%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX186+1 : TPTP v9.3.1. Released v9.3.0.
% 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 : n013.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 11:02:30 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 189 ( 133 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 294 ( 79 ~; 14 |; 0 &; 196 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 127 ( 0 ^; 112 !; 15 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_drop,type,
drop: $i > $i > $i ).
thf(tp_head,type,
head: $i > $i ).
thf(tp_nil,type,
nil: $i ).
thf(tp_proj1S,type,
proj1S: $i > $i ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_tail,type,
tail: $i > $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [Y: $i] :
( ( drop @ z @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(2,axiom,
! [Z: $i,X2: $i,X3: $i] :
( ( drop @ ( s @ Z ) @ ( cons @ X2 @ X3 ) )
= ( drop @ Z @ X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(3,axiom,
! [Z: $i] :
( ( drop @ ( s @ Z ) @ nil )
= nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(4,axiom,
! [X: $i] :
( ( s @ X )
!= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(5,axiom,
! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(6,axiom,
! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(7,axiom,
! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(8,axiom,
! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(9,conjecture,
? [N: $i,Xs: $i,Ys: $i] :
~ ( ( ( drop @ N @ Xs )
= ( drop @ N @ Ys ) )
=> ( Xs = Ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_009) ).
thf(10,negated_conjecture,
( ( ? [N: $i,Xs: $i,Ys: $i] :
~ ( ( ( drop @ N @ Xs )
= ( drop @ N @ Ys ) )
=> ( Xs = Ys ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,plain,
( ( ? [N: $i,Xs: $i,Ys: $i] :
~ ( ( ( drop @ N @ Xs )
= ( drop @ N @ Ys ) )
=> ( Xs = Ys ) ) )
= $false ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [Y: $i] :
( ( drop @ z @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [Z: $i,X2: $i,X3: $i] :
( ( drop @ ( s @ Z ) @ ( cons @ X2 @ X3 ) )
= ( drop @ Z @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [Z: $i] :
( ( drop @ ( s @ Z ) @ nil )
= nil ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [X: $i] :
( ( s @ X )
!= z ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ~ ? [N: $i,Xs: $i,Ys: $i] :
~ ( ( ( drop @ N @ Xs )
= ( drop @ N @ Ys ) )
=> ( Xs = Ys ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(22,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( s @ X )
!= z ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(26,plain,
( ( ! [Z: $i] :
( ( drop @ ( s @ Z ) @ nil )
= nil ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(27,plain,
( ( ! [Z: $i,X2: $i,X3: $i] :
( ( drop @ ( s @ Z ) @ ( cons @ X2 @ X3 ) )
= ( drop @ Z @ X3 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(28,plain,
( ( ! [Y: $i] :
( ( drop @ z @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(29,plain,
( ( ~ ? [N: $i,Xs: $i,Ys: $i] :
~ ( ( ( drop @ N @ Xs )
= ( drop @ N @ Ys ) )
=> ( Xs = Ys ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(30,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ( ( drop @ SX0 @ SX1 )
!= ( drop @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(31,plain,
( ( ! [SX0: $i] :
( ( s @ SX0 )
!= z ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [SX0: $i,SX1: $i] :
( nil
!= ( cons @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(33,plain,
! [SV1: $i] :
( ( ! [SY16: $i] :
( ( head @ ( cons @ SV1 @ SY16 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(34,plain,
! [SV2: $i] :
( ( ! [SY17: $i] :
( ( tail @ ( cons @ SV2 @ SY17 ) )
= SY17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(35,plain,
! [SV3: $i] :
( ( ( proj1S @ ( s @ SV3 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(36,plain,
! [SV4: $i] :
( ( ( drop @ ( s @ SV4 ) @ nil )
= nil )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
! [SV5: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ( drop @ ( s @ SV5 ) @ ( cons @ SY18 @ SY19 ) )
= ( drop @ SV5 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(38,plain,
! [SV6: $i] :
( ( ( drop @ z @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(39,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ( ( drop @ SX0 @ SX1 )
!= ( drop @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(40,plain,
! [SV7: $i] :
( ( ( s @ SV7 )
!= z )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV8: $i] :
( ( ! [SY20: $i] :
( nil
!= ( cons @ SV8 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(42,plain,
! [SV9: $i,SV1: $i] :
( ( ( head @ ( cons @ SV1 @ SV9 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(43,plain,
! [SV10: $i,SV2: $i] :
( ( ( tail @ ( cons @ SV2 @ SV10 ) )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(44,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY21: $i] :
( ( drop @ ( s @ SV5 ) @ ( cons @ SV11 @ SY21 ) )
= ( drop @ SV5 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ( ( drop @ SX0 @ SX1 )
!= ( drop @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(46,plain,
! [SV7: $i] :
( ( ( s @ SV7 )
= z )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV12: $i,SV8: $i] :
( ( nil
!= ( cons @ SV8 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV13: $i,SV11: $i,SV5: $i] :
( ( ( drop @ ( s @ SV5 ) @ ( cons @ SV11 @ SV13 ) )
= ( drop @ SV5 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV14: $i] :
( ( ~ ~ ! [SY22: $i] :
~ ~ ! [SY23: $i] :
~ ~ ( ( ( drop @ SV14 @ SY22 )
!= ( drop @ SV14 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV12: $i,SV8: $i] :
( ( nil
= ( cons @ SV8 @ SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV14: $i] :
( ( ~ ! [SY22: $i] :
~ ~ ! [SY23: $i] :
~ ~ ( ( ( drop @ SV14 @ SY22 )
!= ( drop @ SV14 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV14: $i] :
( ( ! [SY22: $i] :
~ ~ ! [SY23: $i] :
~ ~ ( ( ( drop @ SV14 @ SY22 )
!= ( drop @ SV14 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(53,plain,
! [SV15: $i,SV14: $i] :
( ( ~ ~ ! [SY24: $i] :
~ ~ ( ( ( drop @ SV14 @ SV15 )
!= ( drop @ SV14 @ SY24 ) )
| ( SV15 = SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(54,plain,
! [SV15: $i,SV14: $i] :
( ( ~ ! [SY24: $i] :
~ ~ ( ( ( drop @ SV14 @ SV15 )
!= ( drop @ SV14 @ SY24 ) )
| ( SV15 = SY24 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(55,plain,
! [SV15: $i,SV14: $i] :
( ( ! [SY24: $i] :
~ ~ ( ( ( drop @ SV14 @ SV15 )
!= ( drop @ SV14 @ SY24 ) )
| ( SV15 = SY24 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(56,plain,
! [SV16: $i,SV15: $i,SV14: $i] :
( ( ~ ~ ( ( ( drop @ SV14 @ SV15 )
!= ( drop @ SV14 @ SV16 ) )
| ( SV15 = SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(57,plain,
! [SV16: $i,SV15: $i,SV14: $i] :
( ( ~ ( ( ( drop @ SV14 @ SV15 )
!= ( drop @ SV14 @ SV16 ) )
| ( SV15 = SV16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(58,plain,
! [SV16: $i,SV15: $i,SV14: $i] :
( ( ( ( drop @ SV14 @ SV15 )
!= ( drop @ SV14 @ SV16 ) )
| ( SV15 = SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(59,plain,
! [SV16: $i,SV15: $i,SV14: $i] :
( ( ( ( drop @ SV14 @ SV15 )
!= ( drop @ SV14 @ SV16 ) )
= $true )
| ( ( SV15 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(60,plain,
! [SV16: $i,SV15: $i,SV14: $i] :
( ( ( ( drop @ SV14 @ SV15 )
= ( drop @ SV14 @ SV16 ) )
= $false )
| ( ( SV15 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,60,50,48,46,43,42,38,36]) ).
thf(62,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX186+1 : TPTP v9.3.1. Released v9.3.0.
% 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
% 0.09/0.20 % Computer : n013.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 17:09:51 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:0,axioms:8,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:61,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: 62 ****
% 0.09/0.26 %**** clause counter: 61 ****
% 0.09/0.26
% 0.09/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------