%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU660^2 : 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 : n014.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 10:46:04 AM UTC 2026
% Result : Theorem 0.10s 0.18s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 52 ( 31 unt; 0 typ; 2 def)
% Number of atoms : 281 ( 114 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 686 ( 141 ~; 61 |; 8 &; 456 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 188 ( 0 ^; 180 !; 8 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_cartprodmempair1,type,
cartprodmempair1: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY29,type,
sK2_SY29: $i ).
thf(tp_sK3_SY35,type,
sK3_SY35: $i ).
thf(tp_sK4_SY37,type,
sK4_SY37: $i ).
thf(tp_sK5_SY33,type,
sK5_SY33: $i > $i > $i > $i ).
thf(tp_sK6_SY38,type,
sK6_SY38: $i > $i > $i > $i ).
thf(tp_setukpairinjR,type,
setukpairinjR: $o ).
thf(cartprodmempair1,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(setukpairinjR,definition,
( setukpairinjR
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).
thf(1,conjecture,
( cartprodmempair1
=> ( setukpairinjR
=> ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(2,negated_conjecture,
( ( cartprodmempair1
=> ( setukpairinjR
=> ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) )
=> ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cartprodmempair1,setukpairinjR]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ~ ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,cartprodmempair1,setukpairinjR]) ).
thf(12,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ( SX2
!= ( kpair @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,cartprodmempair1,setukpairinjR]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX3 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,cartprodmempair1,setukpairinjR]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY17: $i,SY18: $i,SY19: $i] :
( ( ( kpair @ SV1 @ SY17 )
!= ( kpair @ SY18 @ SY19 ) )
| ( SY17 = SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ~ ( in @ SY21 @ ( cartprod @ SV2 @ SY20 ) )
| ~ ! [SY22: $i] :
~ ~ ( ~ ( in @ SY22 @ SV2 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY20 )
| ( SY21
!= ( kpair @ SY22 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX3 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i,SV1: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ( ( kpair @ SV1 @ SV3 )
!= ( kpair @ SY24 @ SY25 ) )
| ( SV3 = SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY26: $i] :
( ~ ( in @ SY26 @ ( cartprod @ SV2 @ SV4 ) )
| ~ ! [SY27: $i] :
~ ~ ( ~ ( in @ SY27 @ SV2 )
| ~ ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ SV4 )
| ( SY26
!= ( kpair @ SY27 @ SY28 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY29: $i,SY30: $i,SY31: $i] :
( ~ ( in @ ( kpair @ SY30 @ SY31 ) @ ( cartprod @ sK1_SX0 @ SY29 ) )
| ( in @ SY31 @ SY29 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV5: $i,SV3: $i,SV1: $i] :
( ( ! [SY32: $i] :
( ( ( kpair @ SV1 @ SV3 )
!= ( kpair @ SV5 @ SY32 ) )
| ( SV3 = SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV4: $i,SV2: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
| ~ ! [SY33: $i] :
~ ~ ( ~ ( in @ SY33 @ SV2 )
| ~ ~ ! [SY34: $i] :
~ ~ ( ~ ( in @ SY34 @ SV4 )
| ( SV6
!= ( kpair @ SY33 @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [SY35: $i,SY36: $i] :
( ~ ( in @ ( kpair @ SY35 @ SY36 ) @ ( cartprod @ sK1_SX0 @ sK2_SY29 ) )
| ( in @ SY36 @ sK2_SY29 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(23,plain,
! [SV7: $i,SV5: $i,SV3: $i,SV1: $i] :
( ( ( ( kpair @ SV1 @ SV3 )
!= ( kpair @ SV5 @ SV7 ) )
| ( SV3 = SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: $i,SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) ) )
= $true )
| ( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( in @ SY33 @ SV2 )
| ~ ~ ! [SY34: $i] :
~ ~ ( ~ ( in @ SY34 @ SV4 )
| ( SV6
!= ( kpair @ SY33 @ SY34 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SY37: $i] :
( ~ ( in @ ( kpair @ sK3_SY35 @ SY37 ) @ ( cartprod @ sK1_SX0 @ sK2_SY29 ) )
| ( in @ SY37 @ sK2_SY29 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(26,plain,
! [SV7: $i,SV5: $i,SV3: $i,SV1: $i] :
( ( ( ( kpair @ SV1 @ SV3 )
!= ( kpair @ SV5 @ SV7 ) )
= $true )
| ( ( SV3 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV4: $i,SV2: $i,SV6: $i] :
( ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( in @ SY33 @ SV2 )
| ~ ~ ! [SY34: $i] :
~ ~ ( ~ ( in @ SY34 @ SV4 )
| ( SV6
!= ( kpair @ SY33 @ SY34 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ( in @ ( kpair @ sK3_SY35 @ sK4_SY37 ) @ ( cartprod @ sK1_SX0 @ sK2_SY29 ) )
| ( in @ sK4_SY37 @ sK2_SY29 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(29,plain,
! [SV7: $i,SV5: $i,SV3: $i,SV1: $i] :
( ( ( ( kpair @ SV1 @ SV3 )
= ( kpair @ SV5 @ SV7 ) )
= $false )
| ( ( SV3 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ( ! [SY33: $i] :
~ ~ ( ~ ( in @ SY33 @ SV2 )
| ~ ~ ! [SY34: $i] :
~ ~ ( ~ ( in @ SY34 @ SV4 )
| ( SV6
!= ( kpair @ SY33 @ SY34 ) ) ) ) )
= $false )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ( in @ ( kpair @ sK3_SY35 @ sK4_SY37 ) @ ( cartprod @ sK1_SX0 @ sK2_SY29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( in @ sK4_SY37 @ sK2_SY29 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV4 )
| ( SV6
!= ( kpair @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ SY38 ) ) ) ) )
= $false )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(34,plain,
( ( in @ ( kpair @ sK3_SY35 @ sK4_SY37 ) @ ( cartprod @ sK1_SX0 @ sK2_SY29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV4 )
| ( SV6
!= ( kpair @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ SY38 ) ) ) ) )
= $true )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ SV2 )
| ~ ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV4 )
| ( SV6
!= ( kpair @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ SY38 ) ) ) )
= $false )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(37,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(38,plain,
! [SV2: $i,SV6: $i,SV4: $i] :
( ( ( ~ ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV4 )
| ( SV6
!= ( kpair @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ SY38 ) ) ) )
= $false )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(39,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( in @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ SV2 )
= $true )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(40,plain,
! [SV2: $i,SV6: $i,SV4: $i] :
( ( ( ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV4 )
| ( SV6
!= ( kpair @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ SY38 ) ) ) )
= $true )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(41,plain,
! [SV2: $i,SV6: $i,SV4: $i] :
( ( ( ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV4 )
| ( SV6
!= ( kpair @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ SY38 ) ) ) )
= $false )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
! [SV4: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_SY38 @ SV2 @ SV6 @ SV4 ) @ SV4 )
| ( SV6
!= ( kpair @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ ( sK6_SY38 @ SV2 @ SV6 @ SV4 ) ) ) ) )
= $false )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(43,plain,
! [SV4: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY38 @ SV2 @ SV6 @ SV4 ) @ SV4 )
| ( SV6
!= ( kpair @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ ( sK6_SY38 @ SV2 @ SV6 @ SV4 ) ) ) ) )
= $true )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(44,plain,
! [SV4: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK6_SY38 @ SV2 @ SV6 @ SV4 ) @ SV4 )
| ( SV6
!= ( kpair @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ ( sK6_SY38 @ SV2 @ SV6 @ SV4 ) ) ) )
= $false )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(45,plain,
! [SV4: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK6_SY38 @ SV2 @ SV6 @ SV4 ) @ SV4 ) )
= $false )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(46,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( SV6
!= ( kpair @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ ( sK6_SY38 @ SV2 @ SV6 @ SV4 ) ) )
= $false )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(47,plain,
! [SV4: $i,SV6: $i,SV2: $i] :
( ( ( in @ ( sK6_SY38 @ SV2 @ SV6 @ SV4 ) @ SV4 )
= $true )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(48,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( SV6
= ( kpair @ ( sK5_SY33 @ SV6 @ SV4 @ SV2 ) @ ( sK6_SY38 @ SV2 @ SV6 @ SV4 ) ) )
= $true )
| ( ( in @ SV6 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(49,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,48,47,39,34,32]) ).
thf(50,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU660^2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.15 % Computer : n014.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Oct 6 15:30:41 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.18
% 0.10/0.18 No.of.Axioms: 0
% 0.10/0.18
% 0.10/0.18 Length.of.Defs: 469
% 0.10/0.18
% 0.10/0.18 Contains.Choice.Funs: false
% 0.10/0.18 .
% 0.10/0.18
% 0.10/0.18 ********************************
% 0.10/0.18 * All subproblems solved! *
% 0.10/0.18 ********************************
% 0.10/0.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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:49,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.18
% 0.10/0.18 %**** Beginning of derivation protocol ****
% 0.10/0.18 % SZS output start CNFRefutation
% See solution above
% 0.10/0.18
% 0.10/0.18 %**** End of derivation protocol ****
% 0.10/0.18 %**** no. of clauses in derivation: 50 ****
% 0.10/0.18 %**** clause counter: 49 ****
% 0.10/0.18
% 0.10/0.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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:49,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------