 typ; 2 def)
% Number of atoms : 136 ( 68 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 172 ( 24 ~; 22 |; 4 &; 122 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 4 ^; 41 !; 8 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_beverage,type,
beverage: $tType ).
thf(tp_syrup,type,
syrup: $tType ).
thf(tp_coffee,type,
coffee: beverage ).
thf(tp_cold_mixture,type,
cold_mixture: beverage > syrup > beverage ).
thf(tp_heat,type,
heat: beverage > beverage ).
thf(tp_hot,type,
hot: beverage > $o ).
thf(tp_hot_mixture,type,
hot_mixture: beverage > syrup > beverage ).
thf(tp_mix,type,
mix: beverage > syrup > beverage ).
thf(tp_sK1_S,type,
sK1_S: ( beverage > syrup > beverage ) > syrup ).
thf(cold_mixture,definition,
( cold_mixture
= ( ^ [B: beverage,S: syrup] : ( mix @ B @ S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cold_mixture_definition) ).
thf(hot_mixture,definition,
( hot_mixture
= ( ^ [B: beverage,S: syrup] : ( heat @ ( mix @ B @ S ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hot_mixture_definition) ).
thf(1,axiom,
! [B: beverage] : ( hot @ ( heat @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',its_hot) ).
thf(2,conjecture,
? [Mixture: beverage > syrup > beverage] :
! [S: syrup] :
? [B: beverage] :
( ( ( Mixture @ coffee @ S )
= B )
& ( hot @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hot_coffee) ).
thf(3,negated_conjecture,
( ( ? [Mixture: beverage > syrup > beverage] :
! [S: syrup] :
? [B: beverage] :
( ( ( Mixture @ coffee @ S )
= B )
& ( hot @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ? [Mixture: beverage > syrup > beverage] :
! [S: syrup] :
? [B: beverage] :
( ( ( Mixture @ coffee @ S )
= B )
& ( hot @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3,cold_mixture,hot_mixture]) ).
thf(5,plain,
( ( ! [B: beverage] : ( hot @ ( heat @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,cold_mixture,hot_mixture]) ).
thf(6,plain,
( ( ~ ? [Mixture: beverage > syrup > beverage] :
! [S: syrup] :
? [B: beverage] :
( ( ( Mixture @ coffee @ S )
= B )
& ( hot @ B ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [Mixture: beverage > syrup > beverage,SY4: beverage] :
( ( ( Mixture @ coffee @ ( sK1_S @ Mixture ) )
!= SY4 )
| ~ ( hot @ SY4 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [B: beverage] : ( hot @ ( heat @ B ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [Mixture: beverage > syrup > beverage,SY4: beverage] :
( ( ( Mixture @ coffee @ ( sK1_S @ Mixture ) )
!= SY4 )
| ~ ( hot @ SY4 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
! [SV1: beverage] :
( ( hot @ ( heat @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(11,plain,
! [SV2: beverage > syrup > beverage] :
( ( ! [SY5: beverage] :
( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
!= SY5 )
| ~ ( hot @ SY5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV3: beverage,SV2: beverage > syrup > beverage] :
( ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
!= SV3 )
| ~ ( hot @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(13,plain,
! [SV3: beverage,SV2: beverage > syrup > beverage] :
( ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
!= SV3 )
= $true )
| ( ( ~ ( hot @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(14,plain,
! [SV3: beverage,SV2: beverage > syrup > beverage] :
( ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 )
= $false )
| ( ( ~ ( hot @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(15,plain,
! [SV2: beverage > syrup > beverage,SV3: beverage] :
( ( ( hot @ SV3 )
= $false )
| ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(16,plain,
! [SV2: beverage > syrup > beverage,SV3: beverage] :
( ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 )
= $false )
| ( ( ( hot @ SV3 )
= ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[15]) ).
thf(17,plain,
! [SV2: beverage > syrup > beverage,SV3: beverage] :
( ( ( ~ ( ( hot @ SV3 )
| ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 ) )
| ~ ( ~ ( hot @ SV3 )
| ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
!= SV3 ) ) )
= $false )
| ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: beverage > syrup > beverage,SV3: beverage] :
( ( ( ~ ( ~ ( hot @ SV3 )
| ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
!= SV3 ) ) )
= $false )
| ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV2: beverage > syrup > beverage,SV3: beverage] :
( ( ( ~ ( hot @ SV3 )
| ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
!= SV3 ) )
= $true )
| ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: beverage > syrup > beverage,SV3: beverage] :
( ( ( ~ ( hot @ SV3 ) )
= $true )
| ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
!= SV3 )
= $true )
| ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV2: beverage > syrup > beverage,SV3: beverage] :
( ( ( hot @ SV3 )
= $false )
| ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
!= SV3 )
= $true )
| ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(26,plain,
! [SV3: beverage,SV2: beverage > syrup > beverage] :
( ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 )
= $false )
| ( ( hot @ SV3 )
= $false )
| ( ( ( SV2 @ coffee @ ( sK1_S @ SV2 ) )
= SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV2: beverage > syrup > beverage] :
( ( hot @ ( SV2 @ coffee @ ( sK1_S @ SV2 ) ) )
= $false ),
inference(extuni,[status(esa)],[26:[bind(SV3,$thf( SV2 @ coffee @ ( sK1_S @ SV2 ) ))]]) ).
thf(30,plain,
! [SV4: beverage] :
( ( hot @ ( heat @ SV4 ) )
= $true ),
inference(rename,[status(thm)],[10]) ).
thf(31,plain,
! [SV5: beverage > syrup > beverage] :
( ( hot @ ( SV5 @ coffee @ ( sK1_S @ SV5 ) ) )
= $false ),
inference(rename,[status(thm)],[28]) ).
thf(32,plain,
! [SV5: beverage > syrup > beverage,SV4: beverage] :
( ( ( hot @ ( SV5 @ coffee @ ( sK1_S @ SV5 ) ) )
= ( hot @ ( heat @ SV4 ) ) )
= $false ),
inference(res,[status(thm)],[31,30]) ).
thf(33,plain,
$false = $true,
inference(extuni,[status(esa)],[32:[bind(SV4,$thf( SV10 @ coffee @ ( sK1_S @ ^ [SX0: beverage] : ^ [SX1: syrup] : ( heat @ ( SV10 @ SX0 @ SX1 ) ) ) )),bind(SV5,$thf( ^ [SX0: beverage] : ^ [SX1: syrup] : ( heat @ ( SV10 @ SX0 @ SX1 ) ) ))]]) ).
thf(34,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ140^1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n010.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 14:00:55 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.26
% 0.09/0.26 No.of.Axioms: 1
% 0.09/0.26
% 0.09/0.26 Length.of.Defs: 338
% 0.09/0.26
% 0.09/0.26 Contains.Choice.Funs: false
% 0.09/0.26
% 0.09/0.26 ********************************
% 0.09/0.26 * All subproblems solved! *
% 0.09/0.26 ********************************
% 0.09/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:2,foatp_calls:2,translation:fof_full)
% 0.09/0.26
% 0.09/0.26 %**** Beginning of derivation protocol ****
% 0.09/0.26 % SZS output start CNFRefutation
% See solution above
% 0.09/0.26
% 0.09/0.26 %**** End of derivation protocol ****
% 0.09/0.26 %**** no. of clauses in derivation: 28 ****
% 0.09/0.26 %**** clause counter: 33 ****
% 0.09/0.26
% 0.09/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:2,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------