%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% 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 : n019.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 10:10:25 AM UTC 2026
% Result : Unsatisfiable 6.65s 1.31s
% Output : CNFRefutation 6.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 66 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 211 ( 6 ~; 0 |; 0 &; 205 @)
% ( 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 : 7 ( 4 usr; 4 con; 0-3 aty)
% Number of variables : 80 ( 0 ^; 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( multiply @ X @ Y @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extra_lemma) ).
thf(2,axiom,
! [Y: $i,X: $i] :
( ( multiply @ ( inverse @ Y ) @ Y @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( multiply @ X @ X @ Y )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_2) ).
thf(4,axiom,
! [Y: $i,X: $i] :
( ( multiply @ Y @ X @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_1) ).
thf(5,axiom,
! [V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ V @ W @ X ) @ Y @ ( multiply @ V @ W @ Z ) )
= ( multiply @ V @ W @ ( multiply @ X @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
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,
( ( multiply @ a @ ( inverse @ a ) @ b )
!= b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [Y: $i,X: $i] :
( ( multiply @ ( inverse @ Y ) @ Y @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ X @ Y )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [Y: $i,X: $i] :
( ( multiply @ Y @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ V @ W @ X ) @ Y @ ( multiply @ V @ W @ Z ) )
= ( multiply @ V @ W @ ( multiply @ X @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ( multiply @ a @ ( inverse @ a ) @ b )
!= b )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ( multiply @ a @ ( inverse @ a ) @ b )
!= b )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ V @ W @ X ) @ Y @ ( multiply @ V @ W @ Z ) )
= ( multiply @ V @ W @ ( multiply @ X @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [Y: $i,X: $i] :
( ( multiply @ Y @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ X @ Y )
= X ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ! [Y: $i,X: $i] :
( ( multiply @ ( inverse @ Y ) @ Y @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ Y @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(23,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
( ( ( multiply @ a @ ( inverse @ a ) @ b )
!= b )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(25,plain,
! [SV1: $i] :
( ( ! [SY13: $i,SY14: $i,SY15: $i,SY16: $i] :
( ( multiply @ ( multiply @ SV1 @ SY13 @ SY14 ) @ SY15 @ ( multiply @ SV1 @ SY13 @ SY16 ) )
= ( multiply @ SV1 @ SY13 @ ( multiply @ SY14 @ SY15 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV2: $i] :
( ( ! [SY17: $i] :
( ( multiply @ SV2 @ SY17 @ SY17 )
= SY17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV3: $i] :
( ( ! [SY18: $i] :
( ( multiply @ SV3 @ SV3 @ SY18 )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV4: $i] :
( ( ! [SY19: $i] :
( ( multiply @ ( inverse @ SV4 ) @ SV4 @ SY19 )
= SY19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV5: $i] :
( ( ! [SY20: $i] :
( ( multiply @ SV5 @ SY20 @ SV5 )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(31,plain,
( ( ( multiply @ a @ ( inverse @ a ) @ b )
= b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY21: $i,SY22: $i,SY23: $i] :
( ( multiply @ ( multiply @ SV1 @ SV6 @ SY21 ) @ SY22 @ ( multiply @ SV1 @ SV6 @ SY23 ) )
= ( multiply @ SV1 @ SV6 @ ( multiply @ SY21 @ SY22 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV7: $i,SV2: $i] :
( ( ( multiply @ SV2 @ SV7 @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV8: $i,SV3: $i] :
( ( ( multiply @ SV3 @ SV3 @ SV8 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV9: $i,SV4: $i] :
( ( ( multiply @ ( inverse @ SV4 ) @ SV4 @ SV9 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV10: $i,SV5: $i] :
( ( ( multiply @ SV5 @ SV10 @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ( multiply @ ( multiply @ SV1 @ SV6 @ SV11 ) @ SY24 @ ( multiply @ SV1 @ SV6 @ SY25 ) )
= ( multiply @ SV1 @ SV6 @ ( multiply @ SV11 @ SY24 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV12: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ! [SY26: $i] :
( ( multiply @ ( multiply @ SV1 @ SV6 @ SV11 ) @ SV12 @ ( multiply @ SV1 @ SV6 @ SY26 ) )
= ( multiply @ SV1 @ SV6 @ ( multiply @ SV11 @ SV12 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV13: $i,SV12: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ( multiply @ ( multiply @ SV1 @ SV6 @ SV11 ) @ SV12 @ ( multiply @ SV1 @ SV6 @ SV13 ) )
= ( multiply @ SV1 @ SV6 @ ( multiply @ SV11 @ SV12 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(40,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,39,36,35,34,33,31]) ).
thf(41,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% 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
% 0.13/0.17 % Computer : n019.cluster.edu
% 0.13/0.17 % Model : x86_64 x86_64
% 0.13/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.17 % Memory : 8046.5625MB
% 0.13/0.17 % OS : Linux 6.8.0-71-generic
% 0.13/0.18 % CPULimit : 300
% 0.13/0.18 % WCLimit : 300
% 0.13/0.18 % DateTime : Tue Oct 6 18:25:47 UTC 2026
% 0.13/0.18 % CPUTime :
% 0.13/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.65/1.31
% 6.65/1.31 No.of.Axioms: 6
% 6.65/1.31
% 6.65/1.31 Length.of.Defs: 0
% 6.65/1.31
% 6.65/1.31 Contains.Choice.Funs: false
% 6.65/1.31
% 6.65/1.31 ********************************
% 6.65/1.31 * All subproblems solved! *
% 6.65/1.31 ********************************
% 6.65/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/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:40,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.65/1.31
% 6.65/1.31 %**** Beginning of derivation protocol ****
% 6.65/1.31 % SZS output start CNFRefutation
% See solution above
% 6.65/1.31
% 6.65/1.31 %**** End of derivation protocol ****
% 6.65/1.31 %**** no. of clauses in derivation: 41 ****
% 6.65/1.31 %**** clause counter: 40 ****
% 6.65/1.31
% 6.65/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/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:40,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------