TSTP Solution File: COL066-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL066-2 : TPTP v8.1.2. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 18:22:27 EDT 2023
% Result : Unsatisfiable 0.54s 0.67s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 20 ( 13 unt; 7 typ; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
b: $i ).
tff(decl_23,type,
apply: ( $i * $i ) > $i ).
tff(decl_24,type,
q: $i ).
tff(decl_25,type,
w: $i ).
tff(decl_26,type,
x: $i ).
tff(decl_27,type,
y: $i ).
tff(decl_28,type,
z: $i ).
cnf(prove_p_combinator,negated_conjecture,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p_combinator) ).
cnf(w_definition,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
cnf(q_definition,axiom,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_definition) ).
cnf(c_0_3,negated_conjecture,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
prove_p_combinator ).
cnf(c_0_4,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
w_definition ).
cnf(c_0_5,negated_conjecture,
apply(apply(apply(w,apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x)),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,axiom,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
q_definition ).
cnf(c_0_7,negated_conjecture,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
apply(apply(w,apply(q,X1)),X2) = apply(X2,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_9,plain,
apply(apply(w,apply(apply(q,X1),X2)),X3) = apply(apply(X2,apply(X1,X3)),X3),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_10,negated_conjecture,
apply(apply(apply(w,q),apply(x,y)),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_6]),c_0_6]),c_0_4]) ).
cnf(c_0_11,plain,
apply(apply(apply(w,q),X1),X2) = apply(X1,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : COL066-2 : TPTP v8.1.2. Bugfixed v1.2.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 04:14:11 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.54/0.67 % Version : CSE_E---1.5
% 0.54/0.67 % Problem : theBenchmark.p
% 0.54/0.67 % Proof found
% 0.54/0.67 % SZS status Theorem for theBenchmark.p
% 0.54/0.67 % SZS output start Proof
% See solution above
% 0.54/0.67 % Total time : 0.076000 s
% 0.54/0.67 % SZS output end Proof
% 0.54/0.67 % Total time : 0.078000 s
%------------------------------------------------------------------------------