TSTP Solution File: NUM021-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM021-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 : Thu Aug 31 10:26:11 EDT 2023
% Result : Unsatisfiable 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 34 ( 8 unt; 11 typ; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 20 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 7 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 3 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
n0: $i ).
tff(decl_23,type,
add: ( $i * $i ) > $i ).
tff(decl_24,type,
equalish: ( $i * $i ) > $o ).
tff(decl_25,type,
successor: $i > $i ).
tff(decl_26,type,
multiply: ( $i * $i ) > $i ).
tff(decl_27,type,
less: ( $i * $i ) > $o ).
tff(decl_28,type,
predecessor_of_1st_minus_2nd: ( $i * $i ) > $i ).
tff(decl_29,type,
divides: ( $i * $i ) > $o ).
tff(decl_30,type,
b: $i ).
tff(decl_31,type,
c: $i ).
tff(decl_32,type,
a: $i ).
cnf(transitivity_of_less,axiom,
( less(X3,X2)
| ~ less(X1,X2)
| ~ less(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax',transitivity_of_less) ).
cnf(b_less_than_c,hypothesis,
less(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_less_than_c) ).
cnf(divides_only_less_or_equal,axiom,
( less(X1,X2)
| equalish(X1,X2)
| ~ divides(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-2.ax',divides_only_less_or_equal) ).
cnf(impossible_c_divides_a,negated_conjecture,
divides(c,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impossible_c_divides_a) ).
cnf(b_greater_equal_a,hypothesis,
~ less(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_greater_equal_a) ).
cnf(transitivity,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
cnf(smaller_number,axiom,
( less(X2,X3)
| ~ equalish(add(successor(X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax',smaller_number) ).
cnf(less_lemma,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2)
| ~ less(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax',less_lemma) ).
cnf(c_0_8,axiom,
( less(X3,X2)
| ~ less(X1,X2)
| ~ less(X3,X1) ),
transitivity_of_less ).
cnf(c_0_9,hypothesis,
less(b,c),
b_less_than_c ).
cnf(c_0_10,axiom,
( less(X1,X2)
| equalish(X1,X2)
| ~ divides(X1,X2) ),
divides_only_less_or_equal ).
cnf(c_0_11,negated_conjecture,
divides(c,a),
impossible_c_divides_a ).
cnf(c_0_12,hypothesis,
( less(b,X1)
| ~ less(c,X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( less(c,a)
| equalish(c,a) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,hypothesis,
~ less(b,a),
b_greater_equal_a ).
cnf(c_0_15,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
transitivity ).
cnf(c_0_16,negated_conjecture,
equalish(c,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_17,axiom,
( less(X2,X3)
| ~ equalish(add(successor(X1),X2),X3) ),
smaller_number ).
cnf(c_0_18,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X1,c) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( less(X1,a)
| ~ equalish(add(successor(X2),X1),c) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2)
| ~ less(X1,X2) ),
less_lemma ).
cnf(c_0_21,negated_conjecture,
( less(X1,a)
| ~ less(X1,c) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_21]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM021-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 10:12:11 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
%------------------------------------------------------------------------------