%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP002-3 : 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 : n009.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 10:20:00 AM UTC 2026
% Result : Unsatisfiable 5.68s 1.19s
% Output : CNFRefutation 5.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 56 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 160 ( 6 ~; 0 |; 0 &; 154 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_commutator,type,
commutator: $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,Y: $i] :
( ( commutator @ X @ Y )
= ( multiply @ X @ ( multiply @ Y @ ( multiply @ ( inverse @ X ) @ ( inverse @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(3,axiom,
! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(4,axiom,
! [X: $i] :
( ( multiply @ identity @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(5,axiom,
! [X: $i] :
( ( multiply @ X @ ( multiply @ X @ X ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
( ( commutator @ ( commutator @ a @ b ) @ b )
!= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutator) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i] :
( ( commutator @ X @ Y )
= ( multiply @ X @ ( multiply @ Y @ ( multiply @ ( inverse @ X ) @ ( inverse @ Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( multiply @ X @ X ) )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ( commutator @ ( commutator @ a @ b ) @ b )
!= identity )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ( commutator @ ( commutator @ a @ b ) @ b )
!= identity )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(18,plain,
( ( ( commutator @ ( commutator @ a @ b ) @ b )
!= identity )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [X: $i] :
( ( multiply @ X @ ( multiply @ X @ X ) )
= identity ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ( commutator @ X @ Y )
= ( multiply @ X @ ( multiply @ Y @ ( multiply @ ( inverse @ X ) @ ( inverse @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( ( commutator @ ( commutator @ a @ b ) @ b )
= identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( multiply @ SV1 @ ( multiply @ SV1 @ SV1 ) )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( multiply @ identity @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV3: $i] :
( ( ( multiply @ ( inverse @ SV3 ) @ SV3 )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV4: $i] :
( ( ! [SY8: $i,SY9: $i] :
( ( multiply @ ( multiply @ SV4 @ SY8 ) @ SY9 )
= ( multiply @ SV4 @ ( multiply @ SY8 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV5: $i] :
( ( ! [SY10: $i] :
( ( commutator @ SV5 @ SY10 )
= ( multiply @ SV5 @ ( multiply @ SY10 @ ( multiply @ ( inverse @ SV5 ) @ ( inverse @ SY10 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV6: $i,SV4: $i] :
( ( ! [SY11: $i] :
( ( multiply @ ( multiply @ SV4 @ SV6 ) @ SY11 )
= ( multiply @ SV4 @ ( multiply @ SV6 @ SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV7: $i,SV5: $i] :
( ( ( commutator @ SV5 @ SV7 )
= ( multiply @ SV5 @ ( multiply @ SV7 @ ( multiply @ ( inverse @ SV5 ) @ ( inverse @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV8: $i,SV6: $i,SV4: $i] :
( ( ( multiply @ ( multiply @ SV4 @ SV6 ) @ SV8 )
= ( multiply @ SV4 @ ( multiply @ SV6 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,34,33,31,28,27,26]) ).
thf(36,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-3 : 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
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 10:31:17 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.68/1.19
% 5.68/1.19 No.of.Axioms: 6
% 5.68/1.19
% 5.68/1.19 Length.of.Defs: 0
% 5.68/1.19
% 5.68/1.19 Contains.Choice.Funs: false
% 5.68/1.19
% 5.68/1.19 ********************************
% 5.68/1.19 * All subproblems solved! *
% 5.68/1.19 ********************************
% 5.68/1.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:35,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 5.68/1.19
% 5.68/1.19 %**** Beginning of derivation protocol ****
% 5.68/1.19 % SZS output start CNFRefutation
% See solution above
% 5.68/1.19
% 5.68/1.19 %**** End of derivation protocol ****
% 5.68/1.19 %**** no. of clauses in derivation: 36 ****
% 5.68/1.19 %**** clause counter: 35 ****
% 5.68/1.19
% 5.68/1.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:35,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------