TSTP Solution File: NUM024-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM024-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 10:26:12 EDT 2023
% Result : Unsatisfiable 0.19s 0.73s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 31 ( 13 unt; 8 typ; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 2 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,
a: $i ).
cnf(transitivity,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
cnf(adding_zero,axiom,
equalish(add(X1,n0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',adding_zero) ).
cnf(commutativity_of_plus,axiom,
equalish(add(X1,X2),add(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_plus) ).
cnf(symmetry,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
cnf(less_lemma,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2)
| ~ less(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',less_lemma) ).
cnf(impossible_a_is_less_than_itself,hypothesis,
less(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impossible_a_is_less_than_itself) ).
cnf(plus_substitution,axiom,
( equalish(X1,X3)
| ~ equalish(add(X1,X2),add(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_substitution) ).
cnf(prove_a_contradiction,negated_conjecture,
~ equalish(successor(X1),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_contradiction) ).
cnf(c_0_8,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
transitivity ).
cnf(c_0_9,axiom,
equalish(add(X1,n0),X1),
adding_zero ).
cnf(c_0_10,plain,
( equalish(X1,X2)
| ~ equalish(X1,add(X2,n0)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,axiom,
equalish(add(X1,X2),add(X2,X1)),
commutativity_of_plus ).
cnf(c_0_12,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
symmetry ).
cnf(c_0_13,plain,
equalish(add(n0,X1),X1),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
equalish(X1,add(n0,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2)
| ~ less(X1,X2) ),
less_lemma ).
cnf(c_0_16,hypothesis,
less(a,a),
impossible_a_is_less_than_itself ).
cnf(c_0_17,plain,
( equalish(X1,add(n0,X2))
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_14]) ).
cnf(c_0_18,hypothesis,
equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
( equalish(X1,X3)
| ~ equalish(add(X1,X2),add(X3,X2)) ),
plus_substitution ).
cnf(c_0_20,hypothesis,
equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),add(n0,a)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ equalish(successor(X1),n0),
prove_a_contradiction ).
cnf(c_0_22,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM024-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 12:07:44 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.73 % Version : CSE_E---1.5
% 0.19/0.73 % Problem : theBenchmark.p
% 0.19/0.73 % Proof found
% 0.19/0.73 % SZS status Theorem for theBenchmark.p
% 0.19/0.73 % SZS output start Proof
% See solution above
% 0.19/0.73 % Total time : 0.147000 s
% 0.19/0.73 % SZS output end Proof
% 0.19/0.73 % Total time : 0.150000 s
%------------------------------------------------------------------------------