TSTP Solution File: ALG001^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ALG001^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n026.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 17:22:37 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 22 unt; 10 typ; 0 def)
% Number of atoms : 81 ( 58 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 317 ( 3 ~; 0 |; 8 &; 298 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 0 ^ 93 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_g,type,
g: $tType ).
thf(tp_sK1_Xh1,type,
sK1_Xh1: g > b ).
thf(tp_sK2_SY11,type,
sK2_SY11: b > a ).
thf(tp_sK3_SY21,type,
sK3_SY21: g > g > g ).
thf(tp_sK4_SY30,type,
sK4_SY30: b > b > b ).
thf(tp_sK5_SY38,type,
sK5_SY38: a > a > a ).
thf(tp_sK6_SY49,type,
sK6_SY49: g ).
thf(tp_sK7_SY51,type,
sK7_SY51: g ).
thf(1,conjecture,
! [Xh1: g > b,Xh2: b > a,Xf1: g > g > g,Xf2: b > b > b,Xf3: a > a > a] :
( ( ! [Xx: g,Xy: g] :
( ( Xh1 @ ( Xf1 @ Xx @ Xy ) )
= ( Xf2 @ ( Xh1 @ Xx ) @ ( Xh1 @ Xy ) ) )
& ! [Xx: b,Xy: b] :
( ( Xh2 @ ( Xf2 @ Xx @ Xy ) )
= ( Xf3 @ ( Xh2 @ Xx ) @ ( Xh2 @ Xy ) ) ) )
=> ! [Xx: g,Xy: g] :
( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx @ Xy ) ) )
= ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) @ ( Xh2 @ ( Xh1 @ Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM133_pme) ).
thf(2,negated_conjecture,
( ( ! [Xh1: g > b,Xh2: b > a,Xf1: g > g > g,Xf2: b > b > b,Xf3: a > a > a] :
( ( ! [Xx: g,Xy: g] :
( ( Xh1 @ ( Xf1 @ Xx @ Xy ) )
= ( Xf2 @ ( Xh1 @ Xx ) @ ( Xh1 @ Xy ) ) )
& ! [Xx: b,Xy: b] :
( ( Xh2 @ ( Xf2 @ Xx @ Xy ) )
= ( Xf3 @ ( Xh2 @ Xx ) @ ( Xh2 @ Xy ) ) ) )
=> ! [Xx: g,Xy: g] :
( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx @ Xy ) ) )
= ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) @ ( Xh2 @ ( Xh1 @ Xy ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xh1: g > b,Xh2: b > a,Xf1: g > g > g,Xf2: b > b > b,Xf3: a > a > a] :
( ( ! [Xx: g,Xy: g] :
( ( Xh1 @ ( Xf1 @ Xx @ Xy ) )
= ( Xf2 @ ( Xh1 @ Xx ) @ ( Xh1 @ Xy ) ) )
& ! [Xx: b,Xy: b] :
( ( Xh2 @ ( Xf2 @ Xx @ Xy ) )
= ( Xf3 @ ( Xh2 @ Xx ) @ ( Xh2 @ Xy ) ) ) )
=> ! [Xx: g,Xy: g] :
( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx @ Xy ) ) )
= ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) @ ( Xh2 @ ( Xh1 @ Xy ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY11: b > a,SY12: g > g > g,SY13: b > b > b,SY14: a > a > a] :
( ( ! [SY15: g,SY16: g] :
( ( sK1_Xh1 @ ( SY12 @ SY15 @ SY16 ) )
= ( SY13 @ ( sK1_Xh1 @ SY15 ) @ ( sK1_Xh1 @ SY16 ) ) )
& ! [Xx: b,Xy: b] :
( ( SY11 @ ( SY13 @ Xx @ Xy ) )
= ( SY14 @ ( SY11 @ Xx ) @ ( SY11 @ Xy ) ) ) )
=> ! [SY19: g,SY20: g] :
( ( SY11 @ ( sK1_Xh1 @ ( SY12 @ SY19 @ SY20 ) ) )
= ( SY14 @ ( SY11 @ ( sK1_Xh1 @ SY19 ) ) @ ( SY11 @ ( sK1_Xh1 @ SY20 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY21: g > g > g,SY22: b > b > b,SY23: a > a > a] :
( ( ! [SY15: g,SY16: g] :
( ( sK1_Xh1 @ ( SY21 @ SY15 @ SY16 ) )
= ( SY22 @ ( sK1_Xh1 @ SY15 ) @ ( sK1_Xh1 @ SY16 ) ) )
& ! [SY26: b,SY27: b] :
( ( sK2_SY11 @ ( SY22 @ SY26 @ SY27 ) )
= ( SY23 @ ( sK2_SY11 @ SY26 ) @ ( sK2_SY11 @ SY27 ) ) ) )
=> ! [SY28: g,SY29: g] :
( ( sK2_SY11 @ ( sK1_Xh1 @ ( SY21 @ SY28 @ SY29 ) ) )
= ( SY23 @ ( sK2_SY11 @ ( sK1_Xh1 @ SY28 ) ) @ ( sK2_SY11 @ ( sK1_Xh1 @ SY29 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY30: b > b > b,SY31: a > a > a] :
( ( ! [SY32: g,SY33: g] :
( ( sK1_Xh1 @ ( sK3_SY21 @ SY32 @ SY33 ) )
= ( SY30 @ ( sK1_Xh1 @ SY32 ) @ ( sK1_Xh1 @ SY33 ) ) )
& ! [SY26: b,SY27: b] :
( ( sK2_SY11 @ ( SY30 @ SY26 @ SY27 ) )
= ( SY31 @ ( sK2_SY11 @ SY26 ) @ ( sK2_SY11 @ SY27 ) ) ) )
=> ! [SY36: g,SY37: g] :
( ( sK2_SY11 @ ( sK1_Xh1 @ ( sK3_SY21 @ SY36 @ SY37 ) ) )
= ( SY31 @ ( sK2_SY11 @ ( sK1_Xh1 @ SY36 ) ) @ ( sK2_SY11 @ ( sK1_Xh1 @ SY37 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY38: a > a > a] :
( ( ! [SY39: g,SY40: g] :
( ( sK1_Xh1 @ ( sK3_SY21 @ SY39 @ SY40 ) )
= ( sK4_SY30 @ ( sK1_Xh1 @ SY39 ) @ ( sK1_Xh1 @ SY40 ) ) )
& ! [SY41: b,SY42: b] :
( ( sK2_SY11 @ ( sK4_SY30 @ SY41 @ SY42 ) )
= ( SY38 @ ( sK2_SY11 @ SY41 ) @ ( sK2_SY11 @ SY42 ) ) ) )
=> ! [SY36: g,SY37: g] :
( ( sK2_SY11 @ ( sK1_Xh1 @ ( sK3_SY21 @ SY36 @ SY37 ) ) )
= ( SY38 @ ( sK2_SY11 @ ( sK1_Xh1 @ SY36 ) ) @ ( sK2_SY11 @ ( sK1_Xh1 @ SY37 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ( ! [SY39: g,SY40: g] :
( ( sK1_Xh1 @ ( sK3_SY21 @ SY39 @ SY40 ) )
= ( sK4_SY30 @ ( sK1_Xh1 @ SY39 ) @ ( sK1_Xh1 @ SY40 ) ) )
& ! [SY47: b,SY48: b] :
( ( sK2_SY11 @ ( sK4_SY30 @ SY47 @ SY48 ) )
= ( sK5_SY38 @ ( sK2_SY11 @ SY47 ) @ ( sK2_SY11 @ SY48 ) ) ) )
=> ! [SY49: g,SY50: g] :
( ( sK2_SY11 @ ( sK1_Xh1 @ ( sK3_SY21 @ SY49 @ SY50 ) ) )
= ( sK5_SY38 @ ( sK2_SY11 @ ( sK1_Xh1 @ SY49 ) ) @ ( sK2_SY11 @ ( sK1_Xh1 @ SY50 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY39: g,SY40: g] :
( ( sK1_Xh1 @ ( sK3_SY21 @ SY39 @ SY40 ) )
= ( sK4_SY30 @ ( sK1_Xh1 @ SY39 ) @ ( sK1_Xh1 @ SY40 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY47: b,SY48: b] :
( ( sK2_SY11 @ ( sK4_SY30 @ SY47 @ SY48 ) )
= ( sK5_SY38 @ ( sK2_SY11 @ SY47 ) @ ( sK2_SY11 @ SY48 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SY49: g,SY50: g] :
( ( sK2_SY11 @ ( sK1_Xh1 @ ( sK3_SY21 @ SY49 @ SY50 ) ) )
= ( sK5_SY38 @ ( sK2_SY11 @ ( sK1_Xh1 @ SY49 ) ) @ ( sK2_SY11 @ ( sK1_Xh1 @ SY50 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ! [SY49: g,SY50: g] :
( ( sK2_SY11 @ ( sK1_Xh1 @ ( sK3_SY21 @ SY49 @ SY50 ) ) )
= ( sK5_SY38 @ ( sK2_SY11 @ ( sK1_Xh1 @ SY49 ) ) @ ( sK2_SY11 @ ( sK1_Xh1 @ SY50 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ( ( sK2_SY11 @ ( sK1_Xh1 @ ( sK3_SY21 @ sK6_SY49 @ sK7_SY51 ) ) )
!= ( sK5_SY38 @ ( sK2_SY11 @ ( sK1_Xh1 @ sK6_SY49 ) ) @ ( sK2_SY11 @ ( sK1_Xh1 @ sK7_SY51 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(14,plain,
( ( ! [SY47: b,SY48: b] :
( ( sK2_SY11 @ ( sK4_SY30 @ SY47 @ SY48 ) )
= ( sK5_SY38 @ ( sK2_SY11 @ SY47 ) @ ( sK2_SY11 @ SY48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ! [SY39: g,SY40: g] :
( ( sK1_Xh1 @ ( sK3_SY21 @ SY39 @ SY40 ) )
= ( sK4_SY30 @ ( sK1_Xh1 @ SY39 ) @ ( sK1_Xh1 @ SY40 ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(16,plain,
( ( ( ( sK2_SY11 @ ( sK1_Xh1 @ ( sK3_SY21 @ sK6_SY49 @ sK7_SY51 ) ) )
!= ( sK5_SY38 @ ( sK2_SY11 @ ( sK1_Xh1 @ sK6_SY49 ) ) @ ( sK2_SY11 @ ( sK1_Xh1 @ sK7_SY51 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: b] :
( ( ! [SY52: b] :
( ( sK2_SY11 @ ( sK4_SY30 @ SV1 @ SY52 ) )
= ( sK5_SY38 @ ( sK2_SY11 @ SV1 ) @ ( sK2_SY11 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: g] :
( ( ! [SY53: g] :
( ( sK1_Xh1 @ ( sK3_SY21 @ SV2 @ SY53 ) )
= ( sK4_SY30 @ ( sK1_Xh1 @ SV2 ) @ ( sK1_Xh1 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ( sK2_SY11 @ ( sK1_Xh1 @ ( sK3_SY21 @ sK6_SY49 @ sK7_SY51 ) ) )
= ( sK5_SY38 @ ( sK2_SY11 @ ( sK1_Xh1 @ sK6_SY49 ) ) @ ( sK2_SY11 @ ( sK1_Xh1 @ sK7_SY51 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV3: b,SV1: b] :
( ( ( sK2_SY11 @ ( sK4_SY30 @ SV1 @ SV3 ) )
= ( sK5_SY38 @ ( sK2_SY11 @ SV1 ) @ ( sK2_SY11 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV4: g,SV2: g] :
( ( ( sK1_Xh1 @ ( sK3_SY21 @ SV2 @ SV4 ) )
= ( sK4_SY30 @ ( sK1_Xh1 @ SV2 ) @ ( sK1_Xh1 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,21,20]) ).
thf(23,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG001^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 8 20:06:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (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).
% 0.13/0.39
% 0.13/0.39 ********************************
% 0.13/0.39 * All subproblems solved! *
% 0.13/0.39 ********************************
% 0.13/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:22,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.39
% 0.13/0.39 %**** Beginning of derivation protocol ****
% 0.13/0.39 % SZS output start CNFRefutation
% See solution above
% 0.13/0.39
% 0.13/0.39 %**** End of derivation protocol ****
% 0.13/0.39 %**** no. of clauses in derivation: 23 ****
% 0.13/0.39 %**** clause counter: 22 ****
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:22,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------