TSTP Solution File: COL076-2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL076-2 : 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 : n006.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 18:22:29 EDT 2023
% Result : Unsatisfiable 3.63s 3.79s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 37 ( 23 unt; 9 typ; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 5 |; 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 : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 57 ( 7 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
k: $i ).
tff(decl_23,type,
apply: ( $i * $i ) > $i ).
tff(decl_24,type,
projection1: $i ).
tff(decl_25,type,
pair: ( $i * $i ) > $i ).
tff(decl_26,type,
projection2: $i ).
tff(decl_27,type,
abstraction: $i ).
tff(decl_28,type,
n: ( $i * $i ) > $i ).
tff(decl_29,type,
f: $i ).
tff(decl_30,type,
eq: $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(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(pairwise_application,axiom,
apply(pair(X1,X2),X3) = pair(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairwise_application) ).
cnf(prove_self_referential,negated_conjecture,
X1 != apply(eq,pair(apply(k,X1),apply(k,projection2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_self_referential) ).
cnf(projection2,axiom,
apply(projection2,pair(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection2) ).
cnf(diagonal_combinator,axiom,
apply(apply(f,X1),X2) = apply(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagonal_combinator) ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,apply(k,X3)),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
cnf(c_0_7,axiom,
( X1 = X2
| apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
extensionality2 ).
cnf(c_0_8,axiom,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_9,axiom,
apply(pair(X1,X2),X3) = pair(apply(X1,X3),apply(X2,X3)),
pairwise_application ).
cnf(c_0_10,plain,
( apply(k,X1) = X2
| apply(X2,n(apply(k,X1),X2)) != X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
apply(pair(X1,apply(k,X2)),X3) = pair(apply(X1,X3),X2),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_12,plain,
( apply(k,X1) = pair(X2,apply(k,X3))
| pair(apply(X2,n(apply(k,X1),pair(X2,apply(k,X3)))),X3) != X1 ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,negated_conjecture,
X1 != apply(eq,pair(apply(k,X1),apply(k,projection2))),
prove_self_referential ).
cnf(c_0_14,plain,
pair(apply(k,X1),apply(k,X2)) = apply(k,pair(X1,X2)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_8])]) ).
cnf(c_0_15,axiom,
apply(projection2,pair(X1,X2)) = X2,
projection2 ).
cnf(c_0_16,plain,
( X1 = apply(k,X2)
| apply(X1,n(X1,apply(k,X2))) != X2 ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_17,axiom,
apply(apply(f,X1),X2) = apply(X1,X1),
diagonal_combinator ).
cnf(c_0_18,negated_conjecture,
apply(eq,apply(k,pair(X1,projection2))) != X1,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
pair(apply(X1,pair(X2,X3)),X3) = apply(pair(X1,projection2),pair(X2,X3)),
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_20,plain,
apply(k,apply(X1,X1)) = apply(f,X1),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_21,negated_conjecture,
apply(eq,apply(k,apply(pair(X1,projection2),pair(X2,projection2)))) != apply(X1,pair(X2,projection2)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
apply(k,apply(apply(f,X1),X2)) = apply(f,X1),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_23,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,apply(k,X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_24,negated_conjecture,
apply(eq,apply(f,pair(X1,projection2))) != apply(X1,pair(X1,projection2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_22]) ).
cnf(c_0_25,plain,
apply(apply(apply(abstraction,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_8]) ).
cnf(c_0_26,negated_conjecture,
apply(eq,apply(f,pair(apply(apply(abstraction,apply(k,X1)),X2),projection2))) != apply(X1,apply(X2,pair(apply(apply(abstraction,apply(k,X1)),X2),projection2))),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL076-2 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n006.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 : Sun Aug 27 04:40:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 3.63/3.79 % Version : CSE_E---1.5
% 3.63/3.79 % Problem : theBenchmark.p
% 3.63/3.79 % Proof found
% 3.63/3.79 % SZS status Theorem for theBenchmark.p
% 3.63/3.79 % SZS output start Proof
% See solution above
% 3.63/3.80 % Total time : 3.219000 s
% 3.63/3.80 % SZS output end Proof
% 3.63/3.80 % Total time : 3.221000 s
%------------------------------------------------------------------------------