TSTP Solution File: GRP710+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP710+1 : 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 : n003.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 : Sat Jul 16 10:19:42 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 51 unt; 7 typ; 0 def)
% Number of atoms : 145 ( 97 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 227 ( 8 ~; 0 |; 3 &; 216 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 92 ( 0 ^ 82 !; 10 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_i,type,
i: $i > $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(tp_sK1_X0,type,
sK1_X0: $i ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_X3,type,
sK3_X3: $i ).
thf(tp_sK4_SY16,type,
sK4_SY16: $i ).
thf(tp_unit,type,
unit: $i ).
thf(1,axiom,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
thf(2,axiom,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
thf(4,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
thf(5,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
thf(6,conjecture,
( ! [X0: $i,X1: $i] :
? [X2: $i] :
( ( mult @ X0 @ X2 )
= X1 )
& ! [X3: $i,X4: $i] :
? [X5: $i] :
( ( mult @ X5 @ X4 )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(7,negated_conjecture,
( ( ! [X0: $i,X1: $i] :
? [X2: $i] :
( ( mult @ X0 @ X2 )
= X1 )
& ! [X3: $i,X4: $i] :
? [X5: $i] :
( ( mult @ X5 @ X4 )
= X3 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [X0: $i,X1: $i] :
? [X2: $i] :
( ( mult @ X0 @ X2 )
= X1 )
& ! [X3: $i,X4: $i] :
? [X5: $i] :
( ( mult @ X5 @ X4 )
= X3 ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [X0: $i,X1: $i] :
? [X2: $i] :
( ( mult @ X0 @ X2 )
= X1 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[8]) ).
thf(15,plain,
( ( ! [X3: $i,X4: $i] :
? [X5: $i] :
( ( mult @ X5 @ X4 )
= X3 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[8]) ).
thf(16,plain,
( ( ~ ! [X0: $i,X1: $i] :
? [X2: $i] :
( ( mult @ X0 @ X2 )
= X1 ) )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [X3: $i,X4: $i] :
? [X5: $i] :
( ( mult @ X5 @ X4 )
= X3 ) )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [SY15: $i] :
( ( mult @ sK1_X0 @ SY15 )
!= sK2_SY13 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(19,plain,
( ( ! [SY18: $i] :
( ( mult @ SY18 @ sK4_SY16 )
!= sK3_X3 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(20,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( ! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(25,plain,
( ( ! [SY15: $i] :
( ( mult @ sK1_X0 @ SY15 )
!= sK2_SY13 ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( mult @ SV1 @ unit )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( mult @ unit @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV3: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ( mult @ SY20 @ ( mult @ SY19 @ ( mult @ SY19 @ SV3 ) ) )
= ( mult @ ( mult @ ( mult @ SY20 @ SY19 ) @ SY19 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV4: $i] :
( ( ( mult @ SV4 @ ( i @ SV4 ) )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV5: $i] :
( ( ( mult @ ( i @ SV5 ) @ SV5 )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV6: $i] :
( ( ( ( mult @ sK1_X0 @ SV6 )
!= sK2_SY13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV3: $i,SV7: $i] :
( ( ! [SY21: $i] :
( ( mult @ SY21 @ ( mult @ SV7 @ ( mult @ SV7 @ SV3 ) ) )
= ( mult @ ( mult @ ( mult @ SY21 @ SV7 ) @ SV7 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV6: $i] :
( ( ( mult @ sK1_X0 @ SV6 )
= sK2_SY13 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV3: $i,SV7: $i,SV8: $i] :
( ( ( mult @ SV8 @ ( mult @ SV7 @ ( mult @ SV7 @ SV3 ) ) )
= ( mult @ ( mult @ ( mult @ SV8 @ SV7 ) @ SV7 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,34,33,30,29,27]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(38,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(39,plain,
( ( ! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(41,plain,
( ( ! [SY18: $i] :
( ( mult @ SY18 @ sK4_SY16 )
!= sK3_X3 ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(42,plain,
! [SV9: $i] :
( ( ( mult @ SV9 @ unit )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV10: $i] :
( ( ( mult @ unit @ SV10 )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV11: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ( mult @ SY23 @ ( mult @ SY22 @ ( mult @ SY22 @ SV11 ) ) )
= ( mult @ ( mult @ ( mult @ SY23 @ SY22 ) @ SY22 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV12: $i] :
( ( ( mult @ SV12 @ ( i @ SV12 ) )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV13: $i] :
( ( ( mult @ ( i @ SV13 ) @ SV13 )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV14: $i] :
( ( ( ( mult @ SV14 @ sK4_SY16 )
!= sK3_X3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV11: $i,SV15: $i] :
( ( ! [SY24: $i] :
( ( mult @ SY24 @ ( mult @ SV15 @ ( mult @ SV15 @ SV11 ) ) )
= ( mult @ ( mult @ ( mult @ SY24 @ SV15 ) @ SV15 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV14: $i] :
( ( ( mult @ SV14 @ sK4_SY16 )
= sK3_X3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV11: $i,SV15: $i,SV16: $i] :
( ( ( mult @ SV16 @ ( mult @ SV15 @ ( mult @ SV15 @ SV11 ) ) )
= ( mult @ ( mult @ ( mult @ SV16 @ SV15 ) @ SV15 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[42,50,49,46,45,43]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP710+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 20:12:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 5
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (rf:0,axioms:5,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:7,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.51
% 0.19/0.51 ********************************
% 0.19/0.51 * All subproblems solved! *
% 0.19/0.51 ********************************
% 0.19/0.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:51,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.51
% 0.19/0.51 %**** Beginning of derivation protocol ****
% 0.19/0.51 % SZS output start CNFRefutation
% See solution above
% 0.19/0.51
% 0.19/0.51 %**** End of derivation protocol ****
% 0.19/0.51 %**** no. of clauses in derivation: 52 ****
% 0.19/0.51 %**** clause counter: 51 ****
% 0.19/0.51
% 0.19/0.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:51,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------