%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO262^5 : 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 : 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 11:07:57 AM UTC 2026
% Result : Theorem 1.13s 0.37s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 100 ( 18 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 256 ( 46 ~; 2 |; 5 &; 203 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 38 ^; 25 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cE,type,
cE: ( $i > $o ) > $i ).
thf(tp_cP,type,
cP: $i > $i > $o ).
thf(tp_sK10_E,type,
sK10_E: ( $i > $i > $i > $o ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK11_E,type,
sK11_E: ( $i > $i > $i > $o ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK12_E,type,
sK12_E: ( $i > $i > $i > $o ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK13_E,type,
sK13_E: ( $i > $i > $i > $o ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK1_E,type,
sK1_E: $i ).
thf(tp_sK2_E,type,
sK2_E: ( $i > $i > $o ) > $i ).
thf(tp_sK3_E,type,
sK3_E: ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK4_E,type,
sK4_E: ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK7_E,type,
sK7_E: ( $i > $i > $i ) > ( $i > $i > $i > $o ) > $i ).
thf(tp_sK8_E,type,
sK8_E: ( $i > $i > $i > $o ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK9_E,type,
sK9_E: ( $i > $i > $i > $o ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(1,conjecture,
~ ( ! [Xx: $i] :
( cP @ Xx
@ ( cE
@ ^ [Xy: $i] : ( cP @ Xx @ Xy ) ) )
& ! [Xf: $i > $i] :
~ ( cP
@ ( cE
@ ^ [Xx: $i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) )
@ ( Xf
@ ( cE
@ ^ [Xx: $i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM19SK1) ).
thf(2,negated_conjecture,
( ( ~ ( ! [Xx: $i] :
( cP @ Xx
@ ( cE
@ ^ [Xy: $i] : ( cP @ Xx @ Xy ) ) )
& ! [Xf: $i > $i] :
~ ( cP
@ ( cE
@ ^ [Xx: $i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) )
@ ( Xf
@ ( cE
@ ^ [Xx: $i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ( ! [Xx: $i] :
( cP @ Xx
@ ( cE
@ ^ [Xy: $i] : ( cP @ Xx @ Xy ) ) )
& ! [Xf: $i > $i] :
~ ( cP
@ ( cE
@ ^ [Xx: $i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) )
@ ( Xf
@ ( cE
@ ^ [Xx: $i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: $i] :
( cP @ Xx
@ ( cE
@ ^ [Xy: $i] : ( cP @ Xx @ Xy ) ) )
& ! [Xf: $i > $i] :
~ ( cP
@ ( cE
@ ^ [Xx: $i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) )
@ ( Xf
@ ( cE
@ ^ [Xx: $i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
( cP @ Xx
@ ( cE
@ ^ [Xy: $i] : ( cP @ Xx @ Xy ) ) )
& ! [Xf: $i > $i] :
~ ( cP
@ ( cE
@ ^ [Xx: $i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) )
@ ( Xf
@ ( cE
@ ^ [Xx: $i] :
~ ( cP @ Xx @ ( Xf @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ( ~ ! [SX0: $i] :
( cP @ SX0
@ ( cE
@ ^ [SX1: $i] : ( cP @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i > $i] :
~ ( cP
@ ( cE
@ ^ [SX1: $i] :
~ ( cP @ SX1 @ ( SX0 @ SX1 ) ) )
@ ( SX0
@ ( cE
@ ^ [SX1: $i] :
~ ( cP @ SX1 @ ( SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ! [SX0: $i] :
( cP @ SX0
@ ( cE
@ ^ [SX1: $i] : ( cP @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i > $i] :
~ ( cP
@ ( cE
@ ^ [SX1: $i] :
~ ( cP @ SX1 @ ( SX0 @ SX1 ) ) )
@ ( SX0
@ ( cE
@ ^ [SX1: $i] :
~ ( cP @ SX1 @ ( SX0 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ! [SX0: $i] :
( cP @ SX0
@ ( cE
@ ^ [SX1: $i] : ( cP @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ! [SX0: $i > $i] :
~ ( cP
@ ( cE
@ ^ [SX1: $i] :
~ ( cP @ SX1 @ ( SX0 @ SX1 ) ) )
@ ( SX0
@ ( cE
@ ^ [SX1: $i] :
~ ( cP @ SX1 @ ( SX0 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [SX0: $i] :
( cP @ SX0
@ ( cE
@ ^ [SX1: $i] : ( cP @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SX0: $i > $i] :
~ ( cP
@ ( cE
@ ^ [SX1: $i] :
~ ( cP @ SX1 @ ( SX0 @ SX1 ) ) )
@ ( SX0
@ ( cE
@ ^ [SX1: $i] :
~ ( cP @ SX1 @ ( SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( cP @ SV1
@ ( cE
@ ^ [SY5: $i] : ( cP @ SV1 @ SY5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV2: $i > $i] :
( ( ~ ( cP
@ ( cE
@ ^ [SY6: $i] :
~ ( cP @ SY6 @ ( SV2 @ SY6 ) ) )
@ ( SV2
@ ( cE
@ ^ [SY7: $i] :
~ ( cP @ SY7 @ ( SV2 @ SY7 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: $i > $i] :
( ( cP
@ ( cE
@ ^ [SY6: $i] :
~ ( cP @ SY6 @ ( SV2 @ SY6 ) ) )
@ ( SV2
@ ( cE
@ ^ [SY7: $i] :
~ ( cP @ SY7 @ ( SV2 @ SY7 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(15,plain,
! [SV3: $i] :
( ( cP @ SV3
@ ( cE
@ ^ [SX0: $i] : ( cP @ SV3 @ SX0 ) ) )
= $true ),
inference(rename,[status(thm)],[12]) ).
thf(16,plain,
! [SV4: $i > $i] :
( ( cP
@ ( cE
@ ^ [SX0: $i] :
~ ( cP @ SX0 @ ( SV4 @ SX0 ) ) )
@ ( SV4
@ ( cE
@ ^ [SX0: $i] :
~ ( cP @ SX0 @ ( SV4 @ SX0 ) ) ) ) )
= $false ),
inference(rename,[status(thm)],[14]) ).
thf(17,plain,
! [SV4: $i > $i,SV3: $i] :
( ( ( cP
@ ( cE
@ ^ [SX0: $i] :
~ ( cP @ SX0 @ ( SV4 @ SX0 ) ) )
@ ( SV4
@ ( cE
@ ^ [SX0: $i] :
~ ( cP @ SX0 @ ( SV4 @ SX0 ) ) ) ) )
= ( cP @ SV3
@ ( cE
@ ^ [SX0: $i] : ( cP @ SV3 @ SX0 ) ) ) )
= $false ),
inference(res,[status(thm)],[16,15]) ).
thf(37,plain,
$false = $true,
inference(extuni,[status(esa)],[17:[bind(SV4,$thf( ^ [SX0: $i] : ( cE @ ^ [SX1: $i] : ( cP @ SX0 @ SX1 ) ) )),bind(SV3,$thf( cE @ ^ [SX0: $i] : ~ ( cP @ SX0 @ ( cE @ ^ [SX1: $i] : ( cP @ SX0 @ SX1 ) ) ) ))]]) ).
thf(38,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO262^5 : 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
% 0.09/0.17 % Computer : n026.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 17:37:02 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.13/0.37
% 1.13/0.37 No.of.Axioms: 0
% 1.13/0.37
% 1.13/0.37 Length.of.Defs: 0
% 1.13/0.37
% 1.13/0.37 Contains.Choice.Funs: true
% 1.13/0.37 ..
% 1.13/0.37
% 1.13/0.37 ********************************
% 1.13/0.37 * All subproblems solved! *
% 1.13/0.37 ********************************
% 1.13/0.37 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:37,loop_count:2,foatp_calls:1,translation:fof_full)
% 1.13/0.37
% 1.13/0.37 %**** Beginning of derivation protocol ****
% 1.13/0.37 % SZS output start CNFRefutation
% See solution above
% 1.13/0.37
% 1.13/0.37 %**** End of derivation protocol ****
% 1.13/0.37 %**** no. of clauses in derivation: 19 ****
% 1.13/0.37 %**** clause counter: 37 ****
% 1.13/0.37
% 1.13/0.37 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:37,loop_count:2,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------