TSTP Solution File: SWV167+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV167+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 : 300s
% DateTime : Thu Aug 31 21:36:50 EDT 2023
% Result : Theorem 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 80
% Syntax : Number of formulae : 104 ( 11 unt; 75 typ; 0 def)
% Number of atoms : 203 ( 57 equ)
% Maximal formula atoms : 45 ( 7 avg)
% Number of connectives : 229 ( 55 ~; 52 |; 78 &)
% ( 2 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 144 ( 50 >; 94 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-4 aty)
% Number of functors : 68 ( 68 usr; 23 con; 0-7 aty)
% Number of variables : 59 ( 0 sgn; 48 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
gt: ( $i * $i ) > $o ).
tff(decl_23,type,
leq: ( $i * $i ) > $o ).
tff(decl_24,type,
lt: ( $i * $i ) > $o ).
tff(decl_25,type,
geq: ( $i * $i ) > $o ).
tff(decl_26,type,
pred: $i > $i ).
tff(decl_27,type,
succ: $i > $i ).
tff(decl_28,type,
n0: $i ).
tff(decl_29,type,
uniform_int_rnd: ( $i * $i ) > $i ).
tff(decl_30,type,
dim: ( $i * $i ) > $i ).
tff(decl_31,type,
tptp_const_array1: ( $i * $i ) > $i ).
tff(decl_32,type,
a_select2: ( $i * $i ) > $i ).
tff(decl_33,type,
tptp_const_array2: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
a_select3: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
trans: $i > $i ).
tff(decl_36,type,
inv: $i > $i ).
tff(decl_37,type,
tptp_update3: ( $i * $i * $i * $i ) > $i ).
tff(decl_38,type,
tptp_madd: ( $i * $i ) > $i ).
tff(decl_39,type,
tptp_msub: ( $i * $i ) > $i ).
tff(decl_40,type,
tptp_mmul: ( $i * $i ) > $i ).
tff(decl_41,type,
tptp_minus_1: $i ).
tff(decl_42,type,
sum: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
tptp_float_0_0: $i ).
tff(decl_44,type,
n1: $i ).
tff(decl_45,type,
plus: ( $i * $i ) > $i ).
tff(decl_46,type,
n2: $i ).
tff(decl_47,type,
n3: $i ).
tff(decl_48,type,
n4: $i ).
tff(decl_49,type,
n5: $i ).
tff(decl_50,type,
minus: ( $i * $i ) > $i ).
tff(decl_51,type,
tptp_update2: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
true: $o ).
tff(decl_53,type,
def: $i ).
tff(decl_54,type,
use: $i ).
tff(decl_55,type,
mu_init: $i ).
tff(decl_56,type,
pv40: $i ).
tff(decl_57,type,
init: $i ).
tff(decl_58,type,
sigma_init: $i ).
tff(decl_59,type,
n135299: $i ).
tff(decl_60,type,
q_init: $i ).
tff(decl_61,type,
rho_init: $i ).
tff(decl_62,type,
center_init: $i ).
tff(decl_63,type,
loopcounter: $i ).
tff(decl_64,type,
muold_init: $i ).
tff(decl_65,type,
rhoold_init: $i ).
tff(decl_66,type,
sigmaold_init: $i ).
tff(decl_67,type,
epred1_4: ( $i * $i * $i * $i ) > $o ).
tff(decl_68,type,
epred2_0: $o ).
tff(decl_69,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_71,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_72,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_73,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
esk19_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
esk20_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_89,type,
esk21_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_90,type,
esk22_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
esk23_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
esk24_0: $i ).
tff(decl_93,type,
esk25_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
esk26_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
esk27_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
esk28_4: ( $i * $i * $i * $i ) > $i ).
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(cl5_nebula_init_0011,conjecture,
( ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,n135299) )
=> ! [X18] :
( ( leq(n0,X18)
& leq(X18,n4) )
=> a_select3(q_init,X14,X18) = init ) )
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,n4) )
=> a_select2(rho_init,X4) = init )
& ! [X20] :
( ( leq(n0,X20)
& leq(X20,pred(pv40)) )
=> a_select2(mu_init,X20) = init )
& ! [X21] :
( ( leq(n0,X21)
& leq(X21,pred(pv40)) )
=> a_select2(sigma_init,X21) = init )
& ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select3(center_init,X22,n0) = init )
& ( gt(loopcounter,n1)
=> ! [X28] :
( ( leq(n0,X28)
& leq(X28,n4) )
=> a_select2(muold_init,X28) = init ) )
& ( gt(loopcounter,n1)
=> ! [X29] :
( ( leq(n0,X29)
& leq(X29,n4) )
=> a_select2(rhoold_init,X29) = init ) )
& ( gt(loopcounter,n1)
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select2(sigmaold_init,X5) = init ) ) )
=> ! [X11] :
( ( leq(n0,X11)
& leq(X11,pv40) )
=> a_select2(mu_init,X11) = init ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_init_0011) ).
fof(leq_gt_pred,axiom,
! [X1,X2] :
( leq(X1,pred(X2))
<=> gt(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
fof(leq_gt2,axiom,
! [X1,X2] :
( ( leq(X1,X2)
& X1 != X2 )
=> gt(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt2) ).
fof(c_0_4,plain,
( epred2_0
<=> ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,n135299) )
=> ! [X18] :
( ( leq(n0,X18)
& leq(X18,n4) )
=> a_select3(q_init,X14,X18) = init ) )
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,n4) )
=> a_select2(rho_init,X4) = init )
& ! [X20] :
( ( leq(n0,X20)
& leq(X20,pred(pv40)) )
=> a_select2(mu_init,X20) = init )
& ! [X21] :
( ( leq(n0,X21)
& leq(X21,pred(pv40)) )
=> a_select2(sigma_init,X21) = init )
& ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select3(center_init,X22,n0) = init )
& ( gt(loopcounter,n1)
=> ! [X28] :
( ( leq(n0,X28)
& leq(X28,n4) )
=> a_select2(muold_init,X28) = init ) )
& ( gt(loopcounter,n1)
=> ! [X29] :
( ( leq(n0,X29)
& leq(X29,n4) )
=> a_select2(rhoold_init,X29) = init ) )
& ( gt(loopcounter,n1)
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select2(sigmaold_init,X5) = init ) ) ) ),
introduced(definition) ).
fof(c_0_5,plain,
( epred2_0
=> ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,n135299) )
=> ! [X18] :
( ( leq(n0,X18)
& leq(X18,n4) )
=> a_select3(q_init,X14,X18) = init ) )
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,n4) )
=> a_select2(rho_init,X4) = init )
& ! [X20] :
( ( leq(n0,X20)
& leq(X20,pred(pv40)) )
=> a_select2(mu_init,X20) = init )
& ! [X21] :
( ( leq(n0,X21)
& leq(X21,pred(pv40)) )
=> a_select2(sigma_init,X21) = init )
& ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select3(center_init,X22,n0) = init )
& ( gt(loopcounter,n1)
=> ! [X28] :
( ( leq(n0,X28)
& leq(X28,n4) )
=> a_select2(muold_init,X28) = init ) )
& ( gt(loopcounter,n1)
=> ! [X29] :
( ( leq(n0,X29)
& leq(X29,n4) )
=> a_select2(rhoold_init,X29) = init ) )
& ( gt(loopcounter,n1)
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select2(sigmaold_init,X5) = init ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X203,X204,X205,X206,X207,X208,X209,X210,X211] :
( ( a_select2(mu_init,pv40) = init
| ~ epred2_0 )
& ( a_select2(sigma_init,pv40) = init
| ~ epred2_0 )
& ( leq(n0,pv40)
| ~ epred2_0 )
& ( leq(pv40,n4)
| ~ epred2_0 )
& ( ~ leq(n0,X203)
| ~ leq(X203,n135299)
| ~ leq(n0,X204)
| ~ leq(X204,n4)
| a_select3(q_init,X203,X204) = init
| ~ epred2_0 )
& ( ~ leq(n0,X205)
| ~ leq(X205,n4)
| a_select2(rho_init,X205) = init
| ~ epred2_0 )
& ( ~ leq(n0,X206)
| ~ leq(X206,pred(pv40))
| a_select2(mu_init,X206) = init
| ~ epred2_0 )
& ( ~ leq(n0,X207)
| ~ leq(X207,pred(pv40))
| a_select2(sigma_init,X207) = init
| ~ epred2_0 )
& ( ~ leq(n0,X208)
| ~ leq(X208,n4)
| a_select3(center_init,X208,n0) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n1)
| ~ leq(n0,X209)
| ~ leq(X209,n4)
| a_select2(muold_init,X209) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n1)
| ~ leq(n0,X210)
| ~ leq(X210,n4)
| a_select2(rhoold_init,X210) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n1)
| ~ leq(n0,X211)
| ~ leq(X211,n4)
| a_select2(sigmaold_init,X211) = init
| ~ epred2_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_7,plain,
! [X147] : minus(X147,n1) = pred(X147),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
fof(c_0_8,negated_conjecture,
~ ( epred2_0
=> ! [X11] :
( ( leq(n0,X11)
& leq(X11,pv40) )
=> a_select2(mu_init,X11) = init ) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cl5_nebula_init_0011]),c_0_4]) ).
cnf(c_0_9,plain,
( a_select2(mu_init,X1) = init
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv40))
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( epred2_0
& leq(n0,esk24_0)
& leq(esk24_0,pv40)
& a_select2(mu_init,esk24_0) != init ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X48,X49] :
( ( ~ leq(X48,pred(X49))
| gt(X49,X48) )
& ( ~ gt(X49,X48)
| leq(X48,pred(X49)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt_pred])]) ).
cnf(c_0_13,plain,
( a_select2(mu_init,X1) = init
| ~ epred2_0
| ~ leq(n0,X1)
| ~ leq(X1,minus(pv40,n1)) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
epred2_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( leq(X2,pred(X1))
| ~ gt(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( a_select2(mu_init,X1) = init
| ~ leq(X1,minus(pv40,n1))
| ~ leq(n0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
cnf(c_0_17,plain,
( leq(X2,minus(X1,n1))
| ~ gt(X1,X2) ),
inference(rw,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_18,negated_conjecture,
a_select2(mu_init,esk24_0) != init,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( a_select2(mu_init,X1) = init
| ~ leq(n0,X1)
| ~ gt(pv40,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
leq(n0,esk24_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_21,plain,
! [X46,X47] :
( ~ leq(X46,X47)
| X46 = X47
| gt(X47,X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt2])]) ).
cnf(c_0_22,negated_conjecture,
~ gt(pv40,esk24_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_23,plain,
( X1 = X2
| gt(X2,X1)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
leq(esk24_0,pv40),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,plain,
( a_select2(mu_init,pv40) = init
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
esk24_0 = pv40,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_27,plain,
a_select2(mu_init,pv40) = init,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_14])]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV167+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.34 % Computer : n027.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Aug 29 07:46:08 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.60 % Version : CSE_E---1.5
% 0.21/0.60 % Problem : theBenchmark.p
% 0.21/0.60 % Proof found
% 0.21/0.60 % SZS status Theorem for theBenchmark.p
% 0.21/0.60 % SZS output start Proof
% See solution above
% 0.21/0.61 % Total time : 0.038000 s
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61 % Total time : 0.043000 s
%------------------------------------------------------------------------------