%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT271-1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:14:06 AM UTC 2025
% Result : Unsatisfiable 0.72s 0.90s
% Output : Proof 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 113 ( 54 ~; 50 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 102 ( 90 !; 0 ?; 102 :)
% 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(v_r_type,type,
v_r: $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(v_S_type,type,
v_S: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(c_Tarski_Ointerval_type,type,
c_Tarski_Ointerval: ( $i * $i * $i * $i ) > $i ).
tff(v_b_type,type,
v_b: $i ).
tff(1,plain,
( ~ c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> ~ c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).
tff(3,plain,
~ c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_in(v_x,v_S,t_a)
<=> c_in(v_x,v_S,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_in(v_x,v_S,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(6,plain,
c_in(v_x,v_S,t_a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
<=> c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(9,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
<=> ( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
<=> ! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
<=> ! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
rewrite(( ( ~ c_in(V_x,V_S,T_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_in(V_x,V_S,T_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
<=> ! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_in(V_x,V_S,T_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT006-2.ax',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0) ).
tff(16,plain,
! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_x,v_S,t_a) )
<=> ( ~ ! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_x,v_S,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_x,v_S,t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_x: $i,V_r: $i,V_S: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) )
| c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_x,v_S,t_a) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : LAT271-1 : TPTP v9.0.0. Released v3.2.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.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 : Thu Jun 19 19:58:12 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.72/0.90 % SZS status Unsatisfiable
% 0.72/0.90 % SZS output start Proof
% See solution above
% 0.82/0.98 % E exiting
%------------------------------------------------------------------------------