%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET820-2 : 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 : n005.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 08:39:18 PM UTC 2025
% Result : Unsatisfiable 2.62s 1.59s
% Output : CNFRefutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 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; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 36 ( 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > v_P > c_insert > #nlpp > v_x > v_a > tc_IntDef_Oint > c_emptyset
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_emptyset,type,
c_emptyset: $i ).
tff(tc_IntDef_Oint,type,
tc_IntDef_Oint: $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(v_a,type,
v_a: $i ).
tff(v_x,type,
v_x: $i > $i ).
tff(c_insert,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(v_P,type,
v_P: $i > $o ).
tff(f_30,axiom,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file(unknown,unknown) ).
tff(f_43,axiom,
! [V_V,V_U] :
( ~ c_in(V_V,V_U,tc_IntDef_Oint)
| c_in(v_x(V_U),V_U,tc_IntDef_Oint) ),
file(unknown,unknown) ).
tff(f_37,axiom,
! [V_a,V_b,V_A,T_a] :
( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| ( V_a = V_b ) ),
file(unknown,unknown) ).
tff(f_28,axiom,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
file(unknown,unknown) ).
tff(f_49,axiom,
! [V_W,V_U] :
( ~ c_in(V_W,V_U,tc_IntDef_Oint)
| ~ v_P(v_x(V_U)) ),
file(unknown,unknown) ).
tff(f_38,axiom,
v_P(v_a),
file(unknown,unknown) ).
tff(c_4,plain,
! [V_x_3,V_B_4,T_a_5] : c_in(V_x_3,c_insert(V_x_3,V_B_4,T_a_5),T_a_5),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_16,plain,
! [V_U_21,V_V_22] :
( c_in(v_x(V_U_21),V_U_21,tc_IntDef_Oint)
| ~ c_in(V_V_22,V_U_21,tc_IntDef_Oint) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_20,plain,
! [V_x_3,V_B_4] : c_in(v_x(c_insert(V_x_3,V_B_4,tc_IntDef_Oint)),c_insert(V_x_3,V_B_4,tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolution,[status(thm)],[c_4,c_16]) ).
tff(c_27,plain,
! [V_x_27,V_B_28] : c_in(v_x(c_insert(V_x_27,V_B_28,tc_IntDef_Oint)),c_insert(V_x_27,V_B_28,tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolution,[status(thm)],[c_4,c_16]) ).
tff(c_6,plain,
! [V_b_7,V_a_6,V_A_8,T_a_9] :
( ( V_b_7 = V_a_6 )
| c_in(V_a_6,V_A_8,T_a_9)
| ~ c_in(V_a_6,c_insert(V_b_7,V_A_8,T_a_9),T_a_9) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_36,plain,
! [V_x_29,V_B_30] :
( ( v_x(c_insert(V_x_29,V_B_30,tc_IntDef_Oint)) = V_x_29 )
| c_in(v_x(c_insert(V_x_29,V_B_30,tc_IntDef_Oint)),V_B_30,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[c_27,c_6]) ).
tff(c_2,plain,
! [V_a_1,T_a_2] : ~ c_in(V_a_1,c_emptyset,T_a_2),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_50,plain,
! [V_x_31] : ( v_x(c_insert(V_x_31,c_emptyset,tc_IntDef_Oint)) = V_x_31 ),
inference(resolution,[status(thm)],[c_36,c_2]) ).
tff(c_12,plain,
! [V_U_13,V_W_12] :
( ~ v_P(v_x(V_U_13))
| ~ c_in(V_W_12,V_U_13,tc_IntDef_Oint) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_70,plain,
! [V_x_32,V_W_33] :
( ~ v_P(V_x_32)
| ~ c_in(V_W_33,c_insert(V_x_32,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(superposition,[status(thm),theory(equality)],[c_50,c_12]) ).
tff(c_84,plain,
! [V_x_3] : ~ v_P(V_x_3),
inference(resolution,[status(thm)],[c_20,c_70]) ).
tff(c_8,plain,
v_P(v_a),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_87,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_84,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET820-2 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.13 % 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
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 21:42:12 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.62/1.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.62/1.60
% 2.62/1.60 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------