%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL982+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10:31:12 AM UTC 2026
% Result : Theorem 0.10s 0.22s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 108 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 347 ( 17 ~; 18 |; 0 &; 312 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% 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_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY10,type,
sK2_SY10: $i ).
thf(tp_sK3_SY12,type,
sK3_SY12: $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ ( implies @ C @ ( implies @ D @ E ) ) @ ( implies @ B @ ( implies @ ( not @ D ) @ ( not @ A ) ) ) ) @ ( implies @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( implies @ X @ Y ) )
| ~ ( is_a_theorem @ X )
| ( is_a_theorem @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(3,conjecture,
! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_1) ).
thf(4,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ ( implies @ C @ ( implies @ D @ E ) ) @ ( implies @ B @ ( implies @ ( not @ D ) @ ( not @ A ) ) ) ) @ ( implies @ A @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,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)],[2]) ).
thf(8,plain,
( ( ! [SY10: $i,SY11: $i] : ( is_a_theorem @ ( implies @ ( implies @ sK1_A @ SY10 ) @ ( implies @ ( implies @ SY10 @ SY11 ) @ ( implies @ sK1_A @ SY11 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(9,plain,
( ( ! [SY12: $i] : ( is_a_theorem @ ( implies @ ( implies @ sK1_A @ sK2_SY10 ) @ ( implies @ ( implies @ sK2_SY10 @ SY12 ) @ ( implies @ sK1_A @ SY12 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(10,plain,
( ( is_a_theorem @ ( implies @ ( implies @ sK1_A @ sK2_SY10 ) @ ( implies @ ( implies @ sK2_SY10 @ sK3_SY12 ) @ ( implies @ sK1_A @ sK3_SY12 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(11,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK1_A @ sK2_SY10 ) @ ( implies @ ( implies @ sK2_SY10 @ sK3_SY12 ) @ ( implies @ sK1_A @ sK3_SY12 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( implies @ X @ Y ) )
| ~ ( is_a_theorem @ X )
| ( is_a_theorem @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ ( implies @ C @ ( implies @ D @ E ) ) @ ( implies @ B @ ( implies @ ( not @ D ) @ ( not @ A ) ) ) ) @ ( implies @ A @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(14,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK1_A @ sK2_SY10 ) @ ( implies @ ( implies @ sK2_SY10 @ sK3_SY12 ) @ ( implies @ sK1_A @ sK3_SY12 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ~ ( is_a_theorem @ ( implies @ SV1 @ SY13 ) )
| ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV2: $i] :
( ( ! [SY14: $i,SY15: $i,SY16: $i,SY17: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV2 @ SY14 ) @ ( implies @ ( implies @ ( implies @ SY15 @ ( implies @ SY16 @ SY17 ) ) @ ( implies @ SY14 @ ( implies @ ( not @ SY16 ) @ ( not @ SV2 ) ) ) ) @ ( implies @ SV2 @ SY16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
( ( is_a_theorem @ ( implies @ ( implies @ sK1_A @ sK2_SY10 ) @ ( implies @ ( implies @ sK2_SY10 @ sK3_SY12 ) @ ( implies @ sK1_A @ sK3_SY12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( is_a_theorem @ ( implies @ SV1 @ SV3 ) )
| ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY18: $i,SY19: $i,SY20: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV2 @ SV4 ) @ ( implies @ ( implies @ ( implies @ SY18 @ ( implies @ SY19 @ SY20 ) ) @ ( implies @ SV4 @ ( implies @ ( not @ SY19 ) @ ( not @ SV2 ) ) ) ) @ ( implies @ SV2 @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( is_a_theorem @ ( implies @ SV1 @ SV3 ) )
| ~ ( is_a_theorem @ SV1 ) )
= $true )
| ( ( is_a_theorem @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY21: $i,SY22: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV2 @ SV4 ) @ ( implies @ ( implies @ ( implies @ SV5 @ ( implies @ SY21 @ SY22 ) ) @ ( implies @ SV4 @ ( implies @ ( not @ SY21 ) @ ( not @ SV2 ) ) ) ) @ ( implies @ SV2 @ SY21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( is_a_theorem @ ( implies @ SV1 @ SV3 ) ) )
= $true )
| ( ( ~ ( is_a_theorem @ SV1 ) )
= $true )
| ( ( is_a_theorem @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( ! [SY23: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV2 @ SV4 ) @ ( implies @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ SY23 ) ) @ ( implies @ SV4 @ ( implies @ ( not @ SV6 ) @ ( not @ SV2 ) ) ) ) @ ( implies @ SV2 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV3: $i,SV1: $i] :
( ( ( is_a_theorem @ ( implies @ SV1 @ SV3 ) )
= $false )
| ( ( ~ ( is_a_theorem @ SV1 ) )
= $true )
| ( ( is_a_theorem @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
( ( is_a_theorem @ ( implies @ ( implies @ SV2 @ SV4 ) @ ( implies @ ( implies @ ( implies @ SV5 @ ( implies @ SV6 @ SV7 ) ) @ ( implies @ SV4 @ ( implies @ ( not @ SV6 ) @ ( not @ SV2 ) ) ) ) @ ( implies @ SV2 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV3: $i,SV1: $i] :
( ( ( is_a_theorem @ SV1 )
= $false )
| ( ( is_a_theorem @ ( implies @ SV1 @ SV3 ) )
= $false )
| ( ( is_a_theorem @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,26,25]) ).
thf(28,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL982+1 : TPTP v9.3.1. Released v9.1.0.
% 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
% 0.10/0.17 % Computer : n008.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 12:38:39 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.22
% 0.10/0.22 No.of.Axioms: 2
% 0.10/0.22
% 0.10/0.22 Length.of.Defs: 0
% 0.10/0.22
% 0.10/0.22 Contains.Choice.Funs: false
% 0.10/0.22
% 0.10/0.22 ********************************
% 0.10/0.22 * All subproblems solved! *
% 0.10/0.22 ********************************
% 0.10/0.22 % 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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:27,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.22
% 0.10/0.22 %**** Beginning of derivation protocol ****
% 0.10/0.22 % SZS output start CNFRefutation
% See solution above
% 0.10/0.22
% 0.10/0.22 %**** End of derivation protocol ****
% 0.10/0.22 %**** no. of clauses in derivation: 28 ****
% 0.10/0.22 %**** clause counter: 27 ****
% 0.10/0.22
% 0.10/0.22 % 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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:27,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------