%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU967^5 : 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 : n013.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 10:49:18 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 462 ( 101 ~; 20 |; 15 &; 326 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 150 ( 150 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 188 ( 77 ^; 63 !; 48 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cG_0,type,
cG_0: ( ( $i > $i ) > $o ) > $i > $i ).
thf(tp_cH_0,type,
cH_0: ( ( $i > $i ) > $o ) > $i > $i ).
thf(tp_cP_0,type,
cP_0: $i > $o ).
thf(tp_cY_0,type,
cY_0: ( ( $i > $i ) > $o ) > $i ).
thf(tp_sK1_Xw_2,type,
sK1_Xw_2: ( ( $i > $i ) > $i > $o ) > $i ).
thf(tp_sK2_Xw_2,type,
sK2_Xw_2: ( ( $i > $i ) > $i > $o ) > $i ).
thf(1,conjecture,
~ ! [Xm_5: ( $i > $i ) > $i > $o] :
( ? [Xw_2: $i] :
( Xm_5
@ ( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 ) )
@ Xw_2 )
& ? [Xw_2: $i] :
( Xm_5
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 ) )
@ Xw_2 )
& ( ~ ? [Xw_2: $i] :
( Xm_5
@ ^ [Xx: $i] :
( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ Xx ) )
@ Xw_2 )
| ( ( cP_0
@ ( cY_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 ) ) )
& ~ ( cP_0
@ ( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 )
@ ( cY_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBUGWFFA_pme) ).
thf(2,negated_conjecture,
( ( ~ ! [Xm_5: ( $i > $i ) > $i > $o] :
( ? [Xw_2: $i] :
( Xm_5
@ ( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 ) )
@ Xw_2 )
& ? [Xw_2: $i] :
( Xm_5
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 ) )
@ Xw_2 )
& ( ~ ? [Xw_2: $i] :
( Xm_5
@ ^ [Xx: $i] :
( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ Xx ) )
@ Xw_2 )
| ( ( cP_0
@ ( cY_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 ) ) )
& ~ ( cP_0
@ ( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 )
@ ( cY_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xm_5: ( $i > $i ) > $i > $o] :
( ? [Xw_2: $i] :
( Xm_5
@ ( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 ) )
@ Xw_2 )
& ? [Xw_2: $i] :
( Xm_5
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 ) )
@ Xw_2 )
& ( ~ ? [Xw_2: $i] :
( Xm_5
@ ^ [Xx: $i] :
( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ Xx ) )
@ Xw_2 )
| ( ( cP_0
@ ( cY_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 ) ) )
& ~ ( cP_0
@ ( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 )
@ ( cY_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xm_5: ( $i > $i ) > $i > $o] :
( Xm_5
@ ( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 ) )
@ ( sK2_Xw_2 @ Xm_5 ) )
& ! [Xm_5: ( $i > $i ) > $i > $o] :
( Xm_5
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 ) )
@ ( sK1_Xw_2 @ Xm_5 ) )
& ! [Xm_5: ( $i > $i ) > $i > $o] :
( ! [Xw_2: $i] :
~ ( Xm_5
@ ^ [Xx: $i] :
( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ Xx ) )
@ Xw_2 )
| ( cP_0
@ ( cY_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 ) ) ) )
& ! [Xm_5: ( $i > $i ) > $i > $o] :
( ! [Xw_2: $i] :
~ ( Xm_5
@ ^ [Xx: $i] :
( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ Xx ) )
@ Xw_2 )
| ~ ( cP_0
@ ( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 )
@ ( cY_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [Xm_5: ( $i > $i ) > $i > $o] :
( Xm_5
@ ( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 ) )
@ ( sK2_Xw_2 @ Xm_5 ) )
& ! [Xm_5: ( $i > $i ) > $i > $o] :
( Xm_5
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 ) )
@ ( sK1_Xw_2 @ Xm_5 ) )
& ! [Xm_5: ( $i > $i ) > $i > $o] :
( ! [Xw_2: $i] :
~ ( Xm_5
@ ^ [Xx: $i] :
( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ Xx ) )
@ Xw_2 )
| ( cP_0
@ ( cY_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 ) ) ) )
& ! [Xm_5: ( $i > $i ) > $i > $o] :
( ! [Xw_2: $i] :
~ ( Xm_5
@ ^ [Xx: $i] :
( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ ( cH_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_20: $i] : ( Xm_5 @ Xw_1144 @ Xw_20 )
@ Xx ) )
@ Xw_2 )
| ~ ( cP_0
@ ( cG_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 )
@ ( cY_0
@ ^ [Xw_1144: $i > $i] :
? [Xw_2: $i] : ( Xm_5 @ Xw_1144 @ Xw_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cG_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK2_Xw_2 @ SX0 ) )
| ~ ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cH_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK1_Xw_2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: ( $i > $i ) > $i > $o] :
( ! [SX1: $i] :
~ ( SX0
@ ^ [SX2: $i] :
( cG_0
@ ^ [SX3: $i > $i] :
~ ! [SX4: $i] :
~ ( SX0 @ SX3 @ SX4 )
@ ( cH_0
@ ^ [SX3: $i > $i] :
~ ! [SX4: $i] :
~ ( SX0 @ SX3 @ SX4 )
@ SX2 ) )
@ SX1 )
| ( cP_0
@ ( cY_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: ( $i > $i ) > $i > $o] :
( ! [SX1: $i] :
~ ( SX0
@ ^ [SX2: $i] :
( cG_0
@ ^ [SX3: $i > $i] :
~ ! [SX4: $i] :
~ ( SX0 @ SX3 @ SX4 )
@ ( cH_0
@ ^ [SX3: $i > $i] :
~ ! [SX4: $i] :
~ ( SX0 @ SX3 @ SX4 )
@ SX2 ) )
@ SX1 )
| ~ ( cP_0
@ ( cG_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 )
@ ( cY_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ~ ( ~ ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cG_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK2_Xw_2 @ SX0 ) )
| ~ ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cH_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK1_Xw_2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: ( $i > $i ) > $i > $o] :
( ! [SX1: $i] :
~ ( SX0
@ ^ [SX2: $i] :
( cG_0
@ ^ [SX3: $i > $i] :
~ ! [SX4: $i] :
~ ( SX0 @ SX3 @ SX4 )
@ ( cH_0
@ ^ [SX3: $i > $i] :
~ ! [SX4: $i] :
~ ( SX0 @ SX3 @ SX4 )
@ SX2 ) )
@ SX1 )
| ( cP_0
@ ( cY_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: ( $i > $i ) > $i > $o] :
( ! [SX1: $i] :
~ ( SX0
@ ^ [SX2: $i] :
( cG_0
@ ^ [SX3: $i > $i] :
~ ! [SX4: $i] :
~ ( SX0 @ SX3 @ SX4 )
@ ( cH_0
@ ^ [SX3: $i > $i] :
~ ! [SX4: $i] :
~ ( SX0 @ SX3 @ SX4 )
@ SX2 ) )
@ SX1 )
| ~ ( cP_0
@ ( cG_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 )
@ ( cY_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ~ ( ~ ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cG_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK2_Xw_2 @ SX0 ) )
| ~ ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cH_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK1_Xw_2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cG_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK2_Xw_2 @ SX0 ) )
| ~ ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cH_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK1_Xw_2 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cG_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK2_Xw_2 @ SX0 ) )
| ~ ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cH_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK1_Xw_2 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cG_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK2_Xw_2 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SX0: ( $i > $i ) > $i > $o] :
( SX0
@ ( cG_0
@ ^ [SX1: $i > $i] :
~ ! [SX2: $i] :
~ ( SX0 @ SX1 @ SX2 ) )
@ ( sK2_Xw_2 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(22,plain,
! [SV1: ( $i > $i ) > $i > $o] :
( ( SV1
@ ( cG_0
@ ^ [SY4: $i > $i] :
~ ! [SY5: $i] :
~ ( SV1 @ SY4 @ SY5 ) )
@ ( sK2_Xw_2 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(34,plain,
$false = $true,
inference(prim_subst,[status(thm)],[22:[bind(SV1,$thf( ^ [SV31: $i > $i] : ^ [SV32: $i] : $false ))]]) ).
thf(75,plain,
$false = $true,
inference(sim,[status(thm)],[34]) ).
thf(76,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU967^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:37:51 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.27
% 0.08/0.27 No.of.Axioms: 0
% 0.08/0.27
% 0.08/0.27 Length.of.Defs: 0
% 0.08/0.27
% 0.08/0.27 Contains.Choice.Funs: true
% 0.08/0.27 .....
% 0.08/0.27
% 0.08/0.27 ********************************
% 0.08/0.27 * All subproblems solved! *
% 0.08/0.27 ********************************
% 0.08/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:75,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.08/0.27
% 0.08/0.27 %**** Beginning of derivation protocol ****
% 0.08/0.27 % SZS output start CNFRefutation
% See solution above
% 0.08/0.27
% 0.08/0.27 %**** End of derivation protocol ****
% 0.08/0.27 %**** no. of clauses in derivation: 16 ****
% 0.08/0.27 %**** clause counter: 75 ****
% 0.08/0.27
% 0.08/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:75,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------