%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LAT269-2 : 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/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 : n031.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 07:11:36 PM UTC 2025
% Result : Unsatisfiable 2.76s 1.73s
% Output : CNFRefutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 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 : 16 ( 16 usr; 10 con; 0-5 aty)
% Number of variables : 6 ( 6 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_Tarski_Opotype_Opotype__ext > c_Tarski_Ointerval > c_Tarski_Olub > c_Tarski_Oinduced > tc_Tarski_Opotype_Opotype__ext__type > c_Tarski_OTop > #nlpp > v_r > v_intY1 > v_cl > v_Y > v_A > tc_Product__Type_Ounit > t_a > c_emptyset > c_Tarski_OCompleteLattice > c_Product__Type_OUnity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_emptyset,type,
c_emptyset: $i ).
tff(t_a,type,
t_a: $i ).
tff(v_cl,type,
v_cl: $i ).
tff(tc_Product__Type_Ounit,type,
tc_Product__Type_Ounit: $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(c_Tarski_Oinduced,type,
c_Tarski_Oinduced: ( $i * $i * $i ) > $i ).
tff(c_Tarski_Olub,type,
c_Tarski_Olub: ( $i * $i * $i ) > $i ).
tff(v_r,type,
v_r: $i ).
tff(v_Y,type,
v_Y: $i ).
tff(v_A,type,
v_A: $i ).
tff(c_Product__Type_OUnity,type,
c_Product__Type_OUnity: $i ).
tff(tc_Tarski_Opotype_Opotype__ext__type,type,
tc_Tarski_Opotype_Opotype__ext__type: ( $i * $i ) > $i ).
tff(c_Tarski_Opotype_Opotype__ext,type,
c_Tarski_Opotype_Opotype__ext: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Tarski_OTop,type,
c_Tarski_OTop: ( $i * $i ) > $i ).
tff(c_Tarski_Ointerval,type,
c_Tarski_Ointerval: ( $i * $i * $i * $i ) > $i ).
tff(v_intY1,type,
v_intY1: $i ).
tff(c_Tarski_OCompleteLattice,type,
c_Tarski_OCompleteLattice: $i ).
tff(f_27,axiom,
~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file(unknown,unknown) ).
tff(f_40,axiom,
c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
file(unknown,unknown) ).
tff(f_39,axiom,
v_intY1 = c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),
file(unknown,unknown) ).
tff(f_46,axiom,
! [V_x] :
( ~ c_in(V_x,v_A,t_a)
| ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
file(unknown,unknown) ).
tff(f_28,axiom,
c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
file(unknown,unknown) ).
tff(f_38,axiom,
! [V_b,V_a] :
( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) ),
file(unknown,unknown) ).
tff(c_2,plain,
~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_10,plain,
c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_8,plain,
c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = v_intY1,
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_17,plain,
! [V_x_4] :
( ( c_Tarski_Ointerval(v_r,V_x_4,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset )
| ~ c_in(V_x_4,v_A,t_a) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_20,plain,
( ( v_intY1 != c_emptyset )
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_17]) ).
tff(c_22,plain,
v_intY1 != c_emptyset,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_20]) ).
tff(c_4,plain,
c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_23,plain,
! [V_a_5,V_b_6] :
( ( c_Tarski_Ointerval(v_r,V_a_5,V_b_6,t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a_5,V_b_6,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a_5,V_b_6,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(V_a_5,v_A,t_a)
| ~ c_in(V_b_6,v_A,t_a) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_26,plain,
( ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
| ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_23]) ).
tff(c_31,plain,
( ( v_intY1 = c_emptyset )
| c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10,c_8,c_8,c_26]) ).
tff(c_33,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2,c_22,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT269-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.14 % 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
% 0.15/0.35 % Computer : n031.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 8 03:58:37 EDT 2025
% 0.15/0.36 % CPUTime :
% 2.76/1.73 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.76/1.74
% 2.76/1.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------