TSTP Solution File: ANA034-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ANA034-2 : 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 : n029.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 17:14:02 EDT 2023
% Result : Unsatisfiable 0.20s 0.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 33
% Syntax : Number of formulae : 58 ( 15 unt; 18 typ; 0 def)
% Number of atoms : 88 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 101 ( 53 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 13 >; 7 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 50 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_23,type,
c_times: ( $i * $i * $i ) > $i ).
tff(decl_24,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(decl_25,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_26,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
c_0: $i ).
tff(decl_28,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_29,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_30,type,
c_less: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(decl_32,type,
v_c: $i ).
tff(decl_33,type,
t_b: $i ).
tff(decl_34,type,
v_x: $i ).
tff(decl_35,type,
v_a: $i > $i ).
tff(decl_36,type,
v_f: $i > $i ).
tff(decl_37,type,
v_b: $i > $i ).
tff(decl_38,type,
v_ca: $i ).
tff(decl_39,type,
v_g: $i > $i ).
cnf(cls_Ring__and__Field_Omult__mono_0,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X5,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_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/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
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_conjecture_0,negated_conjecture,
c_less(c_0,v_c,t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_4,negated_conjecture,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
( class_Orderings_Oorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
( c_lessequals(c_0,c_times(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
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(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(c_0_15,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X5,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X5,X1) ),
cls_Ring__and__Field_Omult__mono_0 ).
cnf(c_0_16,axiom,
( c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_Ring__and__Field_Oabs__mult_0 ).
cnf(c_0_17,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_18,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_19,negated_conjecture,
c_less(c_0,v_c,t_b),
cls_conjecture_0 ).
cnf(c_0_20,plain,
( c_lessequals(c_HOL_Oabs(c_times(X1,X2,X3),X3),c_times(X4,X5,X3),X3)
| ~ c_lessequals(c_0,c_HOL_Oabs(X2,X3),X3)
| ~ c_lessequals(c_HOL_Oabs(X1,X3),X4,X3)
| ~ c_lessequals(c_HOL_Oabs(X2,X3),X5,X3)
| ~ c_lessequals(c_0,X4,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,negated_conjecture,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
cls_conjecture_4 ).
cnf(c_0_22,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_23,negated_conjecture,
( c_lessequals(c_0,v_c,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,axiom,
( class_Orderings_Oorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
clsrel_OrderedGroup_Olordered__ab__group__abs_17 ).
cnf(c_0_25,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
cls_conjecture_5 ).
cnf(c_0_26,negated_conjecture,
( c_lessequals(c_HOL_Oabs(c_times(X1,X2,t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X2,t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X2,t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_27,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
cls_conjecture_2 ).
cnf(c_0_28,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
cls_conjecture_3 ).
cnf(c_0_29,axiom,
( c_lessequals(c_0,c_times(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X3,X1) ),
cls_Ring__and__Field_Omult__nonneg__nonneg_0 ).
cnf(c_0_30,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_40 ).
cnf(c_0_31,negated_conjecture,
( c_lessequals(c_0,v_c,t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,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_33,negated_conjecture,
( ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_34,plain,
( c_lessequals(c_0,c_times(X1,X2,X3),X3)
| ~ c_lessequals(c_0,X1,X3)
| ~ c_lessequals(c_0,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
c_lessequals(c_0,v_c,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22])]) ).
cnf(c_0_36,negated_conjecture,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_22])]) ).
cnf(c_0_37,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_38,negated_conjecture,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_37]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_32]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA034-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n029.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 18:49:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.60 start to proof: theBenchmark
% 0.20/0.62 % Version : CSE_E---1.5
% 0.20/0.62 % Problem : theBenchmark.p
% 0.20/0.62 % Proof found
% 0.20/0.62 % SZS status Theorem for theBenchmark.p
% 0.20/0.62 % SZS output start Proof
% See solution above
% 0.20/0.62 % Total time : 0.011000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.014000 s
%------------------------------------------------------------------------------