%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET855-2 : TPTP v9.0.0. Released v3.2.0.
% 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 : n010.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 08:39:27 PM UTC 2025
% Result : Unsatisfiable 2.41s 1.58s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 6 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_Union > #nlpp > tc_set > v_n > v_Y > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(tc_set,type,
tc_set: $i > $i ).
tff(v_n,type,
v_n: $i ).
tff(t_a,type,
t_a: $i ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Union,type,
c_Union: ( $i * $i ) > $i ).
tff(v_Y,type,
v_Y: $i ).
tff(f_37,axiom,
v_n != c_Union(v_Y,tc_set(t_a)),
file(unknown,unknown) ).
tff(f_35,axiom,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_34,axiom,
c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_33,axiom,
! [V_B,V_A,T_a] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) ),
file(unknown,unknown) ).
tff(c_8,plain,
c_Union(v_Y,tc_set(t_a)) != v_n,
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_6,plain,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_4,plain,
c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_9,plain,
! [V_B_4,V_A_5,T_a_6] :
( ( V_B_4 = V_A_5 )
| ~ c_lessequals(V_A_5,V_B_4,tc_set(T_a_6))
| ~ c_lessequals(V_B_4,V_A_5,tc_set(T_a_6)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_11,plain,
( ( c_Union(v_Y,tc_set(t_a)) = v_n )
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_4,c_9]) ).
tff(c_16,plain,
c_Union(v_Y,tc_set(t_a)) = v_n,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_11]) ).
tff(c_18,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET855-2 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % 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
% 0.13/0.34 % Computer : n010.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 : Tue Apr 8 21:46:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.41/1.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.41/1.59
% 2.41/1.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------