%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : KLE002+1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 10:25:45 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 63 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 206 ( 110 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 410 ( 29 ~; 20 |; 0 &; 352 @)
% ( 3 <=>; 6 =>; 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; 7 con; 0-2 aty)
% Number of variables : 112 ( 0 ^; 112 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addition,type,
addition: $i > $i > $i ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_multiplication,type,
multiplication: $i > $i > $i ).
thf(tp_one,type,
one: $i ).
thf(tp_sK1_X0,type,
sK1_X0: $i ).
thf(tp_sK2_SY18,type,
sK2_SY18: $i ).
thf(tp_sK3_SY20,type,
sK3_SY20: $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(2,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(3,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
thf(6,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(7,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(13,conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( leq @ X0 @ X1 )
=> ( leq @ ( multiplication @ X0 @ X2 ) @ ( multiplication @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(14,negated_conjecture,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( leq @ X0 @ X1 )
=> ( leq @ ( multiplication @ X0 @ X2 ) @ ( multiplication @ X1 @ X2 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( leq @ X0 @ X1 )
=> ( leq @ ( multiplication @ X0 @ X2 ) @ ( multiplication @ X1 @ X2 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(23,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( ! [SY18: $i,SY19: $i] :
( ( leq @ sK1_X0 @ SY18 )
=> ( leq @ ( multiplication @ sK1_X0 @ SY19 ) @ ( multiplication @ SY18 @ SY19 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(25,plain,
( ( ! [SY20: $i] :
( ( leq @ sK1_X0 @ sK2_SY18 )
=> ( leq @ ( multiplication @ sK1_X0 @ SY20 ) @ ( multiplication @ sK2_SY18 @ SY20 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(26,plain,
( ( ( leq @ sK1_X0 @ sK2_SY18 )
=> ( leq @ ( multiplication @ sK1_X0 @ sK3_SY20 ) @ ( multiplication @ sK2_SY18 @ sK3_SY20 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(27,plain,
( ( leq @ sK1_X0 @ sK2_SY18 )
= $true ),
inference(standard_cnf,[status(thm)],[26]) ).
thf(28,plain,
( ( leq @ ( multiplication @ sK1_X0 @ sK3_SY20 ) @ ( multiplication @ sK2_SY18 @ sK3_SY20 ) )
= $false ),
inference(standard_cnf,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ( leq @ ( multiplication @ sK1_X0 @ sK3_SY20 ) @ ( multiplication @ sK2_SY18 @ sK3_SY20 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(30,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(31,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ one )
= A ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( multiplication @ one @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(33,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(34,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(35,plain,
( ( ! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( multiplication @ zero @ A )
= zero ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(38,plain,
( ( leq @ sK1_X0 @ sK2_SY18 )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,plain,
( ( ~ ( leq @ ( multiplication @ sK1_X0 @ sK3_SY20 ) @ ( multiplication @ sK2_SY18 @ sK3_SY20 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(40,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ SX0 @ SX1 )
| ( ( addition @ SX0 @ SX1 )
= SX1 ) )
| ~ ( ( ( addition @ SX0 @ SX1 )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(41,plain,
! [SV1: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ( multiplication @ SV1 @ ( multiplication @ SY21 @ SY22 ) )
= ( multiplication @ ( multiplication @ SV1 @ SY21 ) @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(42,plain,
! [SV2: $i] :
( ( ( multiplication @ SV2 @ one )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(43,plain,
! [SV3: $i] :
( ( ( multiplication @ one @ SV3 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(44,plain,
! [SV4: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ( multiplication @ SV4 @ ( addition @ SY23 @ SY24 ) )
= ( addition @ ( multiplication @ SV4 @ SY23 ) @ ( multiplication @ SV4 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(45,plain,
! [SV5: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ( multiplication @ ( addition @ SV5 @ SY25 ) @ SY26 )
= ( addition @ ( multiplication @ SV5 @ SY26 ) @ ( multiplication @ SY25 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(46,plain,
! [SV6: $i] :
( ( ( multiplication @ SV6 @ zero )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(47,plain,
! [SV7: $i] :
( ( ( multiplication @ zero @ SV7 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(48,plain,
( ( leq @ ( multiplication @ sK1_X0 @ sK3_SY20 ) @ ( multiplication @ sK2_SY18 @ sK3_SY20 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(49,plain,
! [SV8: $i] :
( ( ! [SY27: $i] :
~ ( ~ ( ~ ( leq @ SV8 @ SY27 )
| ( ( addition @ SV8 @ SY27 )
= SY27 ) )
| ~ ( ( ( addition @ SV8 @ SY27 )
!= SY27 )
| ( leq @ SV8 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV9: $i,SV1: $i] :
( ( ! [SY28: $i] :
( ( multiplication @ SV1 @ ( multiplication @ SV9 @ SY28 ) )
= ( multiplication @ ( multiplication @ SV1 @ SV9 ) @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY29: $i] :
( ( multiplication @ SV4 @ ( addition @ SV10 @ SY29 ) )
= ( addition @ ( multiplication @ SV4 @ SV10 ) @ ( multiplication @ SV4 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY30: $i] :
( ( multiplication @ ( addition @ SV5 @ SV11 ) @ SY30 )
= ( addition @ ( multiplication @ SV5 @ SY30 ) @ ( multiplication @ SV11 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV12: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( leq @ SV8 @ SV12 )
| ( ( addition @ SV8 @ SV12 )
= SV12 ) )
| ~ ( ( ( addition @ SV8 @ SV12 )
!= SV12 )
| ( leq @ SV8 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV13: $i,SV9: $i,SV1: $i] :
( ( ( multiplication @ SV1 @ ( multiplication @ SV9 @ SV13 ) )
= ( multiplication @ ( multiplication @ SV1 @ SV9 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV14: $i,SV10: $i,SV4: $i] :
( ( ( multiplication @ SV4 @ ( addition @ SV10 @ SV14 ) )
= ( addition @ ( multiplication @ SV4 @ SV10 ) @ ( multiplication @ SV4 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV15: $i,SV11: $i,SV5: $i] :
( ( ( multiplication @ ( addition @ SV5 @ SV11 ) @ SV15 )
= ( addition @ ( multiplication @ SV5 @ SV15 ) @ ( multiplication @ SV11 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV12: $i,SV8: $i] :
( ( ~ ( ~ ( leq @ SV8 @ SV12 )
| ( ( addition @ SV8 @ SV12 )
= SV12 ) )
| ~ ( ( ( addition @ SV8 @ SV12 )
!= SV12 )
| ( leq @ SV8 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV12: $i,SV8: $i] :
( ( ~ ( ~ ( leq @ SV8 @ SV12 )
| ( ( addition @ SV8 @ SV12 )
= SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(59,plain,
! [SV12: $i,SV8: $i] :
( ( ~ ( ( ( addition @ SV8 @ SV12 )
!= SV12 )
| ( leq @ SV8 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(60,plain,
! [SV12: $i,SV8: $i] :
( ( ~ ( leq @ SV8 @ SV12 )
| ( ( addition @ SV8 @ SV12 )
= SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(61,plain,
! [SV12: $i,SV8: $i] :
( ( ( ( addition @ SV8 @ SV12 )
!= SV12 )
| ( leq @ SV8 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(62,plain,
! [SV12: $i,SV8: $i] :
( ( ( ~ ( leq @ SV8 @ SV12 ) )
= $true )
| ( ( ( addition @ SV8 @ SV12 )
= SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV12: $i,SV8: $i] :
( ( ( ( addition @ SV8 @ SV12 )
!= SV12 )
= $true )
| ( ( leq @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV12: $i,SV8: $i] :
( ( ( leq @ SV8 @ SV12 )
= $false )
| ( ( ( addition @ SV8 @ SV12 )
= SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV12: $i,SV8: $i] :
( ( ( ( addition @ SV8 @ SV12 )
= SV12 )
= $false )
| ( ( leq @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,65,64,56,55,54,48,47,46,43,42]) ).
thf(67,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE002+1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n014.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 11:30:26 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.26
% 0.09/0.26 No.of.Axioms: 8
% 0.09/0.26
% 0.09/0.26 Length.of.Defs: 0
% 0.09/0.26
% 0.09/0.26 Contains.Choice.Funs: false
% 0.09/0.26 .
% 0.09/0.26
% 0.09/0.26 ********************************
% 0.09/0.26 * All subproblems solved! *
% 0.09/0.26 ********************************
% 0.09/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:9,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:66,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.26
% 0.09/0.26 %**** Beginning of derivation protocol ****
% 0.09/0.26 % SZS output start CNFRefutation
% See solution above
% 0.09/0.26
% 0.09/0.26 %**** End of derivation protocol ****
% 0.09/0.26 %**** no. of clauses in derivation: 63 ****
% 0.09/0.26 %**** clause counter: 66 ****
% 0.09/0.26
% 0.09/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:9,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:66,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------