%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN056^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n010.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 11:02:48 AM UTC 2026
% Result : Theorem 0.11s 0.26s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 113 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 775 ( 179 equ; 0 cnn)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 958 ( 240 ~; 216 |; 29 &; 414 @)
% ( 0 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 192 ( 0 ^; 176 !; 16 ?; 192 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cP,type,
cP: $i > $o ).
thf(tp_cQ,type,
cQ: $i > $o ).
thf(tp_cR,type,
cR: $i > $o ).
thf(tp_cS,type,
cS: $i > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_sK2_Xx,type,
sK2_Xx: $i ).
thf(tp_sK3_Xx,type,
sK3_Xx: $i ).
thf(tp_sK4_Xx,type,
sK4_Xx: $i ).
thf(1,conjecture,
( ( ( ? [Xx: $i] : ( cP @ Xx )
=> ? [Xx: $i] : ( cQ @ Xx ) )
& ( ? [Xx: $i] : ( cQ @ Xx )
=> ? [Xx: $i] : ( cP @ Xx ) )
& ! [Xx: $i,Xy: $i] :
( ( ( cP @ Xx )
& ( cQ @ Xy ) )
=> ( ( ( cR @ Xx )
=> ( cS @ Xy ) )
& ( ( cS @ Xy )
=> ( cR @ Xx ) ) ) ) )
=> ( ( ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) )
=> ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) ) )
& ( ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) )
=> ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPELL26) ).
thf(2,negated_conjecture,
( ( ( ( ? [Xx: $i] : ( cP @ Xx )
=> ? [Xx: $i] : ( cQ @ Xx ) )
& ( ? [Xx: $i] : ( cQ @ Xx )
=> ? [Xx: $i] : ( cP @ Xx ) )
& ! [Xx: $i,Xy: $i] :
( ( ( cP @ Xx )
& ( cQ @ Xy ) )
=> ( ( ( cR @ Xx )
=> ( cS @ Xy ) )
& ( ( cS @ Xy )
=> ( cR @ Xx ) ) ) ) )
=> ( ( ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) )
=> ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) ) )
& ( ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) )
=> ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( ? [Xx: $i] : ( cP @ Xx )
=> ? [Xx: $i] : ( cQ @ Xx ) )
& ( ? [Xx: $i] : ( cQ @ Xx )
=> ? [Xx: $i] : ( cP @ Xx ) )
& ! [Xx: $i,Xy: $i] :
( ( ( cP @ Xx )
& ( cQ @ Xy ) )
=> ( ( ( cR @ Xx )
=> ( cS @ Xy ) )
& ( ( cS @ Xy )
=> ( cR @ Xx ) ) ) ) )
=> ( ( ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) )
=> ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) ) )
& ( ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) )
=> ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [Xx: $i] : ( cP @ Xx )
=> ? [Xx: $i] : ( cQ @ Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [Xx: $i] : ( cQ @ Xx )
=> ? [Xx: $i] : ( cP @ Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( cP @ Xx )
& ( cQ @ Xy ) )
=> ( ( ( cR @ Xx )
=> ( cS @ Xy ) )
& ( ( cS @ Xy )
=> ( cR @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ( ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) )
=> ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) ) )
& ( ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) )
=> ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) )
=> ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) )
=> ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ~ ( ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) )
=> ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ! [Xx: $i] :
( ( cQ @ Xx )
=> ( cS @ Xx ) )
=> ! [Xx: $i] :
( ( cP @ Xx )
=> ( cR @ Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [Xx: $i] :
( ~ ( cP @ Xx )
| ( cR @ Xx ) )
& ( cQ @ sK1_Xx )
& ~ ( cS @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(13,plain,
( ( ! [Xx: $i] :
( ~ ( cQ @ Xx )
| ( cS @ Xx ) )
& ( cP @ sK2_Xx )
& ~ ( cR @ sK2_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(14,plain,
( ( ! [Xx: $i] :
~ ( cP @ Xx )
| ( cQ @ sK3_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(15,plain,
( ( ! [Xx: $i] :
~ ( cQ @ Xx )
| ( cP @ sK4_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(16,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( cP @ Xx )
| ~ ( cQ @ Xy )
| ~ ( cR @ Xx )
| ( cS @ Xy ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP @ Xx )
| ~ ( cQ @ Xy )
| ~ ( cS @ Xy )
| ( cR @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(17,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( cP @ Xx )
| ~ ( cQ @ Xy )
| ~ ( cR @ Xx )
| ( cS @ Xy ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP @ Xx )
| ~ ( cQ @ Xy )
| ~ ( cS @ Xy )
| ( cR @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [Xx: $i] :
~ ( cQ @ Xx )
| ( cP @ sK4_Xx ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [Xx: $i] :
~ ( cP @ Xx )
| ( cQ @ sK3_Xx ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [Xx: $i] :
( ~ ( cP @ Xx )
| ( cR @ Xx ) )
& ( cQ @ sK1_Xx )
& ~ ( cS @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( cP @ SX0 )
| ( cR @ SX0 ) )
| ~ ~ ( ~ ( cQ @ sK1_Xx )
| ~ ~ ( cS @ sK1_Xx ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cR @ SX0 )
| ( cS @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cS @ SX1 )
| ( cR @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(23,plain,
( ( ( ! [Xx: $i] :
~ ( cQ @ Xx ) )
= $true )
| ( ( cP @ sK4_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(24,plain,
( ( ( ! [Xx: $i] :
~ ( cP @ Xx ) )
= $true )
| ( ( cQ @ sK3_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(25,plain,
( ( ~ ! [SX0: $i] :
( ~ ( cP @ SX0 )
| ( cR @ SX0 ) )
| ~ ~ ( ~ ( cQ @ sK1_Xx )
| ~ ~ ( cS @ sK1_Xx ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cR @ SX0 )
| ( cS @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cS @ SX1 )
| ( cR @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: $i] :
( ( ( ~ ( cQ @ SV1 ) )
= $true )
| ( ( cP @ sK4_Xx )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV2: $i] :
( ( ( ~ ( cP @ SV2 ) )
= $true )
| ( ( cQ @ sK3_Xx )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ! [SX0: $i] :
( ~ ( cP @ SX0 )
| ( cR @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ~ ~ ( ~ ( cQ @ sK1_Xx )
| ~ ~ ( cS @ sK1_Xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cR @ SX0 )
| ( cS @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(32,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cS @ SX1 )
| ( cR @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(33,plain,
! [SV1: $i] :
( ( ( cQ @ SV1 )
= $false )
| ( ( cP @ sK4_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV2: $i] :
( ( ( cP @ SV2 )
= $false )
| ( ( cQ @ sK3_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(35,plain,
( ( ! [SX0: $i] :
( ~ ( cP @ SX0 )
| ( cR @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(36,plain,
( ( ~ ( ~ ( cQ @ sK1_Xx )
| ~ ~ ( cS @ sK1_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(37,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cR @ SX0 )
| ( cS @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(38,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cS @ SX1 )
| ( cR @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(39,plain,
! [SV3: $i] :
( ( ~ ( cP @ SV3 )
| ( cR @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ( cQ @ sK1_Xx )
| ~ ~ ( cS @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV4: $i] :
( ( ! [SY10: $i] :
( ~ ( cP @ SV4 )
| ~ ( cQ @ SY10 )
| ~ ( cR @ SV4 )
| ( cS @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV5: $i] :
( ( ! [SY11: $i] :
( ~ ( cP @ SV5 )
| ~ ( cQ @ SY11 )
| ~ ( cS @ SY11 )
| ( cR @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV3: $i] :
( ( ( ~ ( cP @ SV3 ) )
= $true )
| ( ( cR @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( ~ ( cQ @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
( ( ~ ~ ( cS @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV6: $i,SV4: $i] :
( ( ~ ( cP @ SV4 )
| ~ ( cQ @ SV6 )
| ~ ( cR @ SV4 )
| ( cS @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV7: $i,SV5: $i] :
( ( ~ ( cP @ SV5 )
| ~ ( cQ @ SV7 )
| ~ ( cS @ SV7 )
| ( cR @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV3: $i] :
( ( ( cP @ SV3 )
= $false )
| ( ( cR @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
( ( cQ @ sK1_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(50,plain,
( ( ~ ( cS @ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( cP @ SV4 )
| ~ ( cQ @ SV6 ) )
= $true )
| ( ( ~ ( cR @ SV4 )
| ( cS @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ( cP @ SV5 )
| ~ ( cQ @ SV7 ) )
= $true )
| ( ( ~ ( cS @ SV7 )
| ( cR @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
( ( cS @ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( cP @ SV4 ) )
= $true )
| ( ( ~ ( cQ @ SV6 ) )
= $true )
| ( ( ~ ( cR @ SV4 )
| ( cS @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV7: $i,SV5: $i] :
( ( ( ~ ( cP @ SV5 ) )
= $true )
| ( ( ~ ( cQ @ SV7 ) )
= $true )
| ( ( ~ ( cS @ SV7 )
| ( cR @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV6: $i,SV4: $i] :
( ( ( cP @ SV4 )
= $false )
| ( ( ~ ( cQ @ SV6 ) )
= $true )
| ( ( ~ ( cR @ SV4 )
| ( cS @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV7: $i,SV5: $i] :
( ( ( cP @ SV5 )
= $false )
| ( ( ~ ( cQ @ SV7 ) )
= $true )
| ( ( ~ ( cS @ SV7 )
| ( cR @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV4: $i,SV6: $i] :
( ( ( cQ @ SV6 )
= $false )
| ( ( cP @ SV4 )
= $false )
| ( ( ~ ( cR @ SV4 )
| ( cS @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV5: $i,SV7: $i] :
( ( ( cQ @ SV7 )
= $false )
| ( ( cP @ SV5 )
= $false )
| ( ( ~ ( cS @ SV7 )
| ( cR @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( cR @ SV4 ) )
= $true )
| ( ( cS @ SV6 )
= $true )
| ( ( cP @ SV4 )
= $false )
| ( ( cQ @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ( cS @ SV7 ) )
= $true )
| ( ( cR @ SV5 )
= $true )
| ( ( cP @ SV5 )
= $false )
| ( ( cQ @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV6: $i,SV4: $i] :
( ( ( cR @ SV4 )
= $false )
| ( ( cS @ SV6 )
= $true )
| ( ( cP @ SV4 )
= $false )
| ( ( cQ @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV5: $i,SV7: $i] :
( ( ( cS @ SV7 )
= $false )
| ( ( cR @ SV5 )
= $true )
| ( ( cP @ SV5 )
= $false )
| ( ( cQ @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[33,63,62,53,49,48,34]) ).
thf(65,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( cP @ Xx )
| ~ ( cQ @ Xy )
| ~ ( cR @ Xx )
| ( cS @ Xy ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP @ Xx )
| ~ ( cQ @ Xy )
| ~ ( cS @ Xy )
| ( cR @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(66,plain,
( ( ! [Xx: $i] :
~ ( cQ @ Xx )
| ( cP @ sK4_Xx ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(67,plain,
( ( ! [Xx: $i] :
~ ( cP @ Xx )
| ( cQ @ sK3_Xx ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(68,plain,
( ( ! [Xx: $i] :
( ~ ( cQ @ Xx )
| ( cS @ Xx ) )
& ( cP @ sK2_Xx )
& ~ ( cR @ sK2_Xx ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(69,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cR @ SX0 )
| ( cS @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cS @ SX1 )
| ( cR @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(70,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( cQ @ SX0 )
| ( cS @ SX0 ) )
| ~ ~ ( ~ ( cP @ sK2_Xx )
| ~ ~ ( cR @ sK2_Xx ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(71,plain,
( ( ( ! [Xx: $i] :
~ ( cQ @ Xx ) )
= $true )
| ( ( cP @ sK4_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(72,plain,
( ( ( ! [Xx: $i] :
~ ( cP @ Xx ) )
= $true )
| ( ( cQ @ sK3_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(73,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cR @ SX0 )
| ( cS @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cS @ SX1 )
| ( cR @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(74,plain,
( ( ~ ! [SX0: $i] :
( ~ ( cQ @ SX0 )
| ( cS @ SX0 ) )
| ~ ~ ( ~ ( cP @ sK2_Xx )
| ~ ~ ( cR @ sK2_Xx ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV8: $i] :
( ( ( ~ ( cQ @ SV8 ) )
= $true )
| ( ( cP @ sK4_Xx )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV9: $i] :
( ( ( ~ ( cP @ SV9 ) )
= $true )
| ( ( cQ @ sK3_Xx )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(77,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cR @ SX0 )
| ( cS @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(78,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cS @ SX1 )
| ( cR @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(79,plain,
( ( ~ ! [SX0: $i] :
( ~ ( cQ @ SX0 )
| ( cS @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(80,plain,
( ( ~ ~ ( ~ ( cP @ sK2_Xx )
| ~ ~ ( cR @ sK2_Xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(81,plain,
! [SV8: $i] :
( ( ( cQ @ SV8 )
= $false )
| ( ( cP @ sK4_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV9: $i] :
( ( ( cP @ SV9 )
= $false )
| ( ( cQ @ sK3_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cR @ SX0 )
| ( cS @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP @ SX0 )
| ~ ( cQ @ SX1 )
| ~ ( cS @ SX1 )
| ( cR @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(85,plain,
( ( ! [SX0: $i] :
( ~ ( cQ @ SX0 )
| ( cS @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(86,plain,
( ( ~ ( ~ ( cP @ sK2_Xx )
| ~ ~ ( cR @ sK2_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(87,plain,
! [SV10: $i] :
( ( ! [SY12: $i] :
( ~ ( cP @ SV10 )
| ~ ( cQ @ SY12 )
| ~ ( cR @ SV10 )
| ( cS @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV11: $i] :
( ( ! [SY13: $i] :
( ~ ( cP @ SV11 )
| ~ ( cQ @ SY13 )
| ~ ( cS @ SY13 )
| ( cR @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV12: $i] :
( ( ~ ( cQ @ SV12 )
| ( cS @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(90,plain,
( ( ~ ( cP @ sK2_Xx )
| ~ ~ ( cR @ sK2_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV13: $i,SV10: $i] :
( ( ~ ( cP @ SV10 )
| ~ ( cQ @ SV13 )
| ~ ( cR @ SV10 )
| ( cS @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV14: $i,SV11: $i] :
( ( ~ ( cP @ SV11 )
| ~ ( cQ @ SV14 )
| ~ ( cS @ SV14 )
| ( cR @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(93,plain,
! [SV12: $i] :
( ( ( ~ ( cQ @ SV12 ) )
= $true )
| ( ( cS @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(94,plain,
( ( ~ ( cP @ sK2_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(95,plain,
( ( ~ ~ ( cR @ sK2_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(96,plain,
! [SV13: $i,SV10: $i] :
( ( ( ~ ( cP @ SV10 )
| ~ ( cQ @ SV13 ) )
= $true )
| ( ( ~ ( cR @ SV10 )
| ( cS @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV14: $i,SV11: $i] :
( ( ( ~ ( cP @ SV11 )
| ~ ( cQ @ SV14 ) )
= $true )
| ( ( ~ ( cS @ SV14 )
| ( cR @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV12: $i] :
( ( ( cQ @ SV12 )
= $false )
| ( ( cS @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
( ( cP @ sK2_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(100,plain,
( ( ~ ( cR @ sK2_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(101,plain,
! [SV13: $i,SV10: $i] :
( ( ( ~ ( cP @ SV10 ) )
= $true )
| ( ( ~ ( cQ @ SV13 ) )
= $true )
| ( ( ~ ( cR @ SV10 )
| ( cS @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV14: $i,SV11: $i] :
( ( ( ~ ( cP @ SV11 ) )
= $true )
| ( ( ~ ( cQ @ SV14 ) )
= $true )
| ( ( ~ ( cS @ SV14 )
| ( cR @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(103,plain,
( ( cR @ sK2_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(104,plain,
! [SV13: $i,SV10: $i] :
( ( ( cP @ SV10 )
= $false )
| ( ( ~ ( cQ @ SV13 ) )
= $true )
| ( ( ~ ( cR @ SV10 )
| ( cS @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(105,plain,
! [SV14: $i,SV11: $i] :
( ( ( cP @ SV11 )
= $false )
| ( ( ~ ( cQ @ SV14 ) )
= $true )
| ( ( ~ ( cS @ SV14 )
| ( cR @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(106,plain,
! [SV10: $i,SV13: $i] :
( ( ( cQ @ SV13 )
= $false )
| ( ( cP @ SV10 )
= $false )
| ( ( ~ ( cR @ SV10 )
| ( cS @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(107,plain,
! [SV11: $i,SV14: $i] :
( ( ( cQ @ SV14 )
= $false )
| ( ( cP @ SV11 )
= $false )
| ( ( ~ ( cS @ SV14 )
| ( cR @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(108,plain,
! [SV13: $i,SV10: $i] :
( ( ( ~ ( cR @ SV10 ) )
= $true )
| ( ( cS @ SV13 )
= $true )
| ( ( cP @ SV10 )
= $false )
| ( ( cQ @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(109,plain,
! [SV11: $i,SV14: $i] :
( ( ( ~ ( cS @ SV14 ) )
= $true )
| ( ( cR @ SV11 )
= $true )
| ( ( cP @ SV11 )
= $false )
| ( ( cQ @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(110,plain,
! [SV13: $i,SV10: $i] :
( ( ( cR @ SV10 )
= $false )
| ( ( cS @ SV13 )
= $true )
| ( ( cP @ SV10 )
= $false )
| ( ( cQ @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(111,plain,
! [SV11: $i,SV14: $i] :
( ( ( cS @ SV14 )
= $false )
| ( ( cR @ SV11 )
= $true )
| ( ( cP @ SV11 )
= $false )
| ( ( cQ @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(112,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[81,111,110,103,99,98,82]) ).
thf(113,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[112,64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN056^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.11/0.19 % Computer : n010.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Oct 6 17:16:10 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.26
% 0.11/0.26 No.of.Axioms: 0
% 0.11/0.26
% 0.11/0.26 Length.of.Defs: 0
% 0.11/0.26
% 0.11/0.26 Contains.Choice.Funs: false
% 0.11/0.26 ..
% 0.11/0.26
% 0.11/0.26 ********************************
% 0.11/0.26 * All subproblems solved! *
% 0.11/0.26 ********************************
% 0.11/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:112,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.26
% 0.11/0.26 %**** Beginning of derivation protocol ****
% 0.11/0.26 % SZS output start CNFRefutation
% See solution above
% 0.11/0.26
% 0.11/0.26 %**** End of derivation protocol ****
% 0.11/0.26 %**** no. of clauses in derivation: 113 ****
% 0.11/0.26 %**** clause counter: 112 ****
% 0.11/0.26
% 0.11/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:112,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------