%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV048^5 : 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 : n010.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 10:49:26 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 13 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 140 ( 26 ~; 6 |; 8 &; 96 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 20 !; 4 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Xx,type,
sK1_Xx: ( ( $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 > $o ).
thf(tp_sK4_SV13,type,
sK4_SV13: $i ).
thf(tp_sK5_SV15,type,
sK5_SV15: $i ).
thf(tp_sK6_SV16,type,
sK6_SV16: $i ).
thf(tp_sK7_E,type,
sK7_E: $i ).
thf(tp_sK8_E,type,
sK8_E: $i ).
thf(tp_sK9_E,type,
sK9_E: $i ).
thf(1,conjecture,
? [R: ( $i > $o ) > ( $i > $o ) > $o] :
! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120_pme) ).
thf(2,negated_conjecture,
( ( ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [R: ( $i > $o ) > ( $i > $o ) > $o] :
( ( R @ ( sK1_Xx @ R ) @ ( sK2_SY4 @ R ) )
& ( R @ ( sK2_SY4 @ R ) @ ( sK3_SY6 @ R ) )
& ~ ( R @ ( sK1_Xx @ R ) @ ( sK3_SY6 @ R ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [R: ( $i > $o ) > ( $i > $o ) > $o] :
( ( R @ ( sK1_Xx @ R ) @ ( sK2_SY4 @ R ) )
& ( R @ ( sK2_SY4 @ R ) @ ( sK3_SY6 @ R ) )
& ~ ( R @ ( sK1_Xx @ R ) @ ( sK3_SY6 @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: ( $i > $o ) > ( $i > $o ) > $o] :
~ ( ~ ~ ( ~ ( SX0 @ ( sK1_Xx @ SX0 ) @ ( sK2_SY4 @ SX0 ) )
| ~ ( SX0 @ ( sK2_SY4 @ SX0 ) @ ( sK3_SY6 @ SX0 ) ) )
| ~ ~ ( SX0 @ ( sK1_Xx @ SX0 ) @ ( sK3_SY6 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ( ~ ~ ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK2_SY4 @ SV1 ) )
| ~ ( SV1 @ ( sK2_SY4 @ SV1 ) @ ( sK3_SY6 @ SV1 ) ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK3_SY6 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ~ ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK2_SY4 @ SV1 ) )
| ~ ( SV1 @ ( sK2_SY4 @ SV1 ) @ ( sK3_SY6 @ SV1 ) ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK3_SY6 @ SV1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(11,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK3_SY6 @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(13,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK3_SY6 @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(15,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK3_SY6 @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(20,plain,
$true = $false,
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SV9: $i > $o] : ^ [SV10: $i > $o] : $true ))]]) ).
thf(116,plain,
$false = $true,
inference(sim,[status(thm)],[20]) ).
thf(117,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV048^5 : 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
% 0.07/0.20 % Computer : n010.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 15:40:10 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.25
% 0.07/0.25 No.of.Axioms: 0
% 0.07/0.25
% 0.07/0.25 Length.of.Defs: 0
% 0.07/0.25
% 0.07/0.25 Contains.Choice.Funs: false
% 0.07/0.25 ..
% 0.07/0.25
% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % 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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:116,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.07/0.25
% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25
% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 15 ****
% 0.07/0.25 %**** clause counter: 116 ****
% 0.07/0.25
% 0.07/0.25 % 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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:116,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------