%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COM011-2 : 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 : n004.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 05:50:34 PM UTC 2025
% Result : Unsatisfiable 5.35s 2.42s
% Output : CNFRefutation 5.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 69 ( 33 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 92 ( 92 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_union > c_minus > c_WFair_OleadsTo > c_WFair_Oensures > c_UNITY_Oconstrains > c_Main_OsubsetI__1 > c_WFair_Otransient > #nlpp > tc_set > tc_UNITY_Oprogram > v_F > v_B > v_A > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_UNITY_Oconstrains,type,
c_UNITY_Oconstrains: ( $i * $i * $i ) > $i ).
tff(tc_set,type,
tc_set: $i > $i ).
tff(c_minus,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(t_a,type,
t_a: $i ).
tff(tc_UNITY_Oprogram,type,
tc_UNITY_Oprogram: $i > $i ).
tff(c_WFair_Otransient,type,
c_WFair_Otransient: ( $i * $i ) > $i ).
tff(c_Main_OsubsetI__1,type,
c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(c_WFair_Oensures,type,
c_WFair_Oensures: ( $i * $i * $i ) > $i ).
tff(c_union,type,
c_union: ( $i * $i * $i ) > $i ).
tff(c_WFair_OleadsTo,type,
c_WFair_OleadsTo: ( $i * $i * $i ) > $i ).
tff(v_B,type,
v_B: $i ).
tff(v_F,type,
v_F: $i ).
tff(v_A,type,
v_A: $i ).
tff(f_64,axiom,
! [V_F,V_A,V_B,T_a] :
( ~ c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
| c_in(V_F,c_WFair_OleadsTo(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
file(unknown,unknown) ).
tff(f_29,axiom,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
file(unknown,unknown) ).
tff(f_26,axiom,
c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
file(unknown,unknown) ).
tff(f_27,axiom,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
file(unknown,unknown) ).
tff(f_38,axiom,
! [V_A,V_B,T_a] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file(unknown,unknown) ).
tff(f_34,axiom,
! [V_c,V_A,V_B,T_a] :
( ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| c_in(V_c,V_A,T_a) ),
file(unknown,unknown) ).
tff(f_43,axiom,
! [V_A,V_B,T_a] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [V_F,V_A,T_a,V_B] :
( ~ c_in(V_F,c_WFair_Otransient(V_A,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| c_in(V_F,c_WFair_Otransient(V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
file(unknown,unknown) ).
tff(f_51,axiom,
! [V_F,V_B,T_a,V_A_H,V_A] :
( ~ c_in(V_F,c_UNITY_Oconstrains(V_A,V_A_H,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| c_in(V_F,c_UNITY_Oconstrains(V_B,V_A_H,T_a),tc_UNITY_Oprogram(T_a)) ),
file(unknown,unknown) ).
tff(f_59,axiom,
! [V_F,V_A,V_B,T_a] :
( ~ c_in(V_F,c_UNITY_Oconstrains(c_minus(V_A,V_B,tc_set(T_a)),c_union(V_A,V_B,T_a),T_a),tc_UNITY_Oprogram(T_a))
| ~ c_in(V_F,c_WFair_Otransient(c_minus(V_A,V_B,tc_set(T_a)),T_a),tc_UNITY_Oprogram(T_a))
| c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
file(unknown,unknown) ).
tff(c_34,plain,
! [V_F_40,V_A_41,V_B_42,T_a_43] :
( c_in(V_F_40,c_WFair_OleadsTo(V_A_41,V_B_42,T_a_43),tc_UNITY_Oprogram(T_a_43))
| ~ c_in(V_F_40,c_WFair_Oensures(V_A_41,V_B_42,T_a_43),tc_UNITY_Oprogram(T_a_43)) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_6,plain,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_42,plain,
~ c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(resolution,[status(thm)],[c_34,c_6]) ).
tff(c_2,plain,
c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_4,plain,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_23,plain,
! [V_A_35,V_B_36,T_a_37] :
( c_lessequals(V_A_35,V_B_36,tc_set(T_a_37))
| c_in(c_Main_OsubsetI__1(V_A_35,V_B_36,T_a_37),V_A_35,T_a_37) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_8,plain,
! [V_c_1,V_A_2,T_a_4,V_B_3] :
( c_in(V_c_1,V_A_2,T_a_4)
| ~ c_in(V_c_1,c_minus(V_A_2,V_B_3,tc_set(T_a_4)),T_a_4) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_50,plain,
! [V_A_48,V_B_49,T_a_50,V_B_51] :
( c_in(c_Main_OsubsetI__1(c_minus(V_A_48,V_B_49,tc_set(T_a_50)),V_B_51,T_a_50),V_A_48,T_a_50)
| c_lessequals(c_minus(V_A_48,V_B_49,tc_set(T_a_50)),V_B_51,tc_set(T_a_50)) ),
inference(resolution,[status(thm)],[c_23,c_8]) ).
tff(c_12,plain,
! [V_A_8,V_B_9,T_a_10] :
( c_lessequals(V_A_8,V_B_9,tc_set(T_a_10))
| ~ c_in(c_Main_OsubsetI__1(V_A_8,V_B_9,T_a_10),V_B_9,T_a_10) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_63,plain,
! [V_A_52,V_B_53,T_a_54] : c_lessequals(c_minus(V_A_52,V_B_53,tc_set(T_a_54)),V_A_52,tc_set(T_a_54)),
inference(resolution,[status(thm)],[c_50,c_12]) ).
tff(c_20,plain,
! [V_F_24,V_B_27,T_a_26,V_A_25] :
( c_in(V_F_24,c_WFair_Otransient(V_B_27,T_a_26),tc_UNITY_Oprogram(T_a_26))
| ~ c_lessequals(V_B_27,V_A_25,tc_set(T_a_26))
| ~ c_in(V_F_24,c_WFair_Otransient(V_A_25,T_a_26),tc_UNITY_Oprogram(T_a_26)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_66,plain,
! [V_F_24,V_A_52,V_B_53,T_a_54] :
( c_in(V_F_24,c_WFair_Otransient(c_minus(V_A_52,V_B_53,tc_set(T_a_54)),T_a_54),tc_UNITY_Oprogram(T_a_54))
| ~ c_in(V_F_24,c_WFair_Otransient(V_A_52,T_a_54),tc_UNITY_Oprogram(T_a_54)) ),
inference(resolution,[status(thm)],[c_63,c_20]) ).
tff(c_10,plain,
! [V_A_5,V_B_6,T_a_7] :
( c_lessequals(V_A_5,V_B_6,tc_set(T_a_7))
| c_in(c_Main_OsubsetI__1(V_A_5,V_B_6,T_a_7),V_A_5,T_a_7) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_72,plain,
! [V_A_H_63,V_B_59,V_A_61,T_a_62,V_F_60] :
( c_in(V_F_60,c_UNITY_Oconstrains(V_B_59,V_A_H_63,T_a_62),tc_UNITY_Oprogram(T_a_62))
| ~ c_lessequals(V_B_59,V_A_61,tc_set(T_a_62))
| ~ c_in(V_F_60,c_UNITY_Oconstrains(V_A_61,V_A_H_63,T_a_62),tc_UNITY_Oprogram(T_a_62)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_163,plain,
! [V_A_83,V_A_H_85,V_B_86,V_F_84,T_a_82] :
( c_in(V_F_84,c_UNITY_Oconstrains(V_A_83,V_A_H_85,T_a_82),tc_UNITY_Oprogram(T_a_82))
| ~ c_in(V_F_84,c_UNITY_Oconstrains(V_B_86,V_A_H_85,T_a_82),tc_UNITY_Oprogram(T_a_82))
| c_in(c_Main_OsubsetI__1(V_A_83,V_B_86,T_a_82),V_A_83,T_a_82) ),
inference(resolution,[status(thm)],[c_10,c_72]) ).
tff(c_178,plain,
! [V_A_87] :
( c_in(v_F,c_UNITY_Oconstrains(V_A_87,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| c_in(c_Main_OsubsetI__1(V_A_87,v_A,t_a),V_A_87,t_a) ),
inference(resolution,[status(thm)],[c_2,c_163]) ).
tff(c_308,plain,
! [V_A_119,V_B_120] :
( c_in(c_Main_OsubsetI__1(c_minus(V_A_119,V_B_120,tc_set(t_a)),v_A,t_a),V_A_119,t_a)
| c_in(v_F,c_UNITY_Oconstrains(c_minus(V_A_119,V_B_120,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolution,[status(thm)],[c_178,c_8]) ).
tff(c_16,plain,
! [V_F_16,V_A_17,V_B_18,T_a_19] :
( c_in(V_F_16,c_WFair_Oensures(V_A_17,V_B_18,T_a_19),tc_UNITY_Oprogram(T_a_19))
| ~ c_in(V_F_16,c_WFair_Otransient(c_minus(V_A_17,V_B_18,tc_set(T_a_19)),T_a_19),tc_UNITY_Oprogram(T_a_19))
| ~ c_in(V_F_16,c_UNITY_Oconstrains(c_minus(V_A_17,V_B_18,tc_set(T_a_19)),c_union(V_A_17,V_B_18,T_a_19),T_a_19),tc_UNITY_Oprogram(T_a_19)) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_319,plain,
( c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a))
| ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a))
| c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a) ),
inference(resolution,[status(thm)],[c_308,c_16]) ).
tff(c_324,plain,
( ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a))
| c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a) ),
inference(negUnitSimplification,[status(thm)],[c_42,c_319]) ).
tff(c_325,plain,
~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)),
inference(splitLeft,[status(thm)],[c_324]) ).
tff(c_333,plain,
~ c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
inference(resolution,[status(thm)],[c_66,c_325]) ).
tff(c_338,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_333]) ).
tff(c_340,plain,
c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)),
inference(splitRight,[status(thm)],[c_324]) ).
tff(c_61,plain,
! [V_A_48,V_B_49,T_a_50] : c_lessequals(c_minus(V_A_48,V_B_49,tc_set(T_a_50)),V_A_48,tc_set(T_a_50)),
inference(resolution,[status(thm)],[c_50,c_12]) ).
tff(c_81,plain,
! [V_A_H_63,V_B_49,V_A_48,T_a_50,V_F_60] :
( c_in(V_F_60,c_UNITY_Oconstrains(c_minus(V_A_48,V_B_49,tc_set(T_a_50)),V_A_H_63,T_a_50),tc_UNITY_Oprogram(T_a_50))
| ~ c_in(V_F_60,c_UNITY_Oconstrains(V_A_48,V_A_H_63,T_a_50),tc_UNITY_Oprogram(T_a_50)) ),
inference(resolution,[status(thm)],[c_61,c_72]) ).
tff(c_90,plain,
! [V_F_69,V_A_70,V_B_71,T_a_72] :
( c_in(V_F_69,c_WFair_Oensures(V_A_70,V_B_71,T_a_72),tc_UNITY_Oprogram(T_a_72))
| ~ c_in(V_F_69,c_WFair_Otransient(c_minus(V_A_70,V_B_71,tc_set(T_a_72)),T_a_72),tc_UNITY_Oprogram(T_a_72))
| ~ c_in(V_F_69,c_UNITY_Oconstrains(c_minus(V_A_70,V_B_71,tc_set(T_a_72)),c_union(V_A_70,V_B_71,T_a_72),T_a_72),tc_UNITY_Oprogram(T_a_72)) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_2018,plain,
! [V_F_290,V_A_291,V_B_292,T_a_293] :
( c_in(V_F_290,c_WFair_Oensures(V_A_291,V_B_292,T_a_293),tc_UNITY_Oprogram(T_a_293))
| ~ c_in(V_F_290,c_WFair_Otransient(c_minus(V_A_291,V_B_292,tc_set(T_a_293)),T_a_293),tc_UNITY_Oprogram(T_a_293))
| ~ c_in(V_F_290,c_UNITY_Oconstrains(V_A_291,c_union(V_A_291,V_B_292,T_a_293),T_a_293),tc_UNITY_Oprogram(T_a_293)) ),
inference(resolution,[status(thm)],[c_81,c_90]) ).
tff(c_2069,plain,
( c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a))
| ~ c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolution,[status(thm)],[c_340,c_2018]) ).
tff(c_2104,plain,
c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2069]) ).
tff(c_2106,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_2104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM011-2 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.14/0.34 % Computer : n004.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
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 7 16:11:38 EDT 2025
% 0.14/0.34 % CPUTime :
% 5.35/2.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.35/2.43
% 5.35/2.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------