%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU320+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 : n027.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 08:53:38 PM UTC 2025
% Result : Theorem 3.60s 1.94s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 26 ~; 19 |; 0 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > open_subset > element > closed_subset > top_str > one_sorted_str > subset_complement > #nlpp > the_carrier > powerset > #skF_5 > #skF_2 > #skF_1 > #skF_4 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(open_subset,type,
open_subset: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(closed_subset,type,
closed_subset: ( $i * $i ) > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff(top_str,type,
top_str: $i > $o ).
tff(f_67,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).
tff(f_31,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_46,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] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).
tff(c_28,plain,
element('#skF_5',powerset(the_carrier('#skF_4'))),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_4,plain,
! [A_1,B_2] :
( element(subset_complement(A_1,B_2),powerset(A_1))
| ~ element(B_2,powerset(A_1)) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_32,plain,
( ~ closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4')
| ~ open_subset('#skF_5','#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_54,plain,
~ open_subset('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_30,plain,
top_str('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_38,plain,
( open_subset('#skF_5','#skF_4')
| closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_71,plain,
closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_54,c_38]) ).
tff(c_72,plain,
! [A_24,B_25] :
( ( subset_complement(A_24,subset_complement(A_24,B_25)) = B_25 )
| ~ element(B_25,powerset(A_24)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_81,plain,
subset_complement(the_carrier('#skF_4'),subset_complement(the_carrier('#skF_4'),'#skF_5')) = '#skF_5',
inference(resolution,[status(thm)],[c_28,c_72]) ).
tff(c_249,plain,
! [A_35,B_36] :
( open_subset(subset_complement(the_carrier(A_35),B_36),A_35)
| ~ closed_subset(B_36,A_35)
| ~ element(B_36,powerset(the_carrier(A_35)))
| ~ top_str(A_35) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_264,plain,
( open_subset('#skF_5','#skF_4')
| ~ closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4')
| ~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4')))
| ~ top_str('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_249]) ).
tff(c_266,plain,
( open_subset('#skF_5','#skF_4')
| ~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_71,c_264]) ).
tff(c_267,plain,
~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4'))),
inference(negUnitSimplification,[status(thm)],[c_54,c_266]) ).
tff(c_270,plain,
~ element('#skF_5',powerset(the_carrier('#skF_4'))),
inference(resolution,[status(thm)],[c_4,c_267]) ).
tff(c_277,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_270]) ).
tff(c_278,plain,
~ closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4'),
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_279,plain,
open_subset('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_298,plain,
! [A_42,B_43] :
( ( subset_complement(A_42,subset_complement(A_42,B_43)) = B_43 )
| ~ element(B_43,powerset(A_42)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_307,plain,
subset_complement(the_carrier('#skF_4'),subset_complement(the_carrier('#skF_4'),'#skF_5')) = '#skF_5',
inference(resolution,[status(thm)],[c_28,c_298]) ).
tff(c_475,plain,
! [B_53,A_54] :
( closed_subset(B_53,A_54)
| ~ open_subset(subset_complement(the_carrier(A_54),B_53),A_54)
| ~ element(B_53,powerset(the_carrier(A_54)))
| ~ top_str(A_54) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_490,plain,
( closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4')
| ~ open_subset('#skF_5','#skF_4')
| ~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4')))
| ~ top_str('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_307,c_475]) ).
tff(c_492,plain,
( closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4')
| ~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_279,c_490]) ).
tff(c_493,plain,
~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4'))),
inference(negUnitSimplification,[status(thm)],[c_278,c_492]) ).
tff(c_496,plain,
~ element('#skF_5',powerset(the_carrier('#skF_4'))),
inference(resolution,[status(thm)],[c_4,c_493]) ).
tff(c_503,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU320+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.13 % 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
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 22:48:35 EDT 2025
% 0.13/0.35 % CPUTime :
% 3.60/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.60/1.94
% 3.60/1.94 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------