%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU782^2 : 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 10:48:13 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 105 ( 43 unt; 0 typ; 5 def)
% Number of atoms : 851 ( 241 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 1276 ( 166 ~; 274 |; 0 &; 779 @)
% ( 0 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 316 ( 5 ^; 311 !; 0 ?; 316 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_binunionEcases,type,
binunionEcases: $o ).
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_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY35,type,
sK2_SY35: $i ).
thf(tp_sK3_SY41,type,
sK3_SY41: $i ).
thf(tp_sK4_SY39,type,
sK4_SY39: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetE,type,
subsetE: $o ).
thf(tp_subsetI1,type,
subsetI1: $o ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
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(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetI1,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(1,conjecture,
( subsetI1
=> ( subsetE
=> ( binunionEcases
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionprop) ).
thf(2,negated_conjecture,
( ( subsetI1
=> ( subsetE
=> ( binunionEcases
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) )
=> ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( subset @ SY6 @ ( cartprod @ SY0 @ SY0 ) )
=> ( subset @ ( binunion @ SY1 @ SY6 ) @ ( cartprod @ SY0 @ SY0 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binunionEcases,breln,breln1,subsetE,subsetI1]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( subset @ SY6 @ ( cartprod @ SY0 @ SY0 ) )
=> ( subset @ ( binunion @ SY1 @ SY6 ) @ ( cartprod @ SY0 @ SY0 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( subset @ SY6 @ ( cartprod @ SY0 @ SY0 ) )
=> ( subset @ ( binunion @ SY1 @ SY6 ) @ ( cartprod @ SY0 @ SY0 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( subset @ SY6 @ ( cartprod @ SY0 @ SY0 ) )
=> ( subset @ ( binunion @ SY1 @ SY6 ) @ ( cartprod @ SY0 @ SY0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ ( cartprod @ SX0 @ SX0 ) )
| ! [SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX0 ) )
| ( subset @ ( binunion @ SX1 @ SX2 ) @ ( cartprod @ SX0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,binunionEcases,breln,breln1,subsetE,subsetI1]) ).
thf(14,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $o] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) )
= $true ),
inference(unfold_def,[status(thm)],[9,binunionEcases,breln,breln1,subsetE,subsetI1]) ).
thf(15,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,binunionEcases,breln,breln1,subsetE,subsetI1]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,binunionEcases,breln,breln1,subsetE,subsetI1]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ ( cartprod @ SX0 @ SX0 ) )
| ! [SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX0 ) )
| ( subset @ ( binunion @ SX1 @ SX2 ) @ ( cartprod @ SX0 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV1: $i] :
( ( ! [SY28: $i,SY29: $i,SY30: $o] :
( ~ ( in @ SY29 @ ( binunion @ SV1 @ SY28 ) )
| ~ ( ~ ( in @ SY29 @ SV1 )
| SY30 )
| ~ ( ~ ( in @ SY29 @ SY28 )
| SY30 )
| SY30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV2: $i] :
( ( ! [SY31: $i] :
( ~ ! [SY32: $i] :
( ~ ( in @ SY32 @ SV2 )
| ( in @ SY32 @ SY31 ) )
| ( subset @ SV2 @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV3: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ( subset @ SV3 @ SY33 )
| ~ ( in @ SY34 @ SV3 )
| ( in @ SY34 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [SY35: $i] :
( ~ ( subset @ SY35 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) )
| ! [SY36: $i] :
( ~ ( subset @ SY36 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) )
| ( subset @ ( binunion @ SY35 @ SY36 ) @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(22,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY37: $i,SY38: $o] :
( ~ ( in @ SY37 @ ( binunion @ SV1 @ SV4 ) )
| ~ ( ~ ( in @ SY37 @ SV1 )
| SY38 )
| ~ ( ~ ( in @ SY37 @ SV4 )
| SY38 )
| SY38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV2 )
| ( in @ SY39 @ SV5 ) )
| ( subset @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY40: $i] :
( ~ ( subset @ SV3 @ SV6 )
| ~ ( in @ SY40 @ SV3 )
| ( in @ SY40 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( subset @ sK2_SY35 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) )
| ! [SY41: $i] :
( ~ ( subset @ SY41 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) )
| ( subset @ ( binunion @ sK2_SY35 @ SY41 ) @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(26,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ! [SY42: $o] :
( ~ ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
| ~ ( ~ ( in @ SV7 @ SV1 )
| SY42 )
| ~ ( ~ ( in @ SV7 @ SV4 )
| SY42 )
| SY42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV2 )
| ( in @ SY39 @ SV5 ) ) )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ SV6 )
| ~ ( in @ SV8 @ SV3 )
| ( in @ SV8 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( subset @ sK2_SY35 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ! [SY41: $i] :
( ~ ( subset @ SY41 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) )
| ( subset @ ( binunion @ sK2_SY35 @ SY41 ) @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(31,plain,
! [SV9: $o,SV4: $i,SV1: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
| ~ ( ~ ( in @ SV7 @ SV1 )
| SV9 )
| ~ ( ~ ( in @ SV7 @ SV4 )
| SV9 )
| SV9 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
| ~ ( ~ ( in @ SV7 @ SV1 )
| $true )
| ~ ( ~ ( in @ SV7 @ SV4 )
| $true )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
| ~ ( ~ ( in @ SV7 @ SV1 )
| $false )
| ~ ( ~ ( in @ SV7 @ SV4 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SY39: $i] :
( ~ ( in @ SY39 @ SV2 )
| ( in @ SY39 @ SV5 ) ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV8 @ SV3 )
| ( in @ SV8 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(36,plain,
( ( subset @ sK2_SY35 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(37,plain,
( ( ~ ( subset @ sK3_SY41 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) )
| ( subset @ ( binunion @ sK2_SY35 @ sK3_SY41 ) @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(38,plain,
! [SV9: $o,SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV7 @ SV1 )
| SV9 )
| ~ ( ~ ( in @ SV7 @ SV4 )
| SV9 )
| SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV7 @ SV1 )
| $true )
| ~ ( ~ ( in @ SV7 @ SV4 )
| $true )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV7 @ SV1 )
| $false )
| ~ ( ~ ( in @ SV7 @ SV4 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(41,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK4_SY39 @ SV5 @ SV2 ) @ SV2 )
| ( in @ ( sK4_SY39 @ SV5 @ SV2 ) @ SV5 ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(42,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV6 )
= $false )
| ( ( ~ ( in @ SV8 @ SV3 )
| ( in @ SV8 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(43,plain,
( ( ~ ( subset @ sK3_SY41 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(44,plain,
( ( subset @ ( binunion @ sK2_SY35 @ sK3_SY41 ) @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(45,plain,
! [SV9: $o,SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV1 )
| SV9 )
| ~ ( ~ ( in @ SV7 @ SV4 )
| SV9 )
| SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV1 )
| $true )
| ~ ( ~ ( in @ SV7 @ SV4 )
| $true )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV1 )
| $false )
| ~ ( ~ ( in @ SV7 @ SV4 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK4_SY39 @ SV5 @ SV2 ) @ SV2 ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(49,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ ( sK4_SY39 @ SV5 @ SV2 ) @ SV5 )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(50,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV3 ) )
= $true )
| ( ( in @ SV8 @ SV6 )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(51,plain,
( ( subset @ sK3_SY41 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(52,plain,
! [SV4: $i,SV9: $o,SV1: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV1 )
| SV9 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| SV9 )
| SV9 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV1 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $true )
| $true )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV1 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $false )
| $false )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ ( sK4_SY39 @ SV5 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(56,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( in @ SV8 @ SV3 )
= $false )
| ( ( in @ SV8 @ SV6 )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV4: $i,SV9: $o,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 )
| SV9 )
= $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| SV9 )
| SV9 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $true )
| $true )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $false )
| $false )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV9: $o,SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| SV9 )
| SV9 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(61,plain,
! [SV1: $i,SV4: $i,SV7: $i,SV9: $o] :
( ( SV9 = $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| SV9 )
| SV9 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $true )
| $true )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $true )
| $true )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(64,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $false )
| $false )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(65,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $false )
| $false )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV9: $o,SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $true )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| SV9 )
| SV9 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(67,plain,
! [SV1: $i,SV9: $o,SV4: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| SV9 ) )
= $true )
| ( SV9 = $true )
| ( SV9 = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $true )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $true )
| $true )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(69,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $true )
| ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $false )
| $false )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV1: $i,SV9: $o,SV4: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| SV9 ) )
= $true )
| ( SV9 = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV1: $i,SV9: $o,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 )
| SV9 )
= $false )
| ( SV9 = $true )
| ( SV9 = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV4 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV1: $i,SV9: $o,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 )
| SV9 )
= $false )
| ( SV9 = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV1: $i,SV9: $o,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 ) )
= $false )
| ( SV9 = $true )
| ( SV9 = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(80,plain,
! [SV4: $i,SV1: $i,SV7: $i,SV9: $o] :
( ( SV9 = $false )
| ( SV9 = $true )
| ( SV9 = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(81,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(83,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(84,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(86,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(87,plain,
! [SV1: $i,SV9: $o,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 ) )
= $false )
| ( SV9 = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(88,plain,
! [SV4: $i,SV1: $i,SV7: $i,SV9: $o] :
( ( SV9 = $false )
| ( SV9 = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(89,plain,
! [SV1: $i,SV9: $o,SV4: $i,SV7: $i] :
( ( ( in @ SV7 @ SV4 )
= $true )
| ( SV9 = $true )
| ( SV9 = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(90,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(91,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(92,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( in @ SV7 @ SV4 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(93,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV4 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(94,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(95,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( in @ SV7 @ SV4 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(96,plain,
! [SV1: $i,SV9: $o,SV4: $i,SV7: $i] :
( ( ( in @ SV7 @ SV4 )
= $true )
| ( SV9 = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(97,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( in @ SV7 @ SV4 )
= $true )
| ( $true = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(98,plain,
! [SV1: $i,SV4: $i,SV7: $i] :
( ( ( in @ SV7 @ SV4 )
= $true )
| ( $false = $true )
| ( ( in @ SV7 @ SV1 )
= $true )
| ( ( in @ SV7 @ ( binunion @ SV1 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(99,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,98,97,96,95,94,92,91,89,88,86,83,80,56,55,51,49,44]) ).
thf(100,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU782^2 : 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
% 0.09/0.17 % Computer : n008.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 15:35:09 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.23
% 0.09/0.23 No.of.Axioms: 0
% 0.09/0.23
% 0.09/0.23 Length.of.Defs: 889
% 0.09/0.23
% 0.09/0.23 Contains.Choice.Funs: false
% 0.09/0.23 ..
% 0.09/0.23
% 0.09/0.23 ********************************
% 0.09/0.23 * All subproblems solved! *
% 0.09/0.23 ********************************
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:99,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.23
% 0.09/0.23 %**** Beginning of derivation protocol ****
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23
% 0.09/0.23 %**** End of derivation protocol ****
% 0.09/0.23 %**** no. of clauses in derivation: 100 ****
% 0.09/0.23 %**** clause counter: 99 ****
% 0.09/0.23
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:99,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------