%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL081-2 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n004.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 Apr 9 05:48:00 PM UTC 2025
% Result : Unsatisfiable 13.27s 4.50s
% Output : CNFRefutation 13.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ n > apply > #nlpp > k > identity > b > abstraction
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(identity,type,
identity: $i ).
tff(k,type,
k: $i > $i ).
tff(abstraction,type,
abstraction: $i ).
tff(n,type,
n: ( $i * $i ) > $i ).
tff(f_28,axiom,
! [X,Y,Z] : ( apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_26,axiom,
! [X,Y] : ( apply(k(X),Y) = X ),
file(unknown,unknown) ).
tff(f_33,axiom,
! [X,Y] :
( ( X = Y )
| ( apply(X,n(X,Y)) != apply(Y,n(X,Y)) ) ),
file(unknown,unknown) ).
tff(f_38,axiom,
k(k(b)) != apply(abstraction,k(k(b))),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Z_5,Y_4] : ( apply(apply(X_3,k(Z_5)),apply(Y_4,Z_5)) = apply(apply(apply(abstraction,X_3),Y_4),Z_5) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_2,plain,
! [X_1,Y_2] : ( apply(k(X_1),Y_2) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_61,plain,
! [X_16,Z_17,Y_18] : ( apply(apply(X_16,k(Z_17)),apply(Y_18,Z_17)) = apply(apply(apply(abstraction,X_16),Y_18),Z_17) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_628,plain,
! [X_41,Y_42,Z_43] : ( apply(apply(apply(abstraction,k(X_41)),Y_42),Z_43) = apply(X_41,apply(Y_42,Z_43)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_61]) ).
tff(c_14595,plain,
! [Y_1187,Z_1188,Z_1189] : ( apply(apply(apply(apply(abstraction,abstraction),Y_1187),Z_1188),Z_1189) = apply(Z_1188,apply(apply(Y_1187,Z_1188),Z_1189)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_628]) ).
tff(c_15704,plain,
! [Y_1200,X_1201,Z_1202] : ( apply(apply(apply(apply(abstraction,abstraction),Y_1200),k(X_1201)),Z_1202) = X_1201 ),
inference(superposition,[status(thm),theory(equality)],[c_14595,c_2]) ).
tff(c_33,plain,
! [Y_12,X_13] :
( ( apply(Y_12,n(X_13,Y_12)) != apply(X_13,n(X_13,Y_12)) )
| ( Y_12 = X_13 ) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_37,plain,
! [X_13,X_1] :
( ( apply(X_13,n(X_13,k(X_1))) != X_1 )
| ( k(X_1) = X_13 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_33]) ).
tff(c_19640,plain,
! [Y_1385,X_1386] : ( apply(apply(apply(abstraction,abstraction),Y_1385),k(X_1386)) = k(X_1386) ),
inference(superposition,[status(thm),theory(equality)],[c_15704,c_37]) ).
tff(c_80,plain,
! [X_16,X_1,Y_2] : ( apply(apply(apply(abstraction,X_16),k(X_1)),Y_2) = apply(apply(X_16,k(Y_2)),X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_61]) ).
tff(c_20075,plain,
! [X_1397,X_1398] : ( apply(apply(abstraction,k(k(X_1397))),X_1398) = k(X_1397) ),
inference(superposition,[status(thm),theory(equality)],[c_19640,c_80]) ).
tff(c_26687,plain,
! [X_1397] : ( apply(abstraction,k(k(X_1397))) = k(k(X_1397)) ),
inference(superposition,[status(thm),theory(equality)],[c_20075,c_37]) ).
tff(c_10,plain,
apply(abstraction,k(k(b))) != k(k(b)),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_26696,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_26687,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : COL081-2 : TPTP v9.0.0. Released v1.2.0.
% 0.08/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n004.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 : Mon Apr 7 16:02:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 13.27/4.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.27/4.51
% 13.27/4.51 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------