TSTP Solution File: COL079-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL079-2 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 18:22:30 EDT 2023
% Result : Unsatisfiable 2.65s 2.72s
% Output : CNFRefutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 18 unt; 5 typ; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 6 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
k: $i > $i ).
tff(decl_23,type,
apply: ( $i * $i ) > $i ).
tff(decl_24,type,
abstraction: $i ).
tff(decl_25,type,
n: ( $i * $i ) > $i ).
tff(decl_26,type,
b: $i ).
cnf(extensionality2,axiom,
( X1 = X2
| apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
cnf(k_definition,axiom,
apply(k(X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
cnf(prove_TRC2a,negated_conjecture,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC2a) ).
cnf(c_0_4,axiom,
( X1 = X2
| apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
extensionality2 ).
cnf(c_0_5,axiom,
apply(k(X1),X2) = X1,
k_definition ).
cnf(c_0_6,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_7,plain,
( k(X1) = X2
| apply(X2,n(k(X1),X2)) != X1 ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_8,plain,
apply(apply(apply(abstraction,k(X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_9,plain,
( k(X1) = apply(apply(abstraction,k(X2)),X3)
| apply(X2,apply(X3,n(k(X1),apply(apply(abstraction,k(X2)),X3)))) != X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
apply(apply(abstraction,k(k(X1))),X2) = k(X1),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_5])]) ).
cnf(c_0_11,plain,
apply(abstraction,k(k(X1))) = k(k(X1)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_10])]) ).
cnf(c_0_12,plain,
apply(apply(apply(abstraction,abstraction),X1),k(X2)) = k(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_11]),c_0_5]) ).
cnf(c_0_13,plain,
apply(apply(X1,k(apply(X2,X3))),apply(apply(apply(abstraction,X4),X2),X3)) = apply(apply(apply(abstraction,X1),apply(X4,k(X3))),apply(X2,X3)),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_14,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_12]),c_0_5]) ).
cnf(c_0_15,plain,
apply(apply(apply(abstraction,X1),k(X2)),X3) = apply(apply(X1,k(X3)),X2),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_16,plain,
apply(apply(X1,k(apply(X2,X3))),X3) = apply(apply(apply(abstraction,apply(abstraction,X1)),X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_12]),c_0_6]) ).
cnf(c_0_17,plain,
apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X1))),X2),X3) = apply(apply(apply(abstraction,X1),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_6]) ).
cnf(c_0_18,plain,
( apply(apply(abstraction,apply(abstraction,apply(abstraction,X1))),X2) = X3
| apply(apply(apply(abstraction,X1),X2),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,X1))),X2),X3)) != apply(X3,n(apply(apply(abstraction,apply(abstraction,apply(abstraction,X1))),X2),X3)) ),
inference(spm,[status(thm)],[c_0_4,c_0_17]) ).
cnf(c_0_19,plain,
apply(apply(abstraction,apply(abstraction,apply(abstraction,X1))),X2) = apply(apply(abstraction,X1),X2),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_20,plain,
( apply(abstraction,apply(abstraction,apply(abstraction,X1))) = X2
| apply(apply(abstraction,X1),n(apply(abstraction,apply(abstraction,apply(abstraction,X1))),X2)) != apply(X2,n(apply(abstraction,apply(abstraction,apply(abstraction,X1))),X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_19]) ).
cnf(c_0_21,negated_conjecture,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
prove_TRC2a ).
cnf(c_0_22,plain,
apply(abstraction,apply(abstraction,apply(abstraction,X1))) = apply(abstraction,X1),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : COL079-2 : TPTP v8.1.2. Released v1.2.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 05:06:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 2.65/2.72 % Version : CSE_E---1.5
% 2.65/2.72 % Problem : theBenchmark.p
% 2.65/2.72 % Proof found
% 2.65/2.72 % SZS status Theorem for theBenchmark.p
% 2.65/2.72 % SZS output start Proof
% See solution above
% 2.65/2.73 % Total time : 2.130000 s
% 2.65/2.73 % SZS output end Proof
% 2.65/2.73 % Total time : 2.133000 s
%------------------------------------------------------------------------------