%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO002^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.21s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 24 unt; 0 typ; 1 def)
% Number of atoms : 80 ( 32 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 130 ( 18 ~; 8 |; 2 &; 84 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 2 ^; 29 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_leibeq,type,
leibeq: $i > $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_SY18,type,
sK3_SY18: $i > $i ).
thf(tp_sK4_SY22,type,
sK4_SY22: $i > $o ).
thf(leibeq,definition,
( leibeq
= ( ^ [X: $i,Y: $i] :
! [P: $i > $o] :
( ( P @ X )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq) ).
thf(1,conjecture,
! [X: $i,Y: $i,F: $i > $i] :
( ( leibeq @ X @ Y )
=> ( leibeq @ ( F @ X ) @ ( F @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ! [X: $i,Y: $i,F: $i > $i] :
( ( leibeq @ X @ Y )
=> ( leibeq @ ( F @ X ) @ ( F @ Y ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i > $i] :
( ! [SY5: $i > $o] :
( ( SY5 @ SY0 )
=> ( SY5 @ SY1 ) )
=> ! [SY8: $i > $o] :
( ( SY8 @ ( SY2 @ SY0 ) )
=> ( SY8 @ ( SY2 @ SY1 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,leibeq]) ).
thf(4,plain,
( ( ! [SY14: $i,SY15: $i > $i] :
( ! [SY16: $i > $o] :
( ( SY16 @ sK1_SY0 )
=> ( SY16 @ SY14 ) )
=> ! [SY17: $i > $o] :
( ( SY17 @ ( SY15 @ sK1_SY0 ) )
=> ( SY17 @ ( SY15 @ SY14 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY18: $i > $i] :
( ! [SY19: $i > $o] :
( ( SY19 @ sK1_SY0 )
=> ( SY19 @ sK2_SY14 ) )
=> ! [SY20: $i > $o] :
( ( SY20 @ ( SY18 @ sK1_SY0 ) )
=> ( SY20 @ ( SY18 @ sK2_SY14 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY19: $i > $o] :
( ( SY19 @ sK1_SY0 )
=> ( SY19 @ sK2_SY14 ) )
=> ! [SY22: $i > $o] :
( ( SY22 @ ( sK3_SY18 @ sK1_SY0 ) )
=> ( SY22 @ ( sK3_SY18 @ sK2_SY14 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY19: $i > $o] :
( ( SY19 @ sK1_SY0 )
=> ( SY19 @ sK2_SY14 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY22: $i > $o] :
( ( SY22 @ ( sK3_SY18 @ sK1_SY0 ) )
=> ( SY22 @ ( sK3_SY18 @ sK2_SY14 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SY22: $i > $o] :
( ( SY22 @ ( sK3_SY18 @ sK1_SY0 ) )
=> ( SY22 @ ( sK3_SY18 @ sK2_SY14 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ( sK4_SY22 @ ( sK3_SY18 @ sK1_SY0 ) )
& ~ ( sK4_SY22 @ ( sK3_SY18 @ sK2_SY14 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ! [SY19: $i > $o] :
( ~ ( SY19 @ sK1_SY0 )
| ( SY19 @ sK2_SY14 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(12,plain,
( ( ! [SY19: $i > $o] :
( ~ ( SY19 @ sK1_SY0 )
| ( SY19 @ sK2_SY14 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(13,plain,
( ( ( sK4_SY22 @ ( sK3_SY18 @ sK1_SY0 ) )
& ~ ( sK4_SY22 @ ( sK3_SY18 @ sK2_SY14 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ( ~ ( sK4_SY22 @ ( sK3_SY18 @ sK1_SY0 ) )
| ~ ~ ( sK4_SY22 @ ( sK3_SY18 @ sK2_SY14 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,leibeq]) ).
thf(15,plain,
! [SV1: $i > $o] :
( ( ~ ( SV1 @ sK1_SY0 )
| ( SV1 @ sK2_SY14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ~ ( sK4_SY22 @ ( sK3_SY18 @ sK1_SY0 ) )
| ~ ~ ( sK4_SY22 @ ( sK3_SY18 @ sK2_SY14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ sK1_SY0 ) )
= $true )
| ( ( SV1 @ sK2_SY14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( sK4_SY22 @ ( sK3_SY18 @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ~ ( sK4_SY22 @ ( sK3_SY18 @ sK2_SY14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ sK1_SY0 )
= $false )
| ( ( SV1 @ sK2_SY14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( sK4_SY22 @ ( sK3_SY18 @ sK1_SY0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( sK4_SY22 @ ( sK3_SY18 @ sK2_SY14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( sK4_SY22 @ ( sK3_SY18 @ sK2_SY14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(24,plain,
( ( ( sK1_SY0 = sK1_SY0 )
= $false )
| ( ( sK2_SY14 = sK1_SY0 )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[20:[bind(SV1,$thf( ^ [SV2: $i] : ( SV2 = sK1_SY0 ) ))]]) ).
thf(25,plain,
( ( sK2_SY14 = sK1_SY0 )
= $true ),
inference(sim,[status(thm)],[24]) ).
thf(26,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,25,23]) ).
thf(27,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO002^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.17 % Computer : n026.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Oct 6 17:33:32 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.21
% 0.12/0.21 No.of.Axioms: 0
% 0.12/0.21
% 0.12/0.21 Length.of.Defs: 150
% 0.12/0.21
% 0.12/0.21 Contains.Choice.Funs: false
% 0.12/0.21
% 0.12/0.21 ********************************
% 0.12/0.21 * All subproblems solved! *
% 0.12/0.21 ********************************
% 0.12/0.21 % 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:26,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.12/0.21
% 0.12/0.21 %**** Beginning of derivation protocol ****
% 0.12/0.21 % SZS output start CNFRefutation
% See solution above
% 0.12/0.21
% 0.12/0.21 %**** End of derivation protocol ****
% 0.12/0.21 %**** no. of clauses in derivation: 27 ****
% 0.12/0.21 %**** clause counter: 26 ****
% 0.12/0.21
% 0.12/0.21 % 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:26,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------