%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG279^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 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 : 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 10:08:46 AM UTC 2026
% Result : Theorem 0.09s 0.21s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 28 unt; 0 typ; 2 def)
% Number of atoms : 98 ( 65 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 169 ( 8 ~; 0 |; 10 &; 146 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 77 ( 4 ^; 67 !; 6 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_g,type,
g: $tType ).
thf(tp_cGRP_RIGHT_INVERSE,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(tp_cGRP_RIGHT_UNIT,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: g > g > g ).
thf(tp_sK2_SY23,type,
sK2_SY23: g ).
thf(tp_sK3_SY37,type,
sK3_SY37: g ).
thf(tp_sK4_SY40,type,
sK4_SY40: g > g ).
thf(cGRP_RIGHT_INVERSE,definition,
( cGRP_RIGHT_INVERSE
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
? [Xb: g] :
( ( Xf @ Xa @ Xb )
= Xe ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE_def) ).
thf(cGRP_RIGHT_UNIT,definition,
( cGRP_RIGHT_UNIT
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
( ( Xf @ Xa @ Xe )
= Xa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def) ).
thf(1,conjecture,
! [Xf: g > g > g,Xe: g] :
( ( ! [Xb: g,Xc: g,Xa: g] :
( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
= ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) )
& ( cGRP_RIGHT_UNIT @ Xf @ Xe )
& ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) )
=> ! [Xa: g] :
( ( Xf @ Xe @ Xa )
= Xa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE13A2A) ).
thf(2,negated_conjecture,
( ( ! [Xf: g > g > g,Xe: g] :
( ( ! [Xb: g,Xc: g,Xa: g] :
( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
= ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) )
& ( cGRP_RIGHT_UNIT @ Xf @ Xe )
& ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) )
=> ! [Xa: g] :
( ( Xf @ Xe @ Xa )
= Xa ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: g > g > g,SY1: g] :
( ( ! [Xb: g,Xc: g,Xa: g] :
( ( SY0 @ ( SY0 @ Xa @ Xb ) @ Xc )
= ( SY0 @ Xa @ ( SY0 @ Xb @ Xc ) ) )
& ! [SY7: g] :
( ( SY0 @ SY7 @ SY1 )
= SY7 )
& ! [SY11: g] :
? [SY12: g] :
( ( SY0 @ SY11 @ SY12 )
= SY1 ) )
=> ! [Xa: g] :
( ( SY0 @ SY1 @ Xa )
= Xa ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cGRP_RIGHT_INVERSE,cGRP_RIGHT_UNIT]) ).
thf(4,plain,
( ( ! [SY23: g] :
( ( ! [SY24: g,SY25: g,SY26: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY26 @ SY24 ) @ SY25 )
= ( sK1_SY0 @ SY26 @ ( sK1_SY0 @ SY24 @ SY25 ) ) )
& ! [SY27: g] :
( ( sK1_SY0 @ SY27 @ SY23 )
= SY27 )
& ! [SY28: g] :
? [SY29: g] :
( ( sK1_SY0 @ SY28 @ SY29 )
= SY23 ) )
=> ! [SY30: g] :
( ( sK1_SY0 @ SY23 @ SY30 )
= SY30 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ! [SY24: g,SY25: g,SY26: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY26 @ SY24 ) @ SY25 )
= ( sK1_SY0 @ SY26 @ ( sK1_SY0 @ SY24 @ SY25 ) ) )
& ! [SY34: g] :
( ( sK1_SY0 @ SY34 @ sK2_SY23 )
= SY34 )
& ! [SY35: g] :
? [SY36: g] :
( ( sK1_SY0 @ SY35 @ SY36 )
= sK2_SY23 ) )
=> ! [SY37: g] :
( ( sK1_SY0 @ sK2_SY23 @ SY37 )
= SY37 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY24: g,SY25: g,SY26: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY26 @ SY24 ) @ SY25 )
= ( sK1_SY0 @ SY26 @ ( sK1_SY0 @ SY24 @ SY25 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY34: g] :
( ( sK1_SY0 @ SY34 @ sK2_SY23 )
= SY34 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [SY35: g] :
? [SY36: g] :
( ( sK1_SY0 @ SY35 @ SY36 )
= sK2_SY23 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [SY37: g] :
( ( sK1_SY0 @ sK2_SY23 @ SY37 )
= SY37 ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ ! [SY37: g] :
( ( sK1_SY0 @ sK2_SY23 @ SY37 )
= SY37 ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [SY35: g] :
? [SY36: g] :
( ( sK1_SY0 @ SY35 @ SY36 )
= sK2_SY23 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [SY34: g] :
( ( sK1_SY0 @ SY34 @ sK2_SY23 )
= SY34 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [SY24: g,SY25: g,SY26: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY26 @ SY24 ) @ SY25 )
= ( sK1_SY0 @ SY26 @ ( sK1_SY0 @ SY24 @ SY25 ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(14,plain,
( ( ~ ! [SY37: g] :
( ( sK1_SY0 @ sK2_SY23 @ SY37 )
= SY37 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ! [SX0: g] :
~ ! [SX1: g] :
( ( sK1_SY0 @ SX0 @ SX1 )
!= sK2_SY23 ) )
= $true ),
inference(unfold_def,[status(thm)],[11,cGRP_RIGHT_INVERSE,cGRP_RIGHT_UNIT]) ).
thf(16,plain,
! [SV1: g] :
( ( ( sK1_SY0 @ SV1 @ sK2_SY23 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
! [SV2: g] :
( ( ! [SY38: g,SY39: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY39 @ SV2 ) @ SY38 )
= ( sK1_SY0 @ SY39 @ ( sK1_SY0 @ SV2 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(18,plain,
( ( ! [SY37: g] :
( ( sK1_SY0 @ sK2_SY23 @ SY37 )
= SY37 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV3: g] :
( ( ~ ! [SY40: g] :
( ( sK1_SY0 @ SV3 @ SY40 )
!= sK2_SY23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV4: g,SV2: g] :
( ( ! [SY41: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY41 @ SV2 ) @ SV4 )
= ( sK1_SY0 @ SY41 @ ( sK1_SY0 @ SV2 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ( sK1_SY0 @ sK2_SY23 @ sK3_SY37 )
= sK3_SY37 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(22,plain,
! [SV3: g] :
( ( ! [SY40: g] :
( ( sK1_SY0 @ SV3 @ SY40 )
!= sK2_SY23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV4: g,SV2: g,SV5: g] :
( ( ( sK1_SY0 @ ( sK1_SY0 @ SV5 @ SV2 ) @ SV4 )
= ( sK1_SY0 @ SV5 @ ( sK1_SY0 @ SV2 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV3: g] :
( ( ( sK1_SY0 @ SV3 @ ( sK4_SY40 @ SV3 ) )
!= sK2_SY23 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(25,plain,
! [SV3: g] :
( ( ( sK1_SY0 @ SV3 @ ( sK4_SY40 @ SV3 ) )
= sK2_SY23 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(26,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,25,23,21]) ).
thf(27,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG279^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 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
% 0.09/0.17 % Computer : n007.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 18:08:15 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21
% 0.09/0.21 No.of.Axioms: 0
% 0.09/0.21
% 0.09/0.21 Length.of.Defs: 396
% 0.09/0.21
% 0.09/0.21 Contains.Choice.Funs: false
% 0.09/0.21
% 0.09/0.21 ********************************
% 0.09/0.21 * All subproblems solved! *
% 0.09/0.21 ********************************
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:26,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.21
% 0.09/0.21 %**** Beginning of derivation protocol ****
% 0.09/0.21 % SZS output start CNFRefutation
% See solution above
% 0.09/0.21
% 0.09/0.21 %**** End of derivation protocol ****
% 0.09/0.21 %**** no. of clauses in derivation: 27 ****
% 0.09/0.21 %**** clause counter: 26 ****
% 0.09/0.21
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:26,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------