%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 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 : n006.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 10:28:44 AM UTC 2026
% Result : Theorem 0.11s 0.24s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1
% Syntax : Number of formulae : 45 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 239 ( 50 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 865 ( 152 ~; 74 |; 20 &; 619 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 180 ( 0 ^; 175 !; 5 ?; 180 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_truth,type,
a_truth: $i > $o ).
thf(tp_implies,type,
implies: $i > $i > $i ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(1,conjecture,
~ ( ! [P: $i,Q: $i] :
( ~ ( a_truth @ ( implies @ P @ Q ) )
| ~ ( a_truth @ P )
| ( a_truth @ Q ) )
& ! [P: $i,Q: $i] : ( a_truth @ ( implies @ P @ ( implies @ Q @ P ) ) )
& ! [P: $i,Q: $i,R: $i] : ( a_truth @ ( implies @ ( implies @ P @ ( implies @ Q @ R ) ) @ ( implies @ ( implies @ P @ Q ) @ ( implies @ P @ R ) ) ) )
& ! [P: $i,Q: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ P ) @ ( not @ Q ) ) @ ( implies @ Q @ P ) ) )
& ? [A: $i] :
~ ( a_truth @ ( implies @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm147) ).
thf(2,negated_conjecture,
( ( ~ ( ! [P: $i,Q: $i] :
( ~ ( a_truth @ ( implies @ P @ Q ) )
| ~ ( a_truth @ P )
| ( a_truth @ Q ) )
& ! [P: $i,Q: $i] : ( a_truth @ ( implies @ P @ ( implies @ Q @ P ) ) )
& ! [P: $i,Q: $i,R: $i] : ( a_truth @ ( implies @ ( implies @ P @ ( implies @ Q @ R ) ) @ ( implies @ ( implies @ P @ Q ) @ ( implies @ P @ R ) ) ) )
& ! [P: $i,Q: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ P ) @ ( not @ Q ) ) @ ( implies @ Q @ P ) ) )
& ? [A: $i] :
~ ( a_truth @ ( implies @ A @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ( ! [P: $i,Q: $i] :
( ~ ( a_truth @ ( implies @ P @ Q ) )
| ~ ( a_truth @ P )
| ( a_truth @ Q ) )
& ! [P: $i,Q: $i] : ( a_truth @ ( implies @ P @ ( implies @ Q @ P ) ) )
& ! [P: $i,Q: $i,R: $i] : ( a_truth @ ( implies @ ( implies @ P @ ( implies @ Q @ R ) ) @ ( implies @ ( implies @ P @ Q ) @ ( implies @ P @ R ) ) ) )
& ! [P: $i,Q: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ P ) @ ( not @ Q ) ) @ ( implies @ Q @ P ) ) )
& ? [A: $i] :
~ ( a_truth @ ( implies @ A @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( a_truth @ ( implies @ P @ Q ) )
| ~ ( a_truth @ P )
| ( a_truth @ Q ) )
& ! [P: $i,Q: $i] : ( a_truth @ ( implies @ P @ ( implies @ Q @ P ) ) )
& ! [P: $i,Q: $i,R: $i] : ( a_truth @ ( implies @ ( implies @ P @ ( implies @ Q @ R ) ) @ ( implies @ ( implies @ P @ Q ) @ ( implies @ P @ R ) ) ) )
& ! [P: $i,Q: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ P ) @ ( not @ Q ) ) @ ( implies @ Q @ P ) ) )
& ? [A: $i] :
~ ( a_truth @ ( implies @ A @ A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( a_truth @ ( implies @ P @ Q ) )
| ~ ( a_truth @ P )
| ( a_truth @ Q ) )
& ! [P: $i,Q: $i] : ( a_truth @ ( implies @ P @ ( implies @ Q @ P ) ) )
& ! [P: $i,Q: $i,R: $i] : ( a_truth @ ( implies @ ( implies @ P @ ( implies @ Q @ R ) ) @ ( implies @ ( implies @ P @ Q ) @ ( implies @ P @ R ) ) ) )
& ! [P: $i,Q: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ P ) @ ( not @ Q ) ) @ ( implies @ Q @ P ) ) )
& ? [A: $i] :
~ ( a_truth @ ( implies @ A @ A ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] : ( a_truth @ ( implies @ ( implies @ SX0 @ ( implies @ SX1 @ SX2 ) ) @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ SX0 ) @ ( not @ SX1 ) ) @ ( implies @ SX1 @ SX0 ) ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( a_truth @ ( implies @ SX0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] : ( a_truth @ ( implies @ ( implies @ SX0 @ ( implies @ SX1 @ SX2 ) ) @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ SX0 ) @ ( not @ SX1 ) ) @ ( implies @ SX1 @ SX0 ) ) ) )
| ~ ~ ! [SX0: $i] :
~ ~ ( a_truth @ ( implies @ SX0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] : ( a_truth @ ( implies @ ( implies @ SX0 @ ( implies @ SX1 @ SX2 ) ) @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ SX0 ) @ ( not @ SX1 ) ) @ ( implies @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( a_truth @ ( implies @ SX0 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] : ( a_truth @ ( implies @ ( implies @ SX0 @ ( implies @ SX1 @ SX2 ) ) @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ SX0 ) @ ( not @ SX1 ) ) @ ( implies @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( a_truth @ ( implies @ SX0 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] : ( a_truth @ ( implies @ ( implies @ SX0 @ ( implies @ SX1 @ SX2 ) ) @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ SX0 ) @ ( not @ SX1 ) ) @ ( implies @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SX0: $i] :
~ ~ ( a_truth @ ( implies @ SX0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] : ( a_truth @ ( implies @ ( implies @ SX0 @ ( implies @ SX1 @ SX2 ) ) @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ SX0 ) @ ( not @ SX1 ) ) @ ( implies @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(16,plain,
( ( ~ ~ ( a_truth @ ( implies @ sK1_SX0 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(17,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] : ( a_truth @ ( implies @ ( implies @ SX0 @ ( implies @ SX1 @ SX2 ) ) @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ SX0 ) @ ( not @ SX1 ) ) @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( a_truth @ ( implies @ sK1_SX0 @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] : ( a_truth @ ( implies @ ( implies @ SX0 @ ( implies @ SX1 @ SX2 ) ) @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i] :
( ( ! [SY10: $i] : ( a_truth @ ( implies @ ( implies @ ( not @ SV1 ) @ ( not @ SY10 ) ) @ ( implies @ SY10 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( a_truth @ ( implies @ sK1_SX0 @ sK1_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] : ( a_truth @ ( implies @ ( implies @ SX0 @ ( implies @ SX1 @ SX2 ) ) @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
! [SV2: $i,SV1: $i] :
( ( a_truth @ ( implies @ ( implies @ ( not @ SV1 ) @ ( not @ SV2 ) ) @ ( implies @ SV2 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(27,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( a_truth @ ( implies @ ( implies @ SX0 @ ( implies @ SX1 @ SX2 ) ) @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV3: $i] :
( ( ! [SY11: $i,SY12: $i] : ( a_truth @ ( implies @ ( implies @ SV3 @ ( implies @ SY11 @ SY12 ) ) @ ( implies @ ( implies @ SV3 @ SY11 ) @ ( implies @ SV3 @ SY12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(30,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(31,plain,
( ( ~ ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV4: $i,SV3: $i] :
( ( ! [SY13: $i] : ( a_truth @ ( implies @ ( implies @ SV3 @ ( implies @ SV4 @ SY13 ) ) @ ( implies @ ( implies @ SV3 @ SV4 ) @ ( implies @ SV3 @ SY13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( a_truth @ ( implies @ SX0 @ SX1 ) )
| ~ ( a_truth @ SX0 )
| ( a_truth @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(34,plain,
( ( ! [SX0: $i,SX1: $i] : ( a_truth @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV5: $i,SV4: $i,SV3: $i] :
( ( a_truth @ ( implies @ ( implies @ SV3 @ ( implies @ SV4 @ SV5 ) ) @ ( implies @ ( implies @ SV3 @ SV4 ) @ ( implies @ SV3 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV6: $i] :
( ( ! [SY14: $i] :
( ~ ( a_truth @ ( implies @ SV6 @ SY14 ) )
| ~ ( a_truth @ SV6 )
| ( a_truth @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV7: $i] :
( ( ! [SY15: $i] : ( a_truth @ ( implies @ SV7 @ ( implies @ SY15 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV8: $i,SV6: $i] :
( ( ~ ( a_truth @ ( implies @ SV6 @ SV8 ) )
| ~ ( a_truth @ SV6 )
| ( a_truth @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV9: $i,SV7: $i] :
( ( a_truth @ ( implies @ SV7 @ ( implies @ SV9 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ( a_truth @ ( implies @ SV6 @ SV8 ) )
| ~ ( a_truth @ SV6 ) )
= $true )
| ( ( a_truth @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ( a_truth @ ( implies @ SV6 @ SV8 ) ) )
= $true )
| ( ( ~ ( a_truth @ SV6 ) )
= $true )
| ( ( a_truth @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(42,plain,
! [SV8: $i,SV6: $i] :
( ( ( a_truth @ ( implies @ SV6 @ SV8 ) )
= $false )
| ( ( ~ ( a_truth @ SV6 ) )
= $true )
| ( ( a_truth @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(43,plain,
! [SV8: $i,SV6: $i] :
( ( ( a_truth @ SV6 )
= $false )
| ( ( a_truth @ ( implies @ SV6 @ SV8 ) )
= $false )
| ( ( a_truth @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(44,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,43,39,35,25]) ).
thf(45,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n006.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 12:19:22 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.24
% 0.11/0.24 No.of.Axioms: 0
% 0.11/0.24
% 0.11/0.24 Length.of.Defs: 0
% 0.11/0.24
% 0.11/0.24 Contains.Choice.Funs: false
% 0.11/0.24 .
% 0.11/0.24
% 0.11/0.24 ********************************
% 0.11/0.24 * All subproblems solved! *
% 0.11/0.24 ********************************
% 0.11/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:44,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.24
% 0.11/0.24 %**** Beginning of derivation protocol ****
% 0.11/0.24 % SZS output start CNFRefutation
% See solution above
% 0.11/0.24
% 0.11/0.24 %**** End of derivation protocol ****
% 0.11/0.24 %**** no. of clauses in derivation: 45 ****
% 0.11/0.24 %**** clause counter: 44 ****
% 0.11/0.24
% 0.11/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:44,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------