%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ANA021-2 : 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 : n026.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 05:37:35 PM UTC 2025
% Result : Unsatisfiable 2.52s 1.62s
% Output : CNFRefutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 8 ( 8 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_less > c_times > c_minus > c_HOL_Oabs > #nlpp > v_h > v_f > c_Suc > v_x > v_c > tc_nat > t_a > c_1 > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(v_c,type,
v_c: $i ).
tff(c_minus,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(v_h,type,
v_h: $i > $i ).
tff(t_a,type,
t_a: $i ).
tff(c_HOL_Oabs,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(c_0,type,
c_0: $i ).
tff(c_1,type,
c_1: $i ).
tff(c_times,type,
c_times: ( $i * $i * $i ) > $i ).
tff(c_Suc,type,
c_Suc: $i > $i ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_nat,type,
tc_nat: $i ).
tff(c_less,type,
c_less: ( $i * $i * $i ) > $o ).
tff(v_f,type,
v_f: $i > $i ).
tff(f_38,axiom,
v_x != c_0,
file(unknown,unknown) ).
tff(f_34,axiom,
! [V_n] :
( c_less(c_0,V_n,tc_nat)
| ( V_n = c_0 ) ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [V_x] :
( ~ c_less(c_0,V_x,tc_nat)
| ( V_x = c_Suc(c_minus(V_x,c_1,tc_nat)) ) ),
file(unknown,unknown) ).
tff(f_36,axiom,
! [V_U] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a),
file(unknown,unknown) ).
tff(f_40,axiom,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file(unknown,unknown) ).
tff(c_8,plain,
v_x != c_0,
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_4,plain,
! [V_n_2] :
( ( c_0 = V_n_2 )
| c_less(c_0,V_n_2,tc_nat) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_2,plain,
! [V_x_1] :
( ( c_Suc(c_minus(V_x_1,c_1,tc_nat)) = V_x_1 )
| ~ c_less(c_0,V_x_1,tc_nat) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_21,plain,
! [V_U_6] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U_6)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(V_U_6)),t_a),t_a),t_a),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_28,plain,
! [V_x_7] :
( c_lessequals(c_HOL_Oabs(v_f(V_x_7),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(V_x_7,c_1,tc_nat))),t_a),t_a),t_a)
| ~ c_less(c_0,V_x_7,tc_nat) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_21]) ).
tff(c_36,plain,
! [V_x_9] :
( c_lessequals(c_HOL_Oabs(v_f(V_x_9),t_a),c_times(v_c,c_HOL_Oabs(v_h(V_x_9),t_a),t_a),t_a)
| ~ c_less(c_0,V_x_9,tc_nat)
| ~ c_less(c_0,V_x_9,tc_nat) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_28]) ).
tff(c_10,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_40,plain,
~ c_less(c_0,v_x,tc_nat),
inference(resolution,[status(thm)],[c_36,c_10]) ).
tff(c_43,plain,
v_x = c_0,
inference(resolution,[status(thm)],[c_4,c_40]) ).
tff(c_47,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA021-2 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.13 % 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 : n026.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 : Mon Apr 7 14:52:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.52/1.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.80/1.62
% 2.80/1.62 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------