%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU595^2 : 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 : n001.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 10:45:24 AM UTC 2026
% Result : Theorem 1.44s 0.51s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 25 unt; 0 typ; 2 def)
% Number of atoms : 119 ( 34 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 218 ( 20 ~; 11 |; 2 &; 174 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 10 con; 0-5 aty)
% Number of variables : 76 ( 25 ^; 51 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK10_E,type,
sK10_E: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK11_E,type,
sK11_E: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK12_E,type,
sK12_E: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK13_E,type,
sK13_E: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK14_E,type,
sK14_E: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK15_E,type,
sK15_E: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK16_E,type,
sK16_E: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK17_E,type,
sK17_E: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK18_E,type,
sK18_E: ( $i > $i ) > ( $i > $i ) > $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK19_E,type,
sK19_E: $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK20_E,type,
sK20_E: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_E,type,
sK4_E: $i ).
thf(tp_sK5_E,type,
sK5_E: $i ).
thf(tp_sK6_E,type,
sK6_E: ( $i > $o ) > $i ).
thf(tp_sK7_E,type,
sK7_E: ( $i > $i ) > ( $i > $i > $o ) > $i ).
thf(tp_sK8_E,type,
sK8_E: ( $i > $i ) > ( $i > $i > $i ) > $i ).
thf(tp_sK9_E,type,
sK9_E: ( $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $o ) > $i ).
thf(binintersect,definition,
( binintersect
= ( ^ [A: $i,B: $i] :
( dsetconstr @ A
@ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersect) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(1,conjecture,
( dsetconstrER
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(2,negated_conjecture,
( ( dsetconstrER
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2
@ ( dsetconstr @ SY0
@ ^ [SY5: $i] : ( in @ SY5 @ SY1 ) ) )
=> ( in @ SY2 @ SY1 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binintersect,dsetconstrER]) ).
thf(4,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2
@ ( dsetconstr @ SY0
@ ^ [SY5: $i] : ( in @ SY5 @ SY1 ) ) )
=> ( in @ SY2 @ SY1 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2
@ ( dsetconstr @ SY0
@ ^ [SY5: $i] : ( in @ SY5 @ SY1 ) ) )
=> ( in @ SY2 @ SY1 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SY18: $i] : ( in @ SY18 @ sK2_SY14 ) ) )
& ~ ( in @ sK3_SY17 @ sK2_SY14 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SY18: $i] : ( in @ SY18 @ sK2_SY14 ) ) )
& ~ ( in @ sK3_SY17 @ sK2_SY14 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ~ ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) )
| ~ ~ ( in @ sK3_SY17 @ sK2_SY14 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,binintersect,dsetconstrER]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY20: $i > $o,SY21: $i] :
( ~ ( in @ SY21
@ ( dsetconstr @ SV1
@ ^ [Xy: $i] : ( SY20 @ Xy ) ) )
| ( SY20 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) )
| ~ ~ ( in @ sK3_SY17 @ sK2_SY14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: $i > $o,SV1: $i] :
( ( ! [SY23: $i] :
( ~ ( in @ SY23
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV2 @ SY24 ) ) )
| ( SV2 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( in @ sK3_SY17 @ sK2_SY14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV2 @ SY24 ) ) )
| ( SV2 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( in @ sK3_SY17 @ sK2_SY14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV2 @ SY24 ) ) ) )
= $true )
| ( ( SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( in @ sK3_SY17 @ sK2_SY14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3
@ ( dsetconstr @ SV1
@ ^ [SY24: $i] : ( SV2 @ SY24 ) ) )
= $false )
| ( ( SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(68,plain,
! [SV20: $i > $o,SV21: $i,SV22: $i] :
( ( ( in @ SV22
@ ( dsetconstr @ SV21
@ ^ [SX0: $i] : ( SV20 @ SX0 ) ) )
= $false )
| ( ( SV20 @ SV22 )
= $true ) ),
inference(rename,[status(thm)],[22]) ).
thf(74,plain,
! [SV20: $i > $o,SV21: $i,SV22: $i] :
( ( ( ( in @ SV22
@ ( dsetconstr @ SV21
@ ^ [SX0: $i] : ( SV20 @ SX0 ) ) )
= ( in @ sK3_SY17
@ ( dsetconstr @ sK1_SY0
@ ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) ) ) )
= $false )
| ( ( SV20 @ SV22 )
= $true ) ),
inference(res,[status(thm)],[68,18]) ).
thf(94,plain,
( ( in @ sK3_SY17 @ sK2_SY14 )
= $true ),
inference(extuni,[status(esa)],[74:[bind(SV20,$thf( ^ [SX0: $i] : ( in @ SX0 @ sK2_SY14 ) )),bind(SV21,$thf( sK1_SY0 )),bind(SV22,$thf( sK3_SY17 ))]]) ).
thf(172,plain,
( ( ( in @ sK3_SY17 @ sK2_SY14 )
= ( in @ sK3_SY17 @ sK2_SY14 ) )
= $false ),
inference(res,[status(thm)],[94,21]) ).
thf(173,plain,
$false = $true,
inference(extuni,[status(esa)],[172]) ).
thf(174,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU595^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n001.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 15:34:54 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.44/0.51
% 1.44/0.51 No.of.Axioms: 0
% 1.44/0.51
% 1.44/0.51 Length.of.Defs: 389
% 1.44/0.51
% 1.44/0.51 Contains.Choice.Funs: false
% 1.44/0.51 ....
% 1.44/0.51
% 1.44/0.51 ********************************
% 1.44/0.51 * All subproblems solved! *
% 1.44/0.51 ********************************
% 1.44/0.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:173,loop_count:9,foatp_calls:3,translation:fof_full)
% 1.44/0.51
% 1.44/0.51 %**** Beginning of derivation protocol ****
% 1.44/0.51 % SZS output start CNFRefutation
% See solution above
% 1.44/0.51
% 1.44/0.51 %**** End of derivation protocol ****
% 1.44/0.51 %**** no. of clauses in derivation: 28 ****
% 1.44/0.51 %**** clause counter: 173 ****
% 1.44/0.51
% 1.44/0.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:173,loop_count:9,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------