%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : HWC001-1 : TPTP v9.3.1. Bugfixed v1.1.1.
% 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 : n007.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 10:22:08 AM UTC 2026
% Result : Unsatisfiable 0.62s 0.29s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 66 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 448 ( 31 ~; 30 |; 0 &; 387 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 138 ( 0 ^; 138 !; 0 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_and,type,
and: $i > $i > $i ).
thf(tp_n0,type,
n0: $i ).
thf(tp_n1,type,
n1: $i ).
thf(tp_nand,type,
nand: $i > $i > $i ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_output,type,
output: $i > $i > $i > $i > $o ).
thf(1,axiom,
( ( not @ n1 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition2) ).
thf(2,axiom,
( ( not @ n0 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition1) ).
thf(3,axiom,
! [X: $i] :
( ( and @ X @ n1 )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition2) ).
thf(4,axiom,
! [X: $i] :
( ( and @ X @ n0 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition1) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( nand @ X @ Y )
= ( not @ ( and @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nand_definition) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
~ ( output @ n0 @ n1 @ n1 @ n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cannot_make_or) ).
thf(9,negated_conjecture,
output @ n0 @ n1 @ n0 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',input2) ).
thf(10,negated_conjecture,
output @ n0 @ n0 @ n1 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',input1) ).
thf(11,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i,Y1: $i,Y2: $i,Y3: $i,Y4: $i] :
( ~ ( output @ X1 @ X2 @ X3 @ X4 )
| ~ ( output @ Y1 @ Y2 @ Y3 @ Y4 )
| ( output @ ( nand @ X1 @ Y1 ) @ ( nand @ X2 @ Y2 ) @ ( nand @ X3 @ Y3 ) @ ( nand @ X4 @ Y4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nand_table_definition) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(13,plain,
( ( ( not @ n1 )
= n0 )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ( not @ n0 )
= n1 )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [X: $i] :
( ( and @ X @ n1 )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( and @ X @ n0 )
= n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ( nand @ X @ Y )
= ( not @ ( and @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ~ ( output @ n0 @ n1 @ n1 @ n1 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(19,plain,
( ( output @ n0 @ n1 @ n0 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(20,plain,
( ( output @ n0 @ n0 @ n1 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(21,plain,
( ( ! [X1: $i,X2: $i,X3: $i,X4: $i,Y1: $i,Y2: $i,Y3: $i,Y4: $i] :
( ~ ( output @ X1 @ X2 @ X3 @ X4 )
| ~ ( output @ Y1 @ Y2 @ Y3 @ Y4 )
| ( output @ ( nand @ X1 @ Y1 ) @ ( nand @ X2 @ Y2 ) @ ( nand @ X3 @ Y3 ) @ ( nand @ X4 @ Y4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [X1: $i,X2: $i,X3: $i,X4: $i,Y1: $i,Y2: $i,Y3: $i,Y4: $i] :
( ~ ( output @ X1 @ X2 @ X3 @ X4 )
| ~ ( output @ Y1 @ Y2 @ Y3 @ Y4 )
| ( output @ ( nand @ X1 @ Y1 ) @ ( nand @ X2 @ Y2 ) @ ( nand @ X3 @ Y3 ) @ ( nand @ X4 @ Y4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(24,plain,
( ( output @ n0 @ n0 @ n1 @ n1 )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(25,plain,
( ( output @ n0 @ n1 @ n0 @ n1 )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(26,plain,
( ( ~ ( output @ n0 @ n1 @ n1 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ( nand @ X @ Y )
= ( not @ ( and @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( and @ X @ n0 )
= n0 ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( and @ X @ n1 )
= X ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(30,plain,
( ( ( not @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(31,plain,
( ( ( not @ n1 )
= n0 )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(32,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[22]) ).
thf(33,plain,
! [SV1: $i] :
( ( ! [SY12: $i,SY13: $i,SY14: $i,SY15: $i,SY16: $i,SY17: $i,SY18: $i] :
( ~ ( output @ SV1 @ SY12 @ SY13 @ SY14 )
| ~ ( output @ SY15 @ SY16 @ SY17 @ SY18 )
| ( output @ ( nand @ SV1 @ SY15 ) @ ( nand @ SY12 @ SY16 ) @ ( nand @ SY13 @ SY17 ) @ ( nand @ SY14 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(34,plain,
( ( output @ n0 @ n1 @ n1 @ n1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV2: $i] :
( ( ! [SY19: $i] :
( ( nand @ SV2 @ SY19 )
= ( not @ ( and @ SV2 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
! [SV3: $i] :
( ( ( and @ SV3 @ n0 )
= n0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(37,plain,
! [SV4: $i] :
( ( ( and @ SV4 @ n1 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY20: $i,SY21: $i,SY22: $i,SY23: $i,SY24: $i,SY25: $i] :
( ~ ( output @ SV1 @ SV5 @ SY20 @ SY21 )
| ~ ( output @ SY22 @ SY23 @ SY24 @ SY25 )
| ( output @ ( nand @ SV1 @ SY22 ) @ ( nand @ SV5 @ SY23 ) @ ( nand @ SY20 @ SY24 ) @ ( nand @ SY21 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV6: $i,SV2: $i] :
( ( ( nand @ SV2 @ SV6 )
= ( not @ ( and @ SV2 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV7: $i,SV5: $i,SV1: $i] :
( ( ! [SY26: $i,SY27: $i,SY28: $i,SY29: $i,SY30: $i] :
( ~ ( output @ SV1 @ SV5 @ SV7 @ SY26 )
| ~ ( output @ SY27 @ SY28 @ SY29 @ SY30 )
| ( output @ ( nand @ SV1 @ SY27 ) @ ( nand @ SV5 @ SY28 ) @ ( nand @ SV7 @ SY29 ) @ ( nand @ SY26 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV8: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ! [SY31: $i,SY32: $i,SY33: $i,SY34: $i] :
( ~ ( output @ SV1 @ SV5 @ SV7 @ SV8 )
| ~ ( output @ SY31 @ SY32 @ SY33 @ SY34 )
| ( output @ ( nand @ SV1 @ SY31 ) @ ( nand @ SV5 @ SY32 ) @ ( nand @ SV7 @ SY33 ) @ ( nand @ SV8 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(43,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ! [SY35: $i,SY36: $i,SY37: $i] :
( ~ ( output @ SV1 @ SV5 @ SV7 @ SV8 )
| ~ ( output @ SV9 @ SY35 @ SY36 @ SY37 )
| ( output @ ( nand @ SV1 @ SV9 ) @ ( nand @ SV5 @ SY35 ) @ ( nand @ SV7 @ SY36 ) @ ( nand @ SV8 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ~ ( output @ SV1 @ SV5 @ SV7 @ SV8 )
| ~ ( output @ SV9 @ SV10 @ SY38 @ SY39 )
| ( output @ ( nand @ SV1 @ SV9 ) @ ( nand @ SV5 @ SV10 ) @ ( nand @ SV7 @ SY38 ) @ ( nand @ SV8 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(45,plain,
! [SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ! [SY40: $i] :
( ~ ( output @ SV1 @ SV5 @ SV7 @ SV8 )
| ~ ( output @ SV9 @ SV10 @ SV11 @ SY40 )
| ( output @ ( nand @ SV1 @ SV9 ) @ ( nand @ SV5 @ SV10 ) @ ( nand @ SV7 @ SV11 ) @ ( nand @ SV8 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(46,plain,
! [SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ~ ( output @ SV1 @ SV5 @ SV7 @ SV8 )
| ~ ( output @ SV9 @ SV10 @ SV11 @ SV12 )
| ( output @ ( nand @ SV1 @ SV9 ) @ ( nand @ SV5 @ SV10 ) @ ( nand @ SV7 @ SV11 ) @ ( nand @ SV8 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(47,plain,
! [SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( output @ SV1 @ SV5 @ SV7 @ SV8 ) )
= $true )
| ( ( ~ ( output @ SV9 @ SV10 @ SV11 @ SV12 )
| ( output @ ( nand @ SV1 @ SV9 ) @ ( nand @ SV5 @ SV10 ) @ ( nand @ SV7 @ SV11 ) @ ( nand @ SV8 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(48,plain,
! [SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV5: $i,SV1: $i] :
( ( ( output @ SV1 @ SV5 @ SV7 @ SV8 )
= $false )
| ( ( ~ ( output @ SV9 @ SV10 @ SV11 @ SV12 )
| ( output @ ( nand @ SV1 @ SV9 ) @ ( nand @ SV5 @ SV10 ) @ ( nand @ SV7 @ SV11 ) @ ( nand @ SV8 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV8: $i,SV7: $i,SV5: $i,SV1: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i] :
( ( ( ~ ( output @ SV9 @ SV10 @ SV11 @ SV12 ) )
= $true )
| ( ( output @ ( nand @ SV1 @ SV9 ) @ ( nand @ SV5 @ SV10 ) @ ( nand @ SV7 @ SV11 ) @ ( nand @ SV8 @ SV12 ) )
= $true )
| ( ( output @ SV1 @ SV5 @ SV7 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV8: $i,SV7: $i,SV5: $i,SV1: $i,SV12: $i,SV11: $i,SV10: $i,SV9: $i] :
( ( ( output @ SV9 @ SV10 @ SV11 @ SV12 )
= $false )
| ( ( output @ ( nand @ SV1 @ SV9 ) @ ( nand @ SV5 @ SV10 ) @ ( nand @ SV7 @ SV11 ) @ ( nand @ SV8 @ SV12 ) )
= $true )
| ( ( output @ SV1 @ SV5 @ SV7 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,50,40,38,37,36,34,31,30,25]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HWC001-1 : TPTP v9.3.1. Bugfixed v1.1.1.
% 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
% 0.10/0.16 % Computer : n007.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 10:54:45 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.29
% 0.62/0.29 No.of.Axioms: 9
% 0.62/0.29
% 0.62/0.29 Length.of.Defs: 0
% 0.62/0.29
% 0.62/0.29 Contains.Choice.Funs: false
% 0.62/0.29 .
% 0.62/0.29
% 0.62/0.29 ********************************
% 0.62/0.29 * All subproblems solved! *
% 0.62/0.29 ********************************
% 0.62/0.29 % SZS status Unsatisfiable for /export/starexec/sandbox/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:51,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.62/0.29
% 0.62/0.29 %**** Beginning of derivation protocol ****
% 0.62/0.29 % SZS output start CNFRefutation
% See solution above
% 0.62/0.29
% 0.62/0.29 %**** End of derivation protocol ****
% 0.62/0.29 %**** no. of clauses in derivation: 52 ****
% 0.62/0.29 %**** clause counter: 51 ****
% 0.62/0.29
% 0.62/0.29 % SZS status Unsatisfiable for /export/starexec/sandbox/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:51,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------