%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET825-2 : 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 08:39:19 PM UTC 2025
% Result : Unsatisfiable 2.82s 1.75s
% Output : CNFRefutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 14 ( 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > v_Q > c_Pair > tc_prod > #nlpp > v_xa > v_x > c_Suc > v_n > v_m > tc_nat > c_Relation_OId > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_xa,type,
v_xa: $i > $i ).
tff(v_n,type,
v_n: $i ).
tff(c_0,type,
c_0: $i ).
tff(tc_prod,type,
tc_prod: ( $i * $i ) > $i ).
tff(c_Suc,type,
c_Suc: $i > $i ).
tff(v_Q,type,
v_Q: $i > $o ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_nat,type,
tc_nat: $i ).
tff(v_m,type,
v_m: $i ).
tff(c_Pair,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_x,type,
v_x: $i > $i ).
tff(c_Relation_OId,type,
c_Relation_OId: $i ).
tff(f_35,axiom,
~ v_Q(v_m),
file(unknown,unknown) ).
tff(f_27,axiom,
! [V_a,T_a] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)),
file(unknown,unknown) ).
tff(f_42,axiom,
! [V_U] :
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(V_U),v_xa(V_U),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)) ),
file(unknown,unknown) ).
tff(f_32,axiom,
! [V_a,V_b,T_a] :
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a))
| ( V_a = V_b ) ),
file(unknown,unknown) ).
tff(f_33,axiom,
v_Q(v_n),
file(unknown,unknown) ).
tff(f_50,axiom,
! [V_U] :
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(V_U)),c_Suc(v_xa(V_U)),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)) ),
file(unknown,unknown) ).
tff(c_8,plain,
~ v_Q(v_m),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2,plain,
! [V_a_1,T_a_2] : c_in(c_Pair(V_a_1,V_a_1,T_a_2,T_a_2),c_Relation_OId,tc_prod(T_a_2,T_a_2)),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_20,plain,
! [V_U_13] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U_13,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(V_U_13),v_xa(V_U_13),tc_nat,tc_nat),V_U_13,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U_13,tc_prod(tc_nat,tc_nat)) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_4,plain,
! [V_b_4,V_a_3,T_a_5] :
( ( V_b_4 = V_a_3 )
| ~ c_in(c_Pair(V_a_3,V_b_4,T_a_5,T_a_5),c_Relation_OId,tc_prod(T_a_5,T_a_5)) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_24,plain,
( ( v_xa(c_Relation_OId) = v_x(c_Relation_OId) )
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolution,[status(thm)],[c_20,c_4]) ).
tff(c_27,plain,
( ( v_xa(c_Relation_OId) = v_x(c_Relation_OId) )
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24]) ).
tff(c_29,plain,
c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
inference(splitLeft,[status(thm)],[c_27]) ).
tff(c_33,plain,
v_n = v_m,
inference(resolution,[status(thm)],[c_29,c_4]) ).
tff(c_6,plain,
v_Q(v_n),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_37,plain,
v_Q(v_m),
inference(demodulation,[status(thm),theory(equality)],[c_33,c_6]) ).
tff(c_40,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_37]) ).
tff(c_42,plain,
~ c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
inference(splitRight,[status(thm)],[c_27]) ).
tff(c_41,plain,
v_xa(c_Relation_OId) = v_x(c_Relation_OId),
inference(splitRight,[status(thm)],[c_27]) ).
tff(c_12,plain,
! [V_U_7] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U_7,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(V_U_7)),c_Suc(v_xa(V_U_7)),tc_nat,tc_nat),V_U_7,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U_7,tc_prod(tc_nat,tc_nat)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_46,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(superposition,[status(thm),theory(equality)],[c_41,c_12]) ).
tff(c_53,plain,
c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_46]) ).
tff(c_57,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET825-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % 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
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 8 21:43:33 EDT 2025
% 0.14/0.35 % CPUTime :
% 2.82/1.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.82/1.75
% 2.82/1.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------