TSTP Solution File: ALG278^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ALG278^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:25:41 EDT 2022
% Result : Theorem 0.15s 0.32s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 37 ( 27 unt; 9 typ; 4 def)
% Number of atoms : 93 ( 60 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 150 ( 3 ~; 0 |; 8 &; 134 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 7 ^ 56 !; 5 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_g,type,
g: $tType ).
thf(tp_cGROUP2,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(tp_cGRP_ASSOC,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(tp_cGRP_LEFT_INVERSE,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(tp_cGRP_LEFT_UNIT,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: g > g > g ).
thf(tp_sK2_SY30,type,
sK2_SY30: g ).
thf(tp_sK3_SY44,type,
sK3_SY44: g ).
thf(tp_sK4_SY43,type,
sK4_SY43: g > g ).
thf(cGROUP2,definition,
( cGROUP2
= ( ^ [Xf: g > g > g,Xe: g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_LEFT_UNIT @ Xf @ Xe )
& ( cGRP_LEFT_INVERSE @ Xf @ Xe ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGROUP2) ).
thf(cGRP_ASSOC,definition,
( cGRP_ASSOC
= ( ^ [Xf: g > g > g] :
! [Xa: g,Xb: g,Xc: g] :
( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
= ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_ASSOC) ).
thf(cGRP_LEFT_INVERSE,definition,
( cGRP_LEFT_INVERSE
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
? [Xb: g] :
( ( Xf @ Xb @ Xa )
= Xe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_LEFT_INVERSE) ).
thf(cGRP_LEFT_UNIT,definition,
( cGRP_LEFT_UNIT
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
( ( Xf @ Xe @ Xa )
= Xa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_LEFT_UNIT) ).
thf(1,conjecture,
! [Xf: g > g > g,Xe: g] :
( ( cGROUP2 @ Xf @ Xe )
=> ! [Xa: g] :
( ( Xf @ Xa @ Xe )
= Xa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE12A1) ).
thf(2,negated_conjecture,
( ( ! [Xf: g > g > g,Xe: g] :
( ( cGROUP2 @ Xf @ Xe )
=> ! [Xa: g] :
( ( Xf @ Xa @ Xe )
= Xa ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: g > g > g,SY1: g] :
( ( ! [SY3: g,SY4: g,SY5: g] :
( ( SY0 @ ( SY0 @ SY3 @ SY4 ) @ SY5 )
= ( SY0 @ SY3 @ ( SY0 @ SY4 @ SY5 ) ) )
& ! [SY17: g] :
( ( SY0 @ SY1 @ SY17 )
= SY17 )
& ! [SY18: g] :
? [SY19: g] :
( ( SY0 @ SY19 @ SY18 )
= SY1 ) )
=> ! [Xa: g] :
( ( SY0 @ Xa @ SY1 )
= Xa ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cGROUP2,cGRP_ASSOC,cGRP_LEFT_INVERSE,cGRP_LEFT_UNIT]) ).
thf(4,plain,
( ( ! [SY30: g] :
( ( ! [SY31: g,SY32: g,SY33: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY31 @ SY32 ) @ SY33 )
= ( sK1_SY0 @ SY31 @ ( sK1_SY0 @ SY32 @ SY33 ) ) )
& ! [SY34: g] :
( ( sK1_SY0 @ SY30 @ SY34 )
= SY34 )
& ! [SY35: g] :
? [SY36: g] :
( ( sK1_SY0 @ SY36 @ SY35 )
= SY30 ) )
=> ! [SY37: g] :
( ( sK1_SY0 @ SY37 @ SY30 )
= SY37 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ! [SY31: g,SY32: g,SY33: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY31 @ SY32 ) @ SY33 )
= ( sK1_SY0 @ SY31 @ ( sK1_SY0 @ SY32 @ SY33 ) ) )
& ! [SY41: g] :
( ( sK1_SY0 @ sK2_SY30 @ SY41 )
= SY41 )
& ! [SY42: g] :
? [SY43: g] :
( ( sK1_SY0 @ SY43 @ SY42 )
= sK2_SY30 ) )
=> ! [SY44: g] :
( ( sK1_SY0 @ SY44 @ sK2_SY30 )
= SY44 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY31: g,SY32: g,SY33: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY31 @ SY32 ) @ SY33 )
= ( sK1_SY0 @ SY31 @ ( sK1_SY0 @ SY32 @ SY33 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY41: g] :
( ( sK1_SY0 @ sK2_SY30 @ SY41 )
= SY41 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ! [SY42: g] :
? [SY43: g] :
( ( sK1_SY0 @ SY43 @ SY42 )
= sK2_SY30 ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [SY44: g] :
( ( sK1_SY0 @ SY44 @ sK2_SY30 )
= SY44 ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ ! [SY44: g] :
( ( sK1_SY0 @ SY44 @ sK2_SY30 )
= SY44 ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ( ( sK1_SY0 @ sK3_SY44 @ sK2_SY30 )
!= sK3_SY44 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(12,plain,
( ( ! [SY42: g] :
( ( sK1_SY0 @ ( sK4_SY43 @ SY42 ) @ SY42 )
= sK2_SY30 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(13,plain,
( ( ! [SY42: g] :
( ( sK1_SY0 @ ( sK4_SY43 @ SY42 ) @ SY42 )
= sK2_SY30 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [SY41: g] :
( ( sK1_SY0 @ sK2_SY30 @ SY41 )
= SY41 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(15,plain,
( ( ! [SY31: g,SY32: g,SY33: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SY31 @ SY32 ) @ SY33 )
= ( sK1_SY0 @ SY31 @ ( sK1_SY0 @ SY32 @ SY33 ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(16,plain,
( ( ( ( sK1_SY0 @ sK3_SY44 @ sK2_SY30 )
!= sK3_SY44 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(17,plain,
! [SV1: g] :
( ( ( sK1_SY0 @ ( sK4_SY43 @ SV1 ) @ SV1 )
= sK2_SY30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV2: g] :
( ( ( sK1_SY0 @ sK2_SY30 @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV3: g] :
( ( ! [SY45: g,SY46: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV3 @ SY45 ) @ SY46 )
= ( sK1_SY0 @ SV3 @ ( sK1_SY0 @ SY45 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( ( sK1_SY0 @ sK3_SY44 @ sK2_SY30 )
= sK3_SY44 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV4: g,SV3: g] :
( ( ! [SY47: g] :
( ( sK1_SY0 @ ( sK1_SY0 @ SV3 @ SV4 ) @ SY47 )
= ( sK1_SY0 @ SV3 @ ( sK1_SY0 @ SV4 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV5: g,SV4: g,SV3: g] :
( ( ( sK1_SY0 @ ( sK1_SY0 @ SV3 @ SV4 ) @ SV5 )
= ( sK1_SY0 @ SV3 @ ( sK1_SY0 @ SV4 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(23,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,22,20,18]) ).
thf(24,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : ALG278^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.03/0.10 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Thu Jun 9 03:31:37 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30
% 0.09/0.30 No.of.Axioms: 0
% 0.09/0.30
% 0.09/0.30 Length.of.Defs: 788
% 0.09/0.30
% 0.09/0.30 Contains.Choice.Funs: false
% 0.09/0.30 (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.15/0.32
% 0.15/0.32 ********************************
% 0.15/0.32 * All subproblems solved! *
% 0.15/0.32 ********************************
% 0.15/0.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:23,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.15/0.32
% 0.15/0.32 %**** Beginning of derivation protocol ****
% 0.15/0.32 % SZS output start CNFRefutation
% See solution above
% 0.15/0.32
% 0.15/0.32 %**** End of derivation protocol ****
% 0.15/0.32 %**** no. of clauses in derivation: 24 ****
% 0.15/0.32 %**** clause counter: 23 ****
% 0.15/0.32
% 0.15/0.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:23,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------