%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU813^2 : 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 : n007.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 10:48:48 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 81 ( 55 unt; 0 typ; 5 def)
% Number of atoms : 467 ( 110 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 928 ( 142 ~; 106 |; 8 &; 620 @)
% ( 0 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 180 ( 1 ^; 179 !; 0 ?; 180 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binintersectEL,type,
binintersectEL: $o ).
thf(tp_binintersectER,type,
binintersectER: $o ).
thf(tp_binintersectSubset5,type,
binintersectSubset5: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY40,type,
sK2_SY40: $i ).
thf(tp_sK3_SY44,type,
sK3_SY44: $i ).
thf(tp_sK4_SY15,type,
sK4_SY15: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_transitiveset,type,
transitiveset: $i > $o ).
thf(tp_transitivesetOp1,type,
transitivesetOp1: $o ).
thf(binintersectEL,definition,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(binintersectSubset5,definition,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(transitiveset,definition,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(transitivesetOp1,definition,
( transitivesetOp1
= ( ! [X: $i] :
( ( transitiveset @ X )
=> ! [A: $i] :
( ( in @ A @ X )
=> ( subset @ A @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivesetOp1) ).
thf(1,conjecture,
( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X: $i] :
( ( transitiveset @ X )
=> ! [Y: $i] :
( ( transitiveset @ Y )
=> ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintTransitive) ).
thf(2,negated_conjecture,
( ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X: $i] :
( ( transitiveset @ X )
=> ! [Y: $i] :
( ( transitiveset @ Y )
=> ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) )
=> ( ! [SY14: $i] :
( ! [SY15: $i] :
( ( in @ SY15 @ SY14 )
=> ( subset @ SY15 @ SY14 ) )
=> ! [A: $i] :
( ( in @ A @ SY14 )
=> ( subset @ A @ SY14 ) ) )
=> ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
=> ! [SY2: $i] :
( ! [SY3: $i] :
( ( in @ SY3 @ SY2 )
=> ( subset @ SY3 @ SY2 ) )
=> ! [SY4: $i] :
( ( in @ SY4 @ ( binintersect @ SY0 @ SY2 ) )
=> ( subset @ SY4 @ ( binintersect @ SY0 @ SY2 ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binintersectEL,binintersectER,binintersectSubset5,transitiveset,transitivesetOp1]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [SY14: $i] :
( ! [SY15: $i] :
( ( in @ SY15 @ SY14 )
=> ( subset @ SY15 @ SY14 ) )
=> ! [A: $i] :
( ( in @ A @ SY14 )
=> ( subset @ A @ SY14 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
=> ! [SY2: $i] :
( ! [SY3: $i] :
( ( in @ SY3 @ SY2 )
=> ( subset @ SY3 @ SY2 ) )
=> ! [SY4: $i] :
( ( in @ SY4 @ ( binintersect @ SY0 @ SY2 ) )
=> ( subset @ SY4 @ ( binintersect @ SY0 @ SY2 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ~ ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
=> ! [SY2: $i] :
( ! [SY3: $i] :
( ( in @ SY3 @ SY2 )
=> ( subset @ SY3 @ SY2 ) )
=> ! [SY4: $i] :
( ( in @ SY4 @ ( binintersect @ SY0 @ SY2 ) )
=> ( subset @ SY4 @ ( binintersect @ SY0 @ SY2 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY39: $i] :
( ~ ( in @ SY39 @ sK1_SY0 )
| ( subset @ SY39 @ sK1_SY0 ) )
& ! [SY43: $i] :
( ~ ( in @ SY43 @ sK2_SY40 )
| ( subset @ SY43 @ sK2_SY40 ) )
& ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
& ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ C @ A )
| ~ ( subset @ C @ B )
| ( subset @ C @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(13,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(14,plain,
( ( ! [SY14: $i] :
( ( ( in @ ( sK4_SY15 @ SY14 ) @ SY14 )
& ~ ( subset @ ( sK4_SY15 @ SY14 ) @ SY14 ) )
| ! [A: $i] :
( ~ ( in @ A @ SY14 )
| ( subset @ A @ SY14 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ! [SY14: $i] :
( ( ( in @ ( sK4_SY15 @ SY14 ) @ SY14 )
& ~ ( subset @ ( sK4_SY15 @ SY14 ) @ SY14 ) )
| ! [A: $i] :
( ~ ( in @ A @ SY14 )
| ( subset @ A @ SY14 ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ C @ A )
| ~ ( subset @ C @ B )
| ( subset @ C @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [SY39: $i] :
( ~ ( in @ SY39 @ sK1_SY0 )
| ( subset @ SY39 @ sK1_SY0 ) )
& ! [SY43: $i] :
( ~ ( in @ SY43 @ sK2_SY40 )
| ( subset @ SY43 @ sK2_SY40 ) )
& ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
& ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK4_SY15 @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK4_SY15 @ SX0 ) @ SX0 ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,binintersectEL,binintersectER,binintersectSubset5,transitiveset,transitivesetOp1]) ).
thf(21,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ( subset @ SX0 @ sK1_SY0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY40 )
| ( subset @ SX0 @ sK2_SY40 ) )
| ~ ~ ( ~ ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
| ~ ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,binintersectEL,binintersectER,binintersectSubset5,transitiveset,transitivesetOp1]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ~ ( in @ SY46 @ ( binintersect @ SV1 @ SY45 ) )
| ( in @ SY46 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ( in @ SY48 @ ( binintersect @ SV2 @ SY47 ) )
| ( in @ SY48 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( subset @ SY50 @ SV3 )
| ~ ( subset @ SY50 @ SY49 )
| ( subset @ SY50 @ ( binintersect @ SV3 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV4: $i] :
( ( ~ ( ~ ( in @ ( sK4_SY15 @ SV4 ) @ SV4 )
| ~ ~ ( subset @ ( sK4_SY15 @ SV4 ) @ SV4 ) )
| ! [SY51: $i] :
( ~ ( in @ SY51 @ SV4 )
| ( subset @ SY51 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ( subset @ SX0 @ sK1_SY0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY40 )
| ( subset @ SX0 @ sK2_SY40 ) )
| ~ ~ ( ~ ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
| ~ ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY52: $i] :
( ~ ( in @ SY52 @ ( binintersect @ SV1 @ SV5 ) )
| ( in @ SY52 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY53: $i] :
( ~ ( in @ SY53 @ ( binintersect @ SV2 @ SV6 ) )
| ( in @ SY53 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY54: $i] :
( ~ ( subset @ SY54 @ SV3 )
| ~ ( subset @ SY54 @ SV7 )
| ( subset @ SY54 @ ( binintersect @ SV3 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY15 @ SV4 ) @ SV4 )
| ~ ~ ( subset @ ( sK4_SY15 @ SV4 ) @ SV4 ) ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ SV4 )
| ( subset @ SY51 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ( subset @ SX0 @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(32,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY40 )
| ( subset @ SX0 @ sK2_SY40 ) )
| ~ ~ ( ~ ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
| ~ ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(33,plain,
! [SV5: $i,SV1: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ ( binintersect @ SV1 @ SV5 ) )
| ( in @ SV8 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV6: $i,SV2: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ ( binintersect @ SV2 @ SV6 ) )
| ( in @ SV9 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV7: $i,SV3: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV3 )
| ~ ( subset @ SV10 @ SV7 )
| ( subset @ SV10 @ ( binintersect @ SV3 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV4: $i] :
( ( ( ~ ( in @ ( sK4_SY15 @ SV4 ) @ SV4 )
| ~ ~ ( subset @ ( sK4_SY15 @ SV4 ) @ SV4 ) )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ SV4 )
| ( subset @ SY51 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ( subset @ SX0 @ sK1_SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(38,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY40 )
| ( subset @ SX0 @ sK2_SY40 ) )
| ~ ~ ( ~ ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
| ~ ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(39,plain,
! [SV5: $i,SV1: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( binintersect @ SV1 @ SV5 ) ) )
= $true )
| ( ( in @ SV8 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV6: $i,SV2: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( binintersect @ SV2 @ SV6 ) ) )
= $true )
| ( ( in @ SV9 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV7: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV3 ) )
= $true )
| ( ( ~ ( subset @ SV10 @ SV7 )
| ( subset @ SV10 @ ( binintersect @ SV3 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV4: $i] :
( ( ( ~ ( in @ ( sK4_SY15 @ SV4 ) @ SV4 ) )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ SV4 )
| ( subset @ SY51 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(43,plain,
! [SV4: $i] :
( ( ( ~ ~ ( subset @ ( sK4_SY15 @ SV4 ) @ SV4 ) )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ SV4 )
| ( subset @ SY51 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(44,plain,
! [SV11: $i] :
( ( ~ ( in @ SV11 @ sK1_SY0 )
| ( subset @ SV11 @ sK1_SY0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY40 )
| ( subset @ SX0 @ sK2_SY40 ) )
| ~ ~ ( ~ ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
| ~ ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV5: $i,SV1: $i,SV8: $i] :
( ( ( in @ SV8 @ ( binintersect @ SV1 @ SV5 ) )
= $false )
| ( ( in @ SV8 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV6: $i,SV2: $i,SV9: $i] :
( ( ( in @ SV9 @ ( binintersect @ SV2 @ SV6 ) )
= $false )
| ( ( in @ SV9 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV7: $i,SV3: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV3 )
= $false )
| ( ( ~ ( subset @ SV10 @ SV7 )
| ( subset @ SV10 @ ( binintersect @ SV3 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV4: $i] :
( ( ( in @ ( sK4_SY15 @ SV4 ) @ SV4 )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ SV4 )
| ( subset @ SY51 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(50,plain,
! [SV4: $i] :
( ( ( ~ ( subset @ ( sK4_SY15 @ SV4 ) @ SV4 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ SV4 )
| ( subset @ SY51 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(51,plain,
! [SV11: $i] :
( ( ( ~ ( in @ SV11 @ sK1_SY0 ) )
= $true )
| ( ( subset @ SV11 @ sK1_SY0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(52,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY40 )
| ( subset @ SX0 @ sK2_SY40 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(53,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
| ~ ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(54,plain,
! [SV3: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV7 ) )
= $true )
| ( ( subset @ SV10 @ ( binintersect @ SV3 @ SV7 ) )
= $true )
| ( ( subset @ SV10 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV4: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV4 )
| ( subset @ SV12 @ SV4 ) )
= $true )
| ( ( in @ ( sK4_SY15 @ SV4 ) @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV4: $i] :
( ( ( subset @ ( sK4_SY15 @ SV4 ) @ SV4 )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( in @ SY51 @ SV4 )
| ( subset @ SY51 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV11: $i] :
( ( ( in @ SV11 @ sK1_SY0 )
= $false )
| ( ( subset @ SV11 @ sK1_SY0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(58,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK2_SY40 )
| ( subset @ SX0 @ sK2_SY40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(59,plain,
( ( ~ ( ~ ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
| ~ ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(60,plain,
! [SV3: $i,SV7: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV7 )
= $false )
| ( ( subset @ SV10 @ ( binintersect @ SV3 @ SV7 ) )
= $true )
| ( ( subset @ SV10 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV4: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV4 ) )
= $true )
| ( ( subset @ SV12 @ SV4 )
= $true )
| ( ( in @ ( sK4_SY15 @ SV4 ) @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV4: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV4 )
| ( subset @ SV13 @ SV4 ) )
= $true )
| ( ( subset @ ( sK4_SY15 @ SV4 ) @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV14: $i] :
( ( ~ ( in @ SV14 @ sK2_SY40 )
| ( subset @ SV14 @ sK2_SY40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(64,plain,
( ( ~ ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
| ~ ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV4: $i,SV12: $i] :
( ( ( in @ SV12 @ SV4 )
= $false )
| ( ( subset @ SV12 @ SV4 )
= $true )
| ( ( in @ ( sK4_SY15 @ SV4 ) @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV4: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV4 ) )
= $true )
| ( ( subset @ SV13 @ SV4 )
= $true )
| ( ( subset @ ( sK4_SY15 @ SV4 ) @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV14: $i] :
( ( ( ~ ( in @ SV14 @ sK2_SY40 ) )
= $true )
| ( ( subset @ SV14 @ sK2_SY40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
( ( ~ ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
( ( ~ ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(70,plain,
! [SV4: $i,SV13: $i] :
( ( ( in @ SV13 @ SV4 )
= $false )
| ( ( subset @ SV13 @ SV4 )
= $true )
| ( ( subset @ ( sK4_SY15 @ SV4 ) @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV14: $i] :
( ( ( in @ SV14 @ sK2_SY40 )
= $false )
| ( ( subset @ SV14 @ sK2_SY40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(72,plain,
( ( in @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(73,plain,
( ( ~ ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(74,plain,
( ( subset @ sK3_SY44 @ ( binintersect @ sK1_SY0 @ sK2_SY40 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(75,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[46,74,72,71,70,65,60,57,47]) ).
thf(76,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU813^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:34:53 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 0
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 1007
% 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:1,axioms:4,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:75,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 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: 76 ****
% 0.07/0.22 %**** clause counter: 75 ****
% 0.07/0.22
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:75,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------