%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU775^2 : 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 : 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 10:48:12 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 28 unt; 0 typ; 4 def)
% Number of atoms : 129 ( 39 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 352 ( 14 ~; 5 |; 2 &; 323 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 90 ( 59 ^; 31 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_breln1,type,
breln1: $i > $i > $o ).
thf(tp_breln1invset,type,
breln1invset: $i > $i > $i ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY35,type,
sK2_SY35: $i ).
thf(tp_sK3_E,type,
sK3_E: ( $i > $i > $o ) > $i ).
thf(tp_sK4_E,type,
sK4_E: ( $i > $i > $o ) > $i ).
thf(tp_setOfPairsIsBReln1,type,
setOfPairsIsBReln1: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(breln1,definition,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1) ).
thf(breln1invset,definition,
( breln1invset
= ( ^ [A: $i,R: $i] :
( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invset) ).
thf(setOfPairsIsBReln1,definition,
( setOfPairsIsBReln1
= ( ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln1) ).
thf(1,conjecture,
( setOfPairsIsBReln1
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invprop) ).
thf(2,negated_conjecture,
( ( setOfPairsIsBReln1
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY15: $i,SY16: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY15 @ SY15
@ ^ [Xx: $i,Xy: $i] : ( SY16 @ Xx @ Xy ) )
@ ( cartprod @ SY15 @ SY15 ) )
=> ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ( subset
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [SY13: $i,SY14: $i] : ( in @ ( kpair @ SY14 @ SY13 ) @ SY1 ) )
@ ( cartprod @ SY0 @ SY0 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,breln,breln1,breln1invset,setOfPairsIsBReln1]) ).
thf(4,plain,
( ( ! [SY15: $i,SY16: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY15 @ SY15
@ ^ [Xx: $i,Xy: $i] : ( SY16 @ Xx @ Xy ) )
@ ( cartprod @ SY15 @ SY15 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ( subset
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [SY13: $i,SY14: $i] : ( in @ ( kpair @ SY14 @ SY13 ) @ SY1 ) )
@ ( cartprod @ SY0 @ SY0 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ( subset
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [SY13: $i,SY14: $i] : ( in @ ( kpair @ SY14 @ SY13 ) @ SY1 ) )
@ ( cartprod @ SY0 @ SY0 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( subset @ sK2_SY35 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
& ~ ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SY38: $i,SY39: $i] : ( in @ ( kpair @ SY39 @ SY38 ) @ sK2_SY35 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY15: $i,SY16: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY15 @ SY15
@ ^ [Xx: $i,Xy: $i] : ( SY16 @ Xx @ Xy ) )
@ ( cartprod @ SY15 @ SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(9,plain,
( ( ( subset @ sK2_SY35 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
& ~ ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SY38: $i,SY39: $i] : ( in @ ( kpair @ SY39 @ SY38 ) @ sK2_SY35 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ( subset @ sK2_SY35 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
| ~ ~ ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY35 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,breln,breln1,breln1invset,setOfPairsIsBReln1]) ).
thf(11,plain,
! [SV1: $i] :
( ( ! [SY40: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV1 @ SV1
@ ^ [Xx: $i,Xy: $i] : ( SY40 @ Xx @ Xy ) )
@ ( cartprod @ SV1 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ( subset @ sK2_SY35 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
| ~ ~ ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY35 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV2: $i > $i > $o,SV1: $i] :
( ( subset
@ ( dpsetconstr @ SV1 @ SV1
@ ^ [SY43: $i,SY44: $i] : ( SV2 @ SY43 @ SY44 ) )
@ ( cartprod @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( subset @ sK2_SY35 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ~ ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY35 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(16,plain,
( ( subset @ sK2_SY35 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY35 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY35 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV3: $i > $i > $o,SV4: $i] :
( ( subset
@ ( dpsetconstr @ SV4 @ SV4
@ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) )
@ ( cartprod @ SV4 @ SV4 ) )
= $true ),
inference(rename,[status(thm)],[13]) ).
thf(20,plain,
! [SV3: $i > $i > $o,SV4: $i] :
( ( ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY35 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= ( subset
@ ( dpsetconstr @ SV4 @ SV4
@ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) )
@ ( cartprod @ SV4 @ SV4 ) ) )
= $false ),
inference(res,[status(thm)],[18,19]) ).
thf(21,plain,
( ( ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY35 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= ( subset @ sK2_SY35 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $false ),
inference(res,[status(thm)],[18,16]) ).
thf(22,plain,
( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY35 ) )
= sK2_SY35 )
= $false ),
inference(extuni,[status(esa)],[21]) ).
thf(23,plain,
! [SV3: $i > $i > $o] :
( ( ( in @ ( kpair @ ( sK4_E @ SV3 ) @ ( sK3_E @ SV3 ) ) @ sK2_SY35 )
= $true )
| ( ( SV3 @ ( sK3_E @ SV3 ) @ ( sK4_E @ SV3 ) )
= $true ) ),
inference(extuni,[status(esa)],[20:[bind(SV4,$thf( sK1_SY0 ))]]) ).
thf(24,plain,
! [SV3: $i > $i > $o] :
( ( ( in @ ( kpair @ ( sK4_E @ SV3 ) @ ( sK3_E @ SV3 ) ) @ sK2_SY35 )
= $false )
| ( ( SV3 @ ( sK3_E @ SV3 ) @ ( sK4_E @ SV3 ) )
= $false ) ),
inference(extuni,[status(esa)],[20:[bind(SV4,$thf( sK1_SY0 ))]]) ).
thf(25,plain,
! [SV3: $i > $i > $o] :
( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY35 ) )
= ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) ) )
= $false ),
inference(extuni,[status(esa)],[20:[bind(SV4,$thf( sK1_SY0 ))]]) ).
thf(26,plain,
! [SV3: $i > $i > $o,SV4: $i] :
( ( ( ( cartprod @ sK1_SY0 @ sK1_SY0 )
= ( cartprod @ SV4 @ SV4 ) )
= $false )
| ( ( ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY35 ) )
= ( dpsetconstr @ SV4 @ SV4
@ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[20]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,26,25,24,23,22,19,18]) ).
thf(30,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU775^2 : 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
% 0.07/0.17 % Computer : n008.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 15:34:54 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 0
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 718
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22 .
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % 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:29,loop_count:5,foatp_calls:2,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 28 ****
% 0.07/0.22 %**** clause counter: 29 ****
% 0.07/0.22
% 0.07/0.22 % 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:29,loop_count:5,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------