%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET175+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/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 : n016.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 08:38:11 PM UTC 2025
% Result : Theorem 133.69s 108.16s
% Output : CNFRefutation 133.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 65 ( 25 ~; 33 |; 2 &)
% ( 4 <=>; 1 =>; 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 : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 80 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > intersection > #nlpp > #skF_3 > #skF_5 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
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_50,axiom,
! [B,C] : ( union(B,C) = union(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
tff(f_61,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
tff(f_40,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
tff(f_64,axiom,
! [B] : subset(B,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
tff(f_33,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
tff(f_47,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
tff(f_76,negated_conjecture,
~ ! [B,C] : ( union(B,intersection(B,C)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_absorbtion_for_union) ).
tff(c_20,plain,
! [C_10,B_9] : ( union(C_10,B_9) = union(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_28,plain,
! [B_13,C_14] :
( member('#skF_1'(B_13,C_14),B_13)
| subset(B_13,C_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_134,plain,
! [D_37,B_38,C_39] :
( member(D_37,B_38)
| ~ member(D_37,intersection(B_38,C_39)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_517,plain,
! [B_91,C_92,C_93] :
( member('#skF_1'(intersection(B_91,C_92),C_93),B_91)
| subset(intersection(B_91,C_92),C_93) ),
inference(resolution,[status(thm)],[c_28,c_134]) ).
tff(c_26,plain,
! [B_13,C_14] :
( ~ member('#skF_1'(B_13,C_14),C_14)
| subset(B_13,C_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_554,plain,
! [B_91,C_92] : subset(intersection(B_91,C_92),B_91),
inference(resolution,[status(thm)],[c_517,c_26]) ).
tff(c_30,plain,
! [B_18] : subset(B_18,B_18),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_210,plain,
! [D_53,C_54,B_55] :
( member(D_53,C_54)
| member(D_53,B_55)
| ~ member(D_53,union(B_55,C_54)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_4494,plain,
! [B_348,C_349,C_350] :
( member('#skF_1'(union(B_348,C_349),C_350),C_349)
| member('#skF_1'(union(B_348,C_349),C_350),B_348)
| subset(union(B_348,C_349),C_350) ),
inference(resolution,[status(thm)],[c_28,c_210]) ).
tff(c_24,plain,
! [D_17,C_14,B_13] :
( member(D_17,C_14)
| ~ member(D_17,B_13)
| ~ subset(B_13,C_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_4635,plain,
! [B_348,C_349,C_350,C_14] :
( member('#skF_1'(union(B_348,C_349),C_350),C_14)
| ~ subset(C_349,C_14)
| member('#skF_1'(union(B_348,C_349),C_350),B_348)
| subset(union(B_348,C_349),C_350) ),
inference(resolution,[status(thm)],[c_4494,c_24]) ).
tff(c_459496,plain,
! [C_2680,C_2681,C_2682] :
( ~ subset(C_2680,C_2681)
| subset(union(C_2681,C_2680),C_2682)
| member('#skF_1'(union(C_2681,C_2680),C_2682),C_2681) ),
inference(factorization,[status(thm),theory(equality)],[c_4635]) ).
tff(c_459731,plain,
! [C_2683,C_2684] :
( ~ subset(C_2683,C_2684)
| subset(union(C_2684,C_2683),C_2684) ),
inference(resolution,[status(thm)],[c_459496,c_26]) ).
tff(c_177,plain,
! [D_47,C_48,B_49] :
( member(D_47,C_48)
| ~ member(D_47,B_49)
| ~ subset(B_49,C_48) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_185,plain,
! [B_13,C_14,C_48] :
( member('#skF_1'(B_13,C_14),C_48)
| ~ subset(B_13,C_48)
| subset(B_13,C_14) ),
inference(resolution,[status(thm)],[c_28,c_177]) ).
tff(c_165,plain,
! [D_44,C_45,B_46] :
( ~ member(D_44,C_45)
| member(D_44,union(B_46,C_45)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_410,plain,
! [B_78,B_79,C_80] :
( subset(B_78,union(B_79,C_80))
| ~ member('#skF_1'(B_78,union(B_79,C_80)),C_80) ),
inference(resolution,[status(thm)],[c_165,c_26]) ).
tff(c_481,plain,
! [B_85,C_86,B_87] :
( ~ subset(B_85,C_86)
| subset(B_85,union(B_87,C_86)) ),
inference(resolution,[status(thm)],[c_185,c_410]) ).
tff(c_14,plain,
! [C_8,B_7] :
( ( C_8 = B_7 )
| ~ subset(C_8,B_7)
| ~ subset(B_7,C_8) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_1462,plain,
! [B_172,C_173,B_174] :
( ( union(B_172,C_173) = B_174 )
| ~ subset(union(B_172,C_173),B_174)
| ~ subset(B_174,C_173) ),
inference(resolution,[status(thm)],[c_481,c_14]) ).
tff(c_1481,plain,
! [B_9,C_10,B_174] :
( ( union(B_9,C_10) = B_174 )
| ~ subset(union(C_10,B_9),B_174)
| ~ subset(B_174,C_10) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_1462]) ).
tff(c_459950,plain,
! [C_2683,C_2684] :
( ( union(C_2683,C_2684) = C_2684 )
| ~ subset(C_2684,C_2684)
| ~ subset(C_2683,C_2684) ),
inference(resolution,[status(thm)],[c_459731,c_1481]) ).
tff(c_460149,plain,
! [C_2685,C_2686] :
( ( union(C_2685,C_2686) = C_2686 )
| ~ subset(C_2685,C_2686) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_459950]) ).
tff(c_468414,plain,
! [B_2691,C_2692] : ( union(intersection(B_2691,C_2692),B_2691) = B_2691 ),
inference(resolution,[status(thm)],[c_554,c_460149]) ).
tff(c_471308,plain,
! [B_9,C_2692] : ( union(B_9,intersection(B_9,C_2692)) = B_9 ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_468414]) ).
tff(c_44,plain,
union('#skF_4',intersection('#skF_4','#skF_5')) != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_472698,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_471308,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET175+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/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 : n016.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 : Tue Apr 8 20:16:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 133.69/108.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 133.69/108.17
% 133.69/108.17 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------