%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG030+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n003.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 05:24:01 PM UTC 2025
% Result : Theorem 7.43s 3.25s
% Output : CNFRefutation 7.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 20 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 95 ( 41 ~; 35 |; 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 : 39 ( 39 !; 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_47,axiom,
~ ! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> ( op1(U,V) = op1(V,U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f_32,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
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/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_56,axiom,
~ ~ ! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> ( op2(U,V) = op2(V,U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(c_6,plain,
op1('#skF_2','#skF_1') != op1('#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_10,plain,
sorti1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_8,plain,
sorti1('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_2,plain,
! [U_1,V_3] :
( sorti1(op1(U_1,V_3))
| ~ sorti1(V_3)
| ~ sorti1(U_1) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
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_79,plain,
! [V_31,U_32] :
( ( op2(V_31,U_32) = op2(U_32,V_31) )
| ~ sorti2(V_31)
| ~ sorti2(U_32) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_86,plain,
! [U_33,U_34] :
( ( op2(h(U_33),U_34) = op2(U_34,h(U_33)) )
| ~ sorti2(U_34)
| ~ sorti1(U_33) ),
inference(resolution,[status(thm)],[c_24,c_79]) ).
tff(c_896,plain,
! [U_70,W_71] :
( ( op2(h(U_70),h(W_71)) = h(op1(W_71,U_70)) )
| ~ sorti1(U_70)
| ~ sorti1(W_71)
| ~ sorti2(h(W_71))
| ~ sorti1(U_70) ),
inference(superposition,[status(thm),theory(equality)],[c_86,c_20]) ).
tff(c_2558,plain,
! [X_112,W_113] :
( ( h(op1(X_112,W_113)) = h(op1(W_113,X_112)) )
| ~ sorti1(W_113)
| ~ sorti1(X_112)
| ~ sorti2(h(X_112))
| ~ sorti1(W_113)
| ~ sorti1(X_112)
| ~ sorti1(W_113) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_896]) ).
tff(c_2575,plain,
! [W_114,U_115] :
( ( h(op1(W_114,U_115)) = h(op1(U_115,W_114)) )
| ~ sorti1(W_114)
| ~ sorti1(U_115) ),
inference(resolution,[status(thm)],[c_24,c_2558]) ).
tff(c_14,plain,
! [X2_20] :
( ( j(h(X2_20)) = X2_20 )
| ~ sorti1(X2_20) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_2833,plain,
! [W_118,U_119] :
( ( j(h(op1(W_118,U_119))) = op1(U_119,W_118) )
| ~ sorti1(op1(U_119,W_118))
| ~ sorti1(W_118)
| ~ sorti1(U_119) ),
inference(superposition,[status(thm),theory(equality)],[c_2575,c_14]) ).
tff(c_3006,plain,
! [W_122,U_123] :
( ( op1(W_122,U_123) = op1(U_123,W_122) )
| ~ sorti1(op1(W_122,U_123))
| ~ sorti1(op1(U_123,W_122))
| ~ sorti1(W_122)
| ~ sorti1(U_123) ),
inference(superposition,[status(thm),theory(equality)],[c_2833,c_14]) ).
tff(c_3020,plain,
! [V_124,U_125] :
( ( op1(V_124,U_125) = op1(U_125,V_124) )
| ~ sorti1(op1(V_124,U_125))
| ~ sorti1(V_124)
| ~ sorti1(U_125) ),
inference(resolution,[status(thm)],[c_2,c_3006]) ).
tff(c_3039,plain,
! [V_126,U_127] :
( ( op1(V_126,U_127) = op1(U_127,V_126) )
| ~ sorti1(V_126)
| ~ sorti1(U_127) ),
inference(resolution,[status(thm)],[c_2,c_3020]) ).
tff(c_3290,plain,
! [U_130] :
( ( op1(U_130,'#skF_2') = op1('#skF_2',U_130) )
| ~ sorti1(U_130) ),
inference(resolution,[status(thm)],[c_8,c_3039]) ).
tff(c_3320,plain,
op1('#skF_2','#skF_1') = op1('#skF_1','#skF_2'),
inference(resolution,[status(thm)],[c_10,c_3290]) ).
tff(c_3334,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6,c_3320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ALG030+1 : TPTP v9.0.0. Released v2.7.0.
% 0.05/0.11 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.10/0.30 % Computer : n003.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sun Apr 6 06:55:33 EDT 2025
% 0.10/0.30 % CPUTime :
% 7.43/3.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.43/3.26
% 7.43/3.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------