%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU308+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 : 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 08:53:35 PM UTC 2025
% Result : Theorem 7.34s 2.79s
% Output : CNFRefutation 7.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 12 ~; 8 |; 2 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 33 ( 32 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > v5_membered > v4_membered > v3_membered > v2_membered > v1_xreal_0 > v1_xcmplx_0 > v1_rat_1 > v1_membered > v1_int_1 > one_sorted_str > natural > empty > subset_difference > subset_complement > set_difference > #nlpp > the_carrier > powerset > cast_as_carrier_subset > empty_set > #skF_5 > #skF_2 > #skF_7 > #skF_6 > #skF_1 > #skF_4 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subset_difference,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(v1_int_1,type,
v1_int_1: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(v3_membered,type,
v3_membered: $i > $o ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
tff(empty,type,
empty: $i > $o ).
tff(v1_xreal_0,type,
v1_xreal_0: $i > $o ).
tff(v5_membered,type,
v5_membered: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(v2_membered,type,
v2_membered: $i > $o ).
tff(v1_membered,type,
v1_membered: $i > $o ).
tff(v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(v1_rat_1,type,
v1_rat_1: $i > $o ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff(natural,type,
natural: $i > $o ).
tff(v4_membered,type,
v4_membered: $i > $o ).
tff(f_342,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
tff(f_334,axiom,
! [A] :
( one_sorted_str(A)
=> ( cast_as_carrier_subset(A) = the_carrier(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
tff(f_346,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_259,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
tff(f_281,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_228,axiom,
! [A] : ( set_difference(A,empty_set) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
tff(f_317,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_309,axiom,
! [A,B,C] :
( ( element(B,powerset(A))
& element(C,powerset(A)) )
=> ( subset_difference(A,B,C) = set_difference(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
tff(c_202,plain,
one_sorted_str('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_342]) ).
tff(c_333,plain,
! [A_116] :
( ( the_carrier(A_116) = cast_as_carrier_subset(A_116) )
| ~ one_sorted_str(A_116) ),
inference(cnfTransformation,[status(thm)],[f_334]) ).
tff(c_341,plain,
the_carrier('#skF_6') = cast_as_carrier_subset('#skF_6'),
inference(resolution,[status(thm)],[c_202,c_333]) ).
tff(c_200,plain,
element('#skF_7',powerset(the_carrier('#skF_6'))),
inference(cnfTransformation,[status(thm)],[f_342]) ).
tff(c_347,plain,
element('#skF_7',powerset(cast_as_carrier_subset('#skF_6'))),
inference(demodulation,[status(thm),theory(equality)],[c_341,c_200]) ).
tff(c_2640,plain,
! [A_318,B_319] :
( ( subset_complement(A_318,B_319) = set_difference(A_318,B_319) )
| ~ element(B_319,powerset(A_318)) ),
inference(cnfTransformation,[status(thm)],[f_346]) ).
tff(c_2675,plain,
subset_complement(cast_as_carrier_subset('#skF_6'),'#skF_7') = set_difference(cast_as_carrier_subset('#skF_6'),'#skF_7'),
inference(resolution,[status(thm)],[c_347,c_2640]) ).
tff(c_198,plain,
subset_difference(the_carrier('#skF_6'),cast_as_carrier_subset('#skF_6'),'#skF_7') != subset_complement(the_carrier('#skF_6'),'#skF_7'),
inference(cnfTransformation,[status(thm)],[f_342]) ).
tff(c_346,plain,
subset_difference(cast_as_carrier_subset('#skF_6'),cast_as_carrier_subset('#skF_6'),'#skF_7') != subset_complement(cast_as_carrier_subset('#skF_6'),'#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_341,c_341,c_198]) ).
tff(c_2858,plain,
subset_difference(cast_as_carrier_subset('#skF_6'),cast_as_carrier_subset('#skF_6'),'#skF_7') != set_difference(cast_as_carrier_subset('#skF_6'),'#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_2675,c_346]) ).
tff(c_144,plain,
! [A_61] : empty('#skF_3'(A_61)),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_230,plain,
! [A_98] :
( ( empty_set = A_98 )
| ~ empty(A_98) ),
inference(cnfTransformation,[status(thm)],[f_281]) ).
tff(c_237,plain,
! [A_61] : ( '#skF_3'(A_61) = empty_set ),
inference(resolution,[status(thm)],[c_144,c_230]) ).
tff(c_146,plain,
! [A_61] : element('#skF_3'(A_61),powerset(A_61)),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_320,plain,
! [A_61] : element(empty_set,powerset(A_61)),
inference(demodulation,[status(thm),theory(equality)],[c_237,c_146]) ).
tff(c_130,plain,
! [A_49] : ( set_difference(A_49,empty_set) = A_49 ),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_2664,plain,
! [A_61] : ( subset_complement(A_61,empty_set) = set_difference(A_61,empty_set) ),
inference(resolution,[status(thm)],[c_320,c_2640]) ).
tff(c_2680,plain,
! [A_320] : ( subset_complement(A_320,empty_set) = A_320 ),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_2664]) ).
tff(c_178,plain,
! [A_79,B_80] :
( element(subset_complement(A_79,B_80),powerset(A_79))
| ~ element(B_80,powerset(A_79)) ),
inference(cnfTransformation,[status(thm)],[f_317]) ).
tff(c_2686,plain,
! [A_320] :
( element(A_320,powerset(A_320))
| ~ element(empty_set,powerset(A_320)) ),
inference(superposition,[status(thm),theory(equality)],[c_2680,c_178]) ).
tff(c_2692,plain,
! [A_320] : element(A_320,powerset(A_320)),
inference(demodulation,[status(thm),theory(equality)],[c_320,c_2686]) ).
tff(c_3184,plain,
! [A_337,B_338,C_339] :
( ( subset_difference(A_337,B_338,C_339) = set_difference(B_338,C_339) )
| ~ element(C_339,powerset(A_337))
| ~ element(B_338,powerset(A_337)) ),
inference(cnfTransformation,[status(thm)],[f_309]) ).
tff(c_3238,plain,
! [B_345] :
( ( subset_difference(cast_as_carrier_subset('#skF_6'),B_345,'#skF_7') = set_difference(B_345,'#skF_7') )
| ~ element(B_345,powerset(cast_as_carrier_subset('#skF_6'))) ),
inference(resolution,[status(thm)],[c_347,c_3184]) ).
tff(c_3242,plain,
subset_difference(cast_as_carrier_subset('#skF_6'),cast_as_carrier_subset('#skF_6'),'#skF_7') = set_difference(cast_as_carrier_subset('#skF_6'),'#skF_7'),
inference(resolution,[status(thm)],[c_2692,c_3238]) ).
tff(c_3269,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2858,c_3242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU308+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.13 % 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 : n010.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 22:45:33 EDT 2025
% 0.13/0.35 % CPUTime :
% 7.34/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.34/2.80
% 7.34/2.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------