%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL437-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 02:02:01 PM UTC 2026
% Result : Unsatisfiable 6.16s 1.17s
% Output : Proof 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 15 unt; 0 def)
% Number of atoms : 23 ( 6 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 : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 43 ( 10 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__right_0) ).
fof(f2_nnf,plain,
! [V_q,V_H,T_a,V_p] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_q,V_H,T_a,V_p] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_in(c_PropLog_Opl_Oop_A_N_62(X3,X0,X2),c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
ifeq(c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,c_in(c_PropLog_Opl_Oop_A_N_62(X3,X0,X2),c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f1,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),c_PropLog_Opl_Ofalse,T_a),V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_ODN_0) ).
fof(f1_nnf,plain,
! [V_p,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),c_PropLog_Opl_Ofalse,T_a),V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_p,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),c_PropLog_Opl_Ofalse,T_a),V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,X1),c_PropLog_Opl_Ofalse,X1),X0,X1),c_PropLog_Othms(X2,X1),tc_PropLog_Opl(X1)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi0,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,X1),c_PropLog_Opl_Ofalse,X1),X0,X1),c_PropLog_Othms(X2,X1),tc_PropLog_Opl(X1)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t2,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Ofalse,X3),c_PropLog_Opl_Ofalse,X3),X2,X3),X3),c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi0]) ).
cnf(t5,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Ofalse,X3),c_PropLog_Opl_Ofalse,X3),X2,X3),X3),c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(f0,negated_conjecture,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Opl_Ofalse,t_a),v_pa,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Opl_Ofalse,t_a),v_pa,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Opl_Ofalse,t_a),v_pa,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Opl_Ofalse,t_a),v_pa,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Opl_Ofalse,t_a),v_pa,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t5]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL437-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 23:22:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.16/1.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.16/1.17 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------