%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO209^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 11:07:50 AM UTC 2026
% Result : Theorem 1.60s 0.52s
% Output : CNFRefutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 1
% Syntax : Number of formulae : 32 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 128 ( 46 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 215 ( 46 ~; 18 |; 0 &; 146 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 2 con; 0-4 aty)
% Number of variables : 80 ( 14 ^; 56 !; 10 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK10_E,type,
sK10_E: ( a > a > $o ) > a > ( a > a > $o ) > a ).
thf(tp_sK11_E,type,
sK11_E: ( a > a > a ) > ( a > a > $o ) > a > ( a > a > a > $o ) > a ).
thf(tp_sK12_E,type,
sK12_E: ( a > a > $o ) > a > ( a > a > $o ) > a ).
thf(tp_sK13_E,type,
sK13_E: ( a > a > a ) > ( a > a > $o ) > a > ( a > a > a > $o ) > a ).
thf(tp_sK14_E,type,
sK14_E: ( a > a > $o ) > a ).
thf(tp_sK15_E,type,
sK15_E: ( a > a > a ) > ( a > a > a > a > $o ) > a ).
thf(tp_sK16_E,type,
sK16_E: ( a > a > a ) > ( a > a > a > a > $o ) > a ).
thf(tp_sK17_E,type,
sK17_E: ( a > a ) > a > ( a > a > $o ) > a ).
thf(tp_sK18_E,type,
sK18_E: ( a > a > a ) > ( a > a ) > a > ( a > a > a > $o ) > a ).
thf(tp_sK19_E,type,
sK19_E: ( a > a > $o ) > a ).
thf(tp_sK1_SX0,type,
sK1_SX0: a > a > $o ).
thf(tp_sK20_E,type,
sK20_E: ( a > a ) > a > ( a > a > $o ) > a ).
thf(tp_sK21_SV327,type,
sK21_SV327: ( a > $o ) > ( a > a > $o ) > a > ( a > a > $o ) > a ).
thf(tp_sK22_SV329,type,
sK22_SV329: a > ( a > a > $o ) > ( a > a > $o ) > ( a > $o ) > a ).
thf(tp_sK23_SV333,type,
sK23_SV333: a > ( a > a > $o ) > ( a > a > $o ) > ( a > $o ) > a ).
thf(tp_sK24_SV336,type,
sK24_SV336: a > ( a > a > $o ) > ( a > a > $o ) > ( a > $o ) > a ).
thf(tp_sK25_SV337,type,
sK25_SV337: a > ( a > a > $o ) > ( a > a > $o ) > ( a > $o ) > a ).
thf(tp_sK2_SY7,type,
sK2_SY7: ( a > $o ) > a ).
thf(tp_sK3_E,type,
sK3_E: ( a > a > $o ) > a ).
thf(tp_sK4_E,type,
sK4_E: ( a > a > a ) > ( a > a > a > a > $o ) > a ).
thf(tp_sK5_E,type,
sK5_E: ( a > a > a ) > ( a > a > a > a > $o ) > a ).
thf(tp_sK6_E,type,
sK6_E: ( a > a ) > a > ( a > a > $o ) > a ).
thf(tp_sK7_E,type,
sK7_E: ( a > a > a ) > ( a > a ) > a > ( a > a > a > $o ) > a ).
thf(tp_sK8_E,type,
sK8_E: ( a > a > $o ) > a ).
thf(tp_sK9_E,type,
sK9_E: ( a > a ) > a > ( a > a > $o ) > a ).
thf(1,conjecture,
~ ? [Xg: a > a > $o] :
! [Xf: a > $o] :
? [Xj: a] :
! [Xp: ( a > $o ) > $o] :
( ( Xp @ ( Xg @ Xj ) )
=> ( Xp @ Xf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCT29) ).
thf(2,negated_conjecture,
( ( ~ ? [Xg: a > a > $o] :
! [Xf: a > $o] :
? [Xj: a] :
! [Xp: ( a > $o ) > $o] :
( ( Xp @ ( Xg @ Xj ) )
=> ( Xp @ Xf ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ? [Xg: a > a > $o] :
! [Xf: a > $o] :
? [Xj: a] :
! [Xp: ( a > $o ) > $o] :
( ( Xp @ ( Xg @ Xj ) )
=> ( Xp @ Xf ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [Xg: a > a > $o] :
! [Xf: a > $o] :
? [Xj: a] :
! [Xp: ( a > $o ) > $o] :
( ( Xp @ ( Xg @ Xj ) )
=> ( Xp @ Xf ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [Xg: a > a > $o] :
! [Xf: a > $o] :
? [Xj: a] :
! [Xp: ( a > $o ) > $o] :
( ( Xp @ ( Xg @ Xj ) )
=> ( Xp @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ! [SX0: a > a > $o] :
~ ! [SX1: a > $o] :
~ ! [SX2: a] :
~ ! [SX3: ( a > $o ) > $o] :
( ~ ( SX3 @ ( SX0 @ SX2 ) )
| ( SX3 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: a > a > $o] :
~ ! [SX1: a > $o] :
~ ! [SX2: a] :
~ ! [SX3: ( a > $o ) > $o] :
( ~ ( SX3 @ ( SX0 @ SX2 ) )
| ( SX3 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ! [SY4: a > $o] :
~ ! [SY5: a] :
~ ! [SY6: ( a > $o ) > $o] :
( ~ ( SY6 @ ( sK1_SX0 @ SY5 ) )
| ( SY6 @ SY4 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY4: a > $o] :
~ ! [SY5: a] :
~ ! [SY6: ( a > $o ) > $o] :
( ~ ( SY6 @ ( sK1_SX0 @ SY5 ) )
| ( SY6 @ SY4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: a > $o] :
( ( ~ ! [SY7: a] :
~ ! [SY8: ( a > $o ) > $o] :
( ~ ( SY8 @ ( sK1_SX0 @ SY7 ) )
| ( SY8 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: a > $o] :
( ( ! [SY7: a] :
~ ! [SY8: ( a > $o ) > $o] :
( ~ ( SY8 @ ( sK1_SX0 @ SY7 ) )
| ( SY8 @ SV1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(12,plain,
! [SV1: a > $o] :
( ( ~ ! [SY9: ( a > $o ) > $o] :
( ~ ( SY9 @ ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) ) )
| ( SY9 @ SV1 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(13,plain,
! [SV1: a > $o] :
( ( ! [SY9: ( a > $o ) > $o] :
( ~ ( SY9 @ ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) ) )
| ( SY9 @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(14,plain,
! [SV1: a > $o,SV2: ( a > $o ) > $o] :
( ( ~ ( SV2 @ ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) ) )
| ( SV2 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(15,plain,
! [SV1: a > $o,SV2: ( a > $o ) > $o] :
( ( ( ~ ( SV2 @ ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) ) ) )
= $true )
| ( ( SV2 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(16,plain,
! [SV1: a > $o,SV2: ( a > $o ) > $o] :
( ( ( SV2 @ ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) ) )
= $false )
| ( ( SV2 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV1: a > $o] :
( ( ( ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) )
= ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) ) )
= $false )
| ( ( SV1
= ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[16:[bind(SV2,$thf( ^ [SV3: a > $o] : ( SV3 = ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) ) ) ))]]) ).
thf(18,plain,
! [SV1: a > $o] :
( ( SV1
= ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) ) )
= $true ),
inference(sim,[status(thm)],[17]) ).
thf(19,plain,
! [SV1: a > $o,SV4: a] :
( ( ( SV1 @ SV4 )
= ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) @ SV4 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV1: a > $o,SV4: a] :
( ( ( SV1 @ SV4 )
= $true )
| ( ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) @ SV4 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV1: a > $o,SV4: a] :
( ( ( SV1 @ SV4 )
= $false )
| ( ( sK1_SX0 @ ( sK2_SY7 @ SV1 ) @ SV4 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[19]) ).
thf(63,plain,
! [SV13: a > $o,SV14: a] :
( ( ( SV13 @ SV14 )
= $true )
| ( ( sK1_SX0 @ ( sK2_SY7 @ SV13 ) @ SV14 )
= $false ) ),
inference(rename,[status(thm)],[20]) ).
thf(68,plain,
! [SV13: a > $o,SV14: a] :
( ( ( SV13 @ SV14 )
= $true )
| ( ( ( SV13 @ SV14 )
= ( ~ ( sK1_SX0 @ ( sK2_SY7 @ SV13 ) @ SV14 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[63]) ).
thf(78,plain,
( ( ~ ( sK1_SX0
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) )
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) ) ) )
= $true ),
inference(extuni,[status(esa)],[68:[bind(SV14,$thf( sK2_SY7 @ ^ [SX0: a] : ~ ( sK1_SX0 @ SX0 @ SX0 ) )),bind(SV13,$thf( ^ [SX0: a] : ~ ( sK1_SX0 @ SX0 @ SX0 ) ))]]) ).
thf(87,plain,
( ( sK1_SX0
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) )
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(104,plain,
! [SV127: a > $o,SV128: a] :
( ( ( SV127 @ SV128 )
= $false )
| ( ( sK1_SX0 @ ( sK2_SY7 @ SV127 ) @ SV128 )
= $true ) ),
inference(rename,[status(thm)],[21]) ).
thf(107,plain,
! [SV127: a > $o,SV128: a] :
( ( ( ( sK1_SX0 @ ( sK2_SY7 @ SV127 ) @ SV128 )
= ( sK1_SX0
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) )
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) ) ) )
= $false )
| ( ( SV127 @ SV128 )
= $false ) ),
inference(res,[status(thm)],[104,87]) ).
thf(145,plain,
( ( ~ ( sK1_SX0
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) )
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) ) ) )
= $false ),
inference(extuni,[status(esa)],[107:[bind(SV128,$thf( sK2_SY7 @ ^ [SX0: a] : ~ ( sK1_SX0 @ SX0 @ SX0 ) )),bind(SV127,$thf( ^ [SX0: a] : ~ ( sK1_SX0 @ SX0 @ SX0 ) ))]]) ).
thf(197,plain,
( ( sK1_SX0
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) )
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(655,plain,
( ( ( sK1_SX0
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) )
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) ) )
= ( sK1_SX0
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) )
@ ( sK2_SY7
@ ^ [SX0: a] :
~ ( sK1_SX0 @ SX0 @ SX0 ) ) ) )
= $false ),
inference(res,[status(thm)],[197,87]) ).
thf(659,plain,
$false = $true,
inference(extuni,[status(esa)],[655]) ).
thf(660,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO209^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 17:33:55 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.60/0.52
% 1.60/0.52 No.of.Axioms: 0
% 1.60/0.52
% 1.60/0.52 Length.of.Defs: 0
% 1.60/0.52
% 1.60/0.52 Contains.Choice.Funs: false
% 1.60/0.52 ..........
% 1.60/0.52
% 1.60/0.52 ********************************
% 1.60/0.52 * All subproblems solved! *
% 1.60/0.52 ********************************
% 1.60/0.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,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:659,loop_count:8,foatp_calls:3,translation:fof_full)
% 1.60/0.52
% 1.60/0.52 %**** Beginning of derivation protocol ****
% 1.60/0.52 % SZS output start CNFRefutation
% See solution above
% 1.60/0.52
% 1.60/0.52 %**** End of derivation protocol ****
% 1.60/0.52 %**** no. of clauses in derivation: 32 ****
% 1.60/0.52 %**** clause counter: 659 ****
% 1.60/0.52
% 1.60/0.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,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:659,loop_count:8,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------