TSTP Solution File: ANA002-2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ANA002-2 : TPTP v8.1.2. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 17:13:45 EDT 2023
% Result : Unsatisfiable 35.18s 35.25s
% Output : CNFRefutation 35.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 29
% Syntax : Number of formulae : 82 ( 18 unt; 11 typ; 0 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 171 ( 63 ~; 108 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in_interval: ( $i * $i * $i ) > $o ).
tff(decl_23,type,
less_than_or_equal: ( $i * $i ) > $o ).
tff(decl_24,type,
q: ( $i * $i ) > $i ).
tff(decl_25,type,
f: $i > $i ).
tff(decl_26,type,
n0: $i ).
tff(decl_27,type,
h: $i > $i ).
tff(decl_28,type,
lower_bound: $i ).
tff(decl_29,type,
upper_bound: $i ).
tff(decl_30,type,
k: $i > $i ).
tff(decl_31,type,
l: $i ).
tff(decl_32,type,
g: $i > $i ).
cnf(continuity2,axiom,
( less_than_or_equal(f(X1),n0)
| less_than_or_equal(X2,h(X1))
| ~ less_than_or_equal(X2,X1)
| ~ less_than_or_equal(f(X2),n0)
| ~ in_interval(lower_bound,X1,upper_bound) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity2) ).
cnf(crossover3_and_g_function2,axiom,
( less_than_or_equal(f(g(X1)),n0)
| less_than_or_equal(l,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover3_and_g_function2) ).
cnf(in_interval,axiom,
( in_interval(X1,X2,X3)
| ~ less_than_or_equal(X1,X2)
| ~ less_than_or_equal(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_interval) ).
cnf(crossover1,axiom,
( less_than_or_equal(X1,l)
| ~ less_than_or_equal(X1,upper_bound)
| ~ less_than_or_equal(f(X1),n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover1) ).
cnf(crossover2_and_g_function1,axiom,
( less_than_or_equal(g(X1),upper_bound)
| less_than_or_equal(l,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover2_and_g_function1) ).
cnf(crossover4_and_g_function3,axiom,
( less_than_or_equal(l,X1)
| ~ less_than_or_equal(g(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover4_and_g_function3) ).
cnf(lower_mapping,hypothesis,
less_than_or_equal(f(lower_bound),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_mapping) ).
cnf(the_interval,hypothesis,
less_than_or_equal(lower_bound,upper_bound),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_interval) ).
cnf(transitivity_of_less,axiom,
( less_than_or_equal(X1,X2)
| ~ less_than_or_equal(X1,X3)
| ~ less_than_or_equal(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
cnf(totality_of_less,axiom,
( less_than_or_equal(X1,X2)
| less_than_or_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_less) ).
cnf(interpolation1,axiom,
( less_than_or_equal(X1,X2)
| ~ less_than_or_equal(X1,q(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interpolation1) ).
cnf(continuity1,axiom,
( less_than_or_equal(f(X1),n0)
| ~ less_than_or_equal(X1,h(X1))
| ~ in_interval(lower_bound,X1,upper_bound) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).
cnf(continuity4,axiom,
( less_than_or_equal(n0,f(X1))
| less_than_or_equal(k(X1),X2)
| ~ less_than_or_equal(X1,X2)
| ~ less_than_or_equal(n0,f(X2))
| ~ in_interval(lower_bound,X1,upper_bound) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity4) ).
cnf(prove_there_is_x_which_crosses,negated_conjecture,
~ in_interval(f(l),n0,f(l)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_x_which_crosses) ).
cnf(interpolation2,axiom,
( less_than_or_equal(X2,X1)
| ~ less_than_or_equal(q(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interpolation2) ).
cnf(reflexivity_of_less,axiom,
less_than_or_equal(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_less) ).
cnf(upper_mapping,hypothesis,
less_than_or_equal(n0,f(upper_bound)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_mapping) ).
cnf(continuity3,axiom,
( less_than_or_equal(n0,f(X1))
| ~ less_than_or_equal(k(X1),X1)
| ~ in_interval(lower_bound,X1,upper_bound) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity3) ).
cnf(c_0_18,axiom,
( less_than_or_equal(f(X1),n0)
| less_than_or_equal(X2,h(X1))
| ~ less_than_or_equal(X2,X1)
| ~ less_than_or_equal(f(X2),n0)
| ~ in_interval(lower_bound,X1,upper_bound) ),
continuity2 ).
cnf(c_0_19,axiom,
( less_than_or_equal(f(g(X1)),n0)
| less_than_or_equal(l,X1) ),
crossover3_and_g_function2 ).
cnf(c_0_20,plain,
( less_than_or_equal(g(X1),h(X2))
| less_than_or_equal(f(X2),n0)
| less_than_or_equal(l,X1)
| ~ less_than_or_equal(g(X1),X2)
| ~ in_interval(lower_bound,X2,upper_bound) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
( in_interval(X1,X2,X3)
| ~ less_than_or_equal(X1,X2)
| ~ less_than_or_equal(X2,X3) ),
in_interval ).
cnf(c_0_22,axiom,
( less_than_or_equal(X1,l)
| ~ less_than_or_equal(X1,upper_bound)
| ~ less_than_or_equal(f(X1),n0) ),
crossover1 ).
cnf(c_0_23,axiom,
( less_than_or_equal(g(X1),upper_bound)
| less_than_or_equal(l,X1) ),
crossover2_and_g_function1 ).
cnf(c_0_24,axiom,
( less_than_or_equal(l,X1)
| ~ less_than_or_equal(g(X1),X1) ),
crossover4_and_g_function3 ).
cnf(c_0_25,hypothesis,
less_than_or_equal(f(lower_bound),n0),
lower_mapping ).
cnf(c_0_26,hypothesis,
less_than_or_equal(lower_bound,upper_bound),
the_interval ).
cnf(c_0_27,axiom,
( less_than_or_equal(X1,X2)
| ~ less_than_or_equal(X1,X3)
| ~ less_than_or_equal(X3,X2) ),
transitivity_of_less ).
cnf(c_0_28,axiom,
( less_than_or_equal(X1,X2)
| less_than_or_equal(X2,X1) ),
totality_of_less ).
cnf(c_0_29,plain,
( less_than_or_equal(g(X1),h(X2))
| less_than_or_equal(f(X2),n0)
| less_than_or_equal(l,X1)
| ~ less_than_or_equal(g(X1),X2)
| ~ less_than_or_equal(X2,upper_bound)
| ~ less_than_or_equal(lower_bound,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_30,plain,
( less_than_or_equal(g(X1),l)
| less_than_or_equal(l,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_23]) ).
cnf(c_0_31,plain,
less_than_or_equal(l,upper_bound),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_32,hypothesis,
less_than_or_equal(lower_bound,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_25]),c_0_26])]) ).
cnf(c_0_33,plain,
( less_than_or_equal(X1,X2)
| less_than_or_equal(X3,X1)
| ~ less_than_or_equal(X3,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( less_than_or_equal(g(X1),h(l))
| less_than_or_equal(f(l),n0)
| less_than_or_equal(l,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_35,axiom,
( less_than_or_equal(X1,X2)
| ~ less_than_or_equal(X1,q(X2,X1)) ),
interpolation1 ).
cnf(c_0_36,plain,
( less_than_or_equal(X1,X2)
| less_than_or_equal(X2,X3)
| less_than_or_equal(X3,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_37,plain,
( less_than_or_equal(n0,f(X1))
| less_than_or_equal(X1,l)
| ~ less_than_or_equal(X1,upper_bound) ),
inference(spm,[status(thm)],[c_0_22,c_0_28]) ).
cnf(c_0_38,axiom,
( less_than_or_equal(f(X1),n0)
| ~ less_than_or_equal(X1,h(X1))
| ~ in_interval(lower_bound,X1,upper_bound) ),
continuity1 ).
cnf(c_0_39,plain,
( less_than_or_equal(f(l),n0)
| less_than_or_equal(l,h(l)) ),
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_40,plain,
( less_than_or_equal(q(X1,X2),X3)
| less_than_or_equal(X3,X2)
| less_than_or_equal(X2,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,axiom,
( less_than_or_equal(n0,f(X1))
| less_than_or_equal(k(X1),X2)
| ~ less_than_or_equal(X1,X2)
| ~ less_than_or_equal(n0,f(X2))
| ~ in_interval(lower_bound,X1,upper_bound) ),
continuity4 ).
cnf(c_0_42,plain,
( less_than_or_equal(n0,f(X1))
| less_than_or_equal(upper_bound,X1)
| less_than_or_equal(X1,l) ),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_43,negated_conjecture,
~ in_interval(f(l),n0,f(l)),
prove_there_is_x_which_crosses ).
cnf(c_0_44,plain,
( less_than_or_equal(f(l),n0)
| ~ in_interval(lower_bound,l,upper_bound) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,axiom,
( less_than_or_equal(X2,X1)
| ~ less_than_or_equal(q(X1,X2),X1) ),
interpolation2 ).
cnf(c_0_46,plain,
( less_than_or_equal(q(X1,q(X2,X3)),X3)
| less_than_or_equal(q(X2,X3),X1)
| less_than_or_equal(X3,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_40]) ).
cnf(c_0_47,plain,
( less_than_or_equal(n0,f(X1))
| less_than_or_equal(k(X1),X2)
| less_than_or_equal(X2,l)
| less_than_or_equal(upper_bound,X2)
| ~ less_than_or_equal(X1,X2)
| ~ in_interval(lower_bound,X1,upper_bound) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( ~ less_than_or_equal(n0,f(l))
| ~ less_than_or_equal(f(l),n0) ),
inference(spm,[status(thm)],[c_0_43,c_0_21]) ).
cnf(c_0_49,plain,
less_than_or_equal(f(l),n0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_21]),c_0_31]),c_0_32])]) ).
cnf(c_0_50,plain,
( less_than_or_equal(q(X1,X2),X2)
| less_than_or_equal(X2,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
( less_than_or_equal(n0,f(X1))
| less_than_or_equal(k(X1),X2)
| less_than_or_equal(upper_bound,X2)
| less_than_or_equal(X2,l)
| ~ less_than_or_equal(lower_bound,X1)
| ~ less_than_or_equal(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_21]),c_0_33]) ).
cnf(c_0_52,hypothesis,
( less_than_or_equal(X1,l)
| ~ less_than_or_equal(X1,lower_bound) ),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_53,axiom,
less_than_or_equal(X1,X1),
reflexivity_of_less ).
cnf(c_0_54,negated_conjecture,
~ less_than_or_equal(n0,f(l)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
cnf(c_0_55,hypothesis,
less_than_or_equal(n0,f(upper_bound)),
upper_mapping ).
cnf(c_0_56,plain,
( less_than_or_equal(X1,X2)
| less_than_or_equal(X3,X1)
| ~ less_than_or_equal(X3,q(X2,X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_50]) ).
cnf(c_0_57,hypothesis,
( less_than_or_equal(k(l),X1)
| less_than_or_equal(X1,l)
| less_than_or_equal(upper_bound,X1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]),c_0_54]),c_0_28]) ).
cnf(c_0_58,hypothesis,
( less_than_or_equal(k(X1),upper_bound)
| less_than_or_equal(n0,f(X1))
| ~ less_than_or_equal(X1,upper_bound)
| ~ in_interval(lower_bound,X1,upper_bound) ),
inference(spm,[status(thm)],[c_0_41,c_0_55]) ).
cnf(c_0_59,hypothesis,
( less_than_or_equal(upper_bound,q(X1,X2))
| less_than_or_equal(q(X1,X2),l)
| less_than_or_equal(k(l),X2)
| less_than_or_equal(X2,X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,hypothesis,
( less_than_or_equal(n0,f(X1))
| less_than_or_equal(k(X1),upper_bound)
| ~ less_than_or_equal(X1,upper_bound)
| ~ less_than_or_equal(lower_bound,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_21]) ).
cnf(c_0_61,hypothesis,
( less_than_or_equal(upper_bound,q(l,X1))
| less_than_or_equal(k(l),X1)
| less_than_or_equal(X1,l) ),
inference(spm,[status(thm)],[c_0_45,c_0_59]) ).
cnf(c_0_62,hypothesis,
( less_than_or_equal(k(l),upper_bound)
| less_than_or_equal(n0,f(l)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_31]),c_0_32])]) ).
cnf(c_0_63,hypothesis,
( less_than_or_equal(X1,q(l,X2))
| less_than_or_equal(k(l),X2)
| less_than_or_equal(X2,l)
| ~ less_than_or_equal(X1,upper_bound) ),
inference(spm,[status(thm)],[c_0_27,c_0_61]) ).
cnf(c_0_64,hypothesis,
less_than_or_equal(k(l),upper_bound),
inference(sr,[status(thm)],[c_0_62,c_0_54]) ).
cnf(c_0_65,hypothesis,
( less_than_or_equal(k(l),X1)
| less_than_or_equal(X1,l) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_56]) ).
cnf(c_0_66,hypothesis,
( less_than_or_equal(q(X1,k(l)),l)
| less_than_or_equal(k(l),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_65]) ).
cnf(c_0_67,axiom,
( less_than_or_equal(n0,f(X1))
| ~ less_than_or_equal(k(X1),X1)
| ~ in_interval(lower_bound,X1,upper_bound) ),
continuity3 ).
cnf(c_0_68,hypothesis,
less_than_or_equal(k(l),l),
inference(spm,[status(thm)],[c_0_45,c_0_66]) ).
cnf(c_0_69,hypothesis,
~ in_interval(lower_bound,l,upper_bound),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_54]) ).
cnf(c_0_70,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_21]),c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : ANA002-2 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.09/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Aug 25 18:18:08 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.57 start to proof: theBenchmark
% 35.18/35.25 % Version : CSE_E---1.5
% 35.18/35.25 % Problem : theBenchmark.p
% 35.18/35.25 % Proof found
% 35.18/35.25 % SZS status Theorem for theBenchmark.p
% 35.18/35.25 % SZS output start Proof
% See solution above
% 35.18/35.26 % Total time : 34.647000 s
% 35.18/35.26 % SZS output end Proof
% 35.18/35.26 % Total time : 34.651000 s
%------------------------------------------------------------------------------