%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV409^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 10:50:03 AM UTC 2026
% Result : Theorem 0.07s 0.21s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 15 equ; 0 cnn)
% Maximal formula atoms : 1 ( 5 avg)
% Number of connectives : 243 ( 47 ~; 22 |; 10 &; 156 @)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 22 !; 4 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_X,type,
sK1_X: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(tp_sK2_SY4,type,
sK2_SY4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(tp_sK3_SY6,type,
sK3_SY6: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i ).
thf(tp_sK4_SV13,type,
sK4_SV13: $i ).
thf(tp_sK5_SV14,type,
sK5_SV14: $i ).
thf(tp_sK6_E,type,
sK6_E: $i ).
thf(tp_sK7_E,type,
sK7_E: $i ).
thf(1,conjecture,
? [R: ( $i > $o ) > ( $i > $o ) > $o] :
! [X: $i > $o,Y: $i > $o] :
( ( ( R @ X @ Y )
& ( R @ Y @ X ) )
=> ! [Xx: $i] :
( ( X @ Xx )
<=> ( Y @ Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120_BUG_pme) ).
thf(2,negated_conjecture,
( ( ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
! [X: $i > $o,Y: $i > $o] :
( ( ( R @ X @ Y )
& ( R @ Y @ X ) )
=> ! [Xx: $i] :
( ( X @ Xx )
<=> ( Y @ Xx ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
! [X: $i > $o,Y: $i > $o] :
( ( ( R @ X @ Y )
& ( R @ Y @ X ) )
=> ! [Xx: $i] :
( ( X @ Xx )
<=> ( Y @ Xx ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
! [X: $i > $o,Y: $i > $o] :
( ( ( R @ X @ Y )
& ( R @ Y @ X ) )
=> ! [Xx: $i] :
( ( X @ Xx )
<=> ( Y @ Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [R: ( $i > $o ) > ( $i > $o ) > $o] :
( ( R @ ( sK1_X @ R ) @ ( sK2_SY4 @ R ) )
& ( R @ ( sK2_SY4 @ R ) @ ( sK1_X @ R ) )
& ( ~ ( sK1_X @ R @ ( sK3_SY6 @ R ) )
| ~ ( sK2_SY4 @ R @ ( sK3_SY6 @ R ) ) )
& ( ( sK1_X @ R @ ( sK3_SY6 @ R ) )
| ( sK2_SY4 @ R @ ( sK3_SY6 @ R ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [R: ( $i > $o ) > ( $i > $o ) > $o] :
( ( R @ ( sK1_X @ R ) @ ( sK2_SY4 @ R ) )
& ( R @ ( sK2_SY4 @ R ) @ ( sK1_X @ R ) )
& ( ~ ( sK1_X @ R @ ( sK3_SY6 @ R ) )
| ~ ( sK2_SY4 @ R @ ( sK3_SY6 @ R ) ) )
& ( ( sK1_X @ R @ ( sK3_SY6 @ R ) )
| ( sK2_SY4 @ R @ ( sK3_SY6 @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: ( $i > $o ) > ( $i > $o ) > $o] :
~ ( ~ ~ ( ~ ( SX0 @ ( sK1_X @ SX0 ) @ ( sK2_SY4 @ SX0 ) )
| ~ ( SX0 @ ( sK2_SY4 @ SX0 ) @ ( sK1_X @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( sK1_X @ SX0 @ ( sK3_SY6 @ SX0 ) )
| ~ ( sK2_SY4 @ SX0 @ ( sK3_SY6 @ SX0 ) ) )
| ~ ( ( sK1_X @ SX0 @ ( sK3_SY6 @ SX0 ) )
| ( sK2_SY4 @ SX0 @ ( sK3_SY6 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ( ~ ~ ( ~ ( SV1 @ ( sK1_X @ SV1 ) @ ( sK2_SY4 @ SV1 ) )
| ~ ( SV1 @ ( sK2_SY4 @ SV1 ) @ ( sK1_X @ SV1 ) ) )
| ~ ~ ( ~ ( ~ ( sK1_X @ SV1 @ ( sK3_SY6 @ SV1 ) )
| ~ ( sK2_SY4 @ SV1 @ ( sK3_SY6 @ SV1 ) ) )
| ~ ( ( sK1_X @ SV1 @ ( sK3_SY6 @ SV1 ) )
| ( sK2_SY4 @ SV1 @ ( sK3_SY6 @ SV1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ~ ( ~ ( SV1 @ ( sK1_X @ SV1 ) @ ( sK2_SY4 @ SV1 ) )
| ~ ( SV1 @ ( sK2_SY4 @ SV1 ) @ ( sK1_X @ SV1 ) ) )
| ~ ~ ( ~ ( ~ ( sK1_X @ SV1 @ ( sK3_SY6 @ SV1 ) )
| ~ ( sK2_SY4 @ SV1 @ ( sK3_SY6 @ SV1 ) ) )
| ~ ( ( sK1_X @ SV1 @ ( sK3_SY6 @ SV1 ) )
| ( sK2_SY4 @ SV1 @ ( sK3_SY6 @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ~ ( ~ ( SV1 @ ( sK1_X @ SV1 ) @ ( sK2_SY4 @ SV1 ) )
| ~ ( SV1 @ ( sK2_SY4 @ SV1 ) @ ( sK1_X @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ( ~ ( SV1 @ ( sK1_X @ SV1 ) @ ( sK2_SY4 @ SV1 ) )
| ~ ( SV1 @ ( sK2_SY4 @ SV1 ) @ ( sK1_X @ SV1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(14,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ( SV1 @ ( sK1_X @ SV1 ) @ ( sK2_SY4 @ SV1 ) )
| ~ ( SV1 @ ( sK2_SY4 @ SV1 ) @ ( sK1_X @ SV1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ( SV1 @ ( sK1_X @ SV1 ) @ ( sK2_SY4 @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(20,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( SV1 @ ( sK1_X @ SV1 ) @ ( sK2_SY4 @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(29,plain,
$false = $true,
inference(prim_subst,[status(thm)],[20:[bind(SV1,$thf( ^ [SV7: $i > $o] : ^ [SV8: $i > $o] : $false ))]]) ).
thf(112,plain,
$false = $true,
inference(sim,[status(thm)],[29]) ).
thf(113,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV409^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:49:58 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.21
% 0.07/0.21 No.of.Axioms: 0
% 0.07/0.21
% 0.07/0.21 Length.of.Defs: 0
% 0.07/0.21
% 0.07/0.21 Contains.Choice.Funs: false
% 0.07/0.21 ..
% 0.07/0.21
% 0.07/0.21 ********************************
% 0.07/0.21 * All subproblems solved! *
% 0.07/0.21 ********************************
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/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:112,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.07/0.21
% 0.07/0.21 %**** Beginning of derivation protocol ****
% 0.07/0.21 % SZS output start CNFRefutation
% See solution above
% 0.07/0.21
% 0.07/0.21 %**** End of derivation protocol ****
% 0.07/0.21 %**** no. of clauses in derivation: 17 ****
% 0.07/0.21 %**** clause counter: 112 ****
% 0.07/0.21
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/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:112,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------