%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO307^5 : 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 : n008.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 11:08:02 AM UTC 2026
% Result : Theorem 0.09s 0.20s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 18 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 273 ( 57 ~; 50 |; 18 &; 144 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 ^; 23 !; 4 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cR,type,
cR: $i > $o ).
thf(tp_cT,type,
cT: $i > $o ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_q,type,
q: $i > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: ( $i > $o ) > $i ).
thf(tp_sK2_SY4,type,
sK2_SY4: ( $i > $o ) > $i ).
thf(tp_sK3_SY6,type,
sK3_SY6: ( $i > $o ) > $i ).
thf(1,conjecture,
? [A: $i > $o] :
! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( A @ Xx )
| ( ( A @ Xy )
& ( A @ Xz ) ) )
=> ( ( ( p @ Xx )
& ( cR @ Xy ) )
| ( ( q @ Xx )
& ( cT @ Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE5F) ).
thf(2,negated_conjecture,
( ( ? [A: $i > $o] :
! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( A @ Xx )
| ( ( A @ Xy )
& ( A @ Xz ) ) )
=> ( ( ( p @ Xx )
& ( cR @ Xy ) )
| ( ( q @ Xx )
& ( cT @ Xz ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [A: $i > $o] :
! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( A @ Xx )
| ( ( A @ Xy )
& ( A @ Xz ) ) )
=> ( ( ( p @ Xx )
& ( cR @ Xy ) )
| ( ( q @ Xx )
& ( cT @ Xz ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [A: $i > $o] :
! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( A @ Xx )
| ( ( A @ Xy )
& ( A @ Xz ) ) )
=> ( ( ( p @ Xx )
& ( cR @ Xy ) )
| ( ( q @ Xx )
& ( cT @ Xz ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i > $o] :
( ( ( A @ ( sK2_SY4 @ A ) )
| ( A @ ( sK1_Xx @ A ) ) )
& ( ( A @ ( sK3_SY6 @ A ) )
| ( A @ ( sK1_Xx @ A ) ) )
& ( ~ ( cR @ ( sK2_SY4 @ A ) )
| ~ ( p @ ( sK1_Xx @ A ) ) )
& ( ~ ( cT @ ( sK3_SY6 @ A ) )
| ~ ( q @ ( sK1_Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [A: $i > $o] :
( ( ( A @ ( sK2_SY4 @ A ) )
| ( A @ ( sK1_Xx @ A ) ) )
& ( ( A @ ( sK3_SY6 @ A ) )
| ( A @ ( sK1_Xx @ A ) ) )
& ( ~ ( cR @ ( sK2_SY4 @ A ) )
| ~ ( p @ ( sK1_Xx @ A ) ) )
& ( ~ ( cT @ ( sK3_SY6 @ A ) )
| ~ ( q @ ( sK1_Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: $i > $o] :
~ ( ~ ~ ( ~ ( ( SX0 @ ( sK2_SY4 @ SX0 ) )
| ( SX0 @ ( sK1_Xx @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK3_SY6 @ SX0 ) )
| ( SX0 @ ( sK1_Xx @ SX0 ) ) ) )
| ~ ~ ( ~ ( ~ ( cR @ ( sK2_SY4 @ SX0 ) )
| ~ ( p @ ( sK1_Xx @ SX0 ) ) )
| ~ ( ~ ( cT @ ( sK3_SY6 @ SX0 ) )
| ~ ( q @ ( sK1_Xx @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: $i > $o] :
( ( ~ ( ~ ~ ( ~ ( ( SV1 @ ( sK2_SY4 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) )
| ~ ( ( SV1 @ ( sK3_SY6 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) ) )
| ~ ~ ( ~ ( ~ ( cR @ ( sK2_SY4 @ SV1 ) )
| ~ ( p @ ( sK1_Xx @ SV1 ) ) )
| ~ ( ~ ( cT @ ( sK3_SY6 @ SV1 ) )
| ~ ( q @ ( sK1_Xx @ SV1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i > $o] :
( ( ~ ~ ( ~ ( ( SV1 @ ( sK2_SY4 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) )
| ~ ( ( SV1 @ ( sK3_SY6 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) ) )
| ~ ~ ( ~ ( ~ ( cR @ ( sK2_SY4 @ SV1 ) )
| ~ ( p @ ( sK1_Xx @ SV1 ) ) )
| ~ ( ~ ( cT @ ( sK3_SY6 @ SV1 ) )
| ~ ( q @ ( sK1_Xx @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i > $o] :
( ( ~ ~ ( ~ ( ( SV1 @ ( sK2_SY4 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) )
| ~ ( ( SV1 @ ( sK3_SY6 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i > $o] :
( ( ~ ( ~ ( ( SV1 @ ( sK2_SY4 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) )
| ~ ( ( SV1 @ ( sK3_SY6 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(14,plain,
! [SV1: $i > $o] :
( ( ~ ( ( SV1 @ ( sK2_SY4 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) )
| ~ ( ( SV1 @ ( sK3_SY6 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV1: $i > $o] :
( ( ~ ( ( SV1 @ ( sK2_SY4 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(20,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK2_SY4 @ SV1 ) )
| ( SV1 @ ( sK1_Xx @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(24,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK2_SY4 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK1_Xx @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(33,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[24:[bind(SV1,$thf( ^ [SV4: $i] : $false ))]]) ).
thf(96,plain,
$false = $true,
inference(sim,[status(thm)],[33]) ).
thf(97,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO307^5 : 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
% 0.09/0.16 % Computer : n008.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 17:35:09 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.20
% 0.09/0.20 No.of.Axioms: 0
% 0.09/0.20
% 0.09/0.20 Length.of.Defs: 0
% 0.09/0.20
% 0.09/0.20 Contains.Choice.Funs: false
% 0.09/0.20 .
% 0.09/0.20
% 0.09/0.20 ********************************
% 0.09/0.20 * All subproblems solved! *
% 0.09/0.20 ********************************
% 0.09/0.20 % 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:96,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.09/0.20
% 0.09/0.20 %**** Beginning of derivation protocol ****
% 0.09/0.20 % SZS output start CNFRefutation
% See solution above
% 0.09/0.20
% 0.09/0.20 %**** End of derivation protocol ****
% 0.09/0.20 %**** no. of clauses in derivation: 18 ****
% 0.09/0.20 %**** clause counter: 96 ****
% 0.09/0.20
% 0.09/0.20 % 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:96,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------