%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU514^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 10:44:42 AM UTC 2026
% Result : Theorem 0.06s 0.20s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 27 unt; 0 typ; 1 def)
% Number of atoms : 184 ( 65 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 330 ( 41 ~; 54 |; 0 &; 222 @)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 87 ( 0 ^; 87 !; 0 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY11,type,
sK2_SY11: $i ).
thf(tp_sK3_SY14,type,
sK3_SY14: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(1,conjecture,
( setadjoinAx
=> ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(2,negated_conjecture,
( ( setadjoinAx
=> ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,setadjoinAx]) ).
thf(4,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,setadjoinAx]) ).
thf(10,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,setadjoinAx]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY9: $i,SY10: $i] :
~ ( ~ ( ~ ( in @ SY10 @ ( setadjoin @ SV1 @ SY9 ) )
| ( SY10 = SV1 )
| ( in @ SY10 @ SY9 ) )
| ~ ( ~ ( ( SY10 = SV1 )
| ( in @ SY10 @ SY9 ) )
| ( in @ SY10 @ ( setadjoin @ SV1 @ SY9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SY11: $i,SY12: $i] :
( ~ ( in @ SY12 @ SY11 )
| ( in @ SY12 @ ( setadjoin @ sK1_SX0 @ SY11 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY13: $i] :
~ ( ~ ( ~ ( in @ SY13 @ ( setadjoin @ SV1 @ SV2 ) )
| ( SY13 = SV1 )
| ( in @ SY13 @ SV2 ) )
| ~ ( ~ ( ( SY13 = SV1 )
| ( in @ SY13 @ SV2 ) )
| ( in @ SY13 @ ( setadjoin @ SV1 @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SY14: $i] :
( ~ ( in @ SY14 @ sK2_SY11 )
| ( in @ SY14 @ ( setadjoin @ sK1_SX0 @ sK2_SY11 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) )
| ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) )
| ~ ( ~ ( ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) )
| ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( in @ sK3_SY14 @ sK2_SY11 )
| ( in @ sK3_SY14 @ ( setadjoin @ sK1_SX0 @ sK2_SY11 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(18,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ~ ( ~ ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) )
| ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) )
| ~ ( ~ ( ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) )
| ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( in @ sK3_SY14 @ sK2_SY11 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( in @ sK3_SY14 @ ( setadjoin @ sK1_SX0 @ sK2_SY11 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ~ ( ~ ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) )
| ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ~ ( ~ ( ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) )
| ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( in @ sK3_SY14 @ sK2_SY11 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) )
| ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ~ ( ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) )
| ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) ) )
= $true )
| ( ( ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) ) )
= $true )
| ( ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) )
= $false )
| ( ( ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ( SV3 = SV1 )
| ( in @ SV3 @ SV2 ) )
= $false )
| ( ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( SV3 = SV1 )
= $true )
| ( ( in @ SV3 @ SV2 )
= $true )
| ( ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( SV3 = SV1 )
= $false )
| ( ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(32,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( setadjoin @ SV1 @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,32,31,30,23]) ).
thf(34,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU514^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n014.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 15:27:18 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.20
% 0.06/0.20 No.of.Axioms: 0
% 0.06/0.20
% 0.06/0.20 Length.of.Defs: 200
% 0.06/0.20
% 0.06/0.20 Contains.Choice.Funs: false
% 0.06/0.20 .
% 0.06/0.20
% 0.06/0.20 ********************************
% 0.06/0.20 * All subproblems solved! *
% 0.06/0.20 ********************************
% 0.06/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,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:33,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.20
% 0.06/0.20 %**** Beginning of derivation protocol ****
% 0.06/0.20 % SZS output start CNFRefutation
% See solution above
% 0.06/0.20
% 0.06/0.20 %**** End of derivation protocol ****
% 0.06/0.20 %**** no. of clauses in derivation: 34 ****
% 0.06/0.20 %**** clause counter: 33 ****
% 0.06/0.20
% 0.06/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,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:33,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------