%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:01 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.41s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 32 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 14 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 65 ( 30 ~; 23 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 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 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 72 ( 66 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_PropLog_Opl_type,type,
tc_PropLog_Opl: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_PropLog_Othms_type,type,
c_PropLog_Othms: ( $i * $i ) > $i ).
tff(c_minus_type,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(c_PropLog_Ohyps_type,type,
c_PropLog_Ohyps: ( $i * $i * $i ) > $i ).
tff(v_p_type,type,
v_p: $i ).
tff(c_emptyset_type,type,
c_emptyset: $i ).
tff(c_PropLog_Osat_type,type,
c_PropLog_Osat: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [T_a: $i,V_A: $i] :
refl(( ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset )
<=> ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T_a: $i,V_A: $i] : ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset )
<=> ! [T_a: $i,V_A: $i] : ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_a: $i,V_A: $i] : ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset )
<=> ! [T_a: $i,V_A: $i] : ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T_a: $i,V_A: $i] : ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
tff(5,plain,
! [T_a: $i,V_A: $i] : ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_a: $i,V_A: $i] : ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_a: $i,V_A: $i] : ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_a: $i,V_A: $i] : ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset )
| ( c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))) = c_emptyset ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))) = c_emptyset,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a) = c_PropLog_Othms(c_emptyset,t_a),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
<=> c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a))
<=> c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a))
<=> ~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a))
<=> ~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(16,plain,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
^ [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
refl(( ( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) )
<=> ( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) )
<=> ! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) )
<=> ! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Ocompleteness__0__lemma__dest_0) ).
tff(22,plain,
! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( c_PropLog_Osat(c_emptyset,v_p,t_a)
<=> c_PropLog_Osat(c_emptyset,v_p,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
c_PropLog_Osat(c_emptyset,v_p,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(27,plain,
c_PropLog_Osat(c_emptyset,v_p,t_a),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ( ~ ! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) )
| ~ c_PropLog_Osat(c_emptyset,v_p,t_a)
| c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) )
<=> ( ~ ! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) )
| ~ c_PropLog_Osat(c_emptyset,v_p,t_a)
| c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) )
| ~ c_PropLog_Osat(c_emptyset,v_p,t_a)
| c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V_U: $i,V_t0: $i,T_a: $i,V_p: $i] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) )
| ~ c_PropLog_Osat(c_emptyset,v_p,t_a)
| c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,t_a,t_a),c_PropLog_Ohyps(v_p,t_a,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(unit_resolution,[status(thm)],[30,27,24]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n028.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 17:25:45 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.41 % SZS status Unsatisfiable
% 0.12/0.41 % SZS output start Proof
% See solution above
% 0.12/0.42 % E exiting
%------------------------------------------------------------------------------