%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV373+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 : n018.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 09:30:21 PM UTC 2025
% Result : Theorem 5.08s 2.70s
% Output : CNFRefutation 5.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 4 |; 2 &)
% ( 1 <=>; 3 =>; 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 : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-3 aty)
% Number of variables : 27 ( 27 !; 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
%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(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_276,axiom,
! [U,V,W,X] :
( ( V != create_slb )
=> ( findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax51) ).
tff(f_214,axiom,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_slb(V,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax39) ).
tff(f_300,negated_conjecture,
~ ! [U,V,W] :
( ~ contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W)))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l9_co) ).
tff(f_292,lemma,
! [U,V,W] :
( ok(findmin_cpq_eff(triple(U,V,W)))
=> ( ( V != create_slb )
& contains_slb(V,findmin_pqp_res(U))
& less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l9_l10) ).
tff(f_104,axiom,
! [U] : ~ contains_slb(create_slb,U),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax20) ).
tff(c_96,plain,
! [U_112,V_113,W_114] :
( ( findmin_cpq_res(triple(U_112,V_113,W_114)) = findmin_pqp_res(U_112) )
| ( create_slb = V_113 ) ),
inference(cnfTransformation,[status(thm)],[f_276]) ).
tff(c_294,plain,
! [U_188,V_189,W_190,X_191] :
( contains_cpq(triple(U_188,V_189,W_190),X_191)
| ~ contains_slb(V_189,X_191) ),
inference(cnfTransformation,[status(thm)],[f_214]) ).
tff(c_110,plain,
~ contains_cpq(triple('#skF_1','#skF_2','#skF_3'),findmin_cpq_res(triple('#skF_1','#skF_2','#skF_3'))),
inference(cnfTransformation,[status(thm)],[f_300]) ).
tff(c_302,plain,
~ contains_slb('#skF_2',findmin_cpq_res(triple('#skF_1','#skF_2','#skF_3'))),
inference(resolution,[status(thm)],[c_294,c_110]) ).
tff(c_306,plain,
( ~ contains_slb('#skF_2',findmin_pqp_res('#skF_1'))
| ( create_slb = '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_96,c_302]) ).
tff(c_307,plain,
~ contains_slb('#skF_2',findmin_pqp_res('#skF_1')),
inference(splitLeft,[status(thm)],[c_306]) ).
tff(c_108,plain,
ok(findmin_cpq_eff(triple('#skF_1','#skF_2','#skF_3'))),
inference(cnfTransformation,[status(thm)],[f_300]) ).
tff(c_409,plain,
! [V_202,U_203,W_204] :
( contains_slb(V_202,findmin_pqp_res(U_203))
| ~ ok(findmin_cpq_eff(triple(U_203,V_202,W_204))) ),
inference(cnfTransformation,[status(thm)],[f_292]) ).
tff(c_415,plain,
contains_slb('#skF_2',findmin_pqp_res('#skF_1')),
inference(resolution,[status(thm)],[c_108,c_409]) ).
tff(c_420,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_307,c_415]) ).
tff(c_421,plain,
create_slb = '#skF_2',
inference(splitRight,[status(thm)],[c_306]) ).
tff(c_20,plain,
! [U_13] : ~ contains_slb(create_slb,U_13),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_429,plain,
! [U_13] : ~ contains_slb('#skF_2',U_13),
inference(demodulation,[status(thm),theory(equality)],[c_421,c_20]) ).
tff(c_422,plain,
contains_slb('#skF_2',findmin_pqp_res('#skF_1')),
inference(splitRight,[status(thm)],[c_306]) ).
tff(c_445,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_429,c_422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWV373+1 : TPTP v9.0.0. Released v3.3.0.
% 0.00/0.10 % 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
% 0.10/0.30 % Computer : n018.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Wed Apr 9 03:09:02 EDT 2025
% 0.10/0.30 % CPUTime :
% 5.08/2.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.08/2.71
% 5.08/2.71 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------