TSTP Solution File: ANA004-4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ANA004-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 17:13:47 EDT 2023
% Result : Unsatisfiable 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 27
% Syntax : Number of formulae : 50 ( 4 unt; 14 typ; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 84 ( 35 ~; 49 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 11 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 4 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
absolute: $i > $i ).
tff(decl_23,type,
add: ( $i * $i ) > $i ).
tff(decl_24,type,
less_or_equal: ( $i * $i ) > $o ).
tff(decl_25,type,
minimum: ( $i * $i ) > $i ).
tff(decl_26,type,
n0: $i ).
tff(decl_27,type,
half: $i > $i ).
tff(decl_28,type,
delta_1: $i > $i ).
tff(decl_29,type,
delta_2: $i > $i ).
tff(decl_30,type,
a_real_number: $i ).
tff(decl_31,type,
negate: $i > $i ).
tff(decl_32,type,
f: $i > $i ).
tff(decl_33,type,
g: $i > $i ).
tff(decl_34,type,
epsilon_0: $i ).
tff(decl_35,type,
xs: $i > $i ).
cnf(less_or_equal_sum_of_halves,axiom,
( less_or_equal(add(X1,X3),X2)
| ~ less_or_equal(X1,half(X2))
| ~ less_or_equal(X3,half(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).
cnf(clause_4,hypothesis,
( less_or_equal(X1,n0)
| less_or_equal(absolute(add(g(X2),negate(g(a_real_number)))),X1)
| ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
cnf(absolute_sum_less_or_equal_sum_of_absolutes2,axiom,
( less_or_equal(absolute(add(X1,X2)),X3)
| ~ less_or_equal(add(absolute(X1),absolute(X2)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absolute_sum_less_or_equal_sum_of_absolutes2) ).
cnf(clause_7_1,negated_conjecture,
( less_or_equal(X1,n0)
| ~ less_or_equal(absolute(add(add(f(xs(X1)),negate(f(a_real_number))),add(g(xs(X1)),negate(g(a_real_number))))),epsilon_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_1) ).
cnf(clause_3,hypothesis,
( less_or_equal(X1,n0)
| less_or_equal(absolute(add(f(X2),negate(f(a_real_number)))),X1)
| ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
cnf(minimum3,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,minimum(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum3) ).
cnf(clause_6,hypothesis,
( less_or_equal(X1,n0)
| less_or_equal(absolute(add(xs(X1),negate(a_real_number))),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
cnf(minimum7,axiom,
( less_or_equal(X1,X3)
| ~ less_or_equal(X1,minimum(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum7) ).
cnf(minimum9,axiom,
( less_or_equal(X1,n0)
| less_or_equal(X2,n0)
| ~ less_or_equal(minimum(X1,X2),n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum9) ).
cnf(clause_2,hypothesis,
( less_or_equal(X1,n0)
| ~ less_or_equal(delta_2(X1),n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
cnf(clause_1,hypothesis,
( less_or_equal(X1,n0)
| ~ less_or_equal(delta_1(X1),n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
cnf(zero_and_half,axiom,
( less_or_equal(X1,n0)
| ~ less_or_equal(half(X1),n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_and_half) ).
cnf(clause_5,hypothesis,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
cnf(c_0_13,axiom,
( less_or_equal(add(X1,X3),X2)
| ~ less_or_equal(X1,half(X2))
| ~ less_or_equal(X3,half(X2)) ),
less_or_equal_sum_of_halves ).
cnf(c_0_14,hypothesis,
( less_or_equal(X1,n0)
| less_or_equal(absolute(add(g(X2),negate(g(a_real_number)))),X1)
| ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_2(X1)) ),
clause_4 ).
cnf(c_0_15,axiom,
( less_or_equal(absolute(add(X1,X2)),X3)
| ~ less_or_equal(add(absolute(X1),absolute(X2)),X3) ),
absolute_sum_less_or_equal_sum_of_absolutes2 ).
cnf(c_0_16,hypothesis,
( less_or_equal(add(X1,absolute(add(g(X2),negate(g(a_real_number))))),X3)
| less_or_equal(half(X3),n0)
| ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_2(half(X3)))
| ~ less_or_equal(X1,half(X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( less_or_equal(X1,n0)
| ~ less_or_equal(absolute(add(add(f(xs(X1)),negate(f(a_real_number))),add(g(xs(X1)),negate(g(a_real_number))))),epsilon_0) ),
clause_7_1 ).
cnf(c_0_18,hypothesis,
( less_or_equal(absolute(add(X1,add(g(X2),negate(g(a_real_number))))),X3)
| less_or_equal(half(X3),n0)
| ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_2(half(X3)))
| ~ less_or_equal(absolute(X1),half(X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( less_or_equal(half(epsilon_0),n0)
| less_or_equal(X1,n0)
| ~ less_or_equal(absolute(add(f(xs(X1)),negate(f(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(xs(X1),negate(a_real_number))),delta_2(half(epsilon_0))) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,hypothesis,
( less_or_equal(X1,n0)
| less_or_equal(absolute(add(f(X2),negate(f(a_real_number)))),X1)
| ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_1(X1)) ),
clause_3 ).
cnf(c_0_21,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,minimum(X2,X3)) ),
minimum3 ).
cnf(c_0_22,hypothesis,
( less_or_equal(X1,n0)
| less_or_equal(absolute(add(xs(X1),negate(a_real_number))),X1) ),
clause_6 ).
cnf(c_0_23,hypothesis,
( less_or_equal(half(epsilon_0),n0)
| less_or_equal(X1,n0)
| ~ less_or_equal(absolute(add(xs(X1),negate(a_real_number))),delta_2(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(X1),negate(a_real_number))),delta_1(half(epsilon_0))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,hypothesis,
( less_or_equal(absolute(add(xs(minimum(X1,X2)),negate(a_real_number))),X1)
| less_or_equal(minimum(X1,X2),n0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,axiom,
( less_or_equal(X1,X3)
| ~ less_or_equal(X1,minimum(X2,X3)) ),
minimum7 ).
cnf(c_0_26,hypothesis,
( less_or_equal(minimum(delta_2(half(epsilon_0)),X1),n0)
| less_or_equal(half(epsilon_0),n0)
| ~ less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),X1)),negate(a_real_number))),delta_1(half(epsilon_0))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,hypothesis,
( less_or_equal(absolute(add(xs(minimum(X1,X2)),negate(a_real_number))),X2)
| less_or_equal(minimum(X1,X2),n0) ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_28,axiom,
( less_or_equal(X1,n0)
| less_or_equal(X2,n0)
| ~ less_or_equal(minimum(X1,X2),n0) ),
minimum9 ).
cnf(c_0_29,hypothesis,
( less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,hypothesis,
( less_or_equal(X1,n0)
| ~ less_or_equal(delta_2(X1),n0) ),
clause_2 ).
cnf(c_0_31,hypothesis,
( less_or_equal(X1,n0)
| ~ less_or_equal(delta_1(X1),n0) ),
clause_1 ).
cnf(c_0_32,axiom,
( less_or_equal(X1,n0)
| ~ less_or_equal(half(X1),n0) ),
zero_and_half ).
cnf(c_0_33,hypothesis,
less_or_equal(half(epsilon_0),n0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_34,hypothesis,
~ less_or_equal(epsilon_0,n0),
clause_5 ).
cnf(c_0_35,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA004-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n012.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 18:49:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.59 % Total time : 0.008000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.011000 s
%------------------------------------------------------------------------------