%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG040+1 : TPTP v9.0.0. Released v2.7.0.
% 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 : n016.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 05:24:02 PM UTC 2025
% Result : Theorem 3.52s 1.95s
% Output : CNFRefutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 16 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 81 ( 35 ~; 27 |; 6 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 32 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sorti2 > sorti1 > op2 > op1 > #nlpp > j > h > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(op2,type,
op2: ( $i * $i ) > $i ).
tff(op1,type,
op1: ( $i * $i ) > $i ).
tff(sorti2,type,
sorti2: $i > $o ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(sorti1,type,
sorti1: $i > $o ).
tff(h,type,
h: $i > $i ).
tff(j,type,
j: $i > $i ).
tff(f_91,negated_conjecture,
~ ( ( ! [U] :
( sorti1(U)
=> sorti2(h(U)) )
& ! [V] :
( sorti2(V)
=> sorti1(j(V)) ) )
=> ~ ( ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> ( h(op1(W,X)) = op2(h(W),h(X)) ) ) )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> ( j(op2(Y,Z)) = op1(j(Y),j(Z)) ) ) )
& ! [X1] :
( sorti2(X1)
=> ( h(j(X1)) = X1 ) )
& ! [X2] :
( sorti1(X2)
=> ( j(h(X2)) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_54,axiom,
~ ? [U] :
( sorti2(U)
& ! [V] :
( sorti2(V)
=> ( op2(V,V) = U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(f_39,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(f_46,axiom,
? [U] :
( sorti1(U)
& ! [V] :
( sorti1(V)
=> ( op1(V,V) = U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(c_24,plain,
! [U_11] :
( sorti2(h(U_11))
| ~ sorti1(U_11) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_12,plain,
! [U_9] :
( sorti2('#skF_2'(U_9))
| ~ sorti2(U_9) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_4,plain,
! [U_4,V_6] :
( sorti2(op2(U_4,V_6))
| ~ sorti2(V_6)
| ~ sorti2(U_4) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_157,plain,
! [Y_37,Z_38] :
( ( op1(j(Y_37),j(Z_38)) = j(op2(Y_37,Z_38)) )
| ~ sorti2(Z_38)
| ~ sorti2(Y_37) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_22,plain,
! [V_12] :
( sorti1(j(V_12))
| ~ sorti2(V_12) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_40,plain,
! [V_25] :
( ( op1(V_25,V_25) = '#skF_1' )
| ~ sorti1(V_25) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_45,plain,
! [V_12] :
( ( op1(j(V_12),j(V_12)) = '#skF_1' )
| ~ sorti2(V_12) ),
inference(resolution,[status(thm)],[c_22,c_40]) ).
tff(c_198,plain,
! [Z_39] :
( ( j(op2(Z_39,Z_39)) = '#skF_1' )
| ~ sorti2(Z_39)
| ~ sorti2(Z_39)
| ~ sorti2(Z_39) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_45]) ).
tff(c_16,plain,
! [X1_19] :
( ( h(j(X1_19)) = X1_19 )
| ~ sorti2(X1_19) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_321,plain,
! [Z_46] :
( ( op2(Z_46,Z_46) = h('#skF_1') )
| ~ sorti2(op2(Z_46,Z_46))
| ~ sorti2(Z_46)
| ~ sorti2(Z_46)
| ~ sorti2(Z_46) ),
inference(superposition,[status(thm),theory(equality)],[c_198,c_16]) ).
tff(c_331,plain,
! [V_47] :
( ( op2(V_47,V_47) = h('#skF_1') )
| ~ sorti2(V_47) ),
inference(resolution,[status(thm)],[c_4,c_321]) ).
tff(c_344,plain,
! [U_48] :
( ( op2('#skF_2'(U_48),'#skF_2'(U_48)) = h('#skF_1') )
| ~ sorti2(U_48) ),
inference(resolution,[status(thm)],[c_12,c_331]) ).
tff(c_10,plain,
! [U_9] :
( ( op2('#skF_2'(U_9),'#skF_2'(U_9)) != U_9 )
| ~ sorti2(U_9) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_365,plain,
~ sorti2(h('#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_344,c_10]) ).
tff(c_423,plain,
! [U_52] :
( ( op2(h(U_52),h(U_52)) = h('#skF_1') )
| ~ sorti1(U_52) ),
inference(resolution,[status(thm)],[c_24,c_331]) ).
tff(c_438,plain,
! [U_52] :
( sorti2(h('#skF_1'))
| ~ sorti2(h(U_52))
| ~ sorti2(h(U_52))
| ~ sorti1(U_52) ),
inference(superposition,[status(thm),theory(equality)],[c_423,c_4]) ).
tff(c_458,plain,
! [U_53] :
( ~ sorti2(h(U_53))
| ~ sorti2(h(U_53))
| ~ sorti1(U_53) ),
inference(negUnitSimplification,[status(thm)],[c_365,c_438]) ).
tff(c_467,plain,
! [U_54] :
( ~ sorti2(h(U_54))
| ~ sorti1(U_54) ),
inference(resolution,[status(thm)],[c_24,c_458]) ).
tff(c_474,plain,
! [U_11] : ~ sorti1(U_11),
inference(resolution,[status(thm)],[c_24,c_467]) ).
tff(c_8,plain,
sorti1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_479,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_474,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : ALG040+1 : TPTP v9.0.0. Released v2.7.0.
% 0.13/0.14 % 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
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Apr 6 06:56:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 3.52/1.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.52/1.96
% 3.52/1.96 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------