TSTP Solution File: COL077-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL077-1 : 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 : n019.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 0.19s 0.62s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of formulae : 25 ( 13 unt; 9 typ; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 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,
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,
eq: $i ).
tff(decl_29,type,
n: ( $i * $i ) > $i ).
tff(decl_30,type,
identity: $i ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',abstraction) ).
cnf(k_definition,axiom,
apply(k(X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',k_definition) ).
cnf(extensionality2,axiom,
( X1 = X2
| apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',extensionality2) ).
cnf(identity_definition,axiom,
apply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).
cnf(prove_TRC1a,negated_conjecture,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC1a) ).
cnf(c_0_5,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_6,axiom,
apply(k(X1),X2) = X1,
k_definition ).
cnf(c_0_7,axiom,
( X1 = X2
| apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
extensionality2 ).
cnf(c_0_8,axiom,
apply(identity,X1) = X1,
identity_definition ).
cnf(c_0_9,plain,
apply(apply(apply(apply(abstraction,abstraction),X1),X2),X3) = apply(X2,apply(apply(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_5]),c_0_6]) ).
cnf(c_0_10,negated_conjecture,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
prove_TRC1a ).
cnf(c_0_11,plain,
( identity = X1
| apply(X1,n(identity,X1)) != n(identity,X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_6]) ).
cnf(c_0_13,negated_conjecture,
apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction) != identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_5]),c_0_5]),c_0_6]) ).
cnf(c_0_14,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2) = identity,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL077-1 : 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
% 0.13/0.34 % Computer : n019.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
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 05:13:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.62 % Version : CSE_E---1.5
% 0.19/0.62 % Problem : theBenchmark.p
% 0.19/0.62 % Proof found
% 0.19/0.62 % SZS status Theorem for theBenchmark.p
% 0.19/0.62 % SZS output start Proof
% See solution above
% 0.19/0.62 % Total time : 0.050000 s
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time : 0.053000 s
%------------------------------------------------------------------------------