%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : TOP049-1 : TPTP v9.3.1. Released v8.1.0.
% 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 : n016.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 11:09:44 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.30s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 58 unt; 0 typ; 0 def)
% Number of atoms : 142 ( 92 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 244 ( 6 ~; 0 |; 0 &; 238 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 12 con; 0-9 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a1,type,
a1: $i ).
thf(tp_a10,type,
a10: $i ).
thf(tp_a2,type,
a2: $i ).
thf(tp_a3,type,
a3: $i ).
thf(tp_a4,type,
a4: $i ).
thf(tp_a5,type,
a5: $i ).
thf(tp_a6,type,
a6: $i ).
thf(tp_a7,type,
a7: $i ).
thf(tp_a8,type,
a8: $i ).
thf(tp_a9,type,
a9: $i ).
thf(tp_product,type,
product: $i > $i > $i ).
thf(tp_tuple,type,
tuple: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(1,axiom,
( a9
= ( product @ a4 @ a8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_11) ).
thf(2,axiom,
( a4
= ( product @ a10 @ a3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_10) ).
thf(3,axiom,
( a10
= ( product @ a8 @ a9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_09) ).
thf(4,axiom,
( a8
= ( product @ a7 @ a4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_08) ).
thf(5,axiom,
( a7
= ( product @ a6 @ a1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_07) ).
thf(6,axiom,
( a6
= ( product @ a5 @ a4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_06) ).
thf(7,axiom,
( a5
= ( product @ a2 @ a10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_05) ).
thf(8,axiom,
( a2
= ( product @ a3 @ a4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_04) ).
thf(9,axiom,
( a3
= ( product @ a1 @ a2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_03) ).
thf(10,axiom,
( a1
= ( product @ a9 @ a7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot) ).
thf(11,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( product @ ( product @ X @ Y ) @ Z )
= ( product @ ( product @ X @ Z ) @ ( product @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_02) ).
thf(12,axiom,
! [X: $i,Y: $i] :
( ( product @ ( product @ X @ Y ) @ Y )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).
thf(13,axiom,
! [X: $i] :
( ( product @ X @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle) ).
thf(14,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(15,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,negated_conjecture,
( ( tuple @ a1 @ a9 @ a8 @ a6 @ a7 @ a2 @ a3 @ a4 @ a5 )
!= ( tuple @ a2 @ a10 @ a9 @ a7 @ a8 @ a3 @ a4 @ a5 @ a6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(17,plain,
$false = $false,
inference(unfold_def,[status(thm)],[15]) ).
thf(18,plain,
( ( a9
= ( product @ a4 @ a8 ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(19,plain,
( ( a4
= ( product @ a10 @ a3 ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(20,plain,
( ( a10
= ( product @ a8 @ a9 ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(21,plain,
( ( a8
= ( product @ a7 @ a4 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(22,plain,
( ( a7
= ( product @ a6 @ a1 ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( a6
= ( product @ a5 @ a4 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( a5
= ( product @ a2 @ a10 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( a2
= ( product @ a3 @ a4 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( a3
= ( product @ a1 @ a2 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( a1
= ( product @ a9 @ a7 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( product @ ( product @ X @ Y ) @ Z )
= ( product @ ( product @ X @ Z ) @ ( product @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( product @ ( product @ X @ Y ) @ Y )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(30,plain,
( ( ! [X: $i] :
( ( product @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(31,plain,
( ( ( tuple @ a1 @ a9 @ a8 @ a6 @ a7 @ a2 @ a3 @ a4 @ a5 )
!= ( tuple @ a2 @ a10 @ a9 @ a7 @ a8 @ a3 @ a4 @ a5 @ a6 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(32,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(33,plain,
( ( ( tuple @ a1 @ a9 @ a8 @ a6 @ a7 @ a2 @ a3 @ a4 @ a5 )
!= ( tuple @ a2 @ a10 @ a9 @ a7 @ a8 @ a3 @ a4 @ a5 @ a6 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(34,plain,
( ( ( tuple @ a1 @ a9 @ a8 @ a6 @ a7 @ a2 @ a3 @ a4 @ a5 )
!= ( tuple @ a2 @ a10 @ a9 @ a7 @ a8 @ a3 @ a4 @ a5 @ a6 ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(35,plain,
( ( ! [X: $i] :
( ( product @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i] :
( ( product @ ( product @ X @ Y ) @ Y )
= X ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( product @ ( product @ X @ Y ) @ Z )
= ( product @ ( product @ X @ Z ) @ ( product @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( a1
= ( product @ a9 @ a7 ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,plain,
( ( a3
= ( product @ a1 @ a2 ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( a2
= ( product @ a3 @ a4 ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(41,plain,
( ( a5
= ( product @ a2 @ a10 ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(42,plain,
( ( a6
= ( product @ a5 @ a4 ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(43,plain,
( ( a7
= ( product @ a6 @ a1 ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(44,plain,
( ( a8
= ( product @ a7 @ a4 ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(45,plain,
( ( a10
= ( product @ a8 @ a9 ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(46,plain,
( ( a4
= ( product @ a10 @ a3 ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(47,plain,
( ( a9
= ( product @ a4 @ a8 ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(48,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[32]) ).
thf(49,plain,
( ( ( tuple @ a1 @ a9 @ a8 @ a6 @ a7 @ a2 @ a3 @ a4 @ a5 )
= ( tuple @ a2 @ a10 @ a9 @ a7 @ a8 @ a3 @ a4 @ a5 @ a6 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(50,plain,
! [SV1: $i] :
( ( ( product @ SV1 @ SV1 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(51,plain,
! [SV2: $i] :
( ( ! [SY6: $i] :
( ( product @ ( product @ SV2 @ SY6 ) @ SY6 )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(52,plain,
! [SV3: $i] :
( ( ! [SY7: $i,SY8: $i] :
( ( product @ ( product @ SV3 @ SY7 ) @ SY8 )
= ( product @ ( product @ SV3 @ SY8 ) @ ( product @ SY7 @ SY8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(53,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV4: $i,SV2: $i] :
( ( ( product @ ( product @ SV2 @ SV4 ) @ SV4 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV5: $i,SV3: $i] :
( ( ! [SY9: $i] :
( ( product @ ( product @ SV3 @ SV5 ) @ SY9 )
= ( product @ ( product @ SV3 @ SY9 ) @ ( product @ SV5 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( product @ ( product @ SV3 @ SV5 ) @ SV6 )
= ( product @ ( product @ SV3 @ SV6 ) @ ( product @ SV5 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(57,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,56,54,53,50,49,47,46,45,44,43,42,41,40,39]) ).
thf(58,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP049-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.19 % Computer : n016.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Oct 6 18:01:30 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.30
% 0.12/0.30 No.of.Axioms: 14
% 0.12/0.30
% 0.12/0.30 Length.of.Defs: 0
% 0.12/0.30
% 0.12/0.30 Contains.Choice.Funs: false
% 0.12/0.30 .
% 0.12/0.30
% 0.12/0.30 ********************************
% 0.12/0.30 * All subproblems solved! *
% 0.12/0.30 ********************************
% 0.12/0.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:14,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:57,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.30
% 0.12/0.30 %**** Beginning of derivation protocol ****
% 0.12/0.30 % SZS output start CNFRefutation
% See solution above
% 0.12/0.30
% 0.12/0.30 %**** End of derivation protocol ****
% 0.12/0.30 %**** no. of clauses in derivation: 58 ****
% 0.12/0.30 %**** clause counter: 57 ****
% 0.12/0.30
% 0.12/0.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:14,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:57,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------