%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SCT075-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:24:26 AM UTC 2025
% Result : Unsatisfiable 0.78s 0.96s
% Output : Proof 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 24
% Syntax : Number of formulae : 56 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 217 ( 58 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 249 ( 94 ~; 129 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 89 ( 79 !; 0 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1_type,type,
v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: ( $i * $i ) > $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(v_b_____type,type,
v_b____: $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_thesis_____type,type,
v_thesis____: $o ).
tff(1,plain,
( ( v_b____ = v_a____ )
<=> ( v_a____ = v_b____ ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( ( v_a____ = v_b____ )
<=> ( v_b____ = v_a____ ) ),
inference(symmetry,[status(thm)],[1]) ).
tff(3,plain,
( ( v_a____ != v_b____ )
<=> ( v_b____ != v_a____ ) ),
inference(monotonicity,[status(thm)],[2]) ).
tff(4,plain,
( ( v_a____ != v_b____ )
<=> ( v_a____ != v_b____ ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(6,plain,
v_a____ != v_b____,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
v_b____ != v_a____,
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
^ [V_b: $i,V_a: $i] :
refl(( ( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
^ [V_b: $i,V_a: $i] :
rewrite(( ( c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( V_a = V_b ) )
<=> ( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [V_b: $i,V_a: $i] :
( c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( V_a = V_b ) )
<=> ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [V_b: $i,V_a: $i] :
( c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
tff(14,plain,
! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
( ( ~ ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_b____ = v_a____ )
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ~ ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_b____ = v_a____ )
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_b____ = v_a____ )
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ( v_b____ = v_a____ )
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( v_b____ = v_a____ )
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(unit_resolution,[status(thm)],[20,17]) ).
tff(22,plain,
c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(unit_resolution,[status(thm)],[21,7]) ).
tff(23,plain,
( ~ v_thesis____
<=> ~ v_thesis____ ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(25,plain,
~ v_thesis____,
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
^ [V_Lba: $i] :
refl(( ( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
^ [V_Lba: $i] :
rewrite(( ( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
tff(32,plain,
! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
( ( ~ ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| v_thesis____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ~ ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| v_thesis____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ( v_thesis____
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( v_thesis____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( ~ ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| v_thesis____
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ~ ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| v_thesis____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| v_thesis____
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
<=> ( ~ ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| v_thesis____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
( ~ ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| v_thesis____
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [V_Lba: $i] :
( v_thesis____
| ~ c_in(V_Lba,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_Lba,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| v_thesis____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(unit_resolution,[status(thm)],[41,35,25,22]) ).
tff(43,plain,
^ [V_b: $i,V_a: $i] :
refl(( ( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
^ [V_b: $i,V_a: $i] :
rewrite(( ( c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ( V_a = V_b ) )
<=> ( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [V_b: $i,V_a: $i] :
( c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ( V_a = V_b ) )
<=> ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [V_b: $i,V_a: $i] :
( c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_0) ).
tff(49,plain,
! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ( v_b____ = v_a____ )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
<=> ( ~ ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ( v_b____ = v_a____ )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ( v_b____ = v_a____ )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [V_b: $i,V_a: $i] :
( ( V_a = V_b )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ( v_b____ = v_a____ )
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,52,7,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SCT075-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 03:41:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.78/0.96 % SZS status Unsatisfiable
% 0.78/0.96 % SZS output start Proof
% See solution above
% 0.78/0.99 % E exiting
%------------------------------------------------------------------------------