%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% 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 : n007.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 10:20:56 AM UTC 2026
% Result : Unsatisfiable 6.50s 1.31s
% Output : CNFRefutation 6.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 154 ( 102 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 288 ( 22 ~; 18 |; 0 &; 248 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 100 ( 0 ^; 100 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_commutator,type,
commutator: $i > $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiply @ ( commutator @ A @ B ) @ C )
= ( multiply @ C @ ( commutator @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nilpotency) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ ( multiply @ A @ ( commutator @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation) ).
thf(5,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiply) ).
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 ) @ c )
!= ( commutator @ a @ ( commutator @ b @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutator_is_associative) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiply @ ( commutator @ A @ B ) @ C )
= ( multiply @ C @ ( commutator @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ ( multiply @ A @ ( commutator @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ( commutator @ ( commutator @ a @ b ) @ c )
!= ( commutator @ a @ ( commutator @ b @ c ) ) )
= $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 ) @ c )
!= ( commutator @ a @ ( commutator @ b @ c ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ C @ B ) )
| ( A = C ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( multiply @ A @ B )
!= ( multiply @ A @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ ( multiply @ A @ ( commutator @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( multiply @ ( commutator @ A @ B ) @ C )
= ( multiply @ C @ ( commutator @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(23,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( multiply @ SX0 @ SX1 )
!= ( multiply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(25,plain,
( ( ( commutator @ ( commutator @ a @ b ) @ c )
!= ( commutator @ a @ ( commutator @ b @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(26,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( multiply @ SX0 @ SX1 )
!= ( multiply @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(27,plain,
! [SV1: $i] :
( ( ! [SY14: $i,SY15: $i] :
( ( multiply @ ( multiply @ SV1 @ SY14 ) @ SY15 )
= ( multiply @ SV1 @ ( multiply @ SY14 @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(28,plain,
! [SV2: $i] :
( ( ! [SY16: $i] :
( ( multiply @ SV2 @ SY16 )
= ( multiply @ SY16 @ ( multiply @ SV2 @ ( commutator @ SV2 @ SY16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV3: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ( multiply @ ( commutator @ SV3 @ SY17 ) @ SY18 )
= ( multiply @ SY18 @ ( commutator @ SV3 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV4: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ( ( multiply @ SV4 @ SY19 )
!= ( multiply @ SV4 @ SY20 ) )
| ( SY19 = SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
( ( ( commutator @ ( commutator @ a @ b ) @ c )
= ( commutator @ a @ ( commutator @ b @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV5: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ( ( multiply @ SV5 @ SY21 )
!= ( multiply @ SY22 @ SY21 ) )
| ( SV5 = SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY23: $i] :
( ( multiply @ ( multiply @ SV1 @ SV6 ) @ SY23 )
= ( multiply @ SV1 @ ( multiply @ SV6 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV7: $i,SV2: $i] :
( ( ( multiply @ SV2 @ SV7 )
= ( multiply @ SV7 @ ( multiply @ SV2 @ ( commutator @ SV2 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY24: $i] :
( ( multiply @ ( commutator @ SV3 @ SV8 ) @ SY24 )
= ( multiply @ SY24 @ ( commutator @ SV3 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY25: $i] :
( ( ( multiply @ SV4 @ SV9 )
!= ( multiply @ SV4 @ SY25 ) )
| ( SV9 = SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY26: $i] :
( ( ( multiply @ SV5 @ SV10 )
!= ( multiply @ SY26 @ SV10 ) )
| ( SV5 = SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( multiply @ ( multiply @ SV1 @ SV6 ) @ SV11 )
= ( multiply @ SV1 @ ( multiply @ SV6 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( multiply @ ( commutator @ SV3 @ SV8 ) @ SV12 )
= ( multiply @ SV12 @ ( commutator @ SV3 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ( multiply @ SV4 @ SV9 )
!= ( multiply @ SV4 @ SV13 ) )
| ( SV9 = SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ( multiply @ SV5 @ SV10 )
!= ( multiply @ SV14 @ SV10 ) )
| ( SV5 = SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ( multiply @ SV4 @ SV9 )
!= ( multiply @ SV4 @ SV13 ) )
= $true )
| ( ( SV9 = SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ( multiply @ SV5 @ SV10 )
!= ( multiply @ SV14 @ SV10 ) )
= $true )
| ( ( SV5 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ( multiply @ SV4 @ SV9 )
= ( multiply @ SV4 @ SV13 ) )
= $false )
| ( ( SV9 = SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ( multiply @ SV5 @ SV10 )
= ( multiply @ SV14 @ SV10 ) )
= $false )
| ( ( SV5 = SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,46,45,40,39,35,32]) ).
thf(48,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% 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
% 0.10/0.18 % Computer : n007.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 10:40:30 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.50/1.31
% 6.50/1.31 No.of.Axioms: 6
% 6.50/1.31
% 6.50/1.31 Length.of.Defs: 0
% 6.50/1.31
% 6.50/1.31 Contains.Choice.Funs: false
% 6.50/1.31 .
% 6.50/1.31
% 6.50/1.31 ********************************
% 6.50/1.31 * All subproblems solved! *
% 6.50/1.31 ********************************
% 6.50/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.50/1.31
% 6.50/1.31 %**** Beginning of derivation protocol ****
% 6.50/1.31 % SZS output start CNFRefutation
% See solution above
% 6.50/1.31
% 6.50/1.31 %**** End of derivation protocol ****
% 6.50/1.31 %**** no. of clauses in derivation: 48 ****
% 6.50/1.31 %**** clause counter: 47 ****
% 6.50/1.31
% 6.50/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------