%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU572^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n003.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 10:45:15 AM UTC 2026
% Result : Theorem 0.13s 0.19s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 27 unt; 0 typ; 2 def)
% Number of atoms : 145 ( 36 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 232 ( 21 ~; 21 |; 0 &; 170 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 75 ( 0 ^; 75 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinSub,type,
setadjoinSub: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetTrans,type,
subsetTrans: $o ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(subsetTrans,definition,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(1,conjecture,
( subsetTrans
=> ( setadjoinSub
=> ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(2,negated_conjecture,
( ( subsetTrans
=> ( setadjoinSub
=> ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) )
=> ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) )
=> ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,setadjoinSub,subsetTrans]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ~ ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,setadjoinSub,subsetTrans]) ).
thf(12,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,setadjoinSub,subsetTrans]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY11: $i] : ( subset @ SY11 @ ( setadjoin @ SV1 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(14,plain,
! [SV2: $i] :
( ( ! [SY12: $i,SY13: $i] :
( ~ ( subset @ SV2 @ SY12 )
| ~ ( subset @ SY12 @ SY13 )
| ( subset @ SV2 @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV1: $i,SV3: $i] :
( ( subset @ SV3 @ ( setadjoin @ SV1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY14: $i] :
( ~ ( subset @ SV2 @ SV4 )
| ~ ( subset @ SV4 @ SY14 )
| ( subset @ SV2 @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [SY15: $i,SY16: $i] :
( ~ ( subset @ sK1_SX0 @ SY16 )
| ( subset @ sK1_SX0 @ ( setadjoin @ SY15 @ SY16 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(19,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ SV4 )
| ~ ( subset @ SV4 @ SV5 )
| ( subset @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ! [SY17: $i] :
( ~ ( subset @ sK1_SX0 @ SY17 )
| ( subset @ sK1_SX0 @ ( setadjoin @ sK2_SY15 @ SY17 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(21,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV4 ) )
= $true )
| ( ( ~ ( subset @ SV4 @ SV5 )
| ( subset @ SV2 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ( subset @ sK1_SX0 @ sK3_SY17 )
| ( subset @ sK1_SX0 @ ( setadjoin @ sK2_SY15 @ sK3_SY17 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(23,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( subset @ SV2 @ SV4 )
= $false )
| ( ( ~ ( subset @ SV4 @ SV5 )
| ( subset @ SV2 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ( subset @ sK1_SX0 @ sK3_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( subset @ sK1_SX0 @ ( setadjoin @ sK2_SY15 @ sK3_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV5 ) )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true )
| ( ( subset @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( subset @ sK1_SX0 @ sK3_SY17 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV2: $i,SV5: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV5 )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true )
| ( ( subset @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,28,27,25]) ).
thf(30,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU572^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.13/0.16 % Computer : n003.cluster.edu
% 0.13/0.16 % Model : x86_64 x86_64
% 0.13/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.16 % Memory : 8046.5625MB
% 0.13/0.16 % OS : Linux 6.8.0-71-generic
% 0.13/0.16 % CPULimit : 300
% 0.13/0.16 % WCLimit : 300
% 0.13/0.16 % DateTime : Tue Oct 6 15:30:09 UTC 2026
% 0.13/0.16 % CPUTime :
% 0.13/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.19
% 0.13/0.19 No.of.Axioms: 0
% 0.13/0.19
% 0.13/0.19 Length.of.Defs: 362
% 0.13/0.19
% 0.13/0.19 Contains.Choice.Funs: false
% 0.13/0.19
% 0.13/0.19 ********************************
% 0.13/0.19 * All subproblems solved! *
% 0.13/0.19 ********************************
% 0.13/0.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.19
% 0.13/0.19 %**** Beginning of derivation protocol ****
% 0.13/0.19 % SZS output start CNFRefutation
% See solution above
% 0.13/0.19
% 0.13/0.19 %**** End of derivation protocol ****
% 0.13/0.19 %**** no. of clauses in derivation: 30 ****
% 0.13/0.19 %**** clause counter: 29 ****
% 0.13/0.19
% 0.13/0.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:29,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------