%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM798^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n011.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 10:35:16 AM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 30 ( 30 unt; 0 typ; 14 def)
% Number of atoms : 58 ( 42 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 131 ( 4 ~; 0 |; 0 &; 127 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 2 con; 0-4 aty)
% Number of variables : 95 ( 79 ^; 12 !; 4 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_eight,type,
eight: ( $i > $i ) > $i > $i ).
thf(tp_five,type,
five: ( $i > $i ) > $i > $i ).
thf(tp_four,type,
four: ( $i > $i ) > $i > $i ).
thf(tp_mult,type,
mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_nine,type,
nine: ( $i > $i ) > $i > $i ).
thf(tp_one,type,
one: ( $i > $i ) > $i > $i ).
thf(tp_plus,type,
plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_sK1_SV2,type,
sK1_SV2: ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(tp_sK2_SV3,type,
sK2_SV3: ( ( $i > $i ) > $i > $i ) > $i ).
thf(tp_seven,type,
seven: ( $i > $i ) > $i > $i ).
thf(tp_six,type,
six: ( $i > $i ) > $i > $i ).
thf(tp_succ,type,
succ: ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(tp_ten,type,
ten: ( $i > $i ) > $i > $i ).
thf(tp_three,type,
three: ( $i > $i ) > $i > $i ).
thf(tp_two,type,
two: ( $i > $i ) > $i > $i ).
thf(tp_zero,type,
zero: ( $i > $i ) > $i > $i ).
thf(eight,definition,
( eight
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eight_ax) ).
thf(five,definition,
( five
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',five_ax) ).
thf(four,definition,
( four
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',four_ax) ).
thf(mult,definition,
( mult
= ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ ( N @ X ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mult_ax) ).
thf(nine,definition,
( nine
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nine_ax) ).
thf(one,definition,
( one
= ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_ax) ).
thf(plus,definition,
( plus
= ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ X @ ( N @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_ax) ).
thf(seven,definition,
( seven
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',seven_ax) ).
thf(six,definition,
( six
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',six_ax) ).
thf(succ,definition,
( succ
= ( ^ [N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( X @ ( N @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_ax) ).
thf(ten,definition,
( ten
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ten_ax) ).
thf(three,definition,
( three
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',three_ax) ).
thf(two,definition,
( two
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_ax) ).
thf(zero,definition,
( zero
= ( ^ [X: $i > $i,Y: $i] : Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_ax) ).
thf(1,conjecture,
? [N: ( $i > $i ) > $i > $i] :
( ( mult @ N @ one )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ? [N: ( $i > $i ) > $i > $i] :
( ( mult @ N @ one )
= one ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [SY0: ( $i > $i ) > $i > $i] :
( ( ^ [SY4: $i > $i,SY5: $i] :
( SY0
@ ^ [SY6: $i] : ( SY4 @ SY6 )
@ SY5 ) )
= ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,eight,five,four,mult,nine,one,plus,seven,six,succ,ten,three,two,zero]) ).
thf(4,plain,
( ( ~ ? [SY0: ( $i > $i ) > $i > $i] :
( ( ^ [SY4: $i > $i,SY5: $i] :
( SY0
@ ^ [SY6: $i] : ( SY4 @ SY6 )
@ SY5 ) )
= ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: ( $i > $i ) > $i > $i] :
( ( ^ [SY4: $i > $i,SY5: $i] :
( SY0
@ ^ [SY6: $i] : ( SY4 @ SY6 )
@ SY5 ) )
!= ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY0: ( $i > $i ) > $i > $i] :
( ( ^ [SY4: $i > $i,SY5: $i] :
( SY0
@ ^ [SY6: $i] : ( SY4 @ SY6 )
@ SY5 ) )
!= ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
! [SV1: ( $i > $i ) > $i > $i] :
( ( ( ^ [SY13: $i > $i,SY14: $i] :
( SV1
@ ^ [SY6: $i] : ( SY13 @ SY6 )
@ SY14 ) )
!= ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: ( $i > $i ) > $i > $i] :
( ( ( ^ [SY13: $i > $i,SY14: $i] :
( SV1
@ ^ [SY6: $i] : ( SY13 @ SY6 )
@ SY14 ) )
= ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: ( $i > $i ) > $i > $i] :
( ( ! [SV2: $i > $i] :
( ( ^ [SY18: $i] :
( SV1
@ ^ [SY19: $i] : ( SV2 @ SY19 )
@ SY18 ) )
= ( ^ [SY20: $i] : ( SV2 @ SY20 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: ( $i > $i ) > $i > $i] :
( ( ( ^ [SY13: $i > $i,SY14: $i] :
( SV1
@ ^ [SY6: $i] : ( SY13 @ SY6 )
@ SY14 ) )
= ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[8]) ).
thf(11,plain,
! [SV1: ( $i > $i ) > $i > $i] :
( ( ( ^ [SY21: $i] :
( SV1
@ ^ [SY22: $i] : ( sK1_SV2 @ SV1 @ SY22 )
@ SY21 ) )
= ( ^ [SY23: $i] : ( sK1_SV2 @ SV1 @ SY23 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(12,plain,
! [SV1: ( $i > $i ) > $i > $i] :
( ( ! [SV3: $i] :
( ( SV1
@ ^ [SY22: $i] : ( sK1_SV2 @ SV1 @ SY22 )
@ SV3 )
= ( sK1_SV2 @ SV1 @ SV3 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[11]) ).
thf(13,plain,
! [SV1: ( $i > $i ) > $i > $i] :
( ( ( ^ [SY21: $i] :
( SV1
@ ^ [SY22: $i] : ( sK1_SV2 @ SV1 @ SY22 )
@ SY21 ) )
= ( ^ [SY23: $i] : ( sK1_SV2 @ SV1 @ SY23 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: ( $i > $i ) > $i > $i] :
( ( ( SV1
@ ^ [SY22: $i] : ( sK1_SV2 @ SV1 @ SY22 )
@ ( sK2_SV3 @ SV1 ) )
= ( sK1_SV2 @ SV1 @ ( sK2_SV3 @ SV1 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(15,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[10,14,13]) ).
thf(16,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM798^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 13:39:36 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.23
% 0.07/0.23 No.of.Axioms: 0
% 0.07/0.23
% 0.07/0.23 Length.of.Defs: 2051
% 0.07/0.23
% 0.07/0.23 Contains.Choice.Funs: false
% 0.07/0.23
% 0.07/0.23 ********************************
% 0.07/0.23 * All subproblems solved! *
% 0.07/0.23 ********************************
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:15,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.07/0.23
% 0.07/0.23 %**** Beginning of derivation protocol ****
% 0.07/0.23 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23
% 0.07/0.23 %**** End of derivation protocol ****
% 0.07/0.23 %**** no. of clauses in derivation: 16 ****
% 0.07/0.23 %**** clause counter: 15 ****
% 0.07/0.23
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:15,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------