TSTP Solution File: ANA031-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ANA031-2 : 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 : n017.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 0.93s 1.06s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 26
% Syntax : Number of formulae : 48 ( 9 unt; 15 typ; 0 def)
% Number of atoms : 70 ( 7 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 81 ( 44 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 12 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v_b: $i > $i ).
tff(decl_23,type,
t_b: $i ).
tff(decl_24,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(decl_25,type,
v_c: $i ).
tff(decl_26,type,
v_g: $i > $i ).
tff(decl_27,type,
c_times: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
v_x: $i > $i ).
tff(decl_30,type,
v_f: $i > $i ).
tff(decl_31,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(decl_32,type,
c_0: $i ).
tff(decl_33,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
tff(decl_34,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_35,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_36,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
cnf(cls_OrderedGroup_Omult__ac__2_0,axiom,
( c_times(X2,X3,X1) = c_times(X3,X2,X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_17,axiom,
( class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_0,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
cnf(cls_OrderedGroup_Omult__ac__1_0,axiom,
( c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1)
| ~ class_OrderedGroup_Osemigroup__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X1)),t_b),c_HOL_Oabs(v_f(v_x(X1)),t_b),t_b),c_times(X1,c_times(c_HOL_Oabs(v_f(v_x(X1)),t_b),c_HOL_Oabs(v_g(v_x(X1)),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(X1),t_b),c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( class_Ring__and__Field_Opordered__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
( class_OrderedGroup_Osemigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
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(c_0_11,axiom,
( c_times(X2,X3,X1) = c_times(X3,X2,X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
cls_OrderedGroup_Omult__ac__2_0 ).
cnf(c_0_12,axiom,
( class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_17 ).
cnf(c_0_13,plain,
( c_times(X1,X2,X3) = c_times(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_15,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_0,X4,X1) ),
cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0 ).
cnf(c_0_16,negated_conjecture,
c_times(X1,X2,t_b) = c_times(X2,X1,t_b),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
( c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1)
| ~ class_OrderedGroup_Osemigroup__mult(X1) ),
cls_OrderedGroup_Omult__ac__1_0 ).
cnf(c_0_18,negated_conjecture,
( c_lessequals(c_times(X1,X2,t_b),c_times(X2,X3,t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(X1,X3,t_b) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( c_times(X1,c_times(X2,X3,t_b),t_b) = c_times(X2,c_times(X3,X1,t_b),t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X1)),t_b),c_HOL_Oabs(v_f(v_x(X1)),t_b),t_b),c_times(X1,c_times(c_HOL_Oabs(v_f(v_x(X1)),t_b),c_HOL_Oabs(v_g(v_x(X1)),t_b),t_b),t_b),t_b),
cls_conjecture_1 ).
cnf(c_0_21,negated_conjecture,
( c_lessequals(c_times(X1,X2,t_b),c_times(X3,c_times(X2,X4,t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ c_lessequals(X1,c_times(X4,X3,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(X1)),t_b),c_times(X1,c_HOL_Oabs(v_g(v_x(X1)),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(X1)),t_b),t_b) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_16]) ).
cnf(c_0_23,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(X1),t_b),c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),
cls_conjecture_0 ).
cnf(c_0_24,negated_conjecture,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,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_26,negated_conjecture,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,axiom,
( class_Ring__and__Field_Opordered__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_42 ).
cnf(c_0_28,negated_conjecture,
( ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_14])]) ).
cnf(c_0_29,axiom,
( class_OrderedGroup_Osemigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_21 ).
cnf(c_0_30,negated_conjecture,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_14])]) ).
cnf(c_0_31,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_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA031-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n017.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 : 300
% 0.12/0.33 % DateTime : Fri Aug 25 17:47:25 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 0.93/1.06 % Version : CSE_E---1.5
% 0.93/1.06 % Problem : theBenchmark.p
% 0.93/1.06 % Proof found
% 0.93/1.06 % SZS status Theorem for theBenchmark.p
% 0.93/1.06 % SZS output start Proof
% See solution above
% 0.93/1.07 % Total time : 0.503000 s
% 0.93/1.07 % SZS output end Proof
% 0.93/1.07 % Total time : 0.506000 s
%------------------------------------------------------------------------------