%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n001.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 10:32:47 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.22s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 261 ( 66 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 406 ( 50 ~; 76 |; 0 &; 280 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 112 ( 0 ^; 112 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_divides,type,
divides: $i > $i > $o ).
thf(tp_prime,type,
prime: $i > $o ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(tp_square,type,
square: $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i,U: $i] :
( ~ ( prime @ X )
| ~ ( product @ Y @ Z @ U )
| ~ ( divides @ X @ U )
| ( divides @ X @ Y )
| ( divides @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',remainder) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( divides @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ Y @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity) ).
thf(4,axiom,
! [X: $i] : ( product @ X @ X @ ( square @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square) ).
thf(5,axiom,
product @ a @ ( square @ c ) @ ( square @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b_squared_by_c_squared) ).
thf(6,axiom,
prime @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_prime) ).
thf(7,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(8,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,negated_conjecture,
~ ( divides @ a @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divides_b) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i] :
( ~ ( prime @ X )
| ~ ( product @ Y @ Z @ U )
| ~ ( divides @ X @ U )
| ( divides @ X @ Y )
| ( divides @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( divides @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ Y @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [X: $i] : ( product @ X @ X @ ( square @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( product @ a @ ( square @ c ) @ ( square @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( prime @ a )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ~ ( divides @ a @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( prime @ X )
| ! [Z: $i,U: $i] :
( ~ ( product @ Y @ Z @ U )
| ~ ( divides @ X @ U )
| ( divides @ X @ Y )
| ( divides @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(20,plain,
( ( ~ ( divides @ a @ b ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(21,plain,
( ( prime @ a )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(22,plain,
( ( product @ a @ ( square @ c ) @ ( square @ b ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(23,plain,
( ( ! [X: $i] : ( product @ X @ X @ ( square @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ Y @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( divides @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( prime @ X )
| ! [Z: $i,U: $i] :
( ~ ( product @ Y @ Z @ U )
| ~ ( divides @ X @ U )
| ( divides @ X @ Y )
| ( divides @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(27,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[18]) ).
thf(28,plain,
( ( divides @ a @ b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(29,plain,
! [SV1: $i] :
( ( product @ SV1 @ SV1 @ ( square @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV2: $i] :
( ( ! [SY11: $i,SY12: $i] :
( ~ ( product @ SV2 @ SY11 @ SY12 )
| ( product @ SY11 @ SV2 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV3: $i] :
( ( ! [SY13: $i,SY14: $i] :
( ~ ( product @ SV3 @ SY13 @ SY14 )
| ( divides @ SV3 @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV4: $i] :
( ( ! [SY15: $i] :
( ~ ( prime @ SV4 )
| ! [SY16: $i,SY17: $i] :
( ~ ( product @ SY15 @ SY16 @ SY17 )
| ~ ( divides @ SV4 @ SY17 )
| ( divides @ SV4 @ SY15 )
| ( divides @ SV4 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY18: $i] :
( ~ ( product @ SV2 @ SV5 @ SY18 )
| ( product @ SV5 @ SV2 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY19: $i] :
( ~ ( product @ SV3 @ SV6 @ SY19 )
| ( divides @ SV3 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV7: $i,SV4: $i] :
( ( ~ ( prime @ SV4 )
| ! [SY20: $i,SY21: $i] :
( ~ ( product @ SV7 @ SY20 @ SY21 )
| ~ ( divides @ SV4 @ SY21 )
| ( divides @ SV4 @ SV7 )
| ( divides @ SV4 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV8: $i,SV5: $i,SV2: $i] :
( ( ~ ( product @ SV2 @ SV5 @ SV8 )
| ( product @ SV5 @ SV2 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ~ ( product @ SV3 @ SV6 @ SV9 )
| ( divides @ SV3 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ( prime @ SV4 ) )
= $true )
| ( ( ! [SY20: $i,SY21: $i] :
( ~ ( product @ SV7 @ SY20 @ SY21 )
| ~ ( divides @ SV4 @ SY21 )
| ( divides @ SV4 @ SV7 )
| ( divides @ SV4 @ SY20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV8: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( product @ SV2 @ SV5 @ SV8 ) )
= $true )
| ( ( product @ SV5 @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( product @ SV3 @ SV6 @ SV9 ) )
= $true )
| ( ( divides @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV7: $i,SV4: $i] :
( ( ( prime @ SV4 )
= $false )
| ( ( ! [SY20: $i,SY21: $i] :
( ~ ( product @ SV7 @ SY20 @ SY21 )
| ~ ( divides @ SV4 @ SY21 )
| ( divides @ SV4 @ SV7 )
| ( divides @ SV4 @ SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV8: $i,SV5: $i,SV2: $i] :
( ( ( product @ SV2 @ SV5 @ SV8 )
= $false )
| ( ( product @ SV5 @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ( product @ SV3 @ SV6 @ SV9 )
= $false )
| ( ( divides @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV4: $i,SV10: $i,SV7: $i] :
( ( ( ! [SY22: $i] :
( ~ ( product @ SV7 @ SV10 @ SY22 )
| ~ ( divides @ SV4 @ SY22 )
| ( divides @ SV4 @ SV7 )
| ( divides @ SV4 @ SV10 ) ) )
= $true )
| ( ( prime @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV4: $i,SV11: $i,SV10: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV10 @ SV11 )
| ~ ( divides @ SV4 @ SV11 )
| ( divides @ SV4 @ SV7 )
| ( divides @ SV4 @ SV10 ) )
= $true )
| ( ( prime @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(47,plain,
! [SV4: $i,SV11: $i,SV10: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV10 @ SV11 ) )
= $true )
| ( ( ~ ( divides @ SV4 @ SV11 )
| ( divides @ SV4 @ SV7 )
| ( divides @ SV4 @ SV10 ) )
= $true )
| ( ( prime @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(48,plain,
! [SV4: $i,SV11: $i,SV10: $i,SV7: $i] :
( ( ( product @ SV7 @ SV10 @ SV11 )
= $false )
| ( ( ~ ( divides @ SV4 @ SV11 )
| ( divides @ SV4 @ SV7 )
| ( divides @ SV4 @ SV10 ) )
= $true )
| ( ( prime @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV10: $i,SV7: $i,SV11: $i,SV4: $i] :
( ( ( ~ ( divides @ SV4 @ SV11 ) )
= $true )
| ( ( ( divides @ SV4 @ SV7 )
| ( divides @ SV4 @ SV10 ) )
= $true )
| ( ( product @ SV7 @ SV10 @ SV11 )
= $false )
| ( ( prime @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV10: $i,SV7: $i,SV11: $i,SV4: $i] :
( ( ( divides @ SV4 @ SV11 )
= $false )
| ( ( ( divides @ SV4 @ SV7 )
| ( divides @ SV4 @ SV10 ) )
= $true )
| ( ( product @ SV7 @ SV10 @ SV11 )
= $false )
| ( ( prime @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(51,plain,
! [SV11: $i,SV10: $i,SV7: $i,SV4: $i] :
( ( ( divides @ SV4 @ SV7 )
= $true )
| ( ( divides @ SV4 @ SV10 )
= $true )
| ( ( divides @ SV4 @ SV11 )
= $false )
| ( ( product @ SV7 @ SV10 @ SV11 )
= $false )
| ( ( prime @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(52,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,51,44,43,33,29,28,22]) ).
thf(53,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 13:06:24 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.22
% 0.08/0.22 No.of.Axioms: 7
% 0.08/0.22
% 0.08/0.22 Length.of.Defs: 0
% 0.08/0.22
% 0.08/0.22 Contains.Choice.Funs: false
% 0.08/0.22 .
% 0.08/0.22
% 0.08/0.22 ********************************
% 0.08/0.22 * All subproblems solved! *
% 0.08/0.22 ********************************
% 0.08/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:52,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.22
% 0.08/0.22 %**** Beginning of derivation protocol ****
% 0.08/0.22 % SZS output start CNFRefutation
% See solution above
% 0.08/0.22
% 0.08/0.22 %**** End of derivation protocol ****
% 0.08/0.22 %**** no. of clauses in derivation: 53 ****
% 0.08/0.22 %**** clause counter: 52 ****
% 0.08/0.22
% 0.08/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:52,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------