%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM415^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n006.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 10:33:37 AM UTC 2026
% Result : Theorem 48.66s 8.33s
% Output : CNFRefutation 48.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 28 ( 28 unt; 0 typ; 14 def)
% Number of atoms : 52 ( 38 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 487 ( 2 ~; 0 |; 0 &; 485 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 3 con; 0-4 aty)
% Number of variables : 61 ( 59 ^; 2 !; 0 ?; 61 :)
% 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_SV1,type,
sK1_SV1: $i > $i ).
thf(tp_sK2_SV2,type,
sK2_SV2: $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/sandbox2/benchmark/theBenchmark.p',eight_ax) ).
thf(five,definition,
( five
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',five_ax) ).
thf(four,definition,
( four
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',nine_ax) ).
thf(one,definition,
( one
= ( ^ [X: $i > $i,Y: $i] : ( X @ Y ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',seven_ax) ).
thf(six,definition,
( six
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ten_ax) ).
thf(three,definition,
( three
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',three_ax) ).
thf(two,definition,
( two
= ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_ax) ).
thf(zero,definition,
( zero
= ( ^ [X: $i > $i,Y: $i] : Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_ax) ).
thf(1,conjecture,
( ( mult @ two @ ( plus @ three @ seven ) )
= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ( mult @ two @ ( plus @ three @ seven ) )
= ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ^ [SY11: $i > $i,SY12: $i] : ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ SY12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= ( ^ [SY34: $i > $i,SY35: $i] : ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ SY35 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,eight,five,four,mult,nine,one,plus,seven,six,succ,ten,three,two,zero]) ).
thf(4,plain,
( ( ( ^ [SY11: $i > $i,SY12: $i] : ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ SY12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= ( ^ [SY34: $i > $i,SY35: $i] : ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ SY35 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ( ^ [SY11: $i > $i,SY12: $i] : ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ SY12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= ( ^ [SY34: $i > $i,SY35: $i] : ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ SY35 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ^ [SY11: $i > $i,SY12: $i] : ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ SY12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= ( ^ [SY34: $i > $i,SY35: $i] : ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ SY35 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SV1: $i > $i] :
( ( ^ [SY50: $i] : ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ SY50 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= ( ^ [SY51: $i] : ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ ( SV1 @ SY51 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[6]) ).
thf(8,plain,
( ( ( ^ [SY11: $i > $i,SY12: $i] : ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ ( SY11 @ SY12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= ( ^ [SY34: $i > $i,SY35: $i] : ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ ( SY34 @ SY35 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[6]) ).
thf(9,plain,
( ( ( ^ [SY52: $i] : ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SY52 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= ( ^ [SY53: $i] : ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SY53 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(10,plain,
( ( ! [SV2: $i] :
( ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SV2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SV2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[9]) ).
thf(11,plain,
( ( ( ^ [SY52: $i] : ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SY52 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= ( ^ [SY53: $i] : ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ SY53 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ sK2_SV2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ ( sK1_SV1 @ sK2_SV2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(13,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[8,12,11]) ).
thf(14,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM415^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n006.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 13:14:37 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.66/8.33
% 48.66/8.33 No.of.Axioms: 0
% 48.66/8.33
% 48.66/8.33 Length.of.Defs: 2065
% 48.66/8.33
% 48.66/8.33 Contains.Choice.Funs: false
% 48.66/8.33 .
% 48.66/8.33
% 48.66/8.33 ********************************
% 48.66/8.33 * All subproblems solved! *
% 48.66/8.33 ********************************
% 48.66/8.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:13,loop_count:0,foatp_calls:1,translation:fof_full)
% 48.66/8.33
% 48.66/8.33 %**** Beginning of derivation protocol ****
% 48.66/8.33 % SZS output start CNFRefutation
% See solution above
% 48.66/8.33
% 48.66/8.33 %**** End of derivation protocol ****
% 48.66/8.33 %**** no. of clauses in derivation: 14 ****
% 48.66/8.33 %**** clause counter: 13 ****
% 48.66/8.33
% 48.66/8.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:13,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------