%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV892-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Sat Jun 21 05:36:17 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.53s
% Output : Proof 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 33
% Syntax : Number of formulae : 80 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 282 ( 122 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 354 ( 165 ~; 157 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 13 ( 13 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 144 ( 131 !; 0 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: ( $i * $i ) > $i ).
tff(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
tff(c_Option_Othe_type,type,
c_Option_Othe: ( $i * $i ) > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_pn_type,type,
v_pn: $i ).
tff(c_Com_Obody_type,type,
c_Com_Obody: $i ).
tff(c_Com_Osko__Com__XWTs__elim__cases__7__1_type,type,
c_Com_Osko__Com__XWTs__elim__cases__7__1: $i > $i ).
tff(c_Com_OWT_type,type,
c_Com_OWT: $i > $o ).
tff(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i > $i ).
tff(c_Option_Ooption_ONone_type,type,
c_Option_Ooption_ONone: $i > $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_Map_Odom_type,type,
c_Map_Odom: ( $i * $i * $i ) > $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(c_in_type,type,
c_in: $i > $i ).
tff(c_Com_OWT__bodies_type,type,
c_Com_OWT__bodies: $o ).
tff(1,plain,
^ [V_x: $i,T_a: $i] :
refl(( ( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x )
<=> ( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_x: $i,T_a: $i] : ( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x )
<=> ! [V_x: $i,T_a: $i] : ( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_x: $i,T_a: $i] : ( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x )
<=> ! [V_x: $i,T_a: $i] : ( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_x: $i,T_a: $i] : ( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
tff(5,plain,
! [V_x: $i,T_a: $i] : ( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_x: $i,T_a: $i] : ( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_x: $i,T_a: $i] : ( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_x: $i,T_a: $i] : ( c_Option_Othe(c_Option_Ooption_OSome(V_x,T_a),T_a) = V_x )
| ( c_Option_Othe(c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom),tc_Com_Ocom) = c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_Option_Othe(c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom),tc_Com_Ocom) = c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_pn),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom)))
<=> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_pn),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_pn),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(12,plain,
hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_pn),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
refl(( ( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) )
<=> ( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) )
<=> ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) )
<=> ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domIff_0) ).
tff(17,plain,
! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) )
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_pn),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))) )
<=> ( ~ ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) )
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_pn),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) )
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_pn),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Map_Odom(V_m,T_a,T_b))) )
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_pn),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_ONone(tc_Com_Ocom),
inference(unit_resolution,[status(thm)],[22,19,12]) ).
tff(24,plain,
^ [V_pn: $i] :
refl(( ( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
tff(28,plain,
! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| c_Com_OWT(c_Com_Ocom_OBODY(v_pn))
| ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ( ~ ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| c_Com_OWT(c_Com_Ocom_OBODY(v_pn))
| ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| c_Com_OWT(c_Com_Ocom_OBODY(v_pn))
| ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| c_Com_OWT(c_Com_Ocom_OBODY(v_pn))
| ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
c_Com_OWT(c_Com_Ocom_OBODY(v_pn)),
inference(unit_resolution,[status(thm)],[33,30,23]) ).
tff(35,plain,
^ [V_P: $i] :
refl(( ( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) )
<=> ( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) )
<=> ! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) )
<=> ! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
^ [V_P: $i] :
rewrite(( ( ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) )
| ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P)) )
<=> ( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [V_P: $i] :
( ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) )
| ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P)) )
<=> ! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [V_P: $i] :
( ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) )
| ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I7_J_0) ).
tff(41,plain,
! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) )
| ~ c_Com_OWT(c_Com_Ocom_OBODY(v_pn))
| ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom) ) )
<=> ( ~ ! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) )
| ~ c_Com_OWT(c_Com_Ocom_OBODY(v_pn))
| ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) )
| ~ c_Com_OWT(c_Com_Ocom_OBODY(v_pn))
| ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_P: $i] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(V_P))
| ( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom) ) )
| ~ c_Com_OWT(c_Com_Ocom_OBODY(v_pn))
| ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ~ c_Com_OWT(c_Com_Ocom_OBODY(v_pn))
| ( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom) ) ),
inference(unit_resolution,[status(thm)],[47,44]) ).
tff(49,plain,
hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom),
inference(unit_resolution,[status(thm)],[48,34]) ).
tff(50,plain,
c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom) = hAPP(c_Com_Obody,v_pn),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
c_Option_Othe(c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom),tc_Com_Ocom) = c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom) = c_Option_Othe(c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom),tc_Com_Ocom),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom) = c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),
inference(transitivity,[status(thm)],[52,9]) ).
tff(54,plain,
c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(v_pn),tc_Com_Ocom) = c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom),
inference(transitivity,[status(thm)],[49,55]) ).
tff(57,plain,
( ~ c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom))
<=> ~ c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom)) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
~ c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(59,plain,
~ c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom)),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( c_Com_OWT__bodies
<=> c_Com_OWT__bodies ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(62,plain,
c_Com_OWT__bodies,
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
^ [V_pn: $i,V_b: $i] :
refl(( ( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) )
<=> ( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) )
<=> ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) )
<=> ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
^ [V_pn: $i,V_b: $i] :
trans(monotonicity(rewrite(( ( ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) )
| ~ c_Com_OWT__bodies )
<=> ( ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) ) )),
( ( ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) )
| ~ c_Com_OWT__bodies
| c_Com_OWT(V_b) )
<=> ( ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) )
| c_Com_OWT(V_b) ) )),
rewrite(( ( ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) )
| c_Com_OWT(V_b) )
<=> ( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) ) )),
( ( ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) )
| ~ c_Com_OWT__bodies
| c_Com_OWT(V_b) )
<=> ( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [V_pn: $i,V_b: $i] :
( ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) )
| ~ c_Com_OWT__bodies
| c_Com_OWT(V_b) )
<=> ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [V_pn: $i,V_b: $i] :
( ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) )
| ~ c_Com_OWT__bodies
| c_Com_OWT(V_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__bodiesD_0) ).
tff(69,plain,
! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( ( ~ ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) )
| ~ c_Com_OWT__bodies
| c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom))
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom) ) )
<=> ( ~ ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) )
| ~ c_Com_OWT__bodies
| c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom))
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom))
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom) ) )
<=> ( ~ c_Com_OWT__bodies
| c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom))
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ( ~ ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) )
| c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom))
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom) ) )
<=> ( ~ ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) )
| ~ c_Com_OWT__bodies
| c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom))
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom) ) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) )
| c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom))
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom) ) )
<=> ( ~ ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) )
| ~ c_Com_OWT__bodies
| c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom))
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom) ) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) )
| c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom))
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [V_pn: $i,V_b: $i] :
( c_Com_OWT(V_b)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) ) )
| ~ c_Com_OWT__bodies
| c_Com_OWT(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom))
| ( hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_OSome(c_Option_Othe(hAPP(c_Com_Obody,v_pn),tc_Com_Ocom),tc_Com_Ocom),
inference(unit_resolution,[status(thm)],[78,72,62,59]) ).
tff(80,plain,
$false,
inference(unit_resolution,[status(thm)],[79,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV892-1 : TPTP v9.0.0. Released v4.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 11:02:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.53 % SZS status Unsatisfiable
% 0.19/0.53 % SZS output start Proof
% See solution above
% 0.38/0.57 % E exiting
%------------------------------------------------------------------------------