%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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 : 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 10:20:15 AM UTC 2026
% Result : Unsatisfiable 1.10s 0.45s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 163 ( 109 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 429 ( 33 ~; 33 |; 0 &; 363 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a1,type,
a1: $i ).
thf(tp_a2,type,
a2: $i ).
thf(tp_a3,type,
a3: $i ).
thf(tp_a4,type,
a4: $i ).
thf(tp_b1,type,
b1: $i ).
thf(tp_b2,type,
b2: $i ).
thf(tp_b3,type,
b3: $i ).
thf(tp_b4,type,
b4: $i ).
thf(tp_c3,type,
c3: $i ).
thf(tp_divide,type,
divide: $i > $i > $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [X: $i] :
( identity
= ( divide @ X @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
thf(2,axiom,
! [X: $i] :
( ( inverse @ X )
= ( divide @ identity @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( divide @ X @ ( divide @ identity @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( divide @ ( divide @ identity @ X ) @ ( divide @ ( divide @ ( divide @ Y @ X ) @ Z ) @ Y ) )
= Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) )
| ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
thf(8,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [X: $i] :
( identity
= ( divide @ X @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [X: $i] :
( ( inverse @ X )
= ( divide @ identity @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( divide @ X @ ( divide @ identity @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( divide @ ( divide @ identity @ X ) @ ( divide @ ( divide @ ( divide @ Y @ X ) @ Z ) @ Y ) )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) )
| ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) )
| ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( divide @ ( divide @ identity @ X ) @ ( divide @ ( divide @ ( divide @ Y @ X ) @ Z ) @ Y ) )
= Z ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y )
= ( divide @ X @ ( divide @ identity @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [X: $i] :
( ( inverse @ X )
= ( divide @ identity @ X ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [X: $i] :
( identity
= ( divide @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(20,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) )
| ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY7: $i,SY8: $i] :
( ( divide @ ( divide @ identity @ SV1 ) @ ( divide @ ( divide @ ( divide @ SY7 @ SV1 ) @ SY8 ) @ SY7 ) )
= SY8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY9: $i] :
( ( multiply @ SV2 @ SY9 )
= ( divide @ SV2 @ ( divide @ identity @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV3: $i] :
( ( ( inverse @ SV3 )
= ( divide @ identity @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV4: $i] :
( ( identity
= ( divide @ SV4 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(27,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
!= ( multiply @ ( inverse @ b1 ) @ b1 ) )
= $true )
| ( ( ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY10: $i] :
( ( divide @ ( divide @ identity @ SV1 ) @ ( divide @ ( divide @ ( divide @ SV5 @ SV1 ) @ SY10 ) @ SV5 ) )
= SY10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV6: $i,SV2: $i] :
( ( ( multiply @ SV2 @ SV6 )
= ( divide @ SV2 @ ( divide @ identity @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
( ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= ( multiply @ ( inverse @ b1 ) @ b1 ) )
= $false )
| ( ( ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 )
| ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV7: $i,SV5: $i,SV1: $i] :
( ( ( divide @ ( divide @ identity @ SV1 ) @ ( divide @ ( divide @ ( divide @ SV5 @ SV1 ) @ SV7 ) @ SV5 ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 )
= $true )
| ( ( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) ) )
= $true )
| ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= ( multiply @ ( inverse @ b1 ) @ b1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(33,plain,
( ( ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
= a2 )
= $false )
| ( ( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
| ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) ) )
= $true )
| ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= ( multiply @ ( inverse @ b1 ) @ b1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(34,plain,
( ( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
= $true )
| ( ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) )
= $true )
| ( ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
= a2 )
= $false )
| ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= ( multiply @ ( inverse @ b1 ) @ b1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(35,plain,
( ( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
= $false )
| ( ( ( multiply @ a4 @ b4 )
!= ( multiply @ b4 @ a4 ) )
= $true )
| ( ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
= a2 )
= $false )
| ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= ( multiply @ ( inverse @ b1 ) @ b1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(36,plain,
( ( ( ( multiply @ a4 @ b4 )
= ( multiply @ b4 @ a4 ) )
= $false )
| ( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
= $false )
| ( ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
= a2 )
= $false )
| ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= ( multiply @ ( inverse @ b1 ) @ b1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(37,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,36,31,29,26,25]) ).
thf(38,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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
% 0.11/0.19 % Computer : n013.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Oct 6 10:31:51 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.10/0.45
% 1.10/0.45 No.of.Axioms: 5
% 1.10/0.45
% 1.10/0.45 Length.of.Defs: 0
% 1.10/0.45
% 1.10/0.45 Contains.Choice.Funs: false
% 1.10/0.45
% 1.10/0.45 ********************************
% 1.10/0.45 * All subproblems solved! *
% 1.10/0.45 ********************************
% 1.10/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:37,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.10/0.45
% 1.10/0.45 %**** Beginning of derivation protocol ****
% 1.10/0.45 % SZS output start CNFRefutation
% See solution above
% 1.10/0.45
% 1.10/0.45 %**** End of derivation protocol ****
% 1.10/0.45 %**** no. of clauses in derivation: 38 ****
% 1.10/0.45 %**** clause counter: 37 ****
% 1.10/0.45
% 1.10/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:37,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------