%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU584^2 : 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 : n011.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 10:45:21 AM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 28 unt; 0 typ; 3 def)
% Number of atoms : 144 ( 37 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 292 ( 28 ~; 20 |; 2 &; 225 @)
% ( 0 <=>; 17 =>; 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 : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 2 ^; 63 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY12,type,
sK2_SY12: $i ).
thf(tp_sK3_SY14,type,
sK3_SY14: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionI,type,
setunionI: $o ).
thf(tp_upairset2IR,type,
upairset2IR: $o ).
thf(binunion,definition,
( binunion
= ( ^ [Xx: $i,Xy: $i] : ( setunion @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunion) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(1,conjecture,
( setunionI
=> ( upairset2IR
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(2,negated_conjecture,
( ( setunionI
=> ( upairset2IR
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2 @ SY1 )
=> ( in @ SY2 @ ( setunion @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binunion,setunionI,upairset2IR]) ).
thf(4,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2 @ SY1 )
=> ( in @ SY2 @ ( setunion @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2 @ SY1 )
=> ( in @ SY2 @ ( setunion @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( in @ sK3_SY14 @ sK2_SY12 )
& ~ ( in @ sK3_SY14 @ ( setunion @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY12 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A )
| ( in @ Xx @ ( setunion @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A )
| ( in @ Xx @ ( setunion @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ( in @ sK3_SY14 @ sK2_SY12 )
& ~ ( in @ sK3_SY14 @ ( setunion @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY12 @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ( ~ ( in @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( in @ sK3_SY14 @ ( setunion @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY12 @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,binunion,setunionI,upairset2IR]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY15: $i] : ( in @ SY15 @ ( setadjoin @ SV1 @ ( setadjoin @ SY15 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(15,plain,
! [SV2: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ~ ( in @ SY16 @ SY17 )
| ~ ( in @ SY17 @ SV2 )
| ( in @ SY16 @ ( setunion @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
( ( ~ ( in @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( in @ sK3_SY14 @ ( setunion @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY12 @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: $i,SV3: $i] :
( ( in @ SV3 @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i,SV4: $i] :
( ( ! [SY18: $i] :
( ~ ( in @ SV4 @ SY18 )
| ~ ( in @ SY18 @ SV2 )
| ( in @ SV4 @ ( setunion @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( in @ sK3_SY14 @ sK2_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ~ ( in @ sK3_SY14 @ ( setunion @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY12 @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(21,plain,
! [SV2: $i,SV5: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV5 )
| ~ ( in @ SV5 @ SV2 )
| ( in @ SV4 @ ( setunion @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( in @ sK3_SY14 @ sK2_SY12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( in @ sK3_SY14 @ ( setunion @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY12 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV5 ) )
= $true )
| ( ( ~ ( in @ SV5 @ SV2 )
| ( in @ SV4 @ ( setunion @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( in @ sK3_SY14 @ ( setunion @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY12 @ emptyset ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV2: $i,SV5: $i,SV4: $i] :
( ( ( in @ SV4 @ SV5 )
= $false )
| ( ( ~ ( in @ SV5 @ SV2 )
| ( in @ SV4 @ ( setunion @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV2 ) )
= $true )
| ( ( in @ SV4 @ ( setunion @ SV2 ) )
= $true )
| ( ( in @ SV4 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(28,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ SV4 @ ( setunion @ SV2 ) )
= $true )
| ( ( in @ SV4 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,28,25,22]) ).
thf(30,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU584^2 : 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
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:28:36 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.23
% 0.07/0.23 No.of.Axioms: 0
% 0.07/0.23
% 0.07/0.23 Length.of.Defs: 557
% 0.07/0.23
% 0.07/0.23 Contains.Choice.Funs: false
% 0.07/0.23
% 0.07/0.23 ********************************
% 0.07/0.23 * All subproblems solved! *
% 0.07/0.23 ********************************
% 0.07/0.23 % 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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:29,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.23
% 0.07/0.23 %**** Beginning of derivation protocol ****
% 0.07/0.23 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23
% 0.07/0.23 %**** End of derivation protocol ****
% 0.07/0.23 %**** no. of clauses in derivation: 30 ****
% 0.07/0.23 %**** clause counter: 29 ****
% 0.07/0.23
% 0.07/0.23 % 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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:29,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------