%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU220+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 : n019.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 08:53:15 PM UTC 2025
% Result : Theorem 14.54s 4.66s
% Output : CNFRefutation 14.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 21 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 182 ( 85 ~; 65 |; 18 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 11 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > element > relation_empty_yielding > relation > one_to_one > function > empty > relation_composition > apply > #nlpp > relation_rng > relation_dom > function_inverse > empty_set > #skF_11 > #skF_15 > #skF_1 > #skF_7 > #skF_13 > #skF_12 > #skF_14 > #skF_5 > #skF_6 > #skF_2 > #skF_10 > #skF_3 > #skF_9 > #skF_8 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(relation,type,
relation: $i > $o ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(function_inverse,type,
function_inverse: $i > $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(relation_composition,type,
relation_composition: ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff(f_246,negated_conjecture,
~ ! [A,B] :
( ( relation(B)
& function(B) )
=> ( ( one_to_one(B)
& in(A,relation_rng(B)) )
=> ( ( A = apply(B,apply(function_inverse(B),A)) )
& ( A = apply(relation_composition(function_inverse(B),B),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
tff(f_60,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( relation(function_inverse(A))
& function(function_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
tff(f_223,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( relation(B)
& function(B) )
=> ( ( B = function_inverse(A) )
<=> ( ( relation_dom(B) = relation_rng(A) )
& ! [C,D] :
( ( ( in(C,relation_rng(A))
& ( D = apply(B,C) ) )
=> ( in(D,relation_dom(A))
& ( C = apply(A,D) ) ) )
& ( ( in(D,relation_dom(A))
& ( C = apply(A,D) ) )
=> ( in(C,relation_rng(A))
& ( D = apply(B,C) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
tff(f_255,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
tff(f_233,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> ( ( relation_rng(A) = relation_dom(function_inverse(A)) )
& ( relation_dom(A) = relation_rng(function_inverse(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
tff(f_185,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(B))
=> ( apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
tff(c_146,plain,
relation('#skF_15'),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_144,plain,
function('#skF_15'),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_20,plain,
! [A_6] :
( function(function_inverse(A_6))
| ~ function(A_6)
| ~ relation(A_6) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_142,plain,
one_to_one('#skF_15'),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_22,plain,
! [A_6] :
( relation(function_inverse(A_6))
| ~ function(A_6)
| ~ relation(A_6) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_140,plain,
in('#skF_14',relation_rng('#skF_15')),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_6336,plain,
! [A_265,C_266] :
( in(apply(function_inverse(A_265),C_266),relation_dom(A_265))
| ~ in(C_266,relation_rng(A_265))
| ~ function(function_inverse(A_265))
| ~ relation(function_inverse(A_265))
| ~ one_to_one(A_265)
| ~ function(A_265)
| ~ relation(A_265) ),
inference(cnfTransformation,[status(thm)],[f_223]) ).
tff(c_150,plain,
! [B_49,A_48] :
( ~ empty(B_49)
| ~ in(A_48,B_49) ),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_24464,plain,
! [A_601,C_602] :
( ~ empty(relation_dom(A_601))
| ~ in(C_602,relation_rng(A_601))
| ~ function(function_inverse(A_601))
| ~ relation(function_inverse(A_601))
| ~ one_to_one(A_601)
| ~ function(A_601)
| ~ relation(A_601) ),
inference(resolution,[status(thm)],[c_6336,c_150]) ).
tff(c_24525,plain,
( ~ empty(relation_dom('#skF_15'))
| ~ function(function_inverse('#skF_15'))
| ~ relation(function_inverse('#skF_15'))
| ~ one_to_one('#skF_15')
| ~ function('#skF_15')
| ~ relation('#skF_15') ),
inference(resolution,[status(thm)],[c_140,c_24464]) ).
tff(c_24533,plain,
( ~ empty(relation_dom('#skF_15'))
| ~ function(function_inverse('#skF_15'))
| ~ relation(function_inverse('#skF_15')) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_144,c_142,c_24525]) ).
tff(c_24937,plain,
~ relation(function_inverse('#skF_15')),
inference(splitLeft,[status(thm)],[c_24533]) ).
tff(c_24940,plain,
( ~ function('#skF_15')
| ~ relation('#skF_15') ),
inference(resolution,[status(thm)],[c_22,c_24937]) ).
tff(c_24947,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_146,c_144,c_24940]) ).
tff(c_24949,plain,
relation(function_inverse('#skF_15')),
inference(splitRight,[status(thm)],[c_24533]) ).
tff(c_3420,plain,
! [A_168,C_169] :
( ( apply(A_168,apply(function_inverse(A_168),C_169)) = C_169 )
| ~ in(C_169,relation_rng(A_168))
| ~ function(function_inverse(A_168))
| ~ relation(function_inverse(A_168))
| ~ one_to_one(A_168)
| ~ function(A_168)
| ~ relation(A_168) ),
inference(cnfTransformation,[status(thm)],[f_223]) ).
tff(c_138,plain,
( ( apply(relation_composition(function_inverse('#skF_15'),'#skF_15'),'#skF_14') != '#skF_14' )
| ( apply('#skF_15',apply(function_inverse('#skF_15'),'#skF_14')) != '#skF_14' ) ),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_200,plain,
apply('#skF_15',apply(function_inverse('#skF_15'),'#skF_14')) != '#skF_14',
inference(splitLeft,[status(thm)],[c_138]) ).
tff(c_3440,plain,
( ~ in('#skF_14',relation_rng('#skF_15'))
| ~ function(function_inverse('#skF_15'))
| ~ relation(function_inverse('#skF_15'))
| ~ one_to_one('#skF_15')
| ~ function('#skF_15')
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_3420,c_200]) ).
tff(c_3455,plain,
( ~ function(function_inverse('#skF_15'))
| ~ relation(function_inverse('#skF_15')) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_144,c_142,c_140,c_3440]) ).
tff(c_3458,plain,
~ relation(function_inverse('#skF_15')),
inference(splitLeft,[status(thm)],[c_3455]) ).
tff(c_3461,plain,
( ~ function('#skF_15')
| ~ relation('#skF_15') ),
inference(resolution,[status(thm)],[c_22,c_3458]) ).
tff(c_3468,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_146,c_144,c_3461]) ).
tff(c_3469,plain,
~ function(function_inverse('#skF_15')),
inference(splitRight,[status(thm)],[c_3455]) ).
tff(c_3716,plain,
( ~ function('#skF_15')
| ~ relation('#skF_15') ),
inference(resolution,[status(thm)],[c_20,c_3469]) ).
tff(c_3723,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_146,c_144,c_3716]) ).
tff(c_3725,plain,
apply('#skF_15',apply(function_inverse('#skF_15'),'#skF_14')) = '#skF_14',
inference(splitRight,[status(thm)],[c_138]) ).
tff(c_136,plain,
! [A_46] :
( ( relation_dom(function_inverse(A_46)) = relation_rng(A_46) )
| ~ one_to_one(A_46)
| ~ function(A_46)
| ~ relation(A_46) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_5795,plain,
! [B_253,C_254,A_255] :
( ( apply(relation_composition(B_253,C_254),A_255) = apply(C_254,apply(B_253,A_255)) )
| ~ in(A_255,relation_dom(B_253))
| ~ function(C_254)
| ~ relation(C_254)
| ~ function(B_253)
| ~ relation(B_253) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_26293,plain,
! [A_658,C_659,A_660] :
( ( apply(relation_composition(function_inverse(A_658),C_659),A_660) = apply(C_659,apply(function_inverse(A_658),A_660)) )
| ~ in(A_660,relation_rng(A_658))
| ~ function(C_659)
| ~ relation(C_659)
| ~ function(function_inverse(A_658))
| ~ relation(function_inverse(A_658))
| ~ one_to_one(A_658)
| ~ function(A_658)
| ~ relation(A_658) ),
inference(superposition,[status(thm),theory(equality)],[c_136,c_5795]) ).
tff(c_3724,plain,
apply(relation_composition(function_inverse('#skF_15'),'#skF_15'),'#skF_14') != '#skF_14',
inference(splitRight,[status(thm)],[c_138]) ).
tff(c_26337,plain,
( ( apply('#skF_15',apply(function_inverse('#skF_15'),'#skF_14')) != '#skF_14' )
| ~ in('#skF_14',relation_rng('#skF_15'))
| ~ function('#skF_15')
| ~ relation('#skF_15')
| ~ function(function_inverse('#skF_15'))
| ~ relation(function_inverse('#skF_15'))
| ~ one_to_one('#skF_15')
| ~ function('#skF_15')
| ~ relation('#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_26293,c_3724]) ).
tff(c_26388,plain,
~ function(function_inverse('#skF_15')),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_144,c_142,c_24949,c_146,c_144,c_140,c_3725,c_26337]) ).
tff(c_26398,plain,
( ~ function('#skF_15')
| ~ relation('#skF_15') ),
inference(resolution,[status(thm)],[c_20,c_26388]) ).
tff(c_26405,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_146,c_144,c_26398]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU220+1 : TPTP v9.0.0. Released v3.3.0.
% 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 : n019.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 22:22:47 EDT 2025
% 0.13/0.34 % CPUTime :
% 14.54/4.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.54/4.66
% 14.54/4.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------