%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO527^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 11:08:39 AM UTC 2026
% Result : Theorem 0.10s 0.18s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 18 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 68 ( 15 ~; 0 |; 0 &; 53 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 0 ^; 27 !; 8 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_r,type,
r: a > b > $o ).
thf(tp_sK1_SY4,type,
sK1_SY4: a > b ).
thf(tp_sK2_SY5,type,
sK2_SY5: ( a > b ) > a ).
thf(1,axiom,
! [X: a] :
? [Y: b] : ( r @ X @ Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rtotal) ).
thf(2,conjecture,
? [F: a > b] :
! [X: a] : ( r @ X @ ( F @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',skolem) ).
thf(3,negated_conjecture,
( ( ? [F: a > b] :
! [X: a] : ( r @ X @ ( F @ X ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ? [F: a > b] :
! [X: a] : ( r @ X @ ( F @ X ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [X: a] :
? [Y: b] : ( r @ X @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(6,plain,
( ( ~ ? [F: a > b] :
! [X: a] : ( r @ X @ ( F @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [X: a] :
? [Y: b] : ( r @ X @ Y ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ? [F: a > b] :
! [X: a] : ( r @ X @ ( F @ X ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ~ ! [SX0: a > b] :
~ ! [SX1: a] : ( r @ SX1 @ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SX0: a] :
~ ! [SX1: b] :
~ ( r @ SX0 @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ! [SX0: a > b] :
~ ! [SX1: a] : ( r @ SX1 @ ( SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: a] :
( ( ~ ! [SY4: b] :
~ ( r @ SV1 @ SY4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SX0: a > b] :
~ ! [SX1: a] : ( r @ SX1 @ ( SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: a] :
( ( ! [SY4: b] :
~ ( r @ SV1 @ SY4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV2: a > b] :
( ( ~ ! [SY5: a] : ( r @ SY5 @ ( SV2 @ SY5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: a] :
( ( ~ ( r @ SV1 @ ( sK1_SY4 @ SV1 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(17,plain,
! [SV2: a > b] :
( ( ! [SY5: a] : ( r @ SY5 @ ( SV2 @ SY5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: a] :
( ( r @ SV1 @ ( sK1_SY4 @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
! [SV2: a > b] :
( ( r @ ( sK2_SY5 @ SV2 ) @ ( SV2 @ ( sK2_SY5 @ SV2 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(20,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,19]) ).
thf(21,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO527^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.14 % Computer : n003.cluster.edu
% 0.10/0.14 % Model : x86_64 x86_64
% 0.10/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.14 % Memory : 8046.5625MB
% 0.10/0.14 % OS : Linux 6.8.0-71-generic
% 0.10/0.14 % CPULimit : 300
% 0.10/0.14 % WCLimit : 300
% 0.10/0.14 % DateTime : Tue Oct 6 17:44:09 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.18
% 0.10/0.18 No.of.Axioms: 1
% 0.10/0.18
% 0.10/0.18 Length.of.Defs: 0
% 0.10/0.18
% 0.10/0.18 Contains.Choice.Funs: false
% 0.10/0.18
% 0.10/0.18 ********************************
% 0.10/0.18 * All subproblems solved! *
% 0.10/0.18 ********************************
% 0.10/0.18 % SZS status Theorem for /export/starexec/sandbox/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:20,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.18
% 0.10/0.18 %**** Beginning of derivation protocol ****
% 0.10/0.18 % SZS output start CNFRefutation
% See solution above
% 0.10/0.18
% 0.10/0.18 %**** End of derivation protocol ****
% 0.10/0.18 %**** no. of clauses in derivation: 21 ****
% 0.10/0.18 %**** clause counter: 20 ****
% 0.10/0.18
% 0.10/0.18 % SZS status Theorem for /export/starexec/sandbox/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:20,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------