%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO296^5 : 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 : n006.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 11:08:00 AM UTC 2026
% Result : Theorem 0.11s 0.19s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 15 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 119 ( 20 ~; 21 |; 6 &; 68 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 16 !; 4 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_p,type,
p: $i > $o ).
thf(tp_q,type,
q: $i > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: ( $i > $o ) > $i ).
thf(tp_sK2_SY3,type,
sK2_SY3: ( $i > $o ) > $i ).
thf(1,conjecture,
? [A: $i > $o] :
! [Xx: $i,Xy: $i] :
( ( ( A @ Xx )
| ( A @ Xy ) )
=> ( ( p @ Xx )
& ( q @ Xy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE5D) ).
thf(2,negated_conjecture,
( ( ? [A: $i > $o] :
! [Xx: $i,Xy: $i] :
( ( ( A @ Xx )
| ( A @ Xy ) )
=> ( ( p @ Xx )
& ( q @ Xy ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [A: $i > $o] :
! [Xx: $i,Xy: $i] :
( ( ( A @ Xx )
| ( A @ Xy ) )
=> ( ( p @ Xx )
& ( q @ Xy ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [A: $i > $o] :
! [Xx: $i,Xy: $i] :
( ( ( A @ Xx )
| ( A @ Xy ) )
=> ( ( p @ Xx )
& ( q @ Xy ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i > $o] :
( ( ( A @ ( sK1_Xx @ A ) )
| ( A @ ( sK2_SY3 @ A ) ) )
& ( ~ ( p @ ( sK1_Xx @ A ) )
| ~ ( q @ ( sK2_SY3 @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [A: $i > $o] :
( ( ( A @ ( sK1_Xx @ A ) )
| ( A @ ( sK2_SY3 @ A ) ) )
& ( ~ ( p @ ( sK1_Xx @ A ) )
| ~ ( q @ ( sK2_SY3 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: $i > $o] :
~ ( ~ ( ( SX0 @ ( sK1_Xx @ SX0 ) )
| ( SX0 @ ( sK2_SY3 @ SX0 ) ) )
| ~ ( ~ ( p @ ( sK1_Xx @ SX0 ) )
| ~ ( q @ ( sK2_SY3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: $i > $o] :
( ( ~ ( ~ ( ( SV1 @ ( sK1_Xx @ SV1 ) )
| ( SV1 @ ( sK2_SY3 @ SV1 ) ) )
| ~ ( ~ ( p @ ( sK1_Xx @ SV1 ) )
| ~ ( q @ ( sK2_SY3 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i > $o] :
( ( ~ ( ( SV1 @ ( sK1_Xx @ SV1 ) )
| ( SV1 @ ( sK2_SY3 @ SV1 ) ) )
| ~ ( ~ ( p @ ( sK1_Xx @ SV1 ) )
| ~ ( q @ ( sK2_SY3 @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i > $o] :
( ( ~ ( ( SV1 @ ( sK1_Xx @ SV1 ) )
| ( SV1 @ ( sK2_SY3 @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_Xx @ SV1 ) )
| ( SV1 @ ( sK2_SY3 @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(14,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_Xx @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK2_SY3 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(19,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[14:[bind(SV1,$thf( ^ [SV4: $i] : $false ))]]) ).
thf(50,plain,
$false = $true,
inference(sim,[status(thm)],[19]) ).
thf(51,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO296^5 : 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
% 0.11/0.16 % Computer : n006.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 17:34:07 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.19
% 0.11/0.19 No.of.Axioms: 0
% 0.11/0.19
% 0.11/0.19 Length.of.Defs: 0
% 0.11/0.19
% 0.11/0.19 Contains.Choice.Funs: false
% 0.11/0.19
% 0.11/0.19 ********************************
% 0.11/0.19 * All subproblems solved! *
% 0.11/0.19 ********************************
% 0.11/0.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:50,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.19
% 0.11/0.19 %**** Beginning of derivation protocol ****
% 0.11/0.19 % SZS output start CNFRefutation
% See solution above
% 0.11/0.19
% 0.11/0.19 %**** End of derivation protocol ****
% 0.11/0.19 %**** no. of clauses in derivation: 15 ****
% 0.11/0.19 %**** clause counter: 50 ****
% 0.11/0.19
% 0.11/0.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:50,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------