%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV406+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 : n003.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 09:30:26 PM UTC 2025
% Result : Theorem 10.75s 3.65s
% Output : CNFRefutation 11.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 146 ( 81 unt; 0 typ; 0 def)
% Number of atoms : 242 ( 23 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 178 ( 82 ~; 81 |; 3 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 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 : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 14 con; 0-3 aty)
% Number of variables : 170 ( 170 !; 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_11 > #skF_7 > #skF_3 > #skF_10 > #skF_5 > #skF_6 > #skF_13 > #skF_1 > #skF_9 > #skF_8 > #skF_4 > #skF_2 > #skF_12
%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('#skF_11',type,
'#skF_11': $i ).
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('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(pair_in_list,type,
pair_in_list: ( $i * $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(less_than,type,
less_than: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $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('#skF_9',type,
'#skF_9': $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('#skF_8',type,
'#skF_8': $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('#skF_2',type,
'#skF_2': ( $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('#skF_12',type,
'#skF_12': $i ).
tff(update_slb,type,
update_slb: ( $i * $i ) > $i ).
tff(f_121,axiom,
! [U,V,W,X,Y] :
( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
<=> ( pair_in_list(U,W,Y)
| ( ( V = W )
& ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax23) ).
tff(f_302,negated_conjecture,
~ ! [U] :
( ! [V,W] :
( check_cpq(triple(V,U,W))
<=> ! [X,Y] :
( pair_in_list(U,X,Y)
=> less_than(Y,X) ) )
=> ! [Z,X1,X2,X3] :
( check_cpq(triple(Z,insert_slb(U,pair(X2,X3)),X1))
<=> ! [X4,X5] :
( pair_in_list(insert_slb(U,pair(X2,X3)),X4,X5)
=> less_than(X5,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l42_co) ).
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_210,axiom,
! [U,V,W,X,Y] :
( strictly_less_than(X,Y)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax38) ).
tff(f_204,axiom,
! [U,V,W,X,Y] :
( less_than(Y,X)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax37) ).
tff(f_56,axiom,
! [U,V,W] :
( ( less_than(U,V)
& less_than(V,W) )
=> less_than(U,W) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',transitivity) ).
tff(f_62,axiom,
! [U] : less_than(U,U),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',reflexivity) ).
tff(c_34,plain,
! [U_20,W_22,Y_24] : pair_in_list(insert_slb(U_20,pair(W_22,Y_24)),W_22,Y_24),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_104,plain,
( ~ check_cpq(triple('#skF_4',insert_slb('#skF_1',pair('#skF_6','#skF_7')),'#skF_5'))
| ~ less_than('#skF_13','#skF_12') ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_3650,plain,
~ less_than('#skF_13','#skF_12'),
inference(splitLeft,[status(thm)],[c_104]) ).
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_3657,plain,
less_than('#skF_12','#skF_13'),
inference(resolution,[status(thm)],[c_4,c_3650]) ).
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_110,plain,
! [X5_151,X4_150] :
( less_than(X5_151,X4_150)
| ~ pair_in_list(insert_slb('#skF_1',pair('#skF_6','#skF_7')),X4_150,X5_151)
| pair_in_list(insert_slb('#skF_1',pair('#skF_10','#skF_11')),'#skF_12','#skF_13') ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_4443,plain,
pair_in_list(insert_slb('#skF_1',pair('#skF_10','#skF_11')),'#skF_12','#skF_13'),
inference(splitLeft,[status(thm)],[c_110]) ).
tff(c_4717,plain,
! [V_577,W_580,X_579,Y_578,U_576] :
( ( Y_578 = X_579 )
| pair_in_list(U_576,W_580,Y_578)
| ~ pair_in_list(insert_slb(U_576,pair(V_577,X_579)),W_580,Y_578) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_4727,plain,
( ( '#skF_11' = '#skF_13' )
| pair_in_list('#skF_1','#skF_12','#skF_13') ),
inference(resolution,[status(thm)],[c_4443,c_4717]) ).
tff(c_4731,plain,
pair_in_list('#skF_1','#skF_12','#skF_13'),
inference(splitLeft,[status(thm)],[c_4727]) ).
tff(c_102,plain,
! [Y_147,X_146,V_140,W_141] :
( less_than(Y_147,X_146)
| ~ pair_in_list('#skF_1',X_146,Y_147)
| ~ check_cpq(triple(V_140,'#skF_1',W_141)) ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_141,plain,
! [V_140,W_141] : ~ check_cpq(triple(V_140,'#skF_1',W_141)),
inference(splitLeft,[status(thm)],[c_102]) ).
tff(c_116,plain,
! [V_140,W_141] :
( ~ less_than('#skF_3'(V_140,W_141),'#skF_2'(V_140,W_141))
| check_cpq(triple(V_140,'#skF_1',W_141)) ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_222,plain,
! [V_140,W_141] : ~ less_than('#skF_3'(V_140,W_141),'#skF_2'(V_140,W_141)),
inference(negUnitSimplification,[status(thm)],[c_141,c_116]) ).
tff(c_118,plain,
! [V_140,W_141] :
( pair_in_list('#skF_1','#skF_2'(V_140,W_141),'#skF_3'(V_140,W_141))
| check_cpq(triple(V_140,'#skF_1',W_141)) ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_298,plain,
! [V_140,W_141] : pair_in_list('#skF_1','#skF_2'(V_140,W_141),'#skF_3'(V_140,W_141)),
inference(negUnitSimplification,[status(thm)],[c_141,c_118]) ).
tff(c_36,plain,
! [V_21,U_20,Y_24,X_23,W_22] :
( ~ pair_in_list(U_20,W_22,Y_24)
| pair_in_list(insert_slb(U_20,pair(V_21,X_23)),W_22,Y_24) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_114,plain,
! [X5_151,X4_150] :
( less_than(X5_151,X4_150)
| ~ pair_in_list(insert_slb('#skF_1',pair('#skF_6','#skF_7')),X4_150,X5_151)
| check_cpq(triple('#skF_8',insert_slb('#skF_1',pair('#skF_10','#skF_11')),'#skF_9')) ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_1267,plain,
check_cpq(triple('#skF_8',insert_slb('#skF_1',pair('#skF_10','#skF_11')),'#skF_9')),
inference(splitLeft,[status(thm)],[c_114]) ).
tff(c_68,plain,
! [Y_70,V_67,W_68,U_66,X_69] :
( ~ check_cpq(triple(U_66,insert_slb(V_67,pair(X_69,Y_70)),W_68))
| ~ strictly_less_than(X_69,Y_70) ),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_1271,plain,
~ strictly_less_than('#skF_10','#skF_11'),
inference(resolution,[status(thm)],[c_1267,c_68]) ).
tff(c_1275,plain,
( less_than('#skF_11','#skF_10')
| ~ less_than('#skF_10','#skF_11') ),
inference(resolution,[status(thm)],[c_8,c_1271]) ).
tff(c_1276,plain,
~ less_than('#skF_10','#skF_11'),
inference(splitLeft,[status(thm)],[c_1275]) ).
tff(c_2038,plain,
! [Y_372,X_374,V_375,W_373,U_371] :
( check_cpq(triple(U_371,V_375,W_373))
| ~ check_cpq(triple(U_371,insert_slb(V_375,pair(X_374,Y_372)),W_373))
| ~ less_than(Y_372,X_374) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_2044,plain,
( check_cpq(triple('#skF_8','#skF_1','#skF_9'))
| ~ less_than('#skF_11','#skF_10') ),
inference(resolution,[status(thm)],[c_1267,c_2038]) ).
tff(c_2049,plain,
~ less_than('#skF_11','#skF_10'),
inference(negUnitSimplification,[status(thm)],[c_141,c_2044]) ).
tff(c_2083,plain,
less_than('#skF_10','#skF_11'),
inference(resolution,[status(thm)],[c_4,c_2049]) ).
tff(c_2100,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1276,c_2083]) ).
tff(c_2101,plain,
less_than('#skF_11','#skF_10'),
inference(splitRight,[status(thm)],[c_1275]) ).
tff(c_3568,plain,
! [X_434,Y_432,U_431,V_435,W_433] :
( check_cpq(triple(U_431,V_435,W_433))
| ~ check_cpq(triple(U_431,insert_slb(V_435,pair(X_434,Y_432)),W_433))
| ~ less_than(Y_432,X_434) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_3574,plain,
( check_cpq(triple('#skF_8','#skF_1','#skF_9'))
| ~ less_than('#skF_11','#skF_10') ),
inference(resolution,[status(thm)],[c_1267,c_3568]) ).
tff(c_3579,plain,
check_cpq(triple('#skF_8','#skF_1','#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_2101,c_3574]) ).
tff(c_3581,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_141,c_3579]) ).
tff(c_3584,plain,
! [X5_436,X4_437] :
( less_than(X5_436,X4_437)
| ~ pair_in_list(insert_slb('#skF_1',pair('#skF_6','#skF_7')),X4_437,X5_436) ),
inference(splitRight,[status(thm)],[c_114]) ).
tff(c_3610,plain,
! [Y_438,W_439] :
( less_than(Y_438,W_439)
| ~ pair_in_list('#skF_1',W_439,Y_438) ),
inference(resolution,[status(thm)],[c_36,c_3584]) ).
tff(c_3613,plain,
! [V_140,W_141] : less_than('#skF_3'(V_140,W_141),'#skF_2'(V_140,W_141)),
inference(resolution,[status(thm)],[c_298,c_3610]) ).
tff(c_3617,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_222,c_3613]) ).
tff(c_3618,plain,
! [Y_147,X_146] :
( less_than(Y_147,X_146)
| ~ pair_in_list('#skF_1',X_146,Y_147) ),
inference(splitRight,[status(thm)],[c_102]) ).
tff(c_4734,plain,
less_than('#skF_13','#skF_12'),
inference(resolution,[status(thm)],[c_4731,c_3618]) ).
tff(c_4738,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3650,c_4734]) ).
tff(c_4740,plain,
~ pair_in_list('#skF_1','#skF_12','#skF_13'),
inference(splitRight,[status(thm)],[c_4727]) ).
tff(c_4739,plain,
'#skF_11' = '#skF_13',
inference(splitRight,[status(thm)],[c_4727]) ).
tff(c_4741,plain,
pair_in_list(insert_slb('#skF_1',pair('#skF_10','#skF_13')),'#skF_12','#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_4739,c_4443]) ).
tff(c_4764,plain,
! [Y_583,W_585,V_582,X_584,U_581] :
( ( W_585 = V_582 )
| pair_in_list(U_581,W_585,Y_583)
| ~ pair_in_list(insert_slb(U_581,pair(V_582,X_584)),W_585,Y_583) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_4767,plain,
( ( '#skF_10' = '#skF_12' )
| pair_in_list('#skF_1','#skF_12','#skF_13') ),
inference(resolution,[status(thm)],[c_4741,c_4764]) ).
tff(c_4776,plain,
'#skF_10' = '#skF_12',
inference(negUnitSimplification,[status(thm)],[c_4740,c_4767]) ).
tff(c_4746,plain,
! [X5_151,X4_150] :
( less_than(X5_151,X4_150)
| ~ pair_in_list(insert_slb('#skF_1',pair('#skF_6','#skF_7')),X4_150,X5_151)
| check_cpq(triple('#skF_8',insert_slb('#skF_1',pair('#skF_10','#skF_13')),'#skF_9')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4739,c_114]) ).
tff(c_4747,plain,
check_cpq(triple('#skF_8',insert_slb('#skF_1',pair('#skF_10','#skF_13')),'#skF_9')),
inference(splitLeft,[status(thm)],[c_4746]) ).
tff(c_4758,plain,
~ strictly_less_than('#skF_10','#skF_13'),
inference(resolution,[status(thm)],[c_4747,c_68]) ).
tff(c_4780,plain,
~ strictly_less_than('#skF_12','#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_4776,c_4758]) ).
tff(c_4790,plain,
( less_than('#skF_13','#skF_12')
| ~ less_than('#skF_12','#skF_13') ),
inference(resolution,[status(thm)],[c_8,c_4780]) ).
tff(c_4793,plain,
less_than('#skF_13','#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_3657,c_4790]) ).
tff(c_4795,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3650,c_4793]) ).
tff(c_4806,plain,
! [X5_586,X4_587] :
( less_than(X5_586,X4_587)
| ~ pair_in_list(insert_slb('#skF_1',pair('#skF_6','#skF_7')),X4_587,X5_586) ),
inference(splitRight,[status(thm)],[c_4746]) ).
tff(c_4816,plain,
less_than('#skF_7','#skF_6'),
inference(resolution,[status(thm)],[c_34,c_4806]) ).
tff(c_3795,plain,
! [V_503,W_504] :
( pair_in_list('#skF_1','#skF_2'(V_503,W_504),'#skF_3'(V_503,W_504))
| check_cpq(triple(V_503,'#skF_1',W_504)) ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_4381,plain,
! [V_557,W_558] :
( less_than('#skF_3'(V_557,W_558),'#skF_2'(V_557,W_558))
| check_cpq(triple(V_557,'#skF_1',W_558)) ),
inference(resolution,[status(thm)],[c_3795,c_3618]) ).
tff(c_4397,plain,
! [V_557,W_558] : check_cpq(triple(V_557,'#skF_1',W_558)),
inference(resolution,[status(thm)],[c_4381,c_116]) ).
tff(c_6070,plain,
! [W_674,Y_673,V_676,U_672,X_675] :
( check_cpq(triple(U_672,insert_slb(V_676,pair(X_675,Y_673)),W_674))
| ~ check_cpq(triple(U_672,V_676,W_674))
| ~ less_than(Y_673,X_675) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_108,plain,
( ~ check_cpq(triple('#skF_4',insert_slb('#skF_1',pair('#skF_6','#skF_7')),'#skF_5'))
| pair_in_list(insert_slb('#skF_1',pair('#skF_10','#skF_11')),'#skF_12','#skF_13') ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_4230,plain,
~ check_cpq(triple('#skF_4',insert_slb('#skF_1',pair('#skF_6','#skF_7')),'#skF_5')),
inference(splitLeft,[status(thm)],[c_108]) ).
tff(c_6079,plain,
( ~ check_cpq(triple('#skF_4','#skF_1','#skF_5'))
| ~ less_than('#skF_7','#skF_6') ),
inference(resolution,[status(thm)],[c_6070,c_4230]) ).
tff(c_6096,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4816,c_4397,c_6079]) ).
tff(c_6142,plain,
! [X5_678,X4_679] :
( less_than(X5_678,X4_679)
| ~ pair_in_list(insert_slb('#skF_1',pair('#skF_6','#skF_7')),X4_679,X5_678) ),
inference(splitRight,[status(thm)],[c_110]) ).
tff(c_6152,plain,
less_than('#skF_7','#skF_6'),
inference(resolution,[status(thm)],[c_34,c_6142]) ).
tff(c_7040,plain,
! [X_730,U_727,V_731,W_729,Y_728] :
( check_cpq(triple(U_727,insert_slb(V_731,pair(X_730,Y_728)),W_729))
| ~ check_cpq(triple(U_727,V_731,W_729))
| ~ less_than(Y_728,X_730) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_7043,plain,
( ~ check_cpq(triple('#skF_4','#skF_1','#skF_5'))
| ~ less_than('#skF_7','#skF_6') ),
inference(resolution,[status(thm)],[c_7040,c_4230]) ).
tff(c_7053,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6152,c_4397,c_7043]) ).
tff(c_7054,plain,
pair_in_list(insert_slb('#skF_1',pair('#skF_10','#skF_11')),'#skF_12','#skF_13'),
inference(splitRight,[status(thm)],[c_108]) ).
tff(c_8910,plain,
! [W_844,X_843,U_840,V_841,Y_842] :
( ( W_844 = V_841 )
| pair_in_list(U_840,W_844,Y_842)
| ~ pair_in_list(insert_slb(U_840,pair(V_841,X_843)),W_844,Y_842) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_8921,plain,
( ( '#skF_10' = '#skF_12' )
| pair_in_list('#skF_1','#skF_12','#skF_13') ),
inference(resolution,[status(thm)],[c_7054,c_8910]) ).
tff(c_8924,plain,
pair_in_list('#skF_1','#skF_12','#skF_13'),
inference(splitLeft,[status(thm)],[c_8921]) ).
tff(c_8927,plain,
less_than('#skF_13','#skF_12'),
inference(resolution,[status(thm)],[c_8924,c_3618]) ).
tff(c_8931,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3650,c_8927]) ).
tff(c_8933,plain,
~ pair_in_list('#skF_1','#skF_12','#skF_13'),
inference(splitRight,[status(thm)],[c_8921]) ).
tff(c_8932,plain,
'#skF_10' = '#skF_12',
inference(splitRight,[status(thm)],[c_8921]) ).
tff(c_8951,plain,
pair_in_list(insert_slb('#skF_1',pair('#skF_12','#skF_11')),'#skF_12','#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_8932,c_7054]) ).
tff(c_30,plain,
! [V_21,U_20,Y_24,X_23,W_22] :
( ( Y_24 = X_23 )
| pair_in_list(U_20,W_22,Y_24)
| ~ pair_in_list(insert_slb(U_20,pair(V_21,X_23)),W_22,Y_24) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_9096,plain,
( ( '#skF_11' = '#skF_13' )
| pair_in_list('#skF_1','#skF_12','#skF_13') ),
inference(resolution,[status(thm)],[c_8951,c_30]) ).
tff(c_9102,plain,
'#skF_11' = '#skF_13',
inference(negUnitSimplification,[status(thm)],[c_8933,c_9096]) ).
tff(c_7321,plain,
! [Y_766,W_768,V_765,X_767,U_764] :
( ( W_768 = V_765 )
| pair_in_list(U_764,W_768,Y_766)
| ~ pair_in_list(insert_slb(U_764,pair(V_765,X_767)),W_768,Y_766) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_7332,plain,
( ( '#skF_10' = '#skF_12' )
| pair_in_list('#skF_1','#skF_12','#skF_13') ),
inference(resolution,[status(thm)],[c_7054,c_7321]) ).
tff(c_7335,plain,
pair_in_list('#skF_1','#skF_12','#skF_13'),
inference(splitLeft,[status(thm)],[c_7332]) ).
tff(c_7338,plain,
less_than('#skF_13','#skF_12'),
inference(resolution,[status(thm)],[c_7335,c_3618]) ).
tff(c_7342,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3650,c_7338]) ).
tff(c_7344,plain,
~ pair_in_list('#skF_1','#skF_12','#skF_13'),
inference(splitRight,[status(thm)],[c_7332]) ).
tff(c_7343,plain,
'#skF_10' = '#skF_12',
inference(splitRight,[status(thm)],[c_7332]) ).
tff(c_7348,plain,
pair_in_list(insert_slb('#skF_1',pair('#skF_12','#skF_11')),'#skF_12','#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_7343,c_7054]) ).
tff(c_7373,plain,
! [X_772,V_770,Y_771,W_773,U_769] :
( ( Y_771 = X_772 )
| pair_in_list(U_769,W_773,Y_771)
| ~ pair_in_list(insert_slb(U_769,pair(V_770,X_772)),W_773,Y_771) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_7376,plain,
( ( '#skF_11' = '#skF_13' )
| pair_in_list('#skF_1','#skF_12','#skF_13') ),
inference(resolution,[status(thm)],[c_7348,c_7373]) ).
tff(c_7385,plain,
'#skF_11' = '#skF_13',
inference(negUnitSimplification,[status(thm)],[c_7344,c_7376]) ).
tff(c_7055,plain,
check_cpq(triple('#skF_4',insert_slb('#skF_1',pair('#skF_6','#skF_7')),'#skF_5')),
inference(splitRight,[status(thm)],[c_108]) ).
tff(c_112,plain,
( ~ check_cpq(triple('#skF_4',insert_slb('#skF_1',pair('#skF_6','#skF_7')),'#skF_5'))
| check_cpq(triple('#skF_8',insert_slb('#skF_1',pair('#skF_10','#skF_11')),'#skF_9')) ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_7065,plain,
check_cpq(triple('#skF_8',insert_slb('#skF_1',pair('#skF_10','#skF_11')),'#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_7055,c_112]) ).
tff(c_7069,plain,
~ strictly_less_than('#skF_10','#skF_11'),
inference(resolution,[status(thm)],[c_7065,c_68]) ).
tff(c_7073,plain,
( less_than('#skF_11','#skF_10')
| ~ less_than('#skF_10','#skF_11') ),
inference(resolution,[status(thm)],[c_8,c_7069]) ).
tff(c_7081,plain,
~ less_than('#skF_10','#skF_11'),
inference(splitLeft,[status(thm)],[c_7073]) ).
tff(c_7345,plain,
~ less_than('#skF_12','#skF_11'),
inference(demodulation,[status(thm),theory(equality)],[c_7343,c_7081]) ).
tff(c_7390,plain,
~ less_than('#skF_12','#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_7385,c_7345]) ).
tff(c_7395,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3657,c_7390]) ).
tff(c_7397,plain,
less_than('#skF_10','#skF_11'),
inference(splitRight,[status(thm)],[c_7073]) ).
tff(c_3758,plain,
! [U_498,W_499,V_500] :
( less_than(U_498,W_499)
| ~ less_than(V_500,W_499)
| ~ less_than(U_498,V_500) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_3800,plain,
! [U_505] :
( less_than(U_505,'#skF_13')
| ~ less_than(U_505,'#skF_12') ),
inference(resolution,[status(thm)],[c_3657,c_3758]) ).
tff(c_2,plain,
! [U_1,W_3,V_2] :
( less_than(U_1,W_3)
| ~ less_than(V_2,W_3)
| ~ less_than(U_1,V_2) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_3803,plain,
! [U_1,U_505] :
( less_than(U_1,'#skF_13')
| ~ less_than(U_1,U_505)
| ~ less_than(U_505,'#skF_12') ),
inference(resolution,[status(thm)],[c_3800,c_2]) ).
tff(c_7418,plain,
( less_than('#skF_10','#skF_13')
| ~ less_than('#skF_11','#skF_12') ),
inference(resolution,[status(thm)],[c_7397,c_3803]) ).
tff(c_7580,plain,
~ less_than('#skF_11','#skF_12'),
inference(splitLeft,[status(thm)],[c_7418]) ).
tff(c_7396,plain,
less_than('#skF_11','#skF_10'),
inference(splitRight,[status(thm)],[c_7073]) ).
tff(c_6,plain,
! [U_6] : less_than(U_6,U_6),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_7937,plain,
! [U_805,Y_807,W_809,X_808,V_806] :
( ( W_809 = V_806 )
| pair_in_list(U_805,W_809,Y_807)
| ~ pair_in_list(insert_slb(U_805,pair(V_806,X_808)),W_809,Y_807) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_7948,plain,
( ( '#skF_10' = '#skF_12' )
| pair_in_list('#skF_1','#skF_12','#skF_13') ),
inference(resolution,[status(thm)],[c_7054,c_7937]) ).
tff(c_7951,plain,
pair_in_list('#skF_1','#skF_12','#skF_13'),
inference(splitLeft,[status(thm)],[c_7948]) ).
tff(c_7954,plain,
less_than('#skF_13','#skF_12'),
inference(resolution,[status(thm)],[c_7951,c_3618]) ).
tff(c_7958,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3650,c_7954]) ).
tff(c_7959,plain,
'#skF_10' = '#skF_12',
inference(splitRight,[status(thm)],[c_7948]) ).
tff(c_7406,plain,
( less_than('#skF_11','#skF_13')
| ~ less_than('#skF_10','#skF_12') ),
inference(resolution,[status(thm)],[c_7396,c_3803]) ).
tff(c_7643,plain,
~ less_than('#skF_10','#skF_12'),
inference(splitLeft,[status(thm)],[c_7406]) ).
tff(c_7964,plain,
~ less_than('#skF_12','#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_7959,c_7643]) ).
tff(c_7977,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_7964]) ).
tff(c_7979,plain,
less_than('#skF_10','#skF_12'),
inference(splitRight,[status(thm)],[c_7406]) ).
tff(c_8137,plain,
! [U_819] :
( less_than(U_819,'#skF_12')
| ~ less_than(U_819,'#skF_10') ),
inference(resolution,[status(thm)],[c_7979,c_2]) ).
tff(c_8162,plain,
less_than('#skF_11','#skF_12'),
inference(resolution,[status(thm)],[c_7396,c_8137]) ).
tff(c_8210,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7580,c_8162]) ).
tff(c_8212,plain,
less_than('#skF_11','#skF_12'),
inference(splitRight,[status(thm)],[c_7418]) ).
tff(c_9136,plain,
less_than('#skF_13','#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_9102,c_8212]) ).
tff(c_9141,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3650,c_9136]) ).
tff(c_9143,plain,
less_than('#skF_13','#skF_12'),
inference(splitRight,[status(thm)],[c_104]) ).
tff(c_106,plain,
! [X5_151,X4_150] :
( less_than(X5_151,X4_150)
| ~ pair_in_list(insert_slb('#skF_1',pair('#skF_6','#skF_7')),X4_150,X5_151)
| ~ less_than('#skF_13','#skF_12') ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_9332,plain,
! [X5_910,X4_911] :
( less_than(X5_910,X4_911)
| ~ pair_in_list(insert_slb('#skF_1',pair('#skF_6','#skF_7')),X4_911,X5_910) ),
inference(demodulation,[status(thm),theory(equality)],[c_9143,c_106]) ).
tff(c_9337,plain,
less_than('#skF_7','#skF_6'),
inference(resolution,[status(thm)],[c_34,c_9332]) ).
tff(c_9207,plain,
! [V_888,W_889] :
( pair_in_list('#skF_1','#skF_2'(V_888,W_889),'#skF_3'(V_888,W_889))
| check_cpq(triple(V_888,'#skF_1',W_889)) ),
inference(cnfTransformation,[status(thm)],[f_302]) ).
tff(c_10717,plain,
! [V_985,W_986] :
( less_than('#skF_3'(V_985,W_986),'#skF_2'(V_985,W_986))
| check_cpq(triple(V_985,'#skF_1',W_986)) ),
inference(resolution,[status(thm)],[c_9207,c_3618]) ).
tff(c_10739,plain,
! [V_985,W_986] : check_cpq(triple(V_985,'#skF_1',W_986)),
inference(resolution,[status(thm)],[c_10717,c_116]) ).
tff(c_12670,plain,
! [Y_1081,U_1080,W_1082,V_1084,X_1083] :
( check_cpq(triple(U_1080,insert_slb(V_1084,pair(X_1083,Y_1081)),W_1082))
| ~ check_cpq(triple(U_1080,V_1084,W_1082))
| ~ less_than(Y_1081,X_1083) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_9142,plain,
~ check_cpq(triple('#skF_4',insert_slb('#skF_1',pair('#skF_6','#skF_7')),'#skF_5')),
inference(splitRight,[status(thm)],[c_104]) ).
tff(c_12676,plain,
( ~ check_cpq(triple('#skF_4','#skF_1','#skF_5'))
| ~ less_than('#skF_7','#skF_6') ),
inference(resolution,[status(thm)],[c_12670,c_9142]) ).
tff(c_12687,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9337,c_10739,c_12676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV406+1 : TPTP v9.0.0. Released v3.3.0.
% 0.13/0.13 % 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
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Apr 9 03:11:48 EDT 2025
% 0.14/0.34 % CPUTime :
% 10.75/3.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.06/3.66
% 11.06/3.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------