%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SCT002-1 : 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 05:24:21 AM UTC 2025
% Result : Unsatisfiable 0.44s 0.59s
% Output : Proof 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 32 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 146 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 207 ( 102 ~; 90 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 95 ( 84 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $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(v_L_type,type,
v_L: $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_y_type,type,
v_y: $i ).
tff(c_Relation_Otrans_type,type,
c_Relation_Otrans: ( $i * $i ) > $o ).
tff(1,plain,
( hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
<=> hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(3,plain,
hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
<=> hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(6,plain,
hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
<=> c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(9,plain,
c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
<=> ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
<=> ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
<=> ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
<=> ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) )),
( ( hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a) )
<=> ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a) ) )),
rewrite(( ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a) )
<=> ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) )),
( ( hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a) )
<=> ( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a) )
<=> ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).
tff(16,plain,
! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
| ~ hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
<=> ( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
| ~ hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
| ~ hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_c: $i,V_r: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ hBOOL(c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ hBOOL(c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)))
| ~ c_Relation_Otrans(V_r,T_a)
| hBOOL(c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))) )
| ~ hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).
tff(24,plain,
^ [V_x: $i] :
refl(( ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
<=> ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
<=> ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
<=> ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(28,plain,
! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [V_x: $i] : ~ hBOOL(c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,30,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT002-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 03:32:46 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.44/0.59 % SZS status Unsatisfiable
% 0.44/0.59 % SZS output start Proof
% See solution above
% 0.44/0.62 % E exiting
%------------------------------------------------------------------------------