%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL368+1 : TPTP v9.3.1. Released v9.1.0.
% 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 : n016.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 10:28:36 AM UTC 2026
% Result : Theorem 70.87s 12.10s
% Output : CNFRefutation 70.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 135 ( 38 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 320 ( 26 ~; 18 |; 3 &; 270 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_implies,type,
implies: $i > $i > $i ).
thf(tp_is_a_theorem,type,
is_a_theorem: $i > $o ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_u,type,
u: $i ).
thf(tp_x,type,
x: $i ).
thf(tp_y,type,
y: $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ ( not @ X ) @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
thf(2,axiom,
! [X: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ X ) @ X ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( ( is_a_theorem @ ( implies @ X @ Y ) )
& ( is_a_theorem @ X ) )
=> ( is_a_theorem @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
thf(5,conjecture,
is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_23) ).
thf(6,negated_conjecture,
( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ ( not @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [X: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ X ) @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ ( implies @ X @ Y ) )
& ( is_a_theorem @ X ) )
=> ( is_a_theorem @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ ( implies @ X @ Y ) )
& ( is_a_theorem @ X ) )
=> ( is_a_theorem @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ! [X: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ X ) @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ ( not @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(17,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( is_a_theorem @ ( implies @ SX0 @ SX1 ) )
| ~ ( is_a_theorem @ SX0 ) )
| ( is_a_theorem @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(19,plain,
! [SV1: $i] :
( ( ! [SY8: $i,SY9: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV1 @ SY8 ) @ ( implies @ ( implies @ SY8 @ SY9 ) @ ( implies @ SV1 @ SY9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(20,plain,
! [SV2: $i] :
( ( is_a_theorem @ ( implies @ ( implies @ ( not @ SV2 ) @ SV2 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV3: $i] :
( ( ! [SY10: $i] : ( is_a_theorem @ ( implies @ SV3 @ ( implies @ ( not @ SV3 ) @ SY10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ x @ ( implies @ y @ z ) ) @ u ) @ ( implies @ ( implies @ y @ ( implies @ x @ z ) ) @ u ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(23,plain,
! [SV4: $i] :
( ( ! [SY11: $i] :
( ~ ~ ( ~ ( is_a_theorem @ ( implies @ SV4 @ SY11 ) )
| ~ ( is_a_theorem @ SV4 ) )
| ( is_a_theorem @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY12: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV1 @ SV5 ) @ ( implies @ ( implies @ SV5 @ SY12 ) @ ( implies @ SV1 @ SY12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV6: $i,SV3: $i] :
( ( is_a_theorem @ ( implies @ SV3 @ ( implies @ ( not @ SV3 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV7: $i,SV4: $i] :
( ( ~ ~ ( ~ ( is_a_theorem @ ( implies @ SV4 @ SV7 ) )
| ~ ( is_a_theorem @ SV4 ) )
| ( is_a_theorem @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV8: $i,SV5: $i,SV1: $i] :
( ( is_a_theorem @ ( implies @ ( implies @ SV1 @ SV5 ) @ ( implies @ ( implies @ SV5 @ SV8 ) @ ( implies @ SV1 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( is_a_theorem @ ( implies @ SV4 @ SV7 ) )
| ~ ( is_a_theorem @ SV4 ) ) )
= $true )
| ( ( is_a_theorem @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ( ~ ( is_a_theorem @ ( implies @ SV4 @ SV7 ) )
| ~ ( is_a_theorem @ SV4 ) ) )
= $false )
| ( ( is_a_theorem @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(30,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ( is_a_theorem @ ( implies @ SV4 @ SV7 ) )
| ~ ( is_a_theorem @ SV4 ) )
= $true )
| ( ( is_a_theorem @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(31,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ( is_a_theorem @ ( implies @ SV4 @ SV7 ) ) )
= $true )
| ( ( ~ ( is_a_theorem @ SV4 ) )
= $true )
| ( ( is_a_theorem @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(32,plain,
! [SV7: $i,SV4: $i] :
( ( ( is_a_theorem @ ( implies @ SV4 @ SV7 ) )
= $false )
| ( ( ~ ( is_a_theorem @ SV4 ) )
= $true )
| ( ( is_a_theorem @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(33,plain,
! [SV7: $i,SV4: $i] :
( ( ( is_a_theorem @ SV4 )
= $false )
| ( ( is_a_theorem @ ( implies @ SV4 @ SV7 ) )
= $false )
| ( ( is_a_theorem @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(34,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,33,27,25,22]) ).
thf(35,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL368+1 : TPTP v9.3.1. Released v9.1.0.
% 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
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Oct 6 12:21:59 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 70.87/12.10
% 70.87/12.10 No.of.Axioms: 4
% 70.87/12.10
% 70.87/12.10 Length.of.Defs: 0
% 70.87/12.10
% 70.87/12.10 Contains.Choice.Funs: false
% 70.87/12.10
% 70.87/12.10 ********************************
% 70.87/12.10 * All subproblems solved! *
% 70.87/12.10 ********************************
% 70.87/12.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,ps:0,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:34,loop_count:0,foatp_calls:1,translation:fof_full)
% 70.87/12.10
% 70.87/12.10 %**** Beginning of derivation protocol ****
% 70.87/12.10 % SZS output start CNFRefutation
% See solution above
% 70.87/12.10
% 70.87/12.10 %**** End of derivation protocol ****
% 70.87/12.10 %**** no. of clauses in derivation: 35 ****
% 70.87/12.10 %**** clause counter: 34 ****
% 70.87/12.10
% 70.87/12.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,ps:0,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:34,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------