%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP059-1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 10:20:11 AM UTC 2026
% Result : Unsatisfiable 50.79s 8.76s
% Output : CNFRefutation 50.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 62 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 316 ( 22 ~; 18 |; 0 &; 276 @)
% ( 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 : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a1,type,
a1: $i ).
thf(tp_a2,type,
a2: $i ).
thf(tp_a3,type,
a3: $i ).
thf(tp_b1,type,
b1: $i ).
thf(tp_b2,type,
b2: $i ).
thf(tp_b3,type,
b3: $i ).
thf(tp_c3,type,
c3: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i,U: $i] :
( ( inverse @ ( multiply @ ( multiply @ ( multiply @ ( inverse @ ( multiply @ ( multiply @ X @ Y ) @ Z ) ) @ X ) @ Y ) @ ( multiply @ U @ ( inverse @ U ) ) ) )
= Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
thf(2,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(3,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
thf(5,plain,
$false = $false,
inference(unfold_def,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i] :
( ( inverse @ ( multiply @ ( multiply @ ( multiply @ ( inverse @ ( multiply @ ( multiply @ X @ Y ) @ Z ) ) @ X ) @ Y ) @ ( multiply @ U @ ( inverse @ U ) ) ) )
= Z ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i] :
( ( inverse @ ( multiply @ ( multiply @ ( multiply @ ( inverse @ ( multiply @ ( multiply @ X @ Y ) @ Z ) ) @ X ) @ Y ) @ ( multiply @ U @ ( inverse @ U ) ) ) )
= Z ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( inverse @ ( multiply @ ( multiply @ ( multiply @ ( inverse @ ( multiply @ ( multiply @ SV1 @ SY4 ) @ SY5 ) ) @ SV1 ) @ SY4 ) @ ( multiply @ SY6 @ ( inverse @ SY6 ) ) ) )
= SY5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(15,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 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY7: $i,SY8: $i] :
( ( inverse @ ( multiply @ ( multiply @ ( multiply @ ( inverse @ ( multiply @ ( multiply @ SV1 @ SV2 ) @ SY7 ) ) @ SV1 ) @ SV2 ) @ ( multiply @ SY8 @ ( inverse @ SY8 ) ) ) )
= SY7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,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 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY9: $i] :
( ( inverse @ ( multiply @ ( multiply @ ( multiply @ ( inverse @ ( multiply @ ( multiply @ SV1 @ SV2 ) @ SV3 ) ) @ SV1 ) @ SV2 ) @ ( multiply @ SY9 @ ( inverse @ SY9 ) ) ) )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
!= a2 )
= $true )
| ( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
= $true )
| ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= ( multiply @ ( inverse @ b1 ) @ b1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( inverse @ ( multiply @ ( multiply @ ( multiply @ ( inverse @ ( multiply @ ( multiply @ SV1 @ SV2 ) @ SV3 ) ) @ SV1 ) @ SV2 ) @ ( multiply @ SV4 @ ( inverse @ SV4 ) ) ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
= a2 )
= $false )
| ( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
!= ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
= $true )
| ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
= ( multiply @ ( inverse @ b1 ) @ b1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ( ( 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)],[21]) ).
thf(23,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,22,20]) ).
thf(24,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP059-1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n026.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 10:34:46 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 50.79/8.76
% 50.79/8.76 No.of.Axioms: 2
% 50.79/8.76
% 50.79/8.76 Length.of.Defs: 0
% 50.79/8.76
% 50.79/8.76 Contains.Choice.Funs: false
% 50.79/8.76
% 50.79/8.76 ********************************
% 50.79/8.76 * All subproblems solved! *
% 50.79/8.76 ********************************
% 50.79/8.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:23,loop_count:0,foatp_calls:1,translation:fof_full)
% 50.79/8.76
% 50.79/8.76 %**** Beginning of derivation protocol ****
% 50.79/8.76 % SZS output start CNFRefutation
% See solution above
% 50.79/8.76
% 50.79/8.76 %**** End of derivation protocol ****
% 50.79/8.76 %**** no. of clauses in derivation: 24 ****
% 50.79/8.76 %**** clause counter: 23 ****
% 50.79/8.76
% 50.79/8.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:23,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------