%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET956+1 : TPTP v9.0.0. Released v3.2.0.
% 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 : n007.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 08:39:40 PM UTC 2025
% Result : Theorem 6.54s 2.75s
% Output : CNFRefutation 6.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 52 ( 22 ~; 21 |; 5 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 47 ( 47 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_7 > #skF_6 > #skF_2 > #skF_3 > #skF_9 > #skF_4 > #skF_8 > #skF_5 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $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 ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_77,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(A,cartesian_product2(B,C))
& ! [E,F] :
( in(ordered_pair(E,F),A)
=> in(ordered_pair(E,F),D) ) )
=> subset(A,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).
tff(f_42,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
tff(f_67,axiom,
! [A,B,C,D] :
~ ( subset(A,cartesian_product2(B,C))
& in(D,A)
& ! [E,F] :
~ ( in(E,B)
& in(F,C)
& ( D = ordered_pair(E,F) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
tff(c_28,plain,
~ subset('#skF_6','#skF_9'),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_10,plain,
! [A_5,B_6] :
( in('#skF_1'(A_5,B_6),A_5)
| subset(A_5,B_6) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_22,plain,
! [A_16,B_17,C_18,D_19] :
( ( ordered_pair('#skF_4'(A_16,B_17,C_18,D_19),'#skF_5'(A_16,B_17,C_18,D_19)) = D_19 )
| ~ in(D_19,A_16)
| ~ subset(A_16,cartesian_product2(B_17,C_18)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_356,plain,
! [A_72,B_73,C_74,D_75] :
( ( ordered_pair('#skF_4'(A_72,B_73,C_74,D_75),'#skF_5'(A_72,B_73,C_74,D_75)) = D_75 )
| ~ in(D_75,A_72)
| ~ subset(A_72,cartesian_product2(B_73,C_74)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_30,plain,
! [E_24,F_25] :
( in(ordered_pair(E_24,F_25),'#skF_9')
| ~ in(ordered_pair(E_24,F_25),'#skF_6') ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_429,plain,
! [A_86,B_87,C_88,D_89] :
( in(ordered_pair('#skF_4'(A_86,B_87,C_88,D_89),'#skF_5'(A_86,B_87,C_88,D_89)),'#skF_9')
| ~ in(D_89,'#skF_6')
| ~ in(D_89,A_86)
| ~ subset(A_86,cartesian_product2(B_87,C_88)) ),
inference(superposition,[status(thm),theory(equality)],[c_356,c_30]) ).
tff(c_2768,plain,
! [D_218,A_219,B_220,C_221] :
( in(D_218,'#skF_9')
| ~ in(D_218,'#skF_6')
| ~ in(D_218,A_219)
| ~ subset(A_219,cartesian_product2(B_220,C_221))
| ~ in(D_218,A_219)
| ~ subset(A_219,cartesian_product2(B_220,C_221)) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_429]) ).
tff(c_3034,plain,
! [B_240,A_241,B_242,C_243] :
( in('#skF_1'('#skF_6',B_240),'#skF_9')
| ~ in('#skF_1'('#skF_6',B_240),A_241)
| ~ subset(A_241,cartesian_product2(B_242,C_243))
| subset('#skF_6',B_240) ),
inference(resolution,[status(thm)],[c_10,c_2768]) ).
tff(c_3048,plain,
! [B_6,B_242,C_243] :
( in('#skF_1'('#skF_6',B_6),'#skF_9')
| ~ subset('#skF_6',cartesian_product2(B_242,C_243))
| subset('#skF_6',B_6) ),
inference(resolution,[status(thm)],[c_10,c_3034]) ).
tff(c_3053,plain,
! [B_242,C_243] : ~ subset('#skF_6',cartesian_product2(B_242,C_243)),
inference(splitLeft,[status(thm)],[c_3048]) ).
tff(c_32,plain,
subset('#skF_6',cartesian_product2('#skF_7','#skF_8')),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_3055,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3053,c_32]) ).
tff(c_3057,plain,
! [B_248] :
( in('#skF_1'('#skF_6',B_248),'#skF_9')
| subset('#skF_6',B_248) ),
inference(splitRight,[status(thm)],[c_3048]) ).
tff(c_8,plain,
! [A_5,B_6] :
( ~ in('#skF_1'(A_5,B_6),B_6)
| subset(A_5,B_6) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_3065,plain,
subset('#skF_6','#skF_9'),
inference(resolution,[status(thm)],[c_3057,c_8]) ).
tff(c_3073,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_28,c_3065]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET956+1 : TPTP v9.0.0. Released v3.2.0.
% 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 : n007.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 21:53:09 EDT 2025
% 0.13/0.34 % CPUTime :
% 6.54/2.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.54/2.76
% 6.54/2.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------