TSTP Solution File: COL044-4 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL044-4 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 18:22:14 EDT 2023
% Result : Unsatisfiable 0.84s 0.92s
% Output : CNFRefutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 24 ( 17 unt; 5 typ; 0 def)
% Number of atoms : 21 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
b: $i ).
tff(decl_23,type,
apply: ( $i * $i ) > $i ).
tff(decl_24,type,
n: $i ).
tff(decl_25,type,
fixed_pt: $i ).
tff(decl_26,type,
fixed_point: $i > $o ).
cnf(n_definition,axiom,
apply(apply(apply(n,X1),X2),X3) = apply(apply(apply(X1,X3),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_definition) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(prove_strong_fixed_point,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n)),b)),b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(strong_fixed_point,axiom,
( fixed_point(X1)
| apply(X1,fixed_pt) != apply(fixed_pt,apply(X1,fixed_pt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
cnf(c_0_4,axiom,
apply(apply(apply(n,X1),X2),X3) = apply(apply(apply(X1,X3),X2),X3),
n_definition ).
cnf(c_0_5,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_6,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n)),b)),b)),
prove_strong_fixed_point ).
cnf(c_0_7,axiom,
( fixed_point(X1)
| apply(X1,fixed_pt) != apply(fixed_pt,apply(X1,fixed_pt)) ),
strong_fixed_point ).
cnf(c_0_8,plain,
apply(apply(apply(n,apply(X1,X2)),X2),X3) = apply(apply(apply(n,apply(n,X1)),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_4]),c_0_4]) ).
cnf(c_0_9,plain,
apply(apply(apply(n,apply(apply(b,X1),X2)),X3),X4) = apply(apply(apply(X1,apply(X2,X4)),X3),X4),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_10,plain,
apply(apply(apply(n,apply(b,X1)),X2),X3) = apply(apply(X1,apply(X3,X2)),X3),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_11,negated_conjecture,
apply(fixed_pt,apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_5]),c_0_5]),c_0_5]),c_0_5]) ).
cnf(c_0_12,plain,
apply(apply(apply(n,apply(X1,apply(X2,X3))),X3),X4) = apply(apply(apply(n,apply(n,apply(apply(b,X1),X2))),X3),X4),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_13,plain,
apply(apply(apply(n,apply(apply(b,b),X1)),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_9]) ).
cnf(c_0_14,plain,
apply(apply(apply(apply(n,apply(b,b)),X1),X2),X3) = apply(apply(X2,X1),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
apply(fixed_pt,apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_8]),c_0_12]),c_0_13]),c_0_8]) ).
cnf(c_0_16,plain,
apply(apply(apply(n,apply(n,apply(b,b))),X1),X2) = apply(apply(X1,X2),apply(X1,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_14]) ).
cnf(c_0_17,plain,
apply(apply(apply(n,apply(b,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X3,X2),X3)),
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL044-4 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n027.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
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Sun Aug 27 05:33:36 EDT 2023
% 0.19/0.35 % CPUTime :
% 0.21/0.63 start to proof: theBenchmark
% 0.84/0.92 % Version : CSE_E---1.5
% 0.84/0.92 % Problem : theBenchmark.p
% 0.84/0.92 % Proof found
% 0.84/0.92 % SZS status Theorem for theBenchmark.p
% 0.84/0.92 % SZS output start Proof
% See solution above
% 0.84/0.92 % Total time : 0.283000 s
% 0.84/0.92 % SZS output end Proof
% 0.84/0.92 % Total time : 0.284000 s
%------------------------------------------------------------------------------