%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU170+1 : TPTP v9.0.0. Released v3.3.0.
% 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 : n024.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 08:53:03 PM UTC 2025
% Result : Theorem 22.36s 11.08s
% Output : CNFRefutation 22.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 123 ( 19 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 102 ( 45 ~; 41 |; 6 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 84 ( 83 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > disjoint > empty > subset_complement > set_difference > #nlpp > powerset > empty_set > #skF_7 > #skF_5 > #skF_4 > #skF_11 > #skF_10 > #skF_6 > #skF_2 > #skF_8 > #skF_3 > #skF_1 > #skF_9 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_38,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
tff(f_130,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
tff(f_52,axiom,
! [A,B] :
( element(B,powerset(A))
=> ( subset_complement(A,B) = set_difference(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
tff(f_68,axiom,
! [A,B] :
( element(B,powerset(A))
=> ( subset_complement(A,subset_complement(A,B)) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
tff(f_57,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
tff(f_48,axiom,
! [A,B,C] :
( ( C = set_difference(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
tff(f_120,axiom,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] :
~ ( in(C,A)
& in(C,B) ) )
& ~ ( ? [C] :
( in(C,A)
& in(C,B) )
& disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
tff(c_8,plain,
! [A_3,B_4] :
( in('#skF_1'(A_3,B_4),A_3)
| subset(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_76,plain,
element('#skF_11',powerset('#skF_10')),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_3022,plain,
! [A_320,B_321] :
( ( subset_complement(A_320,B_321) = set_difference(A_320,B_321) )
| ~ element(B_321,powerset(A_320)) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_3043,plain,
subset_complement('#skF_10','#skF_11') = set_difference('#skF_10','#skF_11'),
inference(resolution,[status(thm)],[c_76,c_3022]) ).
tff(c_3076,plain,
! [A_325,B_326] :
( ( subset_complement(A_325,subset_complement(A_325,B_326)) = B_326 )
| ~ element(B_326,powerset(A_325)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_3092,plain,
subset_complement('#skF_10',subset_complement('#skF_10','#skF_11')) = '#skF_11',
inference(resolution,[status(thm)],[c_76,c_3076]) ).
tff(c_3120,plain,
subset_complement('#skF_10',set_difference('#skF_10','#skF_11')) = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_3043,c_3092]) ).
tff(c_3151,plain,
! [A_333,B_334] :
( element(subset_complement(A_333,B_334),powerset(A_333))
| ~ element(B_334,powerset(A_333)) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_3165,plain,
( element(set_difference('#skF_10','#skF_11'),powerset('#skF_10'))
| ~ element('#skF_11',powerset('#skF_10')) ),
inference(superposition,[status(thm),theory(equality)],[c_3043,c_3151]) ).
tff(c_3180,plain,
element(set_difference('#skF_10','#skF_11'),powerset('#skF_10')),
inference(demodulation,[status(thm),theory(equality)],[c_76,c_3165]) ).
tff(c_28,plain,
! [A_14,B_15] :
( ( subset_complement(A_14,B_15) = set_difference(A_14,B_15) )
| ~ element(B_15,powerset(A_14)) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_3231,plain,
subset_complement('#skF_10',set_difference('#skF_10','#skF_11')) = set_difference('#skF_10',set_difference('#skF_10','#skF_11')),
inference(resolution,[status(thm)],[c_3180,c_28]) ).
tff(c_3235,plain,
set_difference('#skF_10',set_difference('#skF_10','#skF_11')) = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_3120,c_3231]) ).
tff(c_14,plain,
! [D_13,A_8,B_9] :
( in(D_13,A_8)
| ~ in(D_13,set_difference(A_8,B_9)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_3265,plain,
! [D_337] :
( in(D_337,'#skF_10')
| ~ in(D_337,'#skF_11') ),
inference(superposition,[status(thm),theory(equality)],[c_3235,c_14]) ).
tff(c_3370,plain,
! [B_348] :
( in('#skF_1'('#skF_11',B_348),'#skF_10')
| subset('#skF_11',B_348) ),
inference(resolution,[status(thm)],[c_8,c_3265]) ).
tff(c_6,plain,
! [A_3,B_4] :
( ~ in('#skF_1'(A_3,B_4),B_4)
| subset(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_3386,plain,
subset('#skF_11','#skF_10'),
inference(resolution,[status(thm)],[c_3370,c_6]) ).
tff(c_2987,plain,
! [C_313,B_314,A_315] :
( in(C_313,B_314)
| ~ in(C_313,A_315)
| ~ subset(A_315,B_314) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_2994,plain,
! [A_3,B_4,B_314] :
( in('#skF_1'(A_3,B_4),B_314)
| ~ subset(A_3,B_314)
| subset(A_3,B_4) ),
inference(resolution,[status(thm)],[c_8,c_2987]) ).
tff(c_3389,plain,
! [D_349,A_350,B_351] :
( in(D_349,set_difference(A_350,B_351))
| in(D_349,B_351)
| ~ in(D_349,A_350) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_11389,plain,
! [A_726,A_727,B_728] :
( subset(A_726,set_difference(A_727,B_728))
| in('#skF_1'(A_726,set_difference(A_727,B_728)),B_728)
| ~ in('#skF_1'(A_726,set_difference(A_727,B_728)),A_727) ),
inference(resolution,[status(thm)],[c_3389,c_6]) ).
tff(c_58261,plain,
! [A_1547,B_1548,B_1549] :
( in('#skF_1'(A_1547,set_difference(B_1548,B_1549)),B_1549)
| ~ subset(A_1547,B_1548)
| subset(A_1547,set_difference(B_1548,B_1549)) ),
inference(resolution,[status(thm)],[c_2994,c_11389]) ).
tff(c_84,plain,
( disjoint('#skF_11','#skF_12')
| subset('#skF_11',subset_complement('#skF_10','#skF_12')) ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_191,plain,
subset('#skF_11',subset_complement('#skF_10','#skF_12')),
inference(splitLeft,[status(thm)],[c_84]) ).
tff(c_78,plain,
( ~ subset('#skF_11',subset_complement('#skF_10','#skF_12'))
| ~ disjoint('#skF_11','#skF_12') ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_217,plain,
~ disjoint('#skF_11','#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_191,c_78]) ).
tff(c_74,plain,
element('#skF_12',powerset('#skF_10')),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_442,plain,
! [A_123,B_124] :
( ( subset_complement(A_123,B_124) = set_difference(A_123,B_124) )
| ~ element(B_124,powerset(A_123)) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_468,plain,
subset_complement('#skF_10','#skF_12') = set_difference('#skF_10','#skF_12'),
inference(resolution,[status(thm)],[c_74,c_442]) ).
tff(c_593,plain,
subset('#skF_11',set_difference('#skF_10','#skF_12')),
inference(demodulation,[status(thm),theory(equality)],[c_468,c_191]) ).
tff(c_361,plain,
! [A_112,B_113] :
( ( subset_complement(A_112,subset_complement(A_112,B_113)) = B_113 )
| ~ element(B_113,powerset(A_112)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_377,plain,
subset_complement('#skF_10',subset_complement('#skF_10','#skF_12')) = '#skF_12',
inference(resolution,[status(thm)],[c_74,c_361]) ).
tff(c_592,plain,
subset_complement('#skF_10',set_difference('#skF_10','#skF_12')) = '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_468,c_377]) ).
tff(c_34,plain,
! [A_16,B_17] :
( element(subset_complement(A_16,B_17),powerset(A_16))
| ~ element(B_17,powerset(A_16)) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_597,plain,
( element(set_difference('#skF_10','#skF_12'),powerset('#skF_10'))
| ~ element('#skF_12',powerset('#skF_10')) ),
inference(superposition,[status(thm),theory(equality)],[c_468,c_34]) ).
tff(c_601,plain,
element(set_difference('#skF_10','#skF_12'),powerset('#skF_10')),
inference(demodulation,[status(thm),theory(equality)],[c_74,c_597]) ).
tff(c_630,plain,
subset_complement('#skF_10',set_difference('#skF_10','#skF_12')) = set_difference('#skF_10',set_difference('#skF_10','#skF_12')),
inference(resolution,[status(thm)],[c_601,c_28]) ).
tff(c_634,plain,
set_difference('#skF_10',set_difference('#skF_10','#skF_12')) = '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_592,c_630]) ).
tff(c_72,plain,
! [A_36,B_37] :
( in('#skF_9'(A_36,B_37),A_36)
| disjoint(A_36,B_37) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_313,plain,
! [C_92,B_93,A_94] :
( in(C_92,B_93)
| ~ in(C_92,A_94)
| ~ subset(A_94,B_93) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_321,plain,
! [A_36,B_37,B_93] :
( in('#skF_9'(A_36,B_37),B_93)
| ~ subset(A_36,B_93)
| disjoint(A_36,B_37) ),
inference(resolution,[status(thm)],[c_72,c_313]) ).
tff(c_70,plain,
! [A_36,B_37] :
( in('#skF_9'(A_36,B_37),B_37)
| disjoint(A_36,B_37) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_239,plain,
! [D_81,B_82,A_83] :
( ~ in(D_81,B_82)
| ~ in(D_81,set_difference(A_83,B_82)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_2463,plain,
! [A_247,A_248,B_249] :
( ~ in('#skF_9'(A_247,set_difference(A_248,B_249)),B_249)
| disjoint(A_247,set_difference(A_248,B_249)) ),
inference(resolution,[status(thm)],[c_70,c_239]) ).
tff(c_2605,plain,
! [A_256,B_257,A_258] :
( ~ subset(A_256,B_257)
| disjoint(A_256,set_difference(A_258,B_257)) ),
inference(resolution,[status(thm)],[c_321,c_2463]) ).
tff(c_2810,plain,
! [A_268] :
( ~ subset(A_268,set_difference('#skF_10','#skF_12'))
| disjoint(A_268,'#skF_12') ),
inference(superposition,[status(thm),theory(equality)],[c_634,c_2605]) ).
tff(c_2813,plain,
disjoint('#skF_11','#skF_12'),
inference(resolution,[status(thm)],[c_593,c_2810]) ).
tff(c_2829,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_217,c_2813]) ).
tff(c_2830,plain,
disjoint('#skF_11','#skF_12'),
inference(splitRight,[status(thm)],[c_84]) ).
tff(c_2955,plain,
! [A_304,B_305,C_306] :
( ~ disjoint(A_304,B_305)
| ~ in(C_306,B_305)
| ~ in(C_306,A_304) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_2968,plain,
! [C_307] :
( ~ in(C_307,'#skF_12')
| ~ in(C_307,'#skF_11') ),
inference(resolution,[status(thm)],[c_2830,c_2955]) ).
tff(c_2981,plain,
! [B_4] :
( ~ in('#skF_1'('#skF_11',B_4),'#skF_12')
| subset('#skF_11',B_4) ),
inference(resolution,[status(thm)],[c_8,c_2968]) ).
tff(c_63428,plain,
! [B_1573] :
( ~ subset('#skF_11',B_1573)
| subset('#skF_11',set_difference(B_1573,'#skF_12')) ),
inference(resolution,[status(thm)],[c_58261,c_2981]) ).
tff(c_3044,plain,
subset_complement('#skF_10','#skF_12') = set_difference('#skF_10','#skF_12'),
inference(resolution,[status(thm)],[c_74,c_3022]) ).
tff(c_2834,plain,
~ subset('#skF_11',subset_complement('#skF_10','#skF_12')),
inference(demodulation,[status(thm),theory(equality)],[c_2830,c_78]) ).
tff(c_3071,plain,
~ subset('#skF_11',set_difference('#skF_10','#skF_12')),
inference(demodulation,[status(thm),theory(equality)],[c_3044,c_2834]) ).
tff(c_63495,plain,
~ subset('#skF_11','#skF_10'),
inference(resolution,[status(thm)],[c_63428,c_3071]) ).
tff(c_63569,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3386,c_63495]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU170+1 : TPTP v9.0.0. Released v3.3.0.
% 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
% 0.12/0.34 % Computer : n024.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 22:11:51 EDT 2025
% 0.12/0.34 % CPUTime :
% 22.36/11.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.36/11.09
% 22.36/11.09 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------