%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG178+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 : n012.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 05:24:42 PM UTC 2025
% Result : Theorem 31.25s 14.01s
% Output : CNFRefutation 31.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 20 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 112 ( 50 ~; 43 |; 4 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 2 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; 2 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sorti2 > sorti1 > op2 > op1 > #nlpp > j > h > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(op2,type,
op2: ( $i * $i ) > $i ).
tff(op1,type,
op1: ( $i * $i ) > $i ).
tff(sorti2,type,
sorti2: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
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_54,axiom,
~ ! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> ( op2(U,op2(U,V)) = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
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_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(U,op1(U,V)) = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(c_10,plain,
sorti2('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_16,plain,
! [X1_19] :
( ( h(j(X1_19)) = X1_19 )
| ~ sorti2(X1_19) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_12,plain,
sorti2('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_22,plain,
! [V_12] :
( sorti1(j(V_12))
| ~ sorti2(V_12) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
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_18,plain,
! [Y_16,Z_18] :
( ( op1(j(Y_16),j(Z_18)) = j(op2(Y_16,Z_18)) )
| ~ sorti2(Z_18)
| ~ sorti2(Y_16) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_99,plain,
! [Y_33,Z_34] :
( ( op1(j(Y_33),j(Z_34)) = j(op2(Y_33,Z_34)) )
| ~ sorti2(Z_34)
| ~ sorti2(Y_33) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_6,plain,
! [U_7,V_9] :
( ( op1(U_7,op1(U_7,V_9)) = V_9 )
| ~ sorti1(V_9)
| ~ sorti1(U_7) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_400,plain,
! [Y_61,Z_62] :
( ( op1(j(Y_61),j(op2(Y_61,Z_62))) = j(Z_62) )
| ~ sorti1(j(Z_62))
| ~ sorti1(j(Y_61))
| ~ sorti2(Z_62)
| ~ sorti2(Y_61) ),
inference(superposition,[status(thm),theory(equality)],[c_99,c_6]) ).
tff(c_1579,plain,
! [Y_103,Z_104] :
( ( j(op2(Y_103,op2(Y_103,Z_104))) = j(Z_104) )
| ~ sorti1(j(Z_104))
| ~ sorti1(j(Y_103))
| ~ sorti2(Z_104)
| ~ sorti2(Y_103)
| ~ sorti2(op2(Y_103,Z_104))
| ~ sorti2(Y_103) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_400]) ).
tff(c_103018,plain,
! [Y_1039,Z_1040] :
( ( op2(Y_1039,op2(Y_1039,Z_1040)) = h(j(Z_1040)) )
| ~ sorti2(op2(Y_1039,op2(Y_1039,Z_1040)))
| ~ sorti1(j(Z_1040))
| ~ sorti1(j(Y_1039))
| ~ sorti2(Z_1040)
| ~ sorti2(Y_1039)
| ~ sorti2(op2(Y_1039,Z_1040))
| ~ sorti2(Y_1039) ),
inference(superposition,[status(thm),theory(equality)],[c_1579,c_16]) ).
tff(c_103106,plain,
! [U_1041,Z_1042] :
( ( op2(U_1041,op2(U_1041,Z_1042)) = h(j(Z_1042)) )
| ~ sorti1(j(Z_1042))
| ~ sorti1(j(U_1041))
| ~ sorti2(Z_1042)
| ~ sorti2(op2(U_1041,Z_1042))
| ~ sorti2(U_1041) ),
inference(resolution,[status(thm)],[c_4,c_103018]) ).
tff(c_103160,plain,
! [U_1043,V_1044] :
( ( op2(U_1043,op2(U_1043,V_1044)) = h(j(V_1044)) )
| ~ sorti1(j(V_1044))
| ~ sorti1(j(U_1043))
| ~ sorti2(V_1044)
| ~ sorti2(U_1043) ),
inference(resolution,[status(thm)],[c_4,c_103106]) ).
tff(c_103362,plain,
! [U_1045,V_1046] :
( ( op2(U_1045,op2(U_1045,V_1046)) = h(j(V_1046)) )
| ~ sorti1(j(U_1045))
| ~ sorti2(U_1045)
| ~ sorti2(V_1046) ),
inference(resolution,[status(thm)],[c_22,c_103160]) ).
tff(c_103564,plain,
! [V_1047,V_1048] :
( ( op2(V_1047,op2(V_1047,V_1048)) = h(j(V_1048)) )
| ~ sorti2(V_1048)
| ~ sorti2(V_1047) ),
inference(resolution,[status(thm)],[c_22,c_103362]) ).
tff(c_8,plain,
op2('#skF_1',op2('#skF_1','#skF_2')) != '#skF_2',
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_103807,plain,
( ( h(j('#skF_2')) != '#skF_2' )
| ~ sorti2('#skF_2')
| ~ sorti2('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_103564,c_8]) ).
tff(c_103888,plain,
h(j('#skF_2')) != '#skF_2',
inference(demodulation,[status(thm),theory(equality)],[c_12,c_10,c_103807]) ).
tff(c_103892,plain,
~ sorti2('#skF_2'),
inference(superposition,[status(thm),theory(equality)],[c_16,c_103888]) ).
tff(c_103896,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_103892]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG178+1 : TPTP v9.0.0. Released v2.7.0.
% 0.12/0.13 % 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 : n012.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 Apr 6 07:07:16 EDT 2025
% 0.20/0.34 % CPUTime :
% 31.25/14.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.25/14.02
% 31.25/14.02 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------