TSTP Solution File: ITP012_2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ITP012_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n029.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 : Tue Aug 22 10:43:12 EDT 2023
% Result : Theorem 42.39s 25.67s
% Output : CNFRefutation 42.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 70
% Syntax : Number of formulae : 184 ( 63 unt; 50 typ; 0 def)
% Number of atoms : 254 ( 87 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 211 ( 91 ~; 107 |; 1 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 5 ( 3 usr)
% Number of type conns : 52 ( 29 >; 23 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 45 ( 45 usr; 18 con; 0-4 aty)
% Number of variables : 126 (; 126 !; 0 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
%$ mem > p > k > fo__c_2Emin_2E_3D_3D_3E > fo__c_2Einteger_2Eint__sub > fo__c_2Einteger_2Eint__divides > fo__c_2Einteger_2Eint__add > fo__c_2Ebool_2E_5C_2F > fo__c_2Ebool_2E_2F_5C > arr > ap > #nlpp > surj__ty_2Einteger_2Eint > surj__o > inj__ty_2Einteger_2Eint > inj__o > i > fo__c_2Einteger_2Eint__neg > fo__c_2Ebool_2E_7E > c_2Emin_2E_3D > c_2Ebool_2E_3F > c_2Ebool_2E_21 > ty_2Einteger_2Eint > ind > fo__c_2Ebool_2ET > fo__c_2Ebool_2EF > c_2Emin_2E_3D_3D_3E > c_2Einteger_2Eint__sub > c_2Einteger_2Eint__neg > c_2Einteger_2Eint__divides > c_2Einteger_2Eint__add > c_2Ebool_2E_7E > c_2Ebool_2E_5C_2F > c_2Ebool_2E_2F_5C > c_2Ebool_2ET > c_2Ebool_2EF > bool > #skF_11 > #skF_6 > #skF_5 > #skF_10 > #skF_4 > #skF_9 > #skF_7 > #skF_8 > #skF_3 > #skF_1 > #skF_2
%Foreground sorts:
tff(tp__ty_2Einteger_2Eint,type,
tp__ty_2Einteger_2Eint: $tType ).
tff(tp__o,type,
tp__o: $tType ).
tff(del,type,
del: $tType ).
%Background operators:
%Foreground operators:
tff(fo__c_2Ebool_2ET,type,
fo__c_2Ebool_2ET: tp__o ).
tff('#skF_11',type,
'#skF_11': tp__ty_2Einteger_2Eint ).
tff('#skF_6',type,
'#skF_6': ( del * $i * $i ) > $i ).
tff(ty_2Einteger_2Eint,type,
ty_2Einteger_2Eint: del ).
tff(c_2Ebool_2EF,type,
c_2Ebool_2EF: $i ).
tff(inj__ty_2Einteger_2Eint,type,
inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i ).
tff('#skF_5',type,
'#skF_5': ( del * $i ) > $i ).
tff(surj__o,type,
surj__o: $i > tp__o ).
tff(i,type,
i: del > $i ).
tff(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F: del > $i ).
tff(fo__c_2Ebool_2E_2F_5C,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(fo__c_2Einteger_2Eint__divides,type,
fo__c_2Einteger_2Eint__divides: ( tp__ty_2Einteger_2Eint * tp__ty_2Einteger_2Eint ) > tp__o ).
tff(fo__c_2Emin_2E_3D_3D_3E,type,
fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(fo__c_2Ebool_2E_7E,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff(surj__ty_2Einteger_2Eint,type,
surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint ).
tff(ap,type,
ap: ( $i * $i ) > $i ).
tff(fo__c_2Ebool_2EF,type,
fo__c_2Ebool_2EF: tp__o ).
tff(p,type,
p: $i > $o ).
tff(k,type,
k: ( del * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': tp__ty_2Einteger_2Eint ).
tff(c_2Ebool_2E_21,type,
c_2Ebool_2E_21: del > $i ).
tff(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $i ).
tff(c_2Einteger_2Eint__add,type,
c_2Einteger_2Eint__add: $i ).
tff(c_2Einteger_2Eint__divides,type,
c_2Einteger_2Eint__divides: $i ).
tff(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $i ).
tff('#skF_4',type,
'#skF_4': ( del * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': tp__ty_2Einteger_2Eint ).
tff(fo__c_2Einteger_2Eint__neg,type,
fo__c_2Einteger_2Eint__neg: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
tff(fo__c_2Einteger_2Eint__sub,type,
fo__c_2Einteger_2Eint__sub: ( tp__ty_2Einteger_2Eint * tp__ty_2Einteger_2Eint ) > tp__ty_2Einteger_2Eint ).
tff('#skF_7',type,
'#skF_7': ( del * $i * $i ) > $i ).
tff(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $i ).
tff(fo__c_2Ebool_2E_5C_2F,type,
fo__c_2Ebool_2E_5C_2F: ( tp__o * tp__o ) > tp__o ).
tff(arr,type,
arr: ( del * del ) > del ).
tff(c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
tff(c_2Emin_2E_3D,type,
c_2Emin_2E_3D: del > $i ).
tff(ind,type,
ind: del ).
tff(mem,type,
mem: ( $i * del ) > $o ).
tff(fo__c_2Einteger_2Eint__add,type,
fo__c_2Einteger_2Eint__add: ( tp__ty_2Einteger_2Eint * tp__ty_2Einteger_2Eint ) > tp__ty_2Einteger_2Eint ).
tff('#skF_8',type,
'#skF_8': ( del * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( del * $i ) > $i ).
tff(bool,type,
bool: del ).
tff(c_2Einteger_2Eint__sub,type,
c_2Einteger_2Eint__sub: $i ).
tff(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $i ).
tff('#skF_1',type,
'#skF_1': ( del * del * $i * $i ) > $i ).
tff(c_2Einteger_2Eint__neg,type,
c_2Einteger_2Eint__neg: $i ).
tff(inj__o,type,
inj__o: tp__o > $i ).
tff('#skF_2',type,
'#skF_2': ( del * $i ) > $i ).
tff(f_107,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_true_p) ).
tff(f_106,axiom,
inj__o(fo__c_2Ebool_2ET) = c_2Ebool_2ET,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2ET) ).
tff(f_98,axiom,
! [X: tp__o] : ( surj__o(inj__o(X)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_surj_o) ).
tff(f_138,axiom,
! [X0: tp__ty_2Einteger_2Eint,X1: tp__ty_2Einteger_2Eint] : ( inj__o(fo__c_2Einteger_2Eint__divides(X0,X1)) = ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(X0)),inj__ty_2Einteger_2Eint(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__divides) ).
tff(f_568,negated_conjecture,
~ ! [V0p: tp__ty_2Einteger_2Eint,V1q: tp__ty_2Einteger_2Eint,V2r: tp__ty_2Einteger_2Eint] :
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)),inj__ty_2Einteger_2Eint(V1q)))
=> ( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)),ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint(V2r)),inj__ty_2Einteger_2Eint(V1q))))
<=> p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)),inj__ty_2Einteger_2Eint(V2r))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__DIVIDES__RSUB) ).
tff(f_100,axiom,
! [X: tp__o] : mem(inj__o(X),bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_mem_o) ).
tff(f_105,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
tff(f_74,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( ( p(Q)
<=> p(R) )
=> ( Q = R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001_2.ax',boolext) ).
tff(f_135,axiom,
! [X0: tp__ty_2Einteger_2Eint] : ( inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X0)) = ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__neg) ).
tff(f_394,axiom,
! [V0p: tp__ty_2Einteger_2Eint,V1q: tp__ty_2Einteger_2Eint] :
( ( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)),ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(V1q))))
<=> p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)),inj__ty_2Einteger_2Eint(V1q))) )
& ( p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(V0p))),inj__ty_2Einteger_2Eint(V1q)))
<=> p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)),inj__ty_2Einteger_2Eint(V1q))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__DIVIDES__NEG) ).
tff(f_142,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_false_p) ).
tff(f_140,axiom,
inj__o(fo__c_2Ebool_2EF) = c_2Ebool_2EF,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2EF) ).
tff(f_139,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
tff(f_129,axiom,
! [X0: tp__ty_2Einteger_2Eint,X1: tp__ty_2Einteger_2Eint] : ( inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__sub(X0,X1)) = ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint(X0)),inj__ty_2Einteger_2Eint(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__sub) ).
tff(f_187,axiom,
! [X0: tp__o] : ( inj__o(fo__c_2Ebool_2E_7E(X0)) = ap(c_2Ebool_2E_7E,inj__o(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2E_7E) ).
tff(f_194,axiom,
! [Q] :
( mem(Q,bool)
=> ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_neg_p) ).
tff(f_120,axiom,
! [X: tp__ty_2Einteger_2Eint] : ( surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(X)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_surj_ty_2Einteger_2Eint) ).
tff(f_132,axiom,
! [X0: tp__ty_2Einteger_2Eint,X1: tp__ty_2Einteger_2Eint] : ( inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__add(X0,X1)) = ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(X0)),inj__ty_2Einteger_2Eint(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__add) ).
tff(f_380,axiom,
! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] : ( surj__ty_2Einteger_2Eint(ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint(V0x)),inj__ty_2Einteger_2Eint(V1y))) = surj__ty_2Einteger_2Eint(ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(V0x)),ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(V1y)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Einteger_2Eint__sub) ).
tff(f_386,axiom,
! [V0p: tp__ty_2Einteger_2Eint,V1q: tp__ty_2Einteger_2Eint,V2r: tp__ty_2Einteger_2Eint] :
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)),inj__ty_2Einteger_2Eint(V1q)))
=> ( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)),ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(V2r)),inj__ty_2Einteger_2Eint(V1q))))
<=> p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)),inj__ty_2Einteger_2Eint(V2r))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__DIVIDES__RADD) ).
tff(c_30,plain,
p(c_2Ebool_2ET),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_28,plain,
inj__o(fo__c_2Ebool_2ET) = c_2Ebool_2ET,
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_1732,plain,
! [X_144: tp__o] : ( surj__o(inj__o(X_144)) = X_144 ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_1744,plain,
surj__o(c_2Ebool_2ET) = fo__c_2Ebool_2ET,
inference(superposition,[status(thm),theory(equality)],[c_28,c_1732]) ).
tff(c_60,plain,
! [X0_39: tp__ty_2Einteger_2Eint,X1_40: tp__ty_2Einteger_2Eint] : ( ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(X0_39)),inj__ty_2Einteger_2Eint(X1_40)) = inj__o(fo__c_2Einteger_2Eint__divides(X0_39,X1_40)) ),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_1686,plain,
p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint('#skF_9')),inj__ty_2Einteger_2Eint('#skF_10'))),
inference(cnfTransformation,[status(thm)],[f_568]) ).
tff(c_1695,plain,
p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_10'))),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1686]) ).
tff(c_22,plain,
! [X_23: tp__o] : mem(inj__o(X_23),bool),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_26,plain,
mem(c_2Ebool_2ET,bool),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_102985,plain,
! [R_6647,Q_6648] :
( ~ p(R_6647)
| ~ p(Q_6648)
| ( R_6647 = Q_6648 )
| ~ mem(R_6647,bool)
| ~ mem(Q_6648,bool) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_102995,plain,
! [Q_6648] :
( ~ p(c_2Ebool_2ET)
| ~ p(Q_6648)
| ( c_2Ebool_2ET = Q_6648 )
| ~ mem(Q_6648,bool) ),
inference(resolution,[status(thm)],[c_26,c_102985]) ).
tff(c_103315,plain,
! [Q_6654] :
( ~ p(Q_6654)
| ( c_2Ebool_2ET = Q_6654 )
| ~ mem(Q_6654,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_102995]) ).
tff(c_103394,plain,
! [X_6655: tp__o] :
( ~ p(inj__o(X_6655))
| ( inj__o(X_6655) = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_22,c_103315]) ).
tff(c_103430,plain,
inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_10')) = c_2Ebool_2ET,
inference(resolution,[status(thm)],[c_1695,c_103394]) ).
tff(c_20,plain,
! [X_22: tp__o] : ( surj__o(inj__o(X_22)) = X_22 ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_103526,plain,
fo__c_2Einteger_2Eint__divides('#skF_9','#skF_10') = surj__o(c_2Ebool_2ET),
inference(superposition,[status(thm),theory(equality)],[c_103430,c_20]) ).
tff(c_103546,plain,
fo__c_2Einteger_2Eint__divides('#skF_9','#skF_10') = fo__c_2Ebool_2ET,
inference(demodulation,[status(thm),theory(equality)],[c_1744,c_103526]) ).
tff(c_56,plain,
! [X0_38: tp__ty_2Einteger_2Eint] : ( ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X0_38)) = inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X0_38)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_218,plain,
! [V0p_121: tp__ty_2Einteger_2Eint,V1q_122: tp__ty_2Einteger_2Eint] :
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_121)),ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(V1q_122))))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_121)),inj__ty_2Einteger_2Eint(V1q_122))) ),
inference(cnfTransformation,[status(thm)],[f_394]) ).
tff(c_1703,plain,
! [V0p_121: tp__ty_2Einteger_2Eint,V1q_122: tp__ty_2Einteger_2Eint] :
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_121)),ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(V1q_122))))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_121,V1q_122))) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_218]) ).
tff(c_1708,plain,
! [V0p_121: tp__ty_2Einteger_2Eint,V1q_122: tp__ty_2Einteger_2Eint] :
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_121)),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(V1q_122))))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_121,V1q_122))) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_1703]) ).
tff(c_1712,plain,
! [V0p_121: tp__ty_2Einteger_2Eint,V1q_122: tp__ty_2Einteger_2Eint] :
( p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_121,fo__c_2Einteger_2Eint__neg(V1q_122))))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_121,V1q_122))) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1708]) ).
tff(c_66,plain,
~ p(c_2Ebool_2EF),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_64,plain,
inj__o(fo__c_2Ebool_2EF) = c_2Ebool_2EF,
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_1741,plain,
surj__o(c_2Ebool_2EF) = fo__c_2Ebool_2EF,
inference(superposition,[status(thm),theory(equality)],[c_64,c_1732]) ).
tff(c_62,plain,
mem(c_2Ebool_2EF,bool),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_102854,plain,
! [Q_6644,R_6645] :
( p(Q_6644)
| p(R_6645)
| ( R_6645 = Q_6644 )
| ~ mem(R_6645,bool)
| ~ mem(Q_6644,bool) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_102870,plain,
! [Q_6644] :
( p(Q_6644)
| p(c_2Ebool_2EF)
| ( c_2Ebool_2EF = Q_6644 )
| ~ mem(Q_6644,bool) ),
inference(resolution,[status(thm)],[c_62,c_102854]) ).
tff(c_102888,plain,
! [Q_6646] :
( p(Q_6646)
| ( c_2Ebool_2EF = Q_6646 )
| ~ mem(Q_6646,bool) ),
inference(negUnitSimplification,[status(thm)],[c_66,c_102870]) ).
tff(c_103009,plain,
! [X_6649: tp__o] :
( p(inj__o(X_6649))
| ( inj__o(X_6649) = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_22,c_102888]) ).
tff(c_2806,plain,
! [R_199,Q_200] :
( ~ p(R_199)
| ~ p(Q_200)
| ( R_199 = Q_200 )
| ~ mem(R_199,bool)
| ~ mem(Q_200,bool) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_2820,plain,
! [Q_200] :
( ~ p(c_2Ebool_2ET)
| ~ p(Q_200)
| ( c_2Ebool_2ET = Q_200 )
| ~ mem(Q_200,bool) ),
inference(resolution,[status(thm)],[c_26,c_2806]) ).
tff(c_2837,plain,
! [Q_201] :
( ~ p(Q_201)
| ( c_2Ebool_2ET = Q_201 )
| ~ mem(Q_201,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_2820]) ).
tff(c_2931,plain,
! [X_204: tp__o] :
( ~ p(inj__o(X_204))
| ( inj__o(X_204) = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_22,c_2837]) ).
tff(c_2968,plain,
inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_10')) = c_2Ebool_2ET,
inference(resolution,[status(thm)],[c_1695,c_2931]) ).
tff(c_3036,plain,
fo__c_2Einteger_2Eint__divides('#skF_9','#skF_10') = surj__o(c_2Ebool_2ET),
inference(superposition,[status(thm),theory(equality)],[c_2968,c_20]) ).
tff(c_3057,plain,
fo__c_2Einteger_2Eint__divides('#skF_9','#skF_10') = fo__c_2Ebool_2ET,
inference(demodulation,[status(thm),theory(equality)],[c_1744,c_3036]) ).
tff(c_48,plain,
! [X0_34: tp__ty_2Einteger_2Eint,X1_35: tp__ty_2Einteger_2Eint] : ( ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint(X0_34)),inj__ty_2Einteger_2Eint(X1_35)) = inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__sub(X0_34,X1_35)) ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_1694,plain,
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint('#skF_9')),ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint('#skF_11')),inj__ty_2Einteger_2Eint('#skF_10'))))
| p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint('#skF_9')),inj__ty_2Einteger_2Eint('#skF_11'))) ),
inference(cnfTransformation,[status(thm)],[f_568]) ).
tff(c_1702,plain,
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint('#skF_9')),ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint('#skF_11')),inj__ty_2Einteger_2Eint('#skF_10'))))
| p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1694]) ).
tff(c_1719,plain,
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint('#skF_9')),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__sub('#skF_11','#skF_10'))))
| p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_1702]) ).
tff(c_1722,plain,
( p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__sub('#skF_11','#skF_10'))))
| p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1719]) ).
tff(c_1787,plain,
p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11'))),
inference(splitLeft,[status(thm)],[c_1722]) ).
tff(c_2967,plain,
inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11')) = c_2Ebool_2ET,
inference(resolution,[status(thm)],[c_1787,c_2931]) ).
tff(c_3130,plain,
fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11') = surj__o(c_2Ebool_2ET),
inference(superposition,[status(thm),theory(equality)],[c_2967,c_20]) ).
tff(c_3151,plain,
fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11') = fo__c_2Ebool_2ET,
inference(demodulation,[status(thm),theory(equality)],[c_1744,c_3130]) ).
tff(c_3807,plain,
! [Q_213,R_214] :
( p(Q_213)
| p(R_214)
| ( R_214 = Q_213 )
| ~ mem(R_214,bool)
| ~ mem(Q_213,bool) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_3817,plain,
! [Q_213] :
( p(Q_213)
| p(c_2Ebool_2EF)
| ( c_2Ebool_2EF = Q_213 )
| ~ mem(Q_213,bool) ),
inference(resolution,[status(thm)],[c_62,c_3807]) ).
tff(c_3977,plain,
! [Q_218] :
( p(Q_218)
| ( c_2Ebool_2EF = Q_218 )
| ~ mem(Q_218,bool) ),
inference(negUnitSimplification,[status(thm)],[c_66,c_3817]) ).
tff(c_4066,plain,
! [X_219: tp__o] :
( p(inj__o(X_219))
| ( inj__o(X_219) = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_22,c_3977]) ).
tff(c_100,plain,
! [X0_56: tp__o] : ( ap(c_2Ebool_2E_7E,inj__o(X0_56)) = inj__o(fo__c_2Ebool_2E_7E(X0_56)) ),
inference(cnfTransformation,[status(thm)],[f_187]) ).
tff(c_1945,plain,
! [Q_164] :
( p(ap(c_2Ebool_2E_7E,Q_164))
| p(Q_164)
| ~ mem(Q_164,bool) ),
inference(cnfTransformation,[status(thm)],[f_194]) ).
tff(c_1954,plain,
! [X0_56: tp__o] :
( p(inj__o(fo__c_2Ebool_2E_7E(X0_56)))
| p(inj__o(X0_56))
| ~ mem(inj__o(X0_56),bool) ),
inference(superposition,[status(thm),theory(equality)],[c_100,c_1945]) ).
tff(c_1960,plain,
! [X0_56: tp__o] :
( p(inj__o(fo__c_2Ebool_2E_7E(X0_56)))
| p(inj__o(X0_56)) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1954]) ).
tff(c_3217,plain,
! [X0_207: tp__o] :
( ( inj__o(fo__c_2Ebool_2E_7E(X0_207)) = c_2Ebool_2ET )
| p(inj__o(X0_207)) ),
inference(resolution,[status(thm)],[c_1960,c_2931]) ).
tff(c_2871,plain,
! [X_23: tp__o] :
( ~ p(inj__o(X_23))
| ( inj__o(X_23) = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_22,c_2837]) ).
tff(c_3263,plain,
! [X0_208: tp__o] :
( ( inj__o(X0_208) = c_2Ebool_2ET )
| ( inj__o(fo__c_2Ebool_2E_7E(X0_208)) = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_3217,c_2871]) ).
tff(c_3343,plain,
! [X0_208: tp__o] :
( ( surj__o(c_2Ebool_2ET) = fo__c_2Ebool_2E_7E(X0_208) )
| ( inj__o(X0_208) = c_2Ebool_2ET ) ),
inference(superposition,[status(thm),theory(equality)],[c_3263,c_20]) ).
tff(c_3389,plain,
! [X0_209: tp__o] :
( ( fo__c_2Ebool_2E_7E(X0_209) = fo__c_2Ebool_2ET )
| ( inj__o(X0_209) = c_2Ebool_2ET ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1744,c_3343]) ).
tff(c_3490,plain,
! [X0_209: tp__o] :
( ( surj__o(c_2Ebool_2ET) = X0_209 )
| ( fo__c_2Ebool_2E_7E(X0_209) = fo__c_2Ebool_2ET ) ),
inference(superposition,[status(thm),theory(equality)],[c_3389,c_20]) ).
tff(c_3561,plain,
! [X0_210: tp__o] :
( ( fo__c_2Ebool_2ET = X0_210 )
| ( fo__c_2Ebool_2E_7E(X0_210) = fo__c_2Ebool_2ET ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1744,c_3490]) ).
tff(c_1920,plain,
! [Q_159] :
( ~ p(Q_159)
| ~ p(ap(c_2Ebool_2E_7E,Q_159))
| ~ mem(Q_159,bool) ),
inference(cnfTransformation,[status(thm)],[f_194]) ).
tff(c_1923,plain,
! [X0_56: tp__o] :
( ~ p(inj__o(X0_56))
| ~ p(inj__o(fo__c_2Ebool_2E_7E(X0_56)))
| ~ mem(inj__o(X0_56),bool) ),
inference(superposition,[status(thm),theory(equality)],[c_100,c_1920]) ).
tff(c_1925,plain,
! [X0_56: tp__o] :
( ~ p(inj__o(X0_56))
| ~ p(inj__o(fo__c_2Ebool_2E_7E(X0_56))) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1923]) ).
tff(c_3585,plain,
! [X0_210: tp__o] :
( ~ p(inj__o(X0_210))
| ~ p(inj__o(fo__c_2Ebool_2ET))
| ( fo__c_2Ebool_2ET = X0_210 ) ),
inference(superposition,[status(thm),theory(equality)],[c_3561,c_1925]) ).
tff(c_3605,plain,
! [X0_210: tp__o] :
( ~ p(inj__o(X0_210))
| ( fo__c_2Ebool_2ET = X0_210 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_28,c_3585]) ).
tff(c_4170,plain,
! [X_224: tp__o] :
( ( fo__c_2Ebool_2ET = X_224 )
| ( inj__o(X_224) = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_4066,c_3605]) ).
tff(c_4286,plain,
! [X_224: tp__o] :
( ( surj__o(c_2Ebool_2EF) = X_224 )
| ( fo__c_2Ebool_2ET = X_224 ) ),
inference(superposition,[status(thm),theory(equality)],[c_4170,c_20]) ).
tff(c_4356,plain,
! [X_225: tp__o] :
( ( fo__c_2Ebool_2EF = X_225 )
| ( fo__c_2Ebool_2ET = X_225 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1741,c_4286]) ).
tff(c_1688,plain,
( ~ p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint('#skF_9')),inj__ty_2Einteger_2Eint('#skF_11')))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint('#skF_9')),ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint('#skF_11')),inj__ty_2Einteger_2Eint('#skF_10')))) ),
inference(cnfTransformation,[status(thm)],[f_568]) ).
tff(c_1696,plain,
( ~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11')))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint('#skF_9')),ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint('#skF_11')),inj__ty_2Einteger_2Eint('#skF_10')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1688]) ).
tff(c_1718,plain,
( ~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11')))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint('#skF_9')),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__sub('#skF_11','#skF_10')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_1696]) ).
tff(c_1721,plain,
( ~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11')))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__sub('#skF_11','#skF_10')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1718]) ).
tff(c_1854,plain,
~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__sub('#skF_11','#skF_10')))),
inference(demodulation,[status(thm),theory(equality)],[c_1787,c_1721]) ).
tff(c_4441,plain,
( ~ p(inj__o(fo__c_2Ebool_2ET))
| ( fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__sub('#skF_11','#skF_10')) = fo__c_2Ebool_2EF ) ),
inference(superposition,[status(thm),theory(equality)],[c_4356,c_1854]) ).
tff(c_4481,plain,
fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__sub('#skF_11','#skF_10')) = fo__c_2Ebool_2EF,
inference(demodulation,[status(thm),theory(equality)],[c_30,c_28,c_4441]) ).
tff(c_40,plain,
! [X_31: tp__ty_2Einteger_2Eint] : ( surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(X_31)) = X_31 ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_52,plain,
! [X0_36: tp__ty_2Einteger_2Eint,X1_37: tp__ty_2Einteger_2Eint] : ( ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(X0_36)),inj__ty_2Einteger_2Eint(X1_37)) = inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__add(X0_36,X1_37)) ),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_210,plain,
! [V0x_116: tp__ty_2Einteger_2Eint,V1y_117: tp__ty_2Einteger_2Eint] : ( surj__ty_2Einteger_2Eint(ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(V0x_116)),ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(V1y_117)))) = surj__ty_2Einteger_2Eint(ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint(V0x_116)),inj__ty_2Einteger_2Eint(V1y_117))) ),
inference(cnfTransformation,[status(thm)],[f_380]) ).
tff(c_1706,plain,
! [V0x_116: tp__ty_2Einteger_2Eint,V1y_117: tp__ty_2Einteger_2Eint] : ( surj__ty_2Einteger_2Eint(ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(V0x_116)),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(V1y_117)))) = surj__ty_2Einteger_2Eint(ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint(V0x_116)),inj__ty_2Einteger_2Eint(V1y_117))) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_210]) ).
tff(c_1715,plain,
! [V0x_116: tp__ty_2Einteger_2Eint,V1y_117: tp__ty_2Einteger_2Eint] : ( surj__ty_2Einteger_2Eint(ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint(V0x_116)),inj__ty_2Einteger_2Eint(V1y_117))) = surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__add(V0x_116,fo__c_2Einteger_2Eint__neg(V1y_117)))) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_1706]) ).
tff(c_1720,plain,
! [V0x_116: tp__ty_2Einteger_2Eint,V1y_117: tp__ty_2Einteger_2Eint] : ( surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__add(V0x_116,fo__c_2Einteger_2Eint__neg(V1y_117)))) = surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__sub(V0x_116,V1y_117))) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_1715]) ).
tff(c_1723,plain,
! [V0x_116: tp__ty_2Einteger_2Eint,V1y_117: tp__ty_2Einteger_2Eint] : ( fo__c_2Einteger_2Eint__add(V0x_116,fo__c_2Einteger_2Eint__neg(V1y_117)) = fo__c_2Einteger_2Eint__sub(V0x_116,V1y_117) ),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_40,c_1720]) ).
tff(c_212,plain,
! [V0p_118: tp__ty_2Einteger_2Eint,V2r_120: tp__ty_2Einteger_2Eint,V1q_119: tp__ty_2Einteger_2Eint] :
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_118)),ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(V2r_120)),inj__ty_2Einteger_2Eint(V1q_119))))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_118)),inj__ty_2Einteger_2Eint(V2r_120)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_118)),inj__ty_2Einteger_2Eint(V1q_119))) ),
inference(cnfTransformation,[status(thm)],[f_386]) ).
tff(c_1700,plain,
! [V0p_118: tp__ty_2Einteger_2Eint,V2r_120: tp__ty_2Einteger_2Eint,V1q_119: tp__ty_2Einteger_2Eint] :
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_118)),ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(V2r_120)),inj__ty_2Einteger_2Eint(V1q_119))))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_118,V2r_120)))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_118,V1q_119))) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_60,c_212]) ).
tff(c_1714,plain,
! [V0p_118: tp__ty_2Einteger_2Eint,V2r_120: tp__ty_2Einteger_2Eint,V1q_119: tp__ty_2Einteger_2Eint] :
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_118)),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__add(V2r_120,V1q_119))))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_118,V2r_120)))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_118,V1q_119))) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_1700]) ).
tff(c_8235,plain,
! [V0p_2021: tp__ty_2Einteger_2Eint,V2r_2022: tp__ty_2Einteger_2Eint,V1q_2023: tp__ty_2Einteger_2Eint] :
( p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_2021,fo__c_2Einteger_2Eint__add(V2r_2022,V1q_2023))))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_2021,V2r_2022)))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_2021,V1q_2023))) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1714]) ).
tff(c_101556,plain,
! [V0p_6567: tp__ty_2Einteger_2Eint,V0x_6568: tp__ty_2Einteger_2Eint,V1y_6569: tp__ty_2Einteger_2Eint] :
( p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_6567,fo__c_2Einteger_2Eint__sub(V0x_6568,V1y_6569))))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_6567,V0x_6568)))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_6567,fo__c_2Einteger_2Eint__neg(V1y_6569)))) ),
inference(superposition,[status(thm),theory(equality)],[c_1723,c_8235]) ).
tff(c_101625,plain,
( p(inj__o(fo__c_2Ebool_2EF))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11')))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__neg('#skF_10')))) ),
inference(superposition,[status(thm),theory(equality)],[c_4481,c_101556]) ).
tff(c_101663,plain,
( p(c_2Ebool_2EF)
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__neg('#skF_10')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_28,c_3151,c_64,c_101625]) ).
tff(c_101664,plain,
~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__neg('#skF_10')))),
inference(negUnitSimplification,[status(thm)],[c_66,c_101663]) ).
tff(c_101770,plain,
~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_10'))),
inference(resolution,[status(thm)],[c_1712,c_101664]) ).
tff(c_101809,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_30,c_28,c_3057,c_101770]) ).
tff(c_101811,plain,
~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11'))),
inference(splitRight,[status(thm)],[c_1722]) ).
tff(c_103043,plain,
inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11')) = c_2Ebool_2EF,
inference(resolution,[status(thm)],[c_103009,c_101811]) ).
tff(c_103107,plain,
fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11') = surj__o(c_2Ebool_2EF),
inference(superposition,[status(thm),theory(equality)],[c_103043,c_20]) ).
tff(c_103128,plain,
fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11') = fo__c_2Ebool_2EF,
inference(demodulation,[status(thm),theory(equality)],[c_1741,c_103107]) ).
tff(c_102924,plain,
! [X_23: tp__o] :
( p(inj__o(X_23))
| ( inj__o(X_23) = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_22,c_102888]) ).
tff(c_103680,plain,
! [X_6659: tp__o] :
( ( inj__o(X_6659) = c_2Ebool_2ET )
| ( inj__o(X_6659) = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_102924,c_103394]) ).
tff(c_103772,plain,
! [X_6659: tp__o] :
( ( surj__o(c_2Ebool_2ET) = X_6659 )
| ( inj__o(X_6659) = c_2Ebool_2EF ) ),
inference(superposition,[status(thm),theory(equality)],[c_103680,c_20]) ).
tff(c_103894,plain,
! [X_6662: tp__o] :
( ( fo__c_2Ebool_2ET = X_6662 )
| ( inj__o(X_6662) = c_2Ebool_2EF ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1744,c_103772]) ).
tff(c_101810,plain,
p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__sub('#skF_11','#skF_10')))),
inference(splitRight,[status(thm)],[c_1722]) ).
tff(c_103984,plain,
( p(c_2Ebool_2EF)
| ( fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__sub('#skF_11','#skF_10')) = fo__c_2Ebool_2ET ) ),
inference(superposition,[status(thm),theory(equality)],[c_103894,c_101810]) ).
tff(c_104044,plain,
fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__sub('#skF_11','#skF_10')) = fo__c_2Ebool_2ET,
inference(negUnitSimplification,[status(thm)],[c_66,c_103984]) ).
tff(c_214,plain,
! [V0p_118: tp__ty_2Einteger_2Eint,V2r_120: tp__ty_2Einteger_2Eint,V1q_119: tp__ty_2Einteger_2Eint] :
( p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_118)),inj__ty_2Einteger_2Eint(V2r_120)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_118)),ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(V2r_120)),inj__ty_2Einteger_2Eint(V1q_119))))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_118)),inj__ty_2Einteger_2Eint(V1q_119))) ),
inference(cnfTransformation,[status(thm)],[f_386]) ).
tff(c_1699,plain,
! [V0p_118: tp__ty_2Einteger_2Eint,V2r_120: tp__ty_2Einteger_2Eint,V1q_119: tp__ty_2Einteger_2Eint] :
( p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_118,V2r_120)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_118)),ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(V2r_120)),inj__ty_2Einteger_2Eint(V1q_119))))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_118,V1q_119))) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_60,c_214]) ).
tff(c_1713,plain,
! [V0p_118: tp__ty_2Einteger_2Eint,V2r_120: tp__ty_2Einteger_2Eint,V1q_119: tp__ty_2Einteger_2Eint] :
( p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_118,V2r_120)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p_118)),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__add(V2r_120,V1q_119))))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_118,V1q_119))) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_1699]) ).
tff(c_109443,plain,
! [V0p_8548: tp__ty_2Einteger_2Eint,V2r_8549: tp__ty_2Einteger_2Eint,V1q_8550: tp__ty_2Einteger_2Eint] :
( p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_8548,V2r_8549)))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_8548,fo__c_2Einteger_2Eint__add(V2r_8549,V1q_8550))))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_8548,V1q_8550))) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1713]) ).
tff(c_292129,plain,
! [V0p_13854: tp__ty_2Einteger_2Eint,V0x_13855: tp__ty_2Einteger_2Eint,V1y_13856: tp__ty_2Einteger_2Eint] :
( p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_13854,V0x_13855)))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_13854,fo__c_2Einteger_2Eint__sub(V0x_13855,V1y_13856))))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides(V0p_13854,fo__c_2Einteger_2Eint__neg(V1y_13856)))) ),
inference(superposition,[status(thm),theory(equality)],[c_1723,c_109443]) ).
tff(c_292229,plain,
( p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_11')))
| ~ p(inj__o(fo__c_2Ebool_2ET))
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__neg('#skF_10')))) ),
inference(superposition,[status(thm),theory(equality)],[c_104044,c_292129]) ).
tff(c_292280,plain,
( p(c_2Ebool_2EF)
| ~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__neg('#skF_10')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_28,c_64,c_103128,c_292229]) ).
tff(c_292281,plain,
~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9',fo__c_2Einteger_2Eint__neg('#skF_10')))),
inference(negUnitSimplification,[status(thm)],[c_66,c_292280]) ).
tff(c_292395,plain,
~ p(inj__o(fo__c_2Einteger_2Eint__divides('#skF_9','#skF_10'))),
inference(resolution,[status(thm)],[c_1712,c_292281]) ).
tff(c_292436,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_30,c_28,c_103546,c_292395]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP012_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34 % Computer : n029.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 : Thu Aug 3 19:11:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 42.39/25.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.39/25.69
% 42.39/25.69 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 42.59/25.73
% 42.59/25.73 Inference rules
% 42.59/25.73 ----------------------
% 42.59/25.73 #Ref : 2
% 42.59/25.73 #Sup : 67797
% 42.59/25.73 #Fact : 16
% 42.59/25.73 #Define : 0
% 42.59/25.73 #Split : 16
% 42.59/25.73 #Chain : 0
% 42.59/25.73 #Close : 0
% 42.59/25.73
% 42.59/25.73 Ordering : KBO
% 42.59/25.73
% 42.59/25.73 Simplification rules
% 42.59/25.73 ----------------------
% 42.59/25.73 #Subsume : 17419
% 42.59/25.73 #Demod : 53352
% 42.59/25.73 #Tautology : 33570
% 42.59/25.73 #SimpNegUnit : 19790
% 42.59/25.73 #BackRed : 295
% 42.59/25.73
% 42.59/25.73 #Partial instantiations: 1199
% 42.59/25.73 #Strategies tried : 1
% 42.59/25.73
% 42.59/25.73 Timing (in seconds)
% 42.59/25.73 ----------------------
% 42.59/25.73 Preprocessing : 0.96
% 42.59/25.73 Parsing : 0.30
% 42.59/25.73 CNF conversion : 0.09
% 42.59/25.73 Main loop : 23.54
% 42.59/25.73 Inferencing : 3.36
% 42.59/25.73 Reduction : 9.43
% 42.59/25.73 Demodulation : 7.67
% 42.59/25.73 BG Simplification : 0.38
% 42.59/25.73 Subsumption : 9.43
% 42.59/25.73 Abstraction : 0.43
% 42.59/25.73 MUC search : 0.00
% 42.59/25.73 Cooper : 0.00
% 42.59/25.73 Total : 24.58
% 42.59/25.73 Index Insertion : 0.00
% 42.59/25.73 Index Deletion : 0.00
% 42.59/25.73 Index Matching : 0.00
% 42.59/25.73 BG Taut test : 0.00
%------------------------------------------------------------------------------