TSTP Solution File: LAT281-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT281-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 Sep 17 18:32:39 EDT 2022
% Result : Unsatisfiable 0.97s 0.95s
% Output : Proof 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 36
% Syntax : Number of formulae : 57 ( 16 unt; 14 typ; 0 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 251 ( 120 ~; 111 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 6 >; 10 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 111 ( 99 !; 0 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Relation_Otrans_type,type,
c_Relation_Otrans: ( $i * $i ) > $o ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Tarski_Opotype_Oorder_type,type,
c_Tarski_Opotype_Oorder: ( $i * $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(v_cl_type,type,
v_cl: $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Tarski_Opotype_Opotype__ext__type_type,type,
tc_Tarski_Opotype_Opotype__ext__type: ( $i * $i ) > $i ).
tff(c_Tarski_OPartialOrder_type,type,
c_Tarski_OPartialOrder: $i ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_c_type,type,
v_c: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(v_r_type,type,
v_r: $i ).
tff(v_b_type,type,
v_b: $i ).
tff(1,plain,
( c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
<=> c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
tff(3,plain,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T_a: $i,V_P: $i] :
refl(
( ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
<=> ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
<=> ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
<=> ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_2) ).
tff(8,plain,
! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
| ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
<=> ( ~ ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
| ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
| ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [T_a: $i,V_P: $i] :
( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
| ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ~ c_in(c_Pair(v_a,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> ~ c_in(c_Pair(v_a,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ~ c_in(c_Pair(v_a,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> ~ 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(17,axiom,
~ c_in(c_Pair(v_a,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(18,plain,
~ 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)],[17,16]) ).
tff(19,plain,
~ c_in(c_Pair(v_a,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
( c_in(c_Pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> c_in(c_Pair(v_b,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( c_in(c_Pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> c_in(c_Pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
c_in(c_Pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(23,plain,
c_in(c_Pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
c_in(c_Pair(v_b,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
( c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> c_in(c_Pair(v_a,v_b,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(28,plain,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
c_in(c_Pair(v_a,v_b,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
^ [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
refl(
( ( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) )
<=> ( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) )
<=> ! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) )
<=> ! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
^ [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( ~ c_Relation_Otrans(V_r,T_a)
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) ) )),
( ( ~ c_Relation_Otrans(V_r,T_a)
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ( ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a)
| c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) )),
rewrite(
( ( ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a)
| c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) ) )),
( ( ~ c_Relation_Otrans(V_r,T_a)
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( ~ c_Relation_Otrans(V_r,T_a)
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( ~ c_Relation_Otrans(V_r,T_a)
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Otrans__def_0) ).
tff(36,plain,
! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) )
| c_in(c_Pair(v_a,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_a,v_b,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_b,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
<=> ( ~ ! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) )
| c_in(c_Pair(v_a,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_a,v_b,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_b,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ~ ! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) )
| c_in(c_Pair(v_a,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_a,v_b,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_b,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [V_W: $i,V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
( c_in(c_Pair(V_U,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_W,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Otrans(V_r,T_a) )
| c_in(c_Pair(v_a,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_a,v_b,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_b,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
$false,
inference(unit_resolution,[status(thm)],[42,39,29,24,19,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT281-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 12:52:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.97/0.95 % SZS status Unsatisfiable
% 0.97/0.95 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------