TSTP Solution File: ANA029-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ANA029-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 17:14:00 EDT 2023
% Result : Unsatisfiable 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 58 ( 8 unt; 16 typ; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 131 ( 67 ~; 64 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 13 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 69 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
c_0: $i ).
tff(decl_23,type,
v_x: $i ).
tff(decl_24,type,
v_f: $i > $i ).
tff(decl_25,type,
v_k: $i > $i ).
tff(decl_26,type,
t_b: $i ).
tff(decl_27,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
c_Orderings_Omax: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
v_g: $i > $i ).
tff(decl_31,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(decl_32,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_33,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(decl_34,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_35,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_36,type,
c_less: ( $i * $i * $i ) > $o ).
tff(decl_37,type,
class_Orderings_Oorder: $i > $o ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(cls_Orderings_Olinorder__not__le_0,axiom,
( c_less(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_10,axiom,
( class_Orderings_Oorder(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
( class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
( c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( c_lessequals(X4,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(cls_OrderedGroup_Odiff__le__0__iff__le_1,axiom,
( c_lessequals(c_minus(X2,X3,X1),c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_OrderedGroup_Odiff__le__0__iff__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_minus(X2,X3,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
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/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(c_0_14,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
cls_Orderings_Oorder__less__imp__le_0 ).
cnf(c_0_15,axiom,
( c_less(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_Orderings_Olinorder__not__le_0 ).
cnf(c_0_16,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
( class_Orderings_Oorder(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
clsrel_OrderedGroup_Opordered__ab__group__add_10 ).
cnf(c_0_18,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,axiom,
( class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_33 ).
cnf(c_0_20,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_54 ).
cnf(c_0_21,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
cls_conjecture_3 ).
cnf(c_0_22,axiom,
( c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2 ).
cnf(c_0_23,axiom,
( c_lessequals(X4,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X2,X1) ),
cls_Orderings_Oorder__class_Oorder__trans_0 ).
cnf(c_0_24,axiom,
( c_lessequals(c_minus(X2,X3,X1),c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_OrderedGroup_Odiff__le__0__iff__le_1 ).
cnf(c_0_25,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_26,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_27,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( c_lessequals(c_minus(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_0,X4,X3)
| ~ c_lessequals(X1,X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]) ).
cnf(c_0_29,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_minus(X2,X3,X1),c_0,X1) ),
cls_OrderedGroup_Odiff__le__0__iff__le_0 ).
cnf(c_0_30,negated_conjecture,
( c_lessequals(X1,X2,t_b)
| c_lessequals(X2,X1,t_b) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(v_f(v_x),v_k(v_x),t_b) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
cls_OrderedGroup_Oabs__ge__zero_0 ).
cnf(c_0_33,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
cls_conjecture_2 ).
cnf(c_0_34,negated_conjecture,
( c_lessequals(c_0,c_minus(X1,X2,t_b),t_b)
| c_lessequals(X1,X2,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(v_f(v_x),v_k(v_x),t_b) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( c_lessequals(v_f(v_x),v_k(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,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_39,negated_conjecture,
( ~ 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_37,c_0_38]),c_0_26])]) ).
cnf(c_0_40,negated_conjecture,
~ class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_19]),c_0_26])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_20]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA029-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 18:28:29 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 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
% 0.21/0.60 % Total time : 0.007000 s
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60 % Total time : 0.010000 s
%------------------------------------------------------------------------------