%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG029+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 : n021.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 05:24:00 PM UTC 2025
% Result : Theorem 7.50s 3.11s
% Output : CNFRefutation 7.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 21 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 97 ( 41 ~; 37 |; 4 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 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; 2 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 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,V) = op2(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_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_46,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> ( op1(U,V) = op1(V,U) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(c_8,plain,
op2('#skF_2','#skF_1') != op2('#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_12,plain,
sorti2('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_10,plain,
sorti2('#skF_2'),
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_22,plain,
! [V_12] :
( sorti1(j(V_12))
| ~ sorti2(V_12) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
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_135,plain,
! [Y_35,Z_36] :
( ( op1(j(Y_35),j(Z_36)) = j(op2(Y_35,Z_36)) )
| ~ sorti2(Z_36)
| ~ sorti2(Y_35) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_79,plain,
! [V_31,U_32] :
( ( op1(V_31,U_32) = op1(U_32,V_31) )
| ~ sorti1(V_31)
| ~ sorti1(U_32) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_85,plain,
! [V_12,U_32] :
( ( op1(j(V_12),U_32) = op1(U_32,j(V_12)) )
| ~ sorti1(U_32)
| ~ sorti2(V_12) ),
inference(resolution,[status(thm)],[c_22,c_79]) ).
tff(c_812,plain,
! [Z_70,Y_71] :
( ( op1(j(Z_70),j(Y_71)) = j(op2(Y_71,Z_70)) )
| ~ sorti1(j(Z_70))
| ~ sorti2(Y_71)
| ~ sorti2(Z_70)
| ~ sorti2(Y_71) ),
inference(superposition,[status(thm),theory(equality)],[c_135,c_85]) ).
tff(c_2691,plain,
! [Z_118,Y_119] :
( ( j(op2(Z_118,Y_119)) = j(op2(Y_119,Z_118)) )
| ~ sorti1(j(Y_119))
| ~ sorti2(Z_118)
| ~ sorti2(Y_119)
| ~ sorti2(Z_118)
| ~ sorti2(Z_118)
| ~ sorti2(Y_119) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_812]) ).
tff(c_2717,plain,
! [Z_120,V_121] :
( ( j(op2(Z_120,V_121)) = j(op2(V_121,Z_120)) )
| ~ sorti2(Z_120)
| ~ sorti2(V_121) ),
inference(resolution,[status(thm)],[c_22,c_2691]) ).
tff(c_16,plain,
! [X1_19] :
( ( h(j(X1_19)) = X1_19 )
| ~ sorti2(X1_19) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_2984,plain,
! [Z_124,V_125] :
( ( h(j(op2(Z_124,V_125))) = op2(V_125,Z_124) )
| ~ sorti2(op2(V_125,Z_124))
| ~ sorti2(Z_124)
| ~ sorti2(V_125) ),
inference(superposition,[status(thm),theory(equality)],[c_2717,c_16]) ).
tff(c_3241,plain,
! [Z_128,V_129] :
( ( op2(Z_128,V_129) = op2(V_129,Z_128) )
| ~ sorti2(op2(Z_128,V_129))
| ~ sorti2(op2(V_129,Z_128))
| ~ sorti2(Z_128)
| ~ sorti2(V_129) ),
inference(superposition,[status(thm),theory(equality)],[c_2984,c_16]) ).
tff(c_3258,plain,
! [V_130,U_131] :
( ( op2(V_130,U_131) = op2(U_131,V_130) )
| ~ sorti2(op2(V_130,U_131))
| ~ sorti2(V_130)
| ~ sorti2(U_131) ),
inference(resolution,[status(thm)],[c_4,c_3241]) ).
tff(c_3281,plain,
! [V_132,U_133] :
( ( op2(V_132,U_133) = op2(U_133,V_132) )
| ~ sorti2(V_132)
| ~ sorti2(U_133) ),
inference(resolution,[status(thm)],[c_4,c_3258]) ).
tff(c_3527,plain,
! [U_136] :
( ( op2(U_136,'#skF_2') = op2('#skF_2',U_136) )
| ~ sorti2(U_136) ),
inference(resolution,[status(thm)],[c_10,c_3281]) ).
tff(c_3551,plain,
op2('#skF_2','#skF_1') = op2('#skF_1','#skF_2'),
inference(resolution,[status(thm)],[c_12,c_3527]) ).
tff(c_3563,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_3551]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : ALG029+1 : TPTP v9.0.0. Released v2.7.0.
% 0.09/0.15 % 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
% 0.16/0.37 % Computer : n021.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun Apr 6 06:55:57 EDT 2025
% 0.16/0.37 % CPUTime :
% 7.50/3.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.66/3.12
% 7.66/3.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------