%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU926^5 : 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 : n014.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 10:49:15 AM UTC 2026
% Result : Theorem 0.07s 0.30s
% 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 : 51 ( 15 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 168 ( 40 ~; 18 |; 6 &; 92 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 12 ^; 34 !; 6 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_P,type,
sK1_P: $i > $o ).
thf(tp_sK2_SY9,type,
sK2_SY9: ( ( $i > $i ) > $o ) > $i > $i ).
thf(tp_sK3_SY13,type,
sK3_SY13: ( ( $i > $i ) > $o ) > $i ).
thf(tp_sK4_E,type,
sK4_E: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
thf(1,conjecture,
! [P: $i > $o] :
? [M: ( $i > $i ) > $o] :
! [G: $i > $i] :
( ( M @ G )
=> ( ( M
@ ^ [Z: $i] : ( G @ ( G @ Z ) ) )
& ! [Y: $i] :
( ( P @ Y )
=> ( P @ ( G @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM113) ).
thf(2,negated_conjecture,
( ( ! [P: $i > $o] :
? [M: ( $i > $i ) > $o] :
! [G: $i > $i] :
( ( M @ G )
=> ( ( M
@ ^ [Z: $i] : ( G @ ( G @ Z ) ) )
& ! [Y: $i] :
( ( P @ Y )
=> ( P @ ( G @ Y ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [P: $i > $o] :
? [M: ( $i > $i ) > $o] :
! [G: $i > $i] :
( ( M @ G )
=> ( ( M
@ ^ [Z: $i] : ( G @ ( G @ Z ) ) )
& ! [Y: $i] :
( ( P @ Y )
=> ( P @ ( G @ Y ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [SY5: ( $i > $i ) > $o] :
! [SY6: $i > $i] :
( ( SY5 @ SY6 )
=> ( ( SY5
@ ^ [Z: $i] : ( SY6 @ ( SY6 @ Z ) ) )
& ! [SY8: $i] :
( ( sK1_P @ SY8 )
=> ( sK1_P @ ( SY6 @ SY8 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ~ ? [SY5: ( $i > $i ) > $o] :
! [SY6: $i > $i] :
( ( SY5 @ SY6 )
=> ( ( SY5
@ ^ [Z: $i] : ( SY6 @ ( SY6 @ Z ) ) )
& ! [SY8: $i] :
( ( sK1_P @ SY8 )
=> ( sK1_P @ ( SY6 @ SY8 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ? [SY5: ( $i > $i ) > $o] :
! [SY6: $i > $i] :
( ( SY5 @ SY6 )
=> ( ( SY5
@ ^ [Z: $i] : ( SY6 @ ( SY6 @ Z ) ) )
& ! [SY8: $i] :
( ( sK1_P @ SY8 )
=> ( sK1_P @ ( SY6 @ SY8 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ~ ! [SX0: ( $i > $i ) > $o] :
~ ! [SX1: $i > $i] :
( ~ ( SX0 @ SX1 )
| ~ ( ~ ( SX0
@ ^ [SX2: $i] : ( SX1 @ ( SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( sK1_P @ SX2 )
| ( sK1_P @ ( SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ! [SX0: ( $i > $i ) > $o] :
~ ! [SX1: $i > $i] :
( ~ ( SX0 @ SX1 )
| ~ ( ~ ( SX0
@ ^ [SX2: $i] : ( SX1 @ ( SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( sK1_P @ SX2 )
| ( sK1_P @ ( SX1 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SX0: ( $i > $i ) > $o] :
~ ! [SX1: $i > $i] :
( ~ ( SX0 @ SX1 )
| ~ ( ~ ( SX0
@ ^ [SX2: $i] : ( SX1 @ ( SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( sK1_P @ SX2 )
| ( sK1_P @ ( SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ~ ! [SY9: $i > $i] :
( ~ ( SV1 @ SY9 )
| ~ ( ~ ( SV1
@ ^ [SX2: $i] : ( SY9 @ ( SY9 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( sK1_P @ SX2 )
| ( sK1_P @ ( SY9 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ! [SY9: $i > $i] :
( ~ ( SV1 @ SY9 )
| ~ ( ~ ( SV1
@ ^ [SX2: $i] : ( SY9 @ ( SY9 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( sK1_P @ SX2 )
| ( sK1_P @ ( SY9 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(12,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ~ ( SV1 @ ( sK2_SY9 @ SV1 ) )
| ~ ( ~ ( SV1
@ ^ [SY12: $i] : ( sK2_SY9 @ SV1 @ ( sK2_SY9 @ SV1 @ SY12 ) ) )
| ~ ! [SY13: $i] :
( ~ ( sK1_P @ SY13 )
| ( sK1_P @ ( sK2_SY9 @ SV1 @ SY13 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(13,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ~ ( SV1 @ ( sK2_SY9 @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: ( $i > $i ) > $o] :
( ( SV1 @ ( sK2_SY9 @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(25,plain,
$false = $true,
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SV4: $i > $i] : $false ))]]) ).
thf(92,plain,
$false = $true,
inference(sim,[status(thm)],[25]) ).
thf(93,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU926^5 : 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
% 0.07/0.19 % Computer : n014.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:37:56 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.30
% 0.07/0.30 No.of.Axioms: 0
% 0.07/0.30
% 0.07/0.30 Length.of.Defs: 0
% 0.07/0.30
% 0.07/0.30 Contains.Choice.Funs: false
% 0.07/0.30 .
% 0.07/0.30
% 0.07/0.30 ********************************
% 0.07/0.30 * All subproblems solved! *
% 0.07/0.30 ********************************
% 0.07/0.30 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:92,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.30
% 0.07/0.30 %**** Beginning of derivation protocol ****
% 0.07/0.30 % SZS output start CNFRefutation
% See solution above
% 0.07/0.30
% 0.07/0.30 %**** End of derivation protocol ****
% 0.07/0.30 %**** no. of clauses in derivation: 17 ****
% 0.07/0.30 %**** clause counter: 92 ****
% 0.07/0.30
% 0.07/0.30 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:92,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------