%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV427^1 : 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 10:50:05 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 26 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 112 ( 25 ~; 15 |; 2 &; 69 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 17 !; 1 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_eps,type,
eps: ( $i > $o ) > $i ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_q,type,
q: $i > $o ).
thf(1,axiom,
! [X: $i] :
( ( p @ X )
| ( q @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pq) ).
thf(2,axiom,
! [P: $i > $o] :
( ? [X: $i] : ( P @ X )
=> ( P @ ( eps @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax) ).
thf(3,conjecture,
( ( p @ ( eps @ p ) )
| ( q @ ( eps @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(4,negated_conjecture,
( ( ( p @ ( eps @ p ) )
| ( q @ ( eps @ q ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ~ ( ( p @ ( eps @ p ) )
| ( q @ ( eps @ q ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ( p @ ( eps @ p ) )
& ~ ( q @ ( eps @ q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [P: $i > $o] :
( ! [X: $i] :
~ ( P @ X )
| ( P @ ( eps @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[2]) ).
thf(8,plain,
( ( ! [P: $i > $o] :
( ! [X: $i] :
~ ( P @ X )
| ( P @ ( eps @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [X: $i] :
( ( p @ X )
| ( q @ X ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(10,plain,
( ( ~ ( p @ ( eps @ p ) )
& ~ ( q @ ( eps @ q ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ ( ~ ~ ( p @ ( eps @ p ) )
| ~ ~ ( q @ ( eps @ q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
! [SV1: $i > $o] :
( ( ! [SY0: $i] :
~ ( SV1 @ SY0 )
| ( SV1 @ ( eps @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(13,plain,
! [SV2: $i] :
( ( ( p @ SV2 )
| ( q @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(14,plain,
( ( ~ ~ ( p @ ( eps @ p ) )
| ~ ~ ( q @ ( eps @ q ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV1: $i > $o] :
( ( ( ! [SY0: $i] :
~ ( SV1 @ SY0 ) )
= $true )
| ( ( SV1 @ ( eps @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV2: $i] :
( ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ~ ( p @ ( eps @ p ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ~ ( q @ ( eps @ q ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(19,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV1 @ ( eps @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( ~ ( p @ ( eps @ p ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( q @ ( eps @ q ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( eps @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( p @ ( eps @ p ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( q @ ( eps @ q ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,24,23,22]) ).
thf(26,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV427^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.22 % Computer : n017.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Oct 6 15:42:01 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.26
% 0.10/0.26 No.of.Axioms: 2
% 0.10/0.26
% 0.10/0.26 Length.of.Defs: 0
% 0.10/0.26
% 0.10/0.26 Contains.Choice.Funs: true
% 0.10/0.26
% 0.10/0.26 ********************************
% 0.10/0.26 * All subproblems solved! *
% 0.10/0.26 ********************************
% 0.10/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:1,ude:false,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:25,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.26
% 0.10/0.26 %**** Beginning of derivation protocol ****
% 0.10/0.26 % SZS output start CNFRefutation
% See solution above
% 0.10/0.26
% 0.10/0.26 %**** End of derivation protocol ****
% 0.10/0.26 %**** no. of clauses in derivation: 26 ****
% 0.10/0.26 %**** clause counter: 25 ****
% 0.10/0.26
% 0.10/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:1,ude:false,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:25,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------