%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO008^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 11:07:21 AM UTC 2026
% Result : Theorem 0.12s 0.22s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 27 unt; 0 typ; 2 def)
% Number of atoms : 86 ( 41 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 131 ( 11 ~; 9 |; 0 &; 93 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 4 ^; 43 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_leibeq1,type,
leibeq1: $i > $i > $o ).
thf(tp_leibeq2,type,
leibeq2: ( $i > $i ) > ( $i > $i ) > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i > $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: ( $i > $i ) > $o ).
thf(tp_sK4_E,type,
sK4_E: $i ).
thf(leibeq1,definition,
( leibeq1
= ( ^ [U: $i,V: $i] :
! [Q: $i > $o] :
( ( Q @ U )
=> ( Q @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leibeq1) ).
thf(leibeq2,definition,
( leibeq2
= ( ^ [X: $i > $i,Y: $i > $i] :
! [P: ( $i > $i ) > $o] :
( ( P @ X )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leibeq2) ).
thf(1,conjecture,
! [F: $i > $i,G: $i > $i] :
( ! [X: $i] : ( leibeq1 @ ( F @ X ) @ ( G @ X ) )
=> ( leibeq2 @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ! [F: $i > $i,G: $i > $i] :
( ! [X: $i] : ( leibeq1 @ ( F @ X ) @ ( G @ X ) )
=> ( leibeq2 @ F @ G ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i,SY1: $i > $i] :
( ! [SY2: $i,SY5: $i > $o] :
( ( SY5 @ ( SY0 @ SY2 ) )
=> ( SY5 @ ( SY1 @ SY2 ) ) )
=> ! [SY8: ( $i > $i ) > $o] :
( ( SY8 @ SY0 )
=> ( SY8 @ SY1 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,leibeq1,leibeq2]) ).
thf(4,plain,
( ( ! [SY14: $i > $i] :
( ! [SY15: $i,SY16: $i > $o] :
( ( SY16 @ ( sK1_SY0 @ SY15 ) )
=> ( SY16 @ ( SY14 @ SY15 ) ) )
=> ! [SY17: ( $i > $i ) > $o] :
( ( SY17 @ sK1_SY0 )
=> ( SY17 @ SY14 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY18: $i,SY19: $i > $o] :
( ( SY19 @ ( sK1_SY0 @ SY18 ) )
=> ( SY19 @ ( sK2_SY14 @ SY18 ) ) )
=> ! [SY20: ( $i > $i ) > $o] :
( ( SY20 @ sK1_SY0 )
=> ( SY20 @ sK2_SY14 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY18: $i,SY19: $i > $o] :
( ( SY19 @ ( sK1_SY0 @ SY18 ) )
=> ( SY19 @ ( sK2_SY14 @ SY18 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY20: ( $i > $i ) > $o] :
( ( SY20 @ sK1_SY0 )
=> ( SY20 @ sK2_SY14 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [SY20: ( $i > $i ) > $o] :
( ( SY20 @ sK1_SY0 )
=> ( SY20 @ sK2_SY14 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY18: $i,SY19: $i > $o] :
( ( SY19 @ ( sK1_SY0 @ SY18 ) )
=> ( SY19 @ ( sK2_SY14 @ SY18 ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ! [SY20: ( $i > $i ) > $o] :
( ( SY20 @ sK1_SY0 )
=> ( SY20 @ sK2_SY14 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( sK1_SY0 @ SX0 ) )
| ( SX1 @ ( sK2_SY14 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,leibeq1,leibeq2]) ).
thf(12,plain,
( ( ~ ! [SX0: ( $i > $i ) > $o] :
( ~ ( SX0 @ sK1_SY0 )
| ( SX0 @ sK2_SY14 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,leibeq1,leibeq2]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY21: $i > $o] :
( ~ ( SY21 @ ( sK1_SY0 @ SV1 ) )
| ( SY21 @ ( sK2_SY14 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SX0: ( $i > $i ) > $o] :
( ~ ( SX0 @ sK1_SY0 )
| ( SX0 @ sK2_SY14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ~ ( SV2 @ ( sK1_SY0 @ SV1 ) )
| ( SV2 @ ( sK2_SY14 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( sK3_SX0 @ sK1_SY0 )
| ( sK3_SX0 @ sK2_SY14 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(17,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ( ~ ( SV2 @ ( sK1_SY0 @ SV1 ) ) )
= $true )
| ( ( SV2 @ ( sK2_SY14 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( sK3_SX0 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( sK3_SX0 @ sK2_SY14 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK1_SY0 @ SV1 ) )
= $false )
| ( ( SV2 @ ( sK2_SY14 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( sK3_SX0 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: $i] :
( ( ( ( sK1_SY0 @ SV1 )
= ( sK1_SY0 @ SV1 ) )
= $false )
| ( ( ( sK2_SY14 @ SV1 )
= ( sK1_SY0 @ SV1 ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[20:[bind(SV2,$thf( ^ [SV3: $i] : ( SV3 = ( sK1_SY0 @ SV1 ) ) ))]]) ).
thf(23,plain,
! [SV1: $i] :
( ( ( sK2_SY14 @ SV1 )
= ( sK1_SY0 @ SV1 ) )
= $true ),
inference(sim,[status(thm)],[22]) ).
thf(24,plain,
( ( ( sK3_SX0 @ sK1_SY0 )
= ( sK3_SX0 @ sK2_SY14 ) )
= $false ),
inference(res,[status(thm)],[21,19]) ).
thf(25,plain,
( ( ( sK1_SY0 @ sK4_E )
= ( sK2_SY14 @ sK4_E ) )
= $false ),
inference(extuni,[status(esa)],[24]) ).
thf(26,plain,
! [SV4: $i] :
( ( ( sK2_SY14 @ SV4 )
= ( sK1_SY0 @ SV4 ) )
= $true ),
inference(rename,[status(thm)],[23]) ).
thf(28,plain,
! [SV4: $i] :
( ( ( ( sK1_SY0 @ sK4_E )
= ( sK2_SY14 @ sK4_E ) )
= ( ( sK2_SY14 @ SV4 )
= ( sK1_SY0 @ SV4 ) ) )
= $false ),
inference(res,[status(thm)],[25,26]) ).
thf(30,plain,
$false = $true,
inference(extuni,[status(esa)],[28:[bind(SV4,$thf( sK4_E ))]]) ).
thf(31,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO008^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.18 % Computer : n014.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Oct 6 17:30:26 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.22
% 0.12/0.22 No.of.Axioms: 0
% 0.12/0.22
% 0.12/0.22 Length.of.Defs: 323
% 0.12/0.22
% 0.12/0.22 Contains.Choice.Funs: false
% 0.12/0.22
% 0.12/0.22 ********************************
% 0.12/0.22 * All subproblems solved! *
% 0.12/0.22 ********************************
% 0.12/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:30,loop_count:4,foatp_calls:2,translation:fof_full)
% 0.12/0.22
% 0.12/0.22 %**** Beginning of derivation protocol ****
% 0.12/0.22 % SZS output start CNFRefutation
% See solution above
% 0.12/0.22
% 0.12/0.22 %**** End of derivation protocol ****
% 0.12/0.22 %**** no. of clauses in derivation: 29 ****
% 0.12/0.22 %**** clause counter: 30 ****
% 0.12/0.22
% 0.12/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:30,loop_count:4,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------