TSTP Solution File: SWV181+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV181+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 : n024.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 21:36:54 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 82
% Syntax : Number of formulae : 112 ( 17 unt; 74 typ; 0 def)
% Number of atoms : 165 ( 29 equ)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 173 ( 46 ~; 38 |; 53 &)
% ( 2 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 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 : 67 ( 67 usr; 22 con; 0-7 aty)
% Number of variables : 61 ( 0 sgn; 45 !; 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,
tptp_float_0_001: $i ).
tff(decl_56,type,
pv76: $i ).
tff(decl_57,type,
loopcounter: $i ).
tff(decl_58,type,
n135299: $i ).
tff(decl_59,type,
q_init: $i ).
tff(decl_60,type,
init: $i ).
tff(decl_61,type,
center_init: $i ).
tff(decl_62,type,
mu_init: $i ).
tff(decl_63,type,
rho_init: $i ).
tff(decl_64,type,
sigma_init: $i ).
tff(decl_65,type,
muold_init: $i ).
tff(decl_66,type,
epred1_4: ( $i * $i * $i * $i ) > $o ).
tff(decl_67,type,
epred2_0: $o ).
tff(decl_68,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_71,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_72,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_73,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
esk19_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
esk20_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
esk21_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_89,type,
esk22_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_90,type,
esk23_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
esk24_0: $i ).
tff(decl_92,type,
esk25_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
esk26_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
esk27_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
esk28_4: ( $i * $i * $i * $i ) > $i ).
fof(leq_succ_gt_equiv,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> gt(succ(X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_succ_gt_equiv) ).
fof(succ_plus_1_r,axiom,
! [X1] : plus(X1,n1) = succ(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_1_r) ).
fof(cl5_nebula_init_0081,conjecture,
( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,X4,n0) = init )
& ( gt(loopcounter,n0)
=> ! [X20] :
( ( leq(n0,X20)
& leq(X20,n4) )
=> a_select2(mu_init,X20) = init ) )
& ( gt(loopcounter,n0)
=> ! [X21] :
( ( leq(n0,X21)
& leq(X21,n4) )
=> a_select2(rho_init,X21) = init ) )
& ( gt(loopcounter,n0)
=> ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select2(sigma_init,X22) = init ) ) )
=> ! [X28] :
( ( leq(n0,X28)
& leq(X28,n4) )
=> a_select2(muold_init,X28) = init ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_init_0081) ).
fof(successor_1,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
fof(irreflexivity_gt,axiom,
! [X1] : ~ gt(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(leq_succ_gt,axiom,
! [X1,X2] :
( leq(succ(X1),X2)
=> gt(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_succ_gt) ).
fof(transitivity_leq,axiom,
! [X1,X2,X3] :
( ( leq(X1,X2)
& leq(X2,X3) )
=> leq(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',transitivity_leq) ).
fof(c_0_7,plain,
( epred2_0
<=> ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,X4,n0) = init )
& ( gt(loopcounter,n0)
=> ! [X20] :
( ( leq(n0,X20)
& leq(X20,n4) )
=> a_select2(mu_init,X20) = init ) )
& ( gt(loopcounter,n0)
=> ! [X21] :
( ( leq(n0,X21)
& leq(X21,n4) )
=> a_select2(rho_init,X21) = init ) )
& ( gt(loopcounter,n0)
=> ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select2(sigma_init,X22) = init ) ) ) ),
introduced(definition) ).
fof(c_0_8,plain,
! [X52,X53] :
( ( ~ leq(X52,X53)
| gt(succ(X53),X52) )
& ( ~ gt(succ(X53),X52)
| leq(X52,X53) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt_equiv])]) ).
fof(c_0_9,plain,
! [X136] : plus(X136,n1) = succ(X136),
inference(variable_rename,[status(thm)],[succ_plus_1_r]) ).
fof(c_0_10,plain,
( epred2_0
=> ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,X4,n0) = init )
& ( gt(loopcounter,n0)
=> ! [X20] :
( ( leq(n0,X20)
& leq(X20,n4) )
=> a_select2(mu_init,X20) = init ) )
& ( gt(loopcounter,n0)
=> ! [X21] :
( ( leq(n0,X21)
& leq(X21,n4) )
=> a_select2(rho_init,X21) = init ) )
& ( gt(loopcounter,n0)
=> ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select2(sigma_init,X22) = init ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
~ ( epred2_0
=> ! [X28] :
( ( leq(n0,X28)
& leq(X28,n4) )
=> a_select2(muold_init,X28) = init ) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cl5_nebula_init_0081]),c_0_7]) ).
cnf(c_0_12,plain,
( leq(X2,X1)
| ~ gt(succ(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
plus(X1,n1) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
succ(n0) = n1,
inference(split_conjunct,[status(thm)],[successor_1]) ).
fof(c_0_15,plain,
! [X202,X203,X204,X205,X206,X207] :
( ( leq(tptp_float_0_001,pv76)
| ~ epred2_0 )
& ( leq(n1,loopcounter)
| ~ epred2_0 )
& ( gt(n1,loopcounter)
| ~ epred2_0 )
& ( ~ leq(n0,X202)
| ~ leq(X202,n135299)
| ~ leq(n0,X203)
| ~ leq(X203,n4)
| a_select3(q_init,X202,X203) = init
| ~ epred2_0 )
& ( ~ leq(n0,X204)
| ~ leq(X204,n4)
| a_select3(center_init,X204,n0) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n0)
| ~ leq(n0,X205)
| ~ leq(X205,n4)
| a_select2(mu_init,X205) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n0)
| ~ leq(n0,X206)
| ~ leq(X206,n4)
| a_select2(rho_init,X206) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n0)
| ~ leq(n0,X207)
| ~ leq(X207,n4)
| a_select2(sigma_init,X207) = init
| ~ epred2_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_16,negated_conjecture,
( epred2_0
& leq(n0,esk24_0)
& leq(esk24_0,n4)
& a_select2(muold_init,esk24_0) != init ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_17,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).
fof(c_0_18,plain,
! [X151,X152] :
( ~ leq(succ(X151),X152)
| gt(X152,X151) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt])]) ).
cnf(c_0_19,plain,
( leq(X2,X1)
| ~ gt(plus(X1,n1),X2) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
plus(n0,n1) = n1,
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_21,plain,
( gt(n1,loopcounter)
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
epred2_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,plain,
! [X34] : ~ gt(X34,X34),
inference(variable_rename,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( gt(X2,X1)
| ~ leq(succ(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X36,X37,X38] :
( ~ leq(X36,X37)
| ~ leq(X37,X38)
| leq(X36,X38) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_leq])]) ).
cnf(c_0_26,plain,
( leq(X1,n0)
| ~ gt(n1,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
gt(n1,loopcounter),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_28,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( gt(X2,X1)
| ~ leq(plus(X1,n1),X2) ),
inference(rw,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_30,plain,
( leq(X1,X3)
| ~ leq(X1,X2)
| ~ leq(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
leq(loopcounter,n0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( leq(n1,loopcounter)
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_33,plain,
~ leq(plus(X1,n1),X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( leq(X1,n0)
| ~ leq(X1,loopcounter) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
leq(n1,loopcounter),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_22])]) ).
cnf(c_0_36,plain,
~ leq(n1,n0),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_37,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV181+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 06:16:23 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.048000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.052000 s
%------------------------------------------------------------------------------