%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU692^2 : 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 : n020.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 10:46:16 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 53 ( 37 unt; 0 typ; 2 def)
% Number of atoms : 359 ( 150 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 911 ( 79 ~; 96 |; 0 &; 686 @)
% ( 0 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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; 0-4 aty)
% Number of variables : 179 ( 0 ^; 179 !; 0 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ap,type,
ap: $i > $i > $i > $i > $i ).
thf(tp_func,type,
func: $i > $i > $i > $o ).
thf(tp_funcSet,type,
funcSet: $i > $i > $i ).
thf(tp_funcext,type,
funcext: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_infuncsetfunc,type,
infuncsetfunc: $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY28,type,
sK2_SY28: $i ).
thf(tp_sK3_SY34,type,
sK3_SY34: $i ).
thf(tp_sK4_SY37,type,
sK4_SY37: $i ).
thf(tp_sK5_SY39,type,
sK5_SY39: $i > $i > $i > $i > $i ).
thf(funcext,definition,
( funcext
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(infuncsetfunc,definition,
( infuncsetfunc
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(1,conjecture,
( infuncsetfunc
=> ( funcext
=> ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(2,negated_conjecture,
( ( infuncsetfunc
=> ( funcext
=> ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) )
=> ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,funcext,infuncsetfunc]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ~ ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( func @ SX0 @ SX1 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
= ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,funcext,infuncsetfunc]) ).
thf(12,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ( func @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,funcext,infuncsetfunc]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( funcSet @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
= ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,funcext,infuncsetfunc]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( func @ SV1 @ SY18 @ SY19 )
| ! [SY20: $i] :
( ~ ( func @ SV1 @ SY18 @ SY20 )
| ~ ! [SY21: $i] :
( ~ ( in @ SY21 @ SV1 )
| ( ( ap @ SV1 @ SY18 @ SY19 @ SY21 )
= ( ap @ SV1 @ SY18 @ SY20 @ SY21 ) ) )
| ( SY19 = SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ~ ( in @ SY23 @ ( funcSet @ SV2 @ SY22 ) )
| ( func @ SV2 @ SY22 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( funcSet @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
= ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
| ( SX2 = SX3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i,SV1: $i] :
( ( ! [SY24: $i] :
( ~ ( func @ SV1 @ SV3 @ SY24 )
| ! [SY25: $i] :
( ~ ( func @ SV1 @ SV3 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( in @ SY26 @ SV1 )
| ( ( ap @ SV1 @ SV3 @ SY24 @ SY26 )
= ( ap @ SV1 @ SV3 @ SY25 @ SY26 ) ) )
| ( SY24 = SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY27: $i] :
( ~ ( in @ SY27 @ ( funcSet @ SV2 @ SV4 ) )
| ( func @ SV2 @ SV4 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY28: $i,SY29: $i] :
( ~ ( in @ SY29 @ ( funcSet @ sK1_SX0 @ SY28 ) )
| ! [SY30: $i] :
( ~ ( in @ SY30 @ ( funcSet @ sK1_SX0 @ SY28 ) )
| ~ ! [SY31: $i] :
( ~ ( in @ SY31 @ sK1_SX0 )
| ( ( ap @ sK1_SX0 @ SY28 @ SY29 @ SY31 )
= ( ap @ sK1_SX0 @ SY28 @ SY30 @ SY31 ) ) )
| ( SY29 = SY30 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV5: $i,SV3: $i,SV1: $i] :
( ( ~ ( func @ SV1 @ SV3 @ SV5 )
| ! [SY32: $i] :
( ~ ( func @ SV1 @ SV3 @ SY32 )
| ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV1 )
| ( ( ap @ SV1 @ SV3 @ SV5 @ SY33 )
= ( ap @ SV1 @ SV3 @ SY32 @ SY33 ) ) )
| ( SV5 = SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV4: $i,SV2: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ ( funcSet @ SV2 @ SV4 ) )
| ( func @ SV2 @ SV4 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ ( funcSet @ sK1_SX0 @ sK2_SY28 ) )
| ! [SY35: $i] :
( ~ ( in @ SY35 @ ( funcSet @ sK1_SX0 @ sK2_SY28 ) )
| ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ( ( ap @ sK1_SX0 @ sK2_SY28 @ SY34 @ SY36 )
= ( ap @ sK1_SX0 @ sK2_SY28 @ SY35 @ SY36 ) ) )
| ( SY34 = SY35 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(23,plain,
! [SV5: $i,SV3: $i,SV1: $i] :
( ( ( ~ ( func @ SV1 @ SV3 @ SV5 ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( func @ SV1 @ SV3 @ SY32 )
| ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV1 )
| ( ( ap @ SV1 @ SV3 @ SV5 @ SY33 )
= ( ap @ SV1 @ SV3 @ SY32 @ SY33 ) ) )
| ( SV5 = SY32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: $i,SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( funcSet @ SV2 @ SV4 ) ) )
= $true )
| ( ( func @ SV2 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ( in @ sK3_SY34 @ ( funcSet @ sK1_SX0 @ sK2_SY28 ) )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ ( funcSet @ sK1_SX0 @ sK2_SY28 ) )
| ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ sK1_SX0 )
| ( ( ap @ sK1_SX0 @ sK2_SY28 @ sK3_SY34 @ SY38 )
= ( ap @ sK1_SX0 @ sK2_SY28 @ SY37 @ SY38 ) ) )
| ( sK3_SY34 = SY37 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(26,plain,
! [SV5: $i,SV3: $i,SV1: $i] :
( ( ( func @ SV1 @ SV3 @ SV5 )
= $false )
| ( ( ! [SY32: $i] :
( ~ ( func @ SV1 @ SV3 @ SY32 )
| ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV1 )
| ( ( ap @ SV1 @ SV3 @ SV5 @ SY33 )
= ( ap @ SV1 @ SV3 @ SY32 @ SY33 ) ) )
| ( SV5 = SY32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV4: $i,SV2: $i,SV6: $i] :
( ( ( in @ SV6 @ ( funcSet @ SV2 @ SV4 ) )
= $false )
| ( ( func @ SV2 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ( in @ sK3_SY34 @ ( funcSet @ sK1_SX0 @ sK2_SY28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(29,plain,
( ( ! [SY37: $i] :
( ~ ( in @ SY37 @ ( funcSet @ sK1_SX0 @ sK2_SY28 ) )
| ~ ! [SY38: $i] :
( ~ ( in @ SY38 @ sK1_SX0 )
| ( ( ap @ sK1_SX0 @ sK2_SY28 @ sK3_SY34 @ SY38 )
= ( ap @ sK1_SX0 @ sK2_SY28 @ SY37 @ SY38 ) ) )
| ( sK3_SY34 = SY37 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
! [SV5: $i,SV7: $i,SV3: $i,SV1: $i] :
( ( ( ~ ( func @ SV1 @ SV3 @ SV7 )
| ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV1 )
| ( ( ap @ SV1 @ SV3 @ SV5 @ SY39 )
= ( ap @ SV1 @ SV3 @ SV7 @ SY39 ) ) )
| ( SV5 = SV7 ) )
= $true )
| ( ( func @ SV1 @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( in @ sK3_SY34 @ ( funcSet @ sK1_SX0 @ sK2_SY28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ( in @ sK4_SY37 @ ( funcSet @ sK1_SX0 @ sK2_SY28 ) )
| ~ ! [SY40: $i] :
( ~ ( in @ SY40 @ sK1_SX0 )
| ( ( ap @ sK1_SX0 @ sK2_SY28 @ sK3_SY34 @ SY40 )
= ( ap @ sK1_SX0 @ sK2_SY28 @ sK4_SY37 @ SY40 ) ) )
| ( sK3_SY34 = sK4_SY37 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(33,plain,
! [SV5: $i,SV7: $i,SV3: $i,SV1: $i] :
( ( ( ~ ( func @ SV1 @ SV3 @ SV7 ) )
= $true )
| ( ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV1 )
| ( ( ap @ SV1 @ SV3 @ SV5 @ SY39 )
= ( ap @ SV1 @ SV3 @ SV7 @ SY39 ) ) )
| ( SV5 = SV7 ) )
= $true )
| ( ( func @ SV1 @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ( in @ sK4_SY37 @ ( funcSet @ sK1_SX0 @ sK2_SY28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(35,plain,
( ( ~ ! [SY40: $i] :
( ~ ( in @ SY40 @ sK1_SX0 )
| ( ( ap @ sK1_SX0 @ sK2_SY28 @ sK3_SY34 @ SY40 )
= ( ap @ sK1_SX0 @ sK2_SY28 @ sK4_SY37 @ SY40 ) ) )
| ( sK3_SY34 = sK4_SY37 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV5: $i,SV7: $i,SV3: $i,SV1: $i] :
( ( ( func @ SV1 @ SV3 @ SV7 )
= $false )
| ( ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV1 )
| ( ( ap @ SV1 @ SV3 @ SV5 @ SY39 )
= ( ap @ SV1 @ SV3 @ SV7 @ SY39 ) ) )
| ( SV5 = SV7 ) )
= $true )
| ( ( func @ SV1 @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
( ( in @ sK4_SY37 @ ( funcSet @ sK1_SX0 @ sK2_SY28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
( ( ~ ! [SY40: $i] :
( ~ ( in @ SY40 @ sK1_SX0 )
| ( ( ap @ sK1_SX0 @ sK2_SY28 @ sK3_SY34 @ SY40 )
= ( ap @ sK1_SX0 @ sK2_SY28 @ sK4_SY37 @ SY40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( sK3_SY34 = sK4_SY37 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV7: $i,SV5: $i,SV3: $i,SV1: $i] :
( ( ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV1 )
| ( ( ap @ SV1 @ SV3 @ SV5 @ SY39 )
= ( ap @ SV1 @ SV3 @ SV7 @ SY39 ) ) ) )
= $true )
| ( ( SV5 = SV7 )
= $true )
| ( ( func @ SV1 @ SV3 @ SV7 )
= $false )
| ( ( func @ SV1 @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
( ( ! [SY40: $i] :
( ~ ( in @ SY40 @ sK1_SX0 )
| ( ( ap @ sK1_SX0 @ sK2_SY28 @ sK3_SY34 @ SY40 )
= ( ap @ sK1_SX0 @ sK2_SY28 @ sK4_SY37 @ SY40 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV7: $i,SV5: $i,SV3: $i,SV1: $i] :
( ( ( ! [SY39: $i] :
( ~ ( in @ SY39 @ SV1 )
| ( ( ap @ SV1 @ SV3 @ SV5 @ SY39 )
= ( ap @ SV1 @ SV3 @ SV7 @ SY39 ) ) ) )
= $false )
| ( ( SV5 = SV7 )
= $true )
| ( ( func @ SV1 @ SV3 @ SV7 )
= $false )
| ( ( func @ SV1 @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV8: $i] :
( ( ~ ( in @ SV8 @ sK1_SX0 )
| ( ( ap @ sK1_SX0 @ sK2_SY28 @ sK3_SY34 @ SV8 )
= ( ap @ sK1_SX0 @ sK2_SY28 @ sK4_SY37 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV1: $i,SV3: $i,SV5: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK5_SY39 @ SV7 @ SV5 @ SV3 @ SV1 ) @ SV1 )
| ( ( ap @ SV1 @ SV3 @ SV5 @ ( sK5_SY39 @ SV7 @ SV5 @ SV3 @ SV1 ) )
= ( ap @ SV1 @ SV3 @ SV7 @ ( sK5_SY39 @ SV7 @ SV5 @ SV3 @ SV1 ) ) ) )
= $false )
| ( ( SV5 = SV7 )
= $true )
| ( ( func @ SV1 @ SV3 @ SV7 )
= $false )
| ( ( func @ SV1 @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(45,plain,
! [SV8: $i] :
( ( ( ~ ( in @ SV8 @ sK1_SX0 ) )
= $true )
| ( ( ( ap @ sK1_SX0 @ sK2_SY28 @ sK3_SY34 @ SV8 )
= ( ap @ sK1_SX0 @ sK2_SY28 @ sK4_SY37 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV1: $i,SV3: $i,SV5: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK5_SY39 @ SV7 @ SV5 @ SV3 @ SV1 ) @ SV1 ) )
= $false )
| ( ( SV5 = SV7 )
= $true )
| ( ( func @ SV1 @ SV3 @ SV7 )
= $false )
| ( ( func @ SV1 @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(47,plain,
! [SV7: $i,SV5: $i,SV3: $i,SV1: $i] :
( ( ( ( ap @ SV1 @ SV3 @ SV5 @ ( sK5_SY39 @ SV7 @ SV5 @ SV3 @ SV1 ) )
= ( ap @ SV1 @ SV3 @ SV7 @ ( sK5_SY39 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV5 = SV7 )
= $true )
| ( ( func @ SV1 @ SV3 @ SV7 )
= $false )
| ( ( func @ SV1 @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV8: $i] :
( ( ( in @ SV8 @ sK1_SX0 )
= $false )
| ( ( ( ap @ sK1_SX0 @ sK2_SY28 @ sK3_SY34 @ SV8 )
= ( ap @ sK1_SX0 @ sK2_SY28 @ sK4_SY37 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV1: $i,SV3: $i,SV5: $i,SV7: $i] :
( ( ( in @ ( sK5_SY39 @ SV7 @ SV5 @ SV3 @ SV1 ) @ SV1 )
= $true )
| ( ( SV5 = SV7 )
= $true )
| ( ( func @ SV1 @ SV3 @ SV7 )
= $false )
| ( ( func @ SV1 @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(50,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,49,48,47,39,37,31]) ).
thf(51,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU692^2 : 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
% 0.07/0.19 % Computer : n020.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:32:36 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.24
% 0.07/0.24 No.of.Axioms: 0
% 0.07/0.24
% 0.07/0.24 Length.of.Defs: 467
% 0.07/0.24
% 0.07/0.24 Contains.Choice.Funs: false
% 0.07/0.24 ..
% 0.07/0.24
% 0.07/0.24 ********************************
% 0.07/0.24 * All subproblems solved! *
% 0.07/0.24 ********************************
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox/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:50,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.24
% 0.07/0.24 %**** Beginning of derivation protocol ****
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.24
% 0.07/0.24 %**** End of derivation protocol ****
% 0.07/0.24 %**** no. of clauses in derivation: 51 ****
% 0.07/0.24 %**** clause counter: 50 ****
% 0.07/0.24
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox/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:50,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------