%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG176+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 : n015.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 05:24:41 PM UTC 2025
% Result : Theorem 5.04s 2.25s
% Output : CNFRefutation 5.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 17 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 99 ( 48 ~; 34 |; 6 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 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; 1 con; 0-2 aty)
% Number of variables : 30 ( 28 !; 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_47,axiom,
? [U] :
( sorti1(U)
& ! [V] :
( sorti1(V)
=> ( op1(V,U) != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f_93,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_56,axiom,
~ ? [U] :
( sorti2(U)
& ! [V] :
( sorti2(V)
=> ( op2(V,U) != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(c_8,plain,
sorti1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_24,plain,
! [U_11] :
( sorti2(h(U_11))
| ~ sorti1(U_11) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_20,plain,
! [W_13,X_15] :
( ( op2(h(W_13),h(X_15)) = h(op1(W_13,X_15)) )
| ~ sorti1(X_15)
| ~ sorti1(W_13) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_14,plain,
! [X2_20] :
( ( j(h(X2_20)) = X2_20 )
| ~ sorti1(X2_20) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_124,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_93]) ).
tff(c_161,plain,
! [Y_45,X2_46] :
( ( j(op2(Y_45,h(X2_46))) = op1(j(Y_45),X2_46) )
| ~ sorti2(h(X2_46))
| ~ sorti2(Y_45)
| ~ sorti1(X2_46) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_124]) ).
tff(c_1247,plain,
! [W_111,X_112] :
( ( op1(j(h(W_111)),X_112) = j(h(op1(W_111,X_112))) )
| ~ sorti2(h(X_112))
| ~ sorti2(h(W_111))
| ~ sorti1(X_112)
| ~ sorti1(X_112)
| ~ sorti1(W_111) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_161]) ).
tff(c_22,plain,
! [V_12] :
( sorti1(j(V_12))
| ~ sorti2(V_12) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_40,plain,
! [V_25] :
( ( op1(V_25,'#skF_1') != V_25 )
| ~ sorti1(V_25) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_47,plain,
! [V_12] :
( ( op1(j(V_12),'#skF_1') != j(V_12) )
| ~ sorti2(V_12) ),
inference(resolution,[status(thm)],[c_22,c_40]) ).
tff(c_1305,plain,
! [W_111] :
( ( j(h(op1(W_111,'#skF_1'))) != j(h(W_111)) )
| ~ sorti2(h(W_111))
| ~ sorti2(h('#skF_1'))
| ~ sorti2(h(W_111))
| ~ sorti1('#skF_1')
| ~ sorti1('#skF_1')
| ~ sorti1(W_111) ),
inference(superposition,[status(thm),theory(equality)],[c_1247,c_47]) ).
tff(c_1336,plain,
! [W_111] :
( ( j(h(op1(W_111,'#skF_1'))) != j(h(W_111)) )
| ~ sorti2(h('#skF_1'))
| ~ sorti2(h(W_111))
| ~ sorti1(W_111) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_8,c_1305]) ).
tff(c_1338,plain,
~ sorti2(h('#skF_1')),
inference(splitLeft,[status(thm)],[c_1336]) ).
tff(c_1341,plain,
~ sorti1('#skF_1'),
inference(resolution,[status(thm)],[c_24,c_1338]) ).
tff(c_1345,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1341]) ).
tff(c_1347,plain,
sorti2(h('#skF_1')),
inference(splitRight,[status(thm)],[c_1336]) ).
tff(c_12,plain,
! [U_9] :
( sorti2('#skF_2'(U_9))
| ~ sorti2(U_9) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_10,plain,
! [U_9] :
( ( op2('#skF_2'(U_9),U_9) = '#skF_2'(U_9) )
| ~ sorti2(U_9) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_1393,plain,
! [X2_115] :
( ( op1(j('#skF_2'(h(X2_115))),X2_115) = j('#skF_2'(h(X2_115))) )
| ~ sorti2(h(X2_115))
| ~ sorti2('#skF_2'(h(X2_115)))
| ~ sorti1(X2_115)
| ~ sorti2(h(X2_115)) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_161]) ).
tff(c_1452,plain,
( ~ sorti2('#skF_2'(h('#skF_1')))
| ~ sorti1('#skF_1')
| ~ sorti2(h('#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_1393,c_47]) ).
tff(c_1484,plain,
~ sorti2('#skF_2'(h('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_1347,c_8,c_1452]) ).
tff(c_1488,plain,
~ sorti2(h('#skF_1')),
inference(resolution,[status(thm)],[c_12,c_1484]) ).
tff(c_1492,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1347,c_1488]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : ALG176+1 : TPTP v9.0.0. Released v2.7.0.
% 0.12/0.14 % 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 : n015.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 07:07:35 EDT 2025
% 0.14/0.36 % CPUTime :
% 5.04/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.04/2.26
% 5.04/2.26 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------