%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM846+2 : TPTP v9.3.1. Released v4.1.0.
% 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 : n004.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 10:35:23 AM UTC 2026
% Result : Theorem 0.09s 0.21s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 120 ( 82 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 356 ( 2 ~; 0 |; 0 &; 354 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_geq,type,
geq: $i > $i > $o ).
thf(tp_greater,type,
greater: $i > $i > $o ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd436,type,
vd436: $i ).
thf(tp_vd437,type,
vd437: $i ).
thf(tp_vd439,type,
vd439: $i ).
thf(tp_vmul,type,
vmul: $i > $i > $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vskolem2,type,
vskolem2: $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(5,axiom,
! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(7,axiom,
! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(8,axiom,
! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(13,axiom,
! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(14,axiom,
! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(16,axiom,
( ( vmul @ vd436 @ ( vsucc @ vd437 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(284, 438, 1)') ).
thf(17,axiom,
( ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ v1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(284, 438, 2)') ).
thf(18,axiom,
( ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(285, 440, 0)') ).
thf(19,axiom,
( ( vmul @ vd436 @ ( vplus @ vd437 @ ( vsucc @ vd439 ) ) )
= ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(286, 441, 0)') ).
thf(20,axiom,
( ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) )
= ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(286, 441, 1)') ).
thf(21,conjecture,
( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(286, 441, 2)') ).
thf(22,negated_conjecture,
( ( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,plain,
( ( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) )
= $false ),
inference(unfold_def,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(25,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(26,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(27,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(28,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(29,plain,
( ( ( vmul @ vd436 @ ( vsucc @ vd437 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(30,plain,
( ( ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(31,plain,
( ( ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(32,plain,
( ( ( vmul @ vd436 @ ( vplus @ vd437 @ ( vsucc @ vd439 ) ) )
= ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(33,plain,
( ( ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) )
= ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(34,plain,
( ( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
!= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(35,plain,
( ( ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) )
= ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(36,plain,
( ( ( vmul @ vd436 @ ( vplus @ vd437 @ ( vsucc @ vd439 ) ) )
= ( vmul @ vd436 @ ( vsucc @ ( vplus @ vd437 @ vd439 ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(37,plain,
( ( ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(38,plain,
( ( ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ v1 ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(39,plain,
( ( ( vmul @ vd436 @ ( vsucc @ vd437 ) )
= ( vplus @ ( vmul @ vd436 @ vd437 ) @ vd436 ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(40,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(41,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(42,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(43,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(44,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(45,plain,
( ( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
!= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(46,plain,
! [SV1: $i] :
( ( ! [SY10: $i] :
( ( vmul @ SV1 @ SY10 )
= ( vmul @ SY10 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV2: $i] :
( ( ( vmul @ v1 @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV3: $i] :
( ( ! [SY11: $i] :
( ( vplus @ SY11 @ SV3 )
= ( vplus @ SV3 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV4: $i] :
( ( ! [SY12: $i] :
( ( vplus @ ( vsucc @ SV4 ) @ SY12 )
= ( vsucc @ ( vplus @ SV4 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV5: $i] :
( ( ! [SY13: $i,SY14: $i] :
( ( vplus @ ( vplus @ SV5 @ SY13 ) @ SY14 )
= ( vplus @ SV5 @ ( vplus @ SY13 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(51,plain,
( ( ( vplus @ ( vmul @ vd436 @ ( vplus @ vd437 @ vd439 ) ) @ vd436 )
= ( vplus @ ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ vd439 ) ) @ vd436 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV6: $i,SV1: $i] :
( ( ( vmul @ SV1 @ SV6 )
= ( vmul @ SV6 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV3: $i,SV7: $i] :
( ( ( vplus @ SV7 @ SV3 )
= ( vplus @ SV3 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV8: $i,SV4: $i] :
( ( ( vplus @ ( vsucc @ SV4 ) @ SV8 )
= ( vsucc @ ( vplus @ SV4 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV9: $i,SV5: $i] :
( ( ! [SY15: $i] :
( ( vplus @ ( vplus @ SV5 @ SV9 ) @ SY15 )
= ( vplus @ SV5 @ ( vplus @ SV9 @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV10: $i,SV9: $i,SV5: $i] :
( ( ( vplus @ ( vplus @ SV5 @ SV9 ) @ SV10 )
= ( vplus @ SV5 @ ( vplus @ SV9 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(57,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,56,54,53,52,51,47,39,38,37,36]) ).
thf(58,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM846+2 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.09/0.15 % Computer : n004.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 13:40:39 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.21
% 0.09/0.21 No.of.Axioms: 10
% 0.09/0.21
% 0.09/0.21 Length.of.Defs: 0
% 0.09/0.21
% 0.09/0.21 Contains.Choice.Funs: false
% 0.09/0.21 .
% 0.09/0.21
% 0.09/0.21 ********************************
% 0.09/0.21 * All subproblems solved! *
% 0.09/0.21 ********************************
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.21
% 0.09/0.21 %**** Beginning of derivation protocol ****
% 0.09/0.21 % SZS output start CNFRefutation
% See solution above
% 0.09/0.21
% 0.09/0.21 %**** End of derivation protocol ****
% 0.09/0.21 %**** no. of clauses in derivation: 48 ****
% 0.09/0.21 %**** clause counter: 57 ****
% 0.09/0.21
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------