%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 : Fri Sep 25 02:01:59 PM UTC 2026
% Result : Unsatisfiable 3.92s 1.38s
% Output : Proof 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 22 unt; 0 def)
% Number of atoms : 30 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 36 ( 14 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
( 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Ocompleteness__0__lemma__dest_0) ).
fof(f2_nnf,plain,
! [V_p,T_a,V_U,V_t0] :
( 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) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_p,T_a,V_U,V_t0] :
( 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) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X0,X2,X1),c_PropLog_Ohyps(X0,X3,X1),tc_set(tc_PropLog_Opl(X1))),X1),tc_PropLog_Opl(X1))
| ~ c_PropLog_Osat(c_emptyset,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
ifeq(c_PropLog_Osat(c_emptyset,X0,X1),true,c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X0,X2,X1),c_PropLog_Ohyps(X0,X3,X1),tc_set(tc_PropLog_Opl(X1))),X1),tc_PropLog_Opl(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f0,negated_conjecture,
c_PropLog_Osat(c_emptyset,v_p,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
c_PropLog_Osat(c_emptyset,v_p,t_a),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_PropLog_Osat(c_emptyset,v_p,t_a),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,negated_conjecture,
c_PropLog_Osat(c_emptyset,v_p,t_a) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t3,plain,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X1,t_a),c_PropLog_Ohyps(v_p,X2,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi0]) ).
cnf(t7,plain,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X1,t_a),c_PropLog_Ohyps(v_p,X2,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f3,axiom,
c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f3_nnf,plain,
! [V_A,T_a] : c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_A,T_a] : c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
c_minus(X0,X0,tc_set(X1)) = c_emptyset,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t1,plain,
c_minus(X1,X1,tc_set(X2)) = c_emptyset,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t9,plain,
c_minus(X1,X1,tc_set(X2)) = c_emptyset,
inference(orient,[status(thm)],[t1]) ).
cnf(t10,plain,
true = c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(cp,[status(thm)],[t7,t9]) ).
cnf(t12,plain,
c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(f1,negated_conjecture,
~ 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) ).
fof(f1_nnf,plain,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)) != true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t12]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.78 % Computer : n016.cluster.edu
% 0.09/0.78 % Model : x86_64 x86_64
% 0.09/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.78 % Memory : 8046.5625MB
% 0.09/0.78 % OS : Linux 6.8.0-71-generic
% 0.09/0.78 % CPULimit : 300
% 0.09/0.78 % WCLimit : 300
% 0.09/0.78 % DateTime : Wed Sep 23 23:24:57 UTC 2026
% 0.09/0.78 % CPUTime :
% 0.09/0.78 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.92/1.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.92/1.38 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------