%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : BOO072-1 : TPTP v9.3.1. Released v2.6.0.
% 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 : n020.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 10:10:36 AM UTC 2026
% Result : Unsatisfiable 9.31s 1.87s
% Output : CNFRefutation 9.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 28 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 159 ( 6 ~; 0 |; 0 &; 153 @)
% ( 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 : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( inverse @ ( add @ ( inverse @ ( add @ ( inverse @ ( add @ A @ B ) ) @ C ) ) @ ( inverse @ ( add @ A @ ( inverse @ ( add @ ( inverse @ C ) @ ( inverse @ ( add @ C @ D ) ) ) ) ) ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dn1) ).
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,
( ( add @ b @ a )
!= ( add @ a @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',huntinton_1) ).
thf(5,plain,
$false = $false,
inference(unfold_def,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( inverse @ ( add @ ( inverse @ ( add @ ( inverse @ ( add @ A @ B ) ) @ C ) ) @ ( inverse @ ( add @ A @ ( inverse @ ( add @ ( inverse @ C ) @ ( inverse @ ( add @ C @ D ) ) ) ) ) ) ) )
= C ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ( add @ b @ a )
!= ( add @ a @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( ( add @ b @ a )
!= ( add @ a @ b ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( inverse @ ( add @ ( inverse @ ( add @ ( inverse @ ( add @ A @ B ) ) @ C ) ) @ ( inverse @ ( add @ A @ ( inverse @ ( add @ ( inverse @ C ) @ ( inverse @ ( add @ C @ D ) ) ) ) ) ) ) )
= C ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ( add @ b @ a )
!= ( add @ a @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( inverse @ ( add @ ( inverse @ ( add @ ( inverse @ ( add @ SV1 @ SY4 ) ) @ SY5 ) ) @ ( inverse @ ( add @ SV1 @ ( inverse @ ( add @ ( inverse @ SY5 ) @ ( inverse @ ( add @ SY5 @ 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,
( ( ( add @ b @ a )
= ( add @ a @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY7: $i,SY8: $i] :
( ( inverse @ ( add @ ( inverse @ ( add @ ( inverse @ ( add @ SV1 @ SV2 ) ) @ SY7 ) ) @ ( inverse @ ( add @ SV1 @ ( inverse @ ( add @ ( inverse @ SY7 ) @ ( inverse @ ( add @ SY7 @ SY8 ) ) ) ) ) ) ) )
= SY7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY9: $i] :
( ( inverse @ ( add @ ( inverse @ ( add @ ( inverse @ ( add @ SV1 @ SV2 ) ) @ SV3 ) ) @ ( inverse @ ( add @ SV1 @ ( inverse @ ( add @ ( inverse @ SV3 ) @ ( inverse @ ( add @ SV3 @ SY9 ) ) ) ) ) ) ) )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( inverse @ ( add @ ( inverse @ ( add @ ( inverse @ ( add @ SV1 @ SV2 ) ) @ SV3 ) ) @ ( inverse @ ( add @ SV1 @ ( inverse @ ( add @ ( inverse @ SV3 ) @ ( inverse @ ( add @ SV3 @ SV4 ) ) ) ) ) ) ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(19,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,18,15]) ).
thf(20,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO072-1 : TPTP v9.3.1. Released v2.6.0.
% 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 : n020.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 18:27:21 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.31/1.87
% 9.31/1.87 No.of.Axioms: 2
% 9.31/1.87
% 9.31/1.87 Length.of.Defs: 0
% 9.31/1.87
% 9.31/1.87 Contains.Choice.Funs: false
% 9.31/1.87
% 9.31/1.87 ********************************
% 9.31/1.87 * All subproblems solved! *
% 9.31/1.87 ********************************
% 9.31/1.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:19,loop_count:0,foatp_calls:1,translation:fof_full)
% 9.31/1.87
% 9.31/1.87 %**** Beginning of derivation protocol ****
% 9.31/1.87 % SZS output start CNFRefutation
% See solution above
% 9.31/1.87
% 9.31/1.87 %**** End of derivation protocol ****
% 9.31/1.87 %**** no. of clauses in derivation: 20 ****
% 9.31/1.87 %**** clause counter: 19 ****
% 9.31/1.87
% 9.31/1.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:19,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------