%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL122-1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:00:52 AM UTC 2025
% Result : Unsatisfiable 0.43s 0.58s
% Output : Proof 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 73 ( 42 ~; 23 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 43 ( 39 !; 0 ?; 43 :)
% 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_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(v_r_type,type,
v_r: $i ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_xaa_type,type,
v_xaa: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(1,plain,
^ [V_U: $i] :
refl(( ( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(5,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( c_in(c_Pair(v_x,v_xaa,t_a,t_a),v_r,tc_prod(t_a,t_a))
<=> c_in(c_Pair(v_x,v_xaa,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_xaa,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(10,plain,
c_in(c_Pair(v_x,v_xaa,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_x,v_xaa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
<=> ( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_x,v_xaa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_x,v_xaa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_U: $i] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ c_in(c_Pair(v_x,v_xaa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ c_in(c_Pair(v_xaa,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [V_r: $i,V_a: $i,T_a: $i] :
refl(( c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
<=> c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_r: $i,V_a: $i,T_a: $i] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
<=> ! [V_r: $i,V_a: $i,T_a: $i] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_r: $i,V_a: $i,T_a: $i] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
<=> ! [V_r: $i,V_a: $i,T_a: $i] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [V_r: $i,V_a: $i,T_a: $i] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
tff(19,plain,
! [V_r: $i,V_a: $i,T_a: $i] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_r: $i,V_a: $i,T_a: $i] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [V_r: $i,V_a: $i,T_a: $i] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [V_r: $i,V_a: $i,T_a: $i] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(v_xaa,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,21,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : COL122-1 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 12:17:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.43/0.58 % SZS status Unsatisfiable
% 0.43/0.58 % SZS output start Proof
% See solution above
% 0.45/0.62 % E exiting
%------------------------------------------------------------------------------