%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU771^2 : 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 : n013.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 10:48:09 AM UTC 2026
% Result : Theorem 5.19s 1.07s
% Output : CNFRefutation 5.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 19 unt; 0 typ; 3 def)
% Number of atoms : 65 ( 19 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 170 ( 3 ~; 0 |; 0 &; 164 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 54 usr; 4 con; 0-3 aty)
% Number of variables : 78 ( 41 ^; 37 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_breln1,type,
breln1: $i > $i > $o ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK10_E,type,
sK10_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK11_E,type,
sK11_E: ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK12_E,type,
sK12_E: ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK13_E,type,
sK13_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK14_E,type,
sK14_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK15_E,type,
sK15_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK16_E,type,
sK16_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK17_E,type,
sK17_E: ( $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK18_E,type,
sK18_E: ( $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK19_E,type,
sK19_E: ( $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK20_E,type,
sK20_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i ) > $i ).
thf(tp_sK21_E,type,
sK21_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK22_E,type,
sK22_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK23_E,type,
sK23_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK24_E,type,
sK24_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK25_E,type,
sK25_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK26_E,type,
sK26_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK27_E,type,
sK27_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK28_E,type,
sK28_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK29_E,type,
sK29_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK2_SY29,type,
sK2_SY29: $i > $i > $o ).
thf(tp_sK30_E,type,
sK30_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK31_E,type,
sK31_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK32_E,type,
sK32_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK33_E,type,
sK33_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK34_E,type,
sK34_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK35_E,type,
sK35_E: ( $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK36_E,type,
sK36_E: ( $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK37_E,type,
sK37_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $o ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK38_E,type,
sK38_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $o ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK39_E,type,
sK39_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK3_E,type,
sK3_E: ( $i > $i > $o ) > $i ).
thf(tp_sK40_E,type,
sK40_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK41_E,type,
sK41_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK42_E,type,
sK42_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK43_E,type,
sK43_E: ( $i > $i > $i > $i > $o ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK44_E,type,
sK44_E: ( $i > $i > $i > $i > $o ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK45_E,type,
sK45_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK46_E,type,
sK46_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK47_E,type,
sK47_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > ( $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK48_E,type,
sK48_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $o ) > ( $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK4_E,type,
sK4_E: ( $i > $i > $o ) > $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK7_E,type,
sK7_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK8_E,type,
sK8_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK9_E,type,
sK9_E: ( $i > $i > $i > $i > $i ) > ( $i > $i > $i > $i > $i > $i > $i > $i > $o ) > $i ).
thf(tp_setOfPairsIsBReln,type,
setOfPairsIsBReln: $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/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(breln1,definition,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1) ).
thf(setOfPairsIsBReln,definition,
( setOfPairsIsBReln
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(1,conjecture,
( setOfPairsIsBReln
=> ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln1) ).
thf(2,negated_conjecture,
( ( setOfPairsIsBReln
=> ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY8: $i,SY9: $i,SY10: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY8 @ SY9
@ ^ [Xx: $i,Xy: $i] : ( SY10 @ Xx @ Xy ) )
@ ( cartprod @ SY8 @ SY9 ) )
=> ! [SY0: $i,SY1: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [Xx: $i,Xy: $i] : ( SY1 @ Xx @ Xy ) )
@ ( cartprod @ SY0 @ SY0 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,breln,breln1,setOfPairsIsBReln]) ).
thf(4,plain,
( ( ! [SY8: $i,SY9: $i,SY10: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY8 @ SY9
@ ^ [Xx: $i,Xy: $i] : ( SY10 @ Xx @ Xy ) )
@ ( cartprod @ SY8 @ SY9 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i,SY1: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [Xx: $i,Xy: $i] : ( SY1 @ Xx @ Xy ) )
@ ( cartprod @ SY0 @ SY0 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [Xx: $i,Xy: $i] : ( SY1 @ Xx @ Xy ) )
@ ( cartprod @ SY0 @ SY0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SY32: $i,SY33: $i] : ( sK2_SY29 @ SY32 @ SY33 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY8: $i,SY9: $i,SY10: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY8 @ SY9
@ ^ [Xx: $i,Xy: $i] : ( SY10 @ Xx @ Xy ) )
@ ( cartprod @ SY8 @ SY9 ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(9,plain,
( ( ~ ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SY32: $i,SY33: $i] : ( sK2_SY29 @ SY32 @ SY33 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
! [SV1: $i] :
( ( ! [SY34: $i,SY35: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV1 @ SY34
@ ^ [Xx: $i,Xy: $i] : ( SY35 @ Xx @ Xy ) )
@ ( cartprod @ SV1 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(11,plain,
( ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SY32: $i,SY33: $i] : ( sK2_SY29 @ SY32 @ SY33 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY38: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [Xx: $i,Xy: $i] : ( SY38 @ Xx @ Xy ) )
@ ( cartprod @ SV1 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i] :
( ( subset
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY41: $i,SY42: $i] : ( SV3 @ SY41 @ SY42 ) )
@ ( cartprod @ SV1 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(14,plain,
! [SV4: $i > $i > $o,SV5: $i,SV6: $i] :
( ( subset
@ ( dpsetconstr @ SV6 @ SV5
@ ^ [SX0: $i,SX1: $i] : ( SV4 @ SX0 @ SX1 ) )
@ ( cartprod @ SV6 @ SV5 ) )
= $true ),
inference(rename,[status(thm)],[13]) ).
thf(15,plain,
! [SV4: $i > $i > $o,SV5: $i,SV6: $i] :
( ( ( subset
@ ( dpsetconstr @ SV6 @ SV5
@ ^ [SX0: $i,SX1: $i] : ( SV4 @ SX0 @ SX1 ) )
@ ( cartprod @ SV6 @ SV5 ) )
= ( subset
@ ( dpsetconstr @ sK1_SY0 @ sK1_SY0
@ ^ [SY32: $i,SY33: $i] : ( sK2_SY29 @ SY32 @ SY33 ) )
@ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $false ),
inference(res,[status(thm)],[14,11]) ).
thf(39,plain,
$false = $true,
inference(extuni,[status(esa)],[15:[bind(SV4,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( sK2_SY29 @ SX0 @ SX1 ) )),bind(SV5,$thf( sK1_SY0 )),bind(SV6,$thf( sK1_SY0 ))]]) ).
thf(40,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU771^2 : 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
% 0.12/0.16 % Computer : n013.cluster.edu
% 0.12/0.16 % Model : x86_64 x86_64
% 0.12/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.16 % Memory : 8046.5625MB
% 0.12/0.16 % OS : Linux 6.8.0-71-generic
% 0.12/0.16 % CPULimit : 300
% 0.12/0.16 % WCLimit : 300
% 0.12/0.16 % DateTime : Tue Oct 6 15:33:36 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.19/1.07
% 5.19/1.07 No.of.Axioms: 0
% 5.19/1.07
% 5.19/1.07 Length.of.Defs: 526
% 5.19/1.07
% 5.19/1.07 Contains.Choice.Funs: false
% 5.19/1.07 .........
% 5.19/1.07
% 5.19/1.07 ********************************
% 5.19/1.07 * All subproblems solved! *
% 5.19/1.07 ********************************
% 5.19/1.07 % SZS status Theorem for /export/starexec/sandbox2/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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:39,loop_count:2,foatp_calls:1,translation:fof_full)
% 5.19/1.07
% 5.19/1.07 %**** Beginning of derivation protocol ****
% 5.19/1.07 % SZS output start CNFRefutation
% See solution above
% 5.19/1.07
% 5.19/1.07 %**** End of derivation protocol ****
% 5.19/1.07 %**** no. of clauses in derivation: 17 ****
% 5.19/1.07 %**** clause counter: 39 ****
% 5.19/1.07
% 5.19/1.07 % SZS status Theorem for /export/starexec/sandbox2/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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:39,loop_count:2,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------