%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL074-3 : 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 : n028.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 05:47:58 PM UTC 2025
% Result : Unsatisfiable 2.89s 1.74s
% Output : CNFRefutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 2 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ pair > n > apply > #nlpp > s > projection2 > projection1 > k_projection2 > k_projection1 > k > eq > abstraction
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(k_projection2,type,
k_projection2: $i ).
tff(s,type,
s: $i ).
tff(k_projection1,type,
k_projection1: $i ).
tff(k,type,
k: $i ).
tff(eq,type,
eq: $i ).
tff(pair,type,
pair: ( $i * $i ) > $i ).
tff(projection1,type,
projection1: $i ).
tff(abstraction,type,
abstraction: $i ).
tff(n,type,
n: ( $i * $i ) > $i ).
tff(projection2,type,
projection2: $i ).
tff(f_57,axiom,
projection1 != projection2,
file(unknown,unknown) ).
tff(f_46,axiom,
! [X] : ( apply(eq,pair(X,X)) = projection1 ),
file(unknown,unknown) ).
tff(f_60,axiom,
apply(k,projection2) = k_projection2,
file(unknown,unknown) ).
tff(f_59,axiom,
apply(k,projection1) = k_projection1,
file(unknown,unknown) ).
tff(f_30,axiom,
! [X,Y] : ( apply(apply(k,X),Y) = X ),
file(unknown,unknown) ).
tff(f_61,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
file(unknown,unknown) ).
tff(f_50,axiom,
! [X,Y] :
( ( X = Y )
| ( apply(eq,pair(X,Y)) = projection2 ) ),
file(unknown,unknown) ).
tff(c_20,plain,
projection2 != projection1,
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_14,plain,
! [X_14] : ( apply(eq,pair(X_14,X_14)) = projection1 ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_24,plain,
apply(k,projection2) = k_projection2,
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_22,plain,
apply(k,projection1) = k_projection1,
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_36,plain,
! [X_19,Y_20] : ( apply(apply(k,X_19),Y_20) = X_19 ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_45,plain,
! [Y_20] : ( apply(k_projection1,Y_20) = projection1 ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_36]) ).
tff(c_26,plain,
apply(eq,pair(apply(k,s),apply(k,projection2))) = s,
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_27,plain,
apply(eq,pair(apply(k,s),k_projection2)) = s,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26]) ).
tff(c_16,plain,
! [X_15,Y_16] :
( ( apply(eq,pair(X_15,Y_16)) = projection2 )
| ( Y_16 = X_15 ) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_143,plain,
( ( s = projection2 )
| ( apply(k,s) = k_projection2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_27,c_16]) ).
tff(c_150,plain,
apply(k,s) = k_projection2,
inference(splitLeft,[status(thm)],[c_143]) ).
tff(c_151,plain,
apply(eq,pair(k_projection2,k_projection2)) = s,
inference(demodulation,[status(thm),theory(equality)],[c_150,c_27]) ).
tff(c_152,plain,
s = projection1,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_151]) ).
tff(c_161,plain,
apply(k,projection1) = k_projection2,
inference(demodulation,[status(thm),theory(equality)],[c_152,c_150]) ).
tff(c_162,plain,
k_projection2 = k_projection1,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_161]) ).
tff(c_48,plain,
! [Y_20] : ( apply(k_projection2,Y_20) = projection2 ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_36]) ).
tff(c_196,plain,
! [Y_20] : ( apply(k_projection1,Y_20) = projection2 ),
inference(demodulation,[status(thm),theory(equality)],[c_162,c_48]) ).
tff(c_198,plain,
projection2 = projection1,
inference(demodulation,[status(thm),theory(equality)],[c_45,c_196]) ).
tff(c_200,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_198]) ).
tff(c_201,plain,
s = projection2,
inference(splitRight,[status(thm)],[c_143]) ).
tff(c_203,plain,
apply(eq,pair(apply(k,projection2),k_projection2)) = projection2,
inference(demodulation,[status(thm),theory(equality)],[c_201,c_201,c_27]) ).
tff(c_204,plain,
projection2 = projection1,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_24,c_203]) ).
tff(c_206,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL074-3 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.13 % 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
% 0.13/0.34 % Computer : n028.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 : Mon Apr 7 16:00:34 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.89/1.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.89/1.74
% 2.89/1.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------