%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV290^5 : TPTP v9.3.1. Bugfixed 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 : n026.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 10:49:52 AM UTC 2026
% Result : Theorem 74.47s 15.23s
% Output : CNFRefutation 74.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 83 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 223 ( 70 ~; 20 |; 19 &; 104 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 80 ( 80 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 19 ^; 25 !; 9 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c0,type,
c0: ( $i > $o ) > $o ).
thf(tp_cSUCC,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(tp_c_less__eq_,type,
c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(tp_sK1_SY1,type,
sK1_SY1: ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).
thf(tp_sK2_SY20,type,
sK2_SY20: ( ( ( $i > $o ) > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(cSUCC,definition,
( cSUCC
= ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
? [Xx: $i] :
( ( Xp @ Xx )
& ( Xn
@ ^ [Xt: $i] :
( ( Xt != Xx )
& ( Xp @ Xt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSUCC_def) ).
thf(c_less__eq_,definition,
( c_less__eq_
= ( ^ [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
! [Xp: ( ( $i > $o ) > $o ) > $o] :
( ( ( Xp @ Xx )
& ! [Xz: ( $i > $o ) > $o] :
( ( Xp @ Xz )
=> ( Xp @ ( cSUCC @ Xz ) ) ) )
=> ( Xp @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_less__eq__def) ).
thf(1,conjecture,
? [A: ( ( $i > $o ) > $o ) > $o] :
! [Xx: ( $i > $o ) > $o] :
( ( A @ Xx )
=> ( c_less__eq_ @ Xx @ c0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE1) ).
thf(2,negated_conjecture,
( ( ? [A: ( ( $i > $o ) > $o ) > $o] :
! [Xx: ( $i > $o ) > $o] :
( ( A @ Xx )
=> ( c_less__eq_ @ Xx @ c0 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [SY0: ( ( $i > $o ) > $o ) > $o] :
! [SY1: ( $i > $o ) > $o] :
( ( SY0 @ SY1 )
=> ! [SY8: ( ( $i > $o ) > $o ) > $o] :
( ( ( SY8 @ SY1 )
& ! [SY4: ( $i > $o ) > $o] :
( ( SY8 @ SY4 )
=> ( SY8
@ ^ [SY5: $i > $o] :
? [SY6: $i] :
( ( SY5 @ SY6 )
& ( SY4
@ ^ [Xt: $i] :
( ( Xt != SY6 )
& ( SY5 @ Xt ) ) ) ) ) ) )
=> ( SY8 @ c0 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cSUCC,c_less__eq_]) ).
thf(4,plain,
( ( ~ ? [SY0: ( ( $i > $o ) > $o ) > $o] :
! [SY1: ( $i > $o ) > $o] :
( ( SY0 @ SY1 )
=> ! [SY8: ( ( $i > $o ) > $o ) > $o] :
( ( ( SY8 @ SY1 )
& ! [SY4: ( $i > $o ) > $o] :
( ( SY8 @ SY4 )
=> ( SY8
@ ^ [SY5: $i > $o] :
? [SY6: $i] :
( ( SY5 @ SY6 )
& ( SY4
@ ^ [Xt: $i] :
( ( Xt != SY6 )
& ( SY5 @ Xt ) ) ) ) ) ) )
=> ( SY8 @ c0 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: ( ( $i > $o ) > $o ) > $o] :
( ( SY0 @ ( sK1_SY1 @ SY0 ) )
& ! [SY25: ( $i > $o ) > $o] :
( ~ ( sK2_SY20 @ SY0 @ SY25 )
| ( sK2_SY20 @ SY0
@ ^ [SY5: $i > $o] :
? [SY6: $i] :
( ( SY5 @ SY6 )
& ( SY25
@ ^ [Xt: $i] :
( ( Xt != SY6 )
& ( SY5 @ Xt ) ) ) ) ) )
& ( sK2_SY20 @ SY0 @ ( sK1_SY1 @ SY0 ) )
& ~ ( sK2_SY20 @ SY0 @ c0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY0: ( ( $i > $o ) > $o ) > $o] :
( ( SY0 @ ( sK1_SY1 @ SY0 ) )
& ! [SY25: ( $i > $o ) > $o] :
( ~ ( sK2_SY20 @ SY0 @ SY25 )
| ( sK2_SY20 @ SY0
@ ^ [SY5: $i > $o] :
? [SY6: $i] :
( ( SY5 @ SY6 )
& ( SY25
@ ^ [Xt: $i] :
( ( Xt != SY6 )
& ( SY5 @ Xt ) ) ) ) ) )
& ( sK2_SY20 @ SY0 @ ( sK1_SY1 @ SY0 ) )
& ~ ( sK2_SY20 @ SY0 @ c0 ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: ( ( $i > $o ) > $o ) > $o] :
~ ( ~ ( SX0 @ ( sK1_SY1 @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX1: ( $i > $o ) > $o] :
( ~ ( sK2_SY20 @ SX0 @ SX1 )
| ( sK2_SY20 @ SX0
@ ^ [SX2: $i > $o] :
~ ! [SX3: $i] :
~ ~ ( ~ ( SX2 @ SX3 )
| ~ ( SX1
@ ^ [SX4: $i] :
~ ( ~ ( ( SX4 != SX3 ) )
| ~ ( SX2 @ SX4 ) ) ) ) ) )
| ~ ( sK2_SY20 @ SX0 @ ( sK1_SY1 @ SX0 ) ) )
| ~ ~ ( sK2_SY20 @ SX0 @ c0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,cSUCC,c_less__eq_]) ).
thf(8,plain,
! [SV1: ( ( $i > $o ) > $o ) > $o] :
( ( ~ ( ~ ( SV1 @ ( sK1_SY1 @ SV1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY29: ( $i > $o ) > $o] :
( ~ ( sK2_SY20 @ SV1 @ SY29 )
| ( sK2_SY20 @ SV1
@ ^ [SX2: $i > $o] :
~ ! [SX3: $i] :
~ ~ ( ~ ( SX2 @ SX3 )
| ~ ( SY29
@ ^ [SX4: $i] :
~ ( ~ ( ( SX4 != SX3 ) )
| ~ ( SX2 @ SX4 ) ) ) ) ) )
| ~ ( sK2_SY20 @ SV1 @ ( sK1_SY1 @ SV1 ) ) )
| ~ ~ ( sK2_SY20 @ SV1 @ c0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: ( ( $i > $o ) > $o ) > $o] :
( ( ~ ( SV1 @ ( sK1_SY1 @ SV1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY29: ( $i > $o ) > $o] :
( ~ ( sK2_SY20 @ SV1 @ SY29 )
| ( sK2_SY20 @ SV1
@ ^ [SX2: $i > $o] :
~ ! [SX3: $i] :
~ ~ ( ~ ( SX2 @ SX3 )
| ~ ( SY29
@ ^ [SX4: $i] :
~ ( ~ ( ( SX4 != SX3 ) )
| ~ ( SX2 @ SX4 ) ) ) ) ) )
| ~ ( sK2_SY20 @ SV1 @ ( sK1_SY1 @ SV1 ) ) )
| ~ ~ ( sK2_SY20 @ SV1 @ c0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: ( ( $i > $o ) > $o ) > $o] :
( ( ~ ( SV1 @ ( sK1_SY1 @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: ( ( $i > $o ) > $o ) > $o] :
( ( SV1 @ ( sK1_SY1 @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(29,plain,
$false = $true,
inference(prim_subst,[status(thm)],[12:[bind(SV1,$thf( ^ [SV6: ( $i > $o ) > $o] : $false ))]]) ).
thf(48,plain,
$false = $true,
inference(sim,[status(thm)],[29]) ).
thf(49,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV290^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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
% 0.10/0.17 % Computer : n026.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 15:47:46 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 74.47/15.23
% 74.47/15.23 No.of.Axioms: 0
% 74.47/15.23
% 74.47/15.23 Length.of.Defs: 460
% 74.47/15.23
% 74.47/15.23 Contains.Choice.Funs: false
% 74.47/15.23 .eprover: CPU time limit exceeded, terminating
% 74.47/15.23
% 74.47/15.23
% 74.47/15.23 ********************************
% 74.47/15.23 * All subproblems solved! *
% 74.47/15.23 ********************************
% 74.47/15.23 % 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:48,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 74.47/15.23
% 74.47/15.23 %**** Beginning of derivation protocol ****
% 74.47/15.23 % SZS output start CNFRefutation
% See solution above
% 74.47/15.23
% 74.47/15.23 %**** End of derivation protocol ****
% 74.47/15.23 %**** no. of clauses in derivation: 14 ****
% 74.47/15.23 %**** clause counter: 48 ****
% 74.47/15.23
% 74.47/15.23 % 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:48,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------