%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET185+3 : TPTP v9.0.0. Released v2.2.0.
% 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 : n014.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 08:38:12 PM UTC 2025
% Result : Theorem 31.00s 17.41s
% Output : CNFRefutation 31.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 11 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 24 ~; 31 |; 1 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 65 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > #nlpp > #skF_3 > #skF_5 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(union,type,
union: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_68,negated_conjecture,
~ ! [B,C] :
( subset(B,C)
=> ( union(B,C) = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_union) ).
tff(f_54,axiom,
! [B] : subset(B,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
tff(f_41,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(f_33,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
tff(f_51,axiom,
! [B,C] : ( union(B,C) = union(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
tff(f_48,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
tff(c_36,plain,
union('#skF_4','#skF_5') != '#skF_5',
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_38,plain,
subset('#skF_4','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_22,plain,
! [B_13] : subset(B_13,B_13),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_12,plain,
! [B_4,C_5] :
( member('#skF_1'(B_4,C_5),B_4)
| subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_128,plain,
! [D_37,C_38,B_39] :
( member(D_37,C_38)
| member(D_37,B_39)
| ~ member(D_37,union(B_39,C_38)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_1984,plain,
! [B_195,C_196,C_197] :
( member('#skF_1'(union(B_195,C_196),C_197),C_196)
| member('#skF_1'(union(B_195,C_196),C_197),B_195)
| subset(union(B_195,C_196),C_197) ),
inference(resolution,[status(thm)],[c_12,c_128]) ).
tff(c_8,plain,
! [D_8,C_5,B_4] :
( member(D_8,C_5)
| ~ member(D_8,B_4)
| ~ subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_26126,plain,
! [B_581,C_582,C_583,C_584] :
( member('#skF_1'(union(B_581,C_582),C_583),C_584)
| ~ subset(C_582,C_584)
| member('#skF_1'(union(B_581,C_582),C_583),B_581)
| subset(union(B_581,C_582),C_583) ),
inference(resolution,[status(thm)],[c_1984,c_8]) ).
tff(c_10,plain,
! [B_4,C_5] :
( ~ member('#skF_1'(B_4,C_5),C_5)
| subset(B_4,C_5) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_87938,plain,
! [B_1283,C_1284,C_1285] :
( member('#skF_1'(union(B_1283,C_1284),B_1283),C_1285)
| ~ subset(C_1284,C_1285)
| subset(union(B_1283,C_1284),B_1283) ),
inference(resolution,[status(thm)],[c_26126,c_10]) ).
tff(c_88134,plain,
! [C_1286,C_1287] :
( ~ subset(C_1286,C_1287)
| subset(union(C_1287,C_1286),C_1287) ),
inference(resolution,[status(thm)],[c_87938,c_10]) ).
tff(c_20,plain,
! [C_12,B_11] : ( union(C_12,B_11) = union(B_11,C_12) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_118,plain,
! [D_34,C_35,B_36] :
( member(D_34,C_35)
| ~ member(D_34,B_36)
| ~ subset(B_36,C_35) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_127,plain,
! [B_4,C_5,C_35] :
( member('#skF_1'(B_4,C_5),C_35)
| ~ subset(B_4,C_35)
| subset(B_4,C_5) ),
inference(resolution,[status(thm)],[c_12,c_118]) ).
tff(c_106,plain,
! [D_31,C_32,B_33] :
( ~ member(D_31,C_32)
| member(D_31,union(B_33,C_32)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_279,plain,
! [B_62,B_63,C_64] :
( subset(B_62,union(B_63,C_64))
| ~ member('#skF_1'(B_62,union(B_63,C_64)),C_64) ),
inference(resolution,[status(thm)],[c_106,c_10]) ).
tff(c_345,plain,
! [B_69,C_70,B_71] :
( ~ subset(B_69,C_70)
| subset(B_69,union(B_71,C_70)) ),
inference(resolution,[status(thm)],[c_127,c_279]) ).
tff(c_14,plain,
! [C_10,B_9] :
( ( C_10 = B_9 )
| ~ subset(C_10,B_9)
| ~ subset(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_864,plain,
! [B_116,C_117,B_118] :
( ( union(B_116,C_117) = B_118 )
| ~ subset(union(B_116,C_117),B_118)
| ~ subset(B_118,C_117) ),
inference(resolution,[status(thm)],[c_345,c_14]) ).
tff(c_883,plain,
! [B_11,C_12,B_118] :
( ( union(B_11,C_12) = B_118 )
| ~ subset(union(C_12,B_11),B_118)
| ~ subset(B_118,C_12) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_864]) ).
tff(c_88354,plain,
! [C_1286,C_1287] :
( ( union(C_1286,C_1287) = C_1287 )
| ~ subset(C_1287,C_1287)
| ~ subset(C_1286,C_1287) ),
inference(resolution,[status(thm)],[c_88134,c_883]) ).
tff(c_88550,plain,
! [C_1288,C_1289] :
( ( union(C_1288,C_1289) = C_1289 )
| ~ subset(C_1288,C_1289) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_88354]) ).
tff(c_88862,plain,
union('#skF_4','#skF_5') = '#skF_5',
inference(resolution,[status(thm)],[c_38,c_88550]) ).
tff(c_88974,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_88862]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET185+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.13 % 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
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 20:17:34 EDT 2025
% 0.13/0.35 % CPUTime :
% 31.00/17.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.00/17.42
% 31.00/17.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------