TSTP Solution File: COL081-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL081-1 : 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 : n001.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 18:22:31 EDT 2023
% Result : Unsatisfiable 0.19s 0.63s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 26 ( 13 unt; 10 typ; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 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 ).
tff(decl_31,type,
b: $i ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/COL001-0.ax',abstraction) ).
cnf(k_definition,axiom,
apply(k(X1),X2) = X1,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/COL001-0.ax',extensionality2) ).
cnf(prove_TRC2c,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_TRC2c) ).
cnf(c_0_4,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_5,axiom,
apply(k(X1),X2) = X1,
k_definition ).
cnf(c_0_6,axiom,
( X1 = X2
| apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
extensionality2 ).
cnf(c_0_7,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_4,c_0_4]),c_0_5]) ).
cnf(c_0_8,plain,
( k(X1) = X2
| apply(X2,n(k(X1),X2)) != X1 ),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_9,plain,
apply(apply(apply(apply(abstraction,abstraction),X1),k(X2)),X3) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_10,plain,
apply(apply(apply(abstraction,X1),k(X2)),X3) = apply(apply(X1,k(X3)),X2),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_11,plain,
apply(apply(apply(abstraction,abstraction),X1),k(X2)) = k(X2),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9])]) ).
cnf(c_0_12,plain,
apply(apply(abstraction,k(k(X1))),X2) = k(X1),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
prove_TRC2c ).
cnf(c_0_14,plain,
apply(abstraction,k(k(X1))) = k(k(X1)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_8,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 : COL081-1 : 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 : n001.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 05:04:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.63 % Version : CSE_E---1.5
% 0.19/0.63 % Problem : theBenchmark.p
% 0.19/0.63 % Proof found
% 0.19/0.63 % SZS status Theorem for theBenchmark.p
% 0.19/0.63 % SZS output start Proof
% See solution above
% 0.19/0.63 % Total time : 0.057000 s
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63 % Total time : 0.060000 s
%------------------------------------------------------------------------------