%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV378+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 : n015.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 09:30:22 PM UTC 2025
% Result : Theorem 6.23s 2.57s
% Output : CNFRefutation 6.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 29 ~; 21 |; 3 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-3 aty)
% Number of variables : 63 ( 63 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ pair_in_list > succ_cpq > strictly_less_than > less_than > contains_slb > contains_cpq > ok > isnonempty_slb > check_cpq > triple > update_slb > remove_slb > remove_pqp > remove_cpq > pair > lookup_slb > insert_slb > insert_pqp > insert_cpq > #nlpp > removemin_cpq_res > removemin_cpq_eff > findmin_pqp_res > findmin_cpq_res > findmin_cpq_eff > create_slb > bottom > bad > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(bad,type,
bad: $i ).
tff(insert_cpq,type,
insert_cpq: ( $i * $i ) > $i ).
tff(succ_cpq,type,
succ_cpq: ( $i * $i ) > $o ).
tff(remove_cpq,type,
remove_cpq: ( $i * $i ) > $i ).
tff(contains_slb,type,
contains_slb: ( $i * $i ) > $o ).
tff(lookup_slb,type,
lookup_slb: ( $i * $i ) > $i ).
tff(pair_in_list,type,
pair_in_list: ( $i * $i * $i ) > $o ).
tff(less_than,type,
less_than: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(contains_cpq,type,
contains_cpq: ( $i * $i ) > $o ).
tff(strictly_less_than,type,
strictly_less_than: ( $i * $i ) > $o ).
tff(pair,type,
pair: ( $i * $i ) > $i ).
tff(ok,type,
ok: $i > $o ).
tff(insert_pqp,type,
insert_pqp: ( $i * $i ) > $i ).
tff(findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
tff(remove_pqp,type,
remove_pqp: ( $i * $i ) > $i ).
tff(bottom,type,
bottom: $i ).
tff(triple,type,
triple: ( $i * $i * $i ) > $i ).
tff(removemin_cpq_res,type,
removemin_cpq_res: $i > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(isnonempty_slb,type,
isnonempty_slb: $i > $o ).
tff(check_cpq,type,
check_cpq: $i > $o ).
tff(remove_slb,type,
remove_slb: ( $i * $i ) > $i ).
tff(findmin_cpq_eff,type,
findmin_cpq_eff: $i > $i ).
tff(removemin_cpq_eff,type,
removemin_cpq_eff: $i > $i ).
tff(create_slb,type,
create_slb: $i ).
tff(findmin_cpq_res,type,
findmin_cpq_res: $i > $i ).
tff(insert_slb,type,
insert_slb: ( $i * $i ) > $i ).
tff(update_slb,type,
update_slb: ( $i * $i ) > $i ).
tff(f_222,axiom,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ( W = bad ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax41) ).
tff(f_292,negated_conjecture,
~ ! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(remove_cpq(triple(U,V,W),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l14_co) ).
tff(f_217,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax40) ).
tff(f_229,axiom,
! [U,V,W,X] :
( ~ contains_slb(V,X)
=> ( remove_cpq(triple(U,V,W),X) = triple(U,V,bad) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax43) ).
tff(f_235,axiom,
! [U,V,W,X] :
( ( contains_slb(V,X)
& less_than(lookup_slb(V,X),X) )
=> ( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax44) ).
tff(f_60,axiom,
! [U,V] :
( less_than(U,V)
| less_than(V,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
tff(f_69,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( less_than(U,V)
& ~ less_than(V,U) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
tff(f_241,axiom,
! [U,V,W,X] :
( ( contains_slb(V,X)
& strictly_less_than(X,lookup_slb(V,X)) )
=> ( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax45) ).
tff(c_170,plain,
! [W_149,U_150,V_151] :
( ( bad = W_149 )
| ok(triple(U_150,V_151,W_149)) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_104,plain,
~ ok(triple('#skF_1','#skF_2','#skF_3')),
inference(cnfTransformation,[status(thm)],[f_292]) ).
tff(c_180,plain,
bad = '#skF_3',
inference(resolution,[status(thm)],[c_170,c_104]) ).
tff(c_74,plain,
! [U_75,V_76] : ~ ok(triple(U_75,V_76,bad)),
inference(cnfTransformation,[status(thm)],[f_217]) ).
tff(c_182,plain,
! [U_75,V_76] : ~ ok(triple(U_75,V_76,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_180,c_74]) ).
tff(c_80,plain,
! [U_84,V_85,W_86,X_87] :
( ( remove_cpq(triple(U_84,V_85,W_86),X_87) = triple(U_84,V_85,bad) )
| contains_slb(V_85,X_87) ),
inference(cnfTransformation,[status(thm)],[f_229]) ).
tff(c_494,plain,
! [U_223,V_224,W_225,X_226] :
( ( remove_cpq(triple(U_223,V_224,W_225),X_226) = triple(U_223,V_224,'#skF_3') )
| contains_slb(V_224,X_226) ),
inference(demodulation,[status(thm),theory(equality)],[c_180,c_80]) ).
tff(c_102,plain,
ok(remove_cpq(triple('#skF_1','#skF_2','#skF_3'),'#skF_4')),
inference(cnfTransformation,[status(thm)],[f_292]) ).
tff(c_507,plain,
( ok(triple('#skF_1','#skF_2','#skF_3'))
| contains_slb('#skF_2','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_494,c_102]) ).
tff(c_516,plain,
contains_slb('#skF_2','#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_182,c_507]) ).
tff(c_1423,plain,
! [U_394,X_395,V_396,W_397] :
( ( triple(remove_pqp(U_394,X_395),remove_slb(V_396,X_395),W_397) = remove_cpq(triple(U_394,V_396,W_397),X_395) )
| ~ less_than(lookup_slb(V_396,X_395),X_395)
| ~ contains_slb(V_396,X_395) ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_1607,plain,
! [U_427,V_428,X_429] :
( ~ ok(remove_cpq(triple(U_427,V_428,'#skF_3'),X_429))
| ~ less_than(lookup_slb(V_428,X_429),X_429)
| ~ contains_slb(V_428,X_429) ),
inference(superposition,[status(thm),theory(equality)],[c_1423,c_182]) ).
tff(c_1624,plain,
( ~ less_than(lookup_slb('#skF_2','#skF_4'),'#skF_4')
| ~ contains_slb('#skF_2','#skF_4') ),
inference(resolution,[status(thm)],[c_102,c_1607]) ).
tff(c_1627,plain,
~ less_than(lookup_slb('#skF_2','#skF_4'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_516,c_1624]) ).
tff(c_4,plain,
! [V_5,U_4] :
( less_than(V_5,U_4)
| less_than(U_4,V_5) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_1662,plain,
less_than('#skF_4',lookup_slb('#skF_2','#skF_4')),
inference(resolution,[status(thm)],[c_4,c_1627]) ).
tff(c_8,plain,
! [U_7,V_8] :
( strictly_less_than(U_7,V_8)
| less_than(V_8,U_7)
| ~ less_than(U_7,V_8) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_84,plain,
! [U_92,X_95,V_93,W_94] :
( ( triple(remove_pqp(U_92,X_95),remove_slb(V_93,X_95),bad) = remove_cpq(triple(U_92,V_93,W_94),X_95) )
| ~ strictly_less_than(X_95,lookup_slb(V_93,X_95))
| ~ contains_slb(V_93,X_95) ),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_1318,plain,
! [U_376,X_377,V_378,W_379] :
( ( triple(remove_pqp(U_376,X_377),remove_slb(V_378,X_377),'#skF_3') = remove_cpq(triple(U_376,V_378,W_379),X_377) )
| ~ strictly_less_than(X_377,lookup_slb(V_378,X_377))
| ~ contains_slb(V_378,X_377) ),
inference(demodulation,[status(thm),theory(equality)],[c_180,c_84]) ).
tff(c_3487,plain,
! [U_501,V_502,W_503,X_504] :
( ~ ok(remove_cpq(triple(U_501,V_502,W_503),X_504))
| ~ strictly_less_than(X_504,lookup_slb(V_502,X_504))
| ~ contains_slb(V_502,X_504) ),
inference(superposition,[status(thm),theory(equality)],[c_1318,c_182]) ).
tff(c_3503,plain,
( ~ strictly_less_than('#skF_4',lookup_slb('#skF_2','#skF_4'))
| ~ contains_slb('#skF_2','#skF_4') ),
inference(resolution,[status(thm)],[c_102,c_3487]) ).
tff(c_3506,plain,
~ strictly_less_than('#skF_4',lookup_slb('#skF_2','#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_516,c_3503]) ).
tff(c_3509,plain,
( less_than(lookup_slb('#skF_2','#skF_4'),'#skF_4')
| ~ less_than('#skF_4',lookup_slb('#skF_2','#skF_4')) ),
inference(resolution,[status(thm)],[c_8,c_3506]) ).
tff(c_3512,plain,
less_than(lookup_slb('#skF_2','#skF_4'),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1662,c_3509]) ).
tff(c_3514,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1627,c_3512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV378+1 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.12 % 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
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Apr 9 03:09:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 6.23/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.23/2.58
% 6.23/2.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------