%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT277-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:14:08 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 50 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 146 ( 10 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 173 ( 80 ~; 73 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 94 ( 84 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
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_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_r_type,type,
v_r: $i ).
tff(c_Tarski_Opotype_Opset_type,type,
c_Tarski_Opotype_Opset: ( $i * $i * $i ) > $i ).
tff(v_A_type,type,
v_A: $i ).
tff(c_Relation_Orefl_type,type,
c_Relation_Orefl: ( $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(1,plain,
( ( v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) )
<=> ( v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
tff(3,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( c_in(c_Pair(v_x,v_x,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_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> c_in(c_Pair(v_x,v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ~ c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> ~ c_in(c_Pair(v_x,v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ~ c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> ~ c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
~ c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(10,plain,
~ c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
~ c_in(c_Pair(v_x,v_x,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)],[10,7]) ).
tff(12,plain,
( ( v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) )
<=> ( v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
tff(14,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( c_in(v_x,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
<=> c_in(v_x,v_A,t_a) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( c_in(v_x,v_A,t_a)
<=> c_in(v_x,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( c_in(v_x,v_A,t_a)
<=> c_in(v_x,v_A,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
c_in(v_x,v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(20,plain,
c_in(v_x,v_A,t_a),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
c_in(v_x,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,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(23,axiom,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
tff(24,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)],[23,22]) ).
tff(25,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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(26,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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_0) ).
tff(29,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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),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_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),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_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),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_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),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_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(unit_resolution,[status(thm)],[34,31,24]) ).
tff(36,plain,
^ [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
refl(( ( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) )
<=> ( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) )
<=> ! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) )
<=> ! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
rewrite(( ( ~ c_Relation_Orefl(V_A,V_r,T_a)
| ~ c_in(V_a,V_A,T_a)
| c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_Relation_Orefl(V_A,V_r,T_a)
| ~ c_in(V_a,V_A,T_a)
| c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_Relation_Orefl(V_A,V_r,T_a)
| ~ c_in(V_a,V_A,T_a)
| c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OreflD_0) ).
tff(42,plain,
! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) )
| c_in(c_Pair(v_x,v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(v_x,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| ~ c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
<=> ( ~ ! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) )
| c_in(c_Pair(v_x,v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(v_x,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| ~ c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) )
| c_in(c_Pair(v_x,v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(v_x,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| ~ c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_r: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) )
| c_in(c_Pair(v_x,v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(v_x,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| ~ c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( c_in(c_Pair(v_x,v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(v_x,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,21,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT277-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.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 : Thu Jun 19 19:58:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------