TSTP Solution File: COL003-14 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : COL003-14 : TPTP v8.1.2. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %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 : Tue Aug 22 10:34:47 EDT 2023
% Result : Unsatisfiable 25.01s 14.28s
% Output : CNFRefutation 25.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 25 ( 20 unt; 5 typ; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 28 (; 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ apply > #nlpp > w > strong_fixed_point > fixed_pt > b
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(w,type,
w: $i ).
tff(fixed_pt,type,
fixed_pt: $i ).
tff(b,type,
b: $i ).
tff(strong_fixed_point,type,
strong_fixed_point: $i ).
tff(f_29,axiom,
! [X,Y,Z] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_32,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),
file(unknown,unknown) ).
tff(f_31,axiom,
! [X,Y] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
file(unknown,unknown) ).
tff(f_34,axiom,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1,Y_2,Z_3] : ( apply(apply(apply(b,X_1),Y_2),Z_3) = apply(X_1,apply(Y_2,Z_3)) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_6,plain,
apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b) = strong_fixed_point,
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_1719,plain,
! [Z_30] : ( apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,Z_30)) = apply(strong_fixed_point,Z_30) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_2]) ).
tff(c_1740,plain,
! [Z_30] : ( apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,Z_30))) = apply(strong_fixed_point,Z_30) ),
inference(superposition,[status(thm),theory(equality)],[c_1719,c_2]) ).
tff(c_1757,plain,
! [Z_30] : ( apply(apply(w,w),apply(w,apply(b,apply(b,Z_30)))) = apply(strong_fixed_point,Z_30) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1740]) ).
tff(c_4,plain,
! [X_4,Y_5] : ( apply(apply(w,X_4),Y_5) = apply(apply(X_4,Y_5),Y_5) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_91,plain,
! [X_9,Y_10,Z_11] : ( apply(apply(apply(b,X_9),Y_10),Z_11) = apply(X_9,apply(Y_10,Z_11)) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_127,plain,
! [X_12,Y_13] : ( apply(apply(w,apply(b,X_12)),Y_13) = apply(X_12,apply(Y_13,Y_13)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_91]) ).
tff(c_5742,plain,
! [X_55,Y_56,Z_57] : ( apply(apply(apply(w,apply(b,apply(b,X_55))),Y_56),Z_57) = apply(X_55,apply(apply(Y_56,Y_56),Z_57)) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_2]) ).
tff(c_38176,plain,
! [X_132,Y_133] : ( apply(apply(apply(w,apply(b,apply(b,X_132))),Y_133),Y_133) = apply(X_132,apply(apply(w,Y_133),Y_133)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_5742]) ).
tff(c_9,plain,
! [X_6,Y_7] : ( apply(apply(w,X_6),Y_7) = apply(apply(X_6,Y_7),Y_7) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_13,plain,
! [Y_7] : ( apply(apply(w,w),Y_7) = apply(apply(Y_7,Y_7),Y_7) ),
inference(superposition,[status(thm),theory(equality)],[c_9,c_4]) ).
tff(c_38349,plain,
! [X_132] : ( apply(X_132,apply(apply(w,apply(w,apply(b,apply(b,X_132)))),apply(w,apply(b,apply(b,X_132))))) = apply(apply(w,w),apply(w,apply(b,apply(b,X_132)))) ),
inference(superposition,[status(thm),theory(equality)],[c_38176,c_13]) ).
tff(c_38610,plain,
! [X_132] : ( apply(X_132,apply(strong_fixed_point,X_132)) = apply(strong_fixed_point,X_132) ),
inference(demodulation,[status(thm),theory(equality)],[c_1757,c_1757,c_4,c_38349]) ).
tff(c_8,plain,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) != apply(strong_fixed_point,fixed_pt),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_38654,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_38610,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : COL003-14 : TPTP v8.1.2. Released v2.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 18:09:57 EDT 2023
% 0.15/0.36 % CPUTime :
% 25.01/14.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.01/14.28
% 25.01/14.28 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.01/14.31
% 25.01/14.31 Inference rules
% 25.01/14.31 ----------------------
% 25.01/14.31 #Ref : 0
% 25.01/14.31 #Sup : 9392
% 25.01/14.31 #Fact : 0
% 25.01/14.31 #Define : 0
% 25.01/14.31 #Split : 0
% 25.01/14.31 #Chain : 0
% 25.01/14.31 #Close : 0
% 25.01/14.31
% 25.01/14.31 Ordering : KBO
% 25.01/14.31
% 25.01/14.31 Simplification rules
% 25.01/14.31 ----------------------
% 25.01/14.31 #Subsume : 421
% 25.01/14.31 #Demod : 9087
% 25.01/14.31 #Tautology : 1070
% 25.01/14.31 #SimpNegUnit : 0
% 25.01/14.31 #BackRed : 1
% 25.01/14.31
% 25.01/14.31 #Partial instantiations: 0
% 25.01/14.31 #Strategies tried : 1
% 25.01/14.31
% 25.01/14.31 Timing (in seconds)
% 25.01/14.31 ----------------------
% 25.01/14.32 Preprocessing : 0.40
% 25.01/14.32 Parsing : 0.22
% 25.01/14.32 CNF conversion : 0.02
% 25.01/14.32 Main loop : 12.84
% 25.01/14.32 Inferencing : 1.51
% 25.01/14.32 Reduction : 9.79
% 25.01/14.32 Demodulation : 9.50
% 25.01/14.32 BG Simplification : 0.24
% 25.01/14.32 Subsumption : 1.11
% 25.01/14.32 Abstraction : 0.38
% 25.01/14.32 MUC search : 0.00
% 25.01/14.32 Cooper : 0.00
% 25.01/14.32 Total : 13.29
% 25.01/14.32 Index Insertion : 0.00
% 25.01/14.32 Index Deletion : 0.00
% 25.01/14.32 Index Matching : 0.00
% 25.01/14.32 BG Taut test : 0.00
%------------------------------------------------------------------------------