TSTP Solution File: ANA030-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ANA030-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 : Wed Aug 30 17:14:01 EDT 2023
% Result : Unsatisfiable 0.19s 0.58s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 35
% Syntax : Number of formulae : 70 ( 9 unt; 19 typ; 0 def)
% Number of atoms : 102 ( 22 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 107 ( 56 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 16 >; 12 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 99 ( 4 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v_f: $i > $i ).
tff(decl_23,type,
v_g: $i > $i ).
tff(decl_24,type,
t_b: $i ).
tff(decl_25,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
c_0: $i ).
tff(decl_27,type,
c_Orderings_Omax: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(decl_29,type,
v_c: $i ).
tff(decl_30,type,
v_h: $i > $i ).
tff(decl_31,type,
c_times: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
v_x: $i > $i ).
tff(decl_34,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_36,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(decl_37,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_38,type,
c_uminus: ( $i * $i ) > $i ).
tff(decl_39,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_40,type,
class_Orderings_Olinorder: $i > $o ).
cnf(cls_OrderedGroup_Ominus__diff__eq_0,axiom,
( c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
cnf(cls_OrderedGroup_Odiff__minus__eq__add_0,axiom,
( c_minus(X2,c_uminus(X3,X1),X1) = c_plus(X2,X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__1_0,axiom,
( c_plus(X2,c_uminus(X3,X1),X1) = c_minus(X2,X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__1_0) ).
cnf(cls_OrderedGroup_Ominus__add__distrib_0,axiom,
( c_uminus(c_plus(X2,X3,X1),X1) = c_plus(c_uminus(X2,X1),c_uminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( c_HOL_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(cls_OrderedGroup_Ominus__minus_0,axiom,
( c_uminus(c_uminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(X1),v_g(X1),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(X1),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0,axiom,
( c_lessequals(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
cnf(cls_Orderings_Ole__maxI2_0,axiom,
( c_lessequals(X2,c_Orderings_Omax(X3,X2,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Ole__maxI2_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__8_0,axiom,
( c_lessequals(X2,c_plus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_minus(X2,X3,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(v_f(v_x(X1)),c_plus(v_g(v_x(X1)),c_times(X1,c_HOL_Oabs(v_h(v_x(X1)),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
( class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(c_0_16,axiom,
( c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ominus__diff__eq_0 ).
cnf(c_0_17,axiom,
( c_minus(X2,c_uminus(X3,X1),X1) = c_plus(X2,X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Odiff__minus__eq__add_0 ).
cnf(c_0_18,axiom,
( c_plus(X2,c_uminus(X3,X1),X1) = c_minus(X2,X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ocompare__rls__1_0 ).
cnf(c_0_19,axiom,
( c_uminus(c_plus(X2,X3,X1),X1) = c_plus(c_uminus(X2,X1),c_uminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ominus__add__distrib_0 ).
cnf(c_0_20,axiom,
( c_HOL_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X2,X1) ),
cls_OrderedGroup_Oabs__of__nonneg_0 ).
cnf(c_0_21,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_50 ).
cnf(c_0_22,plain,
( c_minus(c_uminus(X1,X2),X3,X2) = c_uminus(c_plus(X3,X1,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,axiom,
( c_uminus(c_uminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ominus__minus_0 ).
cnf(c_0_24,plain,
( c_minus(c_uminus(X1,X2),X3,X2) = c_uminus(c_plus(X1,X3,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(X1),v_g(X1),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(X1),t_b),t_b),t_b),
cls_conjecture_1 ).
cnf(c_0_26,plain,
( c_HOL_Oabs(X1,X2) = X1
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_lessequals(c_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_28,plain,
( c_uminus(c_plus(X1,c_uminus(X2,X3),X3),X3) = c_minus(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( c_uminus(c_plus(c_uminus(X1,X2),X3,X2),X2) = c_minus(X1,X3,X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_30,axiom,
( c_lessequals(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(c_Orderings_Omax(X2,X3,X1),X4,X1) ),
cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0 ).
cnf(c_0_31,negated_conjecture,
( c_lessequals(c_Orderings_Omax(c_minus(v_f(X1),v_g(X1),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(X1),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_Orderings_Omax(c_minus(v_f(X1),v_g(X1),t_b),c_0,t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_32,axiom,
( c_lessequals(X2,c_Orderings_Omax(X3,X2,X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_Orderings_Ole__maxI2_0 ).
cnf(c_0_33,plain,
( c_plus(X1,c_uminus(X2,X3),X3) = c_uminus(c_minus(X2,X1,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_34,plain,
( c_plus(c_uminus(X1,X2),X3,X2) = c_uminus(c_minus(X1,X3,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_35,axiom,
( c_lessequals(X2,c_plus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_minus(X2,X3,X1),X4,X1) ),
cls_OrderedGroup_Ocompare__rls__8_0 ).
cnf(c_0_36,negated_conjecture,
( c_lessequals(c_minus(v_f(X1),v_g(X1),t_b),c_times(v_c,c_HOL_Oabs(v_h(X1),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_37,plain,
( c_uminus(c_minus(c_uminus(X1,X2),X3,X2),X2) = c_plus(X3,X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_38,plain,
( c_uminus(c_minus(c_uminus(X1,X2),X3,X2),X2) = c_plus(X1,X3,X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_23]) ).
cnf(c_0_39,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_4 ).
cnf(c_0_40,negated_conjecture,
( c_lessequals(v_f(X1),c_plus(c_times(v_c,c_HOL_Oabs(v_h(X1),t_b),t_b),v_g(X1),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( c_plus(X1,X2,X3) = c_plus(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
class_OrderedGroup_Oab__group__add(t_b),
inference(spm,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_43,negated_conjecture,
~ c_lessequals(v_f(v_x(X1)),c_plus(v_g(v_x(X1)),c_times(X1,c_HOL_Oabs(v_h(v_x(X1)),t_b),t_b),t_b),t_b),
cls_conjecture_2 ).
cnf(c_0_44,negated_conjecture,
( c_lessequals(v_f(X1),c_plus(v_g(X1),c_times(v_c,c_HOL_Oabs(v_h(X1),t_b),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_45,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
clsrel_OrderedGroup_Olordered__ab__group__abs_1 ).
cnf(c_0_47,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_48,axiom,
( class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_33 ).
cnf(c_0_49,negated_conjecture,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_27])]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_21]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA030-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n014.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 : 300
% 0.13/0.34 % DateTime : Fri Aug 25 18:33:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.58 % Version : CSE_E---1.5
% 0.19/0.58 % Problem : theBenchmark.p
% 0.19/0.58 % Proof found
% 0.19/0.58 % SZS status Theorem for theBenchmark.p
% 0.19/0.58 % SZS output start Proof
% See solution above
% 0.19/0.58 % Total time : 0.007000 s
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58 % Total time : 0.010000 s
%------------------------------------------------------------------------------