%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO552^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n017.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 11:08:43 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 38 ( 9 ~; 0 |; 0 &; 29 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 10 con; 0-2 aty)
% Number of variables : 33 ( 0 ^; 28 !; 5 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK10_E,type,
sK10_E: $i ).
thf(tp_sK11_E,type,
sK11_E: ( $i > $i > $i > $i > $i > $i > $i > $i > $i ) > $i ).
thf(tp_sK12_E,type,
sK12_E: ( $i > $i > $i > $i > $i > $i > $i > $i > $i ) > $i ).
thf(tp_sK13_E,type,
sK13_E: $i ).
thf(tp_sK14_E,type,
sK14_E: $i ).
thf(tp_sK15_E,type,
sK15_E: ( $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ) > $i ).
thf(tp_sK16_E,type,
sK16_E: ( $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ) > $i ).
thf(tp_sK17_E,type,
sK17_E: $i ).
thf(tp_sK18_E,type,
sK18_E: $i ).
thf(tp_sK19_E,type,
sK19_E: ( $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ) > $i ).
thf(tp_sK1_SY3,type,
sK1_SY3: ( $i > $i > $i ) > $i ).
thf(tp_sK20_E,type,
sK20_E: ( $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ) > $i ).
thf(tp_sK2_SY5,type,
sK2_SY5: ( $i > $i > $i ) > $i ).
thf(tp_sK3_E,type,
sK3_E: ( $i > $i > $i > $i > $i ) > $i ).
thf(tp_sK4_E,type,
sK4_E: ( $i > $i > $i > $i > $i ) > $i ).
thf(tp_sK5_E,type,
sK5_E: $i ).
thf(tp_sK6_E,type,
sK6_E: $i ).
thf(tp_sK7_E,type,
sK7_E: ( $i > $i > $i > $i > $i > $i > $i ) > $i ).
thf(tp_sK8_E,type,
sK8_E: ( $i > $i > $i > $i > $i > $i > $i ) > $i ).
thf(tp_sK9_E,type,
sK9_E: $i ).
thf(1,conjecture,
? [F: $i > $i > $i] :
! [X: $i,Y: $i] :
( ( F @ X @ Y )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',claim) ).
thf(2,negated_conjecture,
( ( ? [F: $i > $i > $i] :
! [X: $i,Y: $i] :
( ( F @ X @ Y )
= X ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [F: $i > $i > $i] :
! [X: $i,Y: $i] :
( ( F @ X @ Y )
= X ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [F: $i > $i > $i] :
! [X: $i,Y: $i] :
( ( F @ X @ Y )
= X ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ ? [F: $i > $i > $i] :
! [X: $i,Y: $i] :
( ( F @ X @ Y )
= X ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ~ ! [SX0: $i > $i > $i] :
~ ! [SX1: $i,SX2: $i] :
( ( SX0 @ SX1 @ SX2 )
= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ! [SX0: $i > $i > $i] :
~ ! [SX1: $i,SX2: $i] :
( ( SX0 @ SX1 @ SX2 )
= SX1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SX0: $i > $i > $i] :
~ ! [SX1: $i,SX2: $i] :
( ( SX0 @ SX1 @ SX2 )
= SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i > $i > $i] :
( ( ~ ! [SY3: $i,SY4: $i] :
( ( SV1 @ SY3 @ SY4 )
= SY3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i > $i > $i] :
( ( ! [SY3: $i,SY4: $i] :
( ( SV1 @ SY3 @ SY4 )
= SY3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i > $i > $i] :
( ( ! [SY5: $i] :
( ( SV1 @ ( sK1_SY3 @ SV1 ) @ SY5 )
= ( sK1_SY3 @ SV1 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
! [SV1: $i > $i > $i] :
( ( ( SV1 @ ( sK1_SY3 @ SV1 ) @ ( sK2_SY5 @ SV1 ) )
= ( sK1_SY3 @ SV1 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(51,plain,
$false = $true,
inference(extuni,[status(esa)],[12:[bind(SV1,$thf( ^ [SX0: $i] : ^ [SX1: $i] : SX0 ))]]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO552^1 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 17:37:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.27
% 0.08/0.27 No.of.Axioms: 0
% 0.08/0.27
% 0.08/0.27 Length.of.Defs: 0
% 0.08/0.27
% 0.08/0.27 Contains.Choice.Funs: false
% 0.08/0.27 ....
% 0.08/0.27
% 0.08/0.27 ********************************
% 0.08/0.27 * All subproblems solved! *
% 0.08/0.27 ********************************
% 0.08/0.27 % 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:51,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.27
% 0.08/0.27 %**** Beginning of derivation protocol ****
% 0.08/0.27 % SZS output start CNFRefutation
% See solution above
% 0.08/0.27
% 0.08/0.27 %**** End of derivation protocol ****
% 0.08/0.27 %**** no. of clauses in derivation: 14 ****
% 0.08/0.27 %**** clause counter: 51 ****
% 0.08/0.27
% 0.08/0.27 % 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:51,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------