%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL434-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 02:02:00 PM UTC 2026
% Result : Unsatisfiable 83.78s 16.34s
% Output : Proof 83.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 18 unt; 0 def)
% Number of atoms : 59 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 22 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 74 ( 7 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1371,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms__I_0) ).
fof(f1371_nnf,plain,
! [V_p,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(nnf_transformation,[status(thm)],[f1371]) ).
fof(f1371_sk,plain,
! [V_p,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_p,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(skolemisation,[status(esa)],[f1371_nnf]) ).
cnf(c1371,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X0,X0,X1),c_PropLog_Othms(X2,X1),tc_PropLog_Opl(X1)),
inference(cnf_transformation,[status(esa)],[f1371_sk]) ).
cnf(f1369,axiom,
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ 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_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
fof(f1369_nnf,plain,
! [V_p,V_H,T_a,V_q] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ 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_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(nnf_transformation,[status(thm)],[f1369]) ).
fof(f1369_sk,plain,
! [V_p,V_H,T_a,V_q] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ 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_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(skolemisation,[status(esa)],[f1369_nnf]) ).
cnf(c1369,plain,
( c_in(X3,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,X3,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)],[f1369_sk]) ).
cnf(f186,axiom,
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f186_nnf,plain,
! [V_a,V_b,V_A,T_a] :
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(nnf_transformation,[status(thm)],[f186]) ).
fof(f186_sk,plain,
! [V_a,V_b,V_A,T_a] :
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(skolemisation,[status(esa)],[f186_nnf]) ).
cnf(c186,plain,
( X0 = X1
| c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(esa)],[f186_sk]) ).
cnf(f1373,negated_conjecture,
c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1373_nnf,plain,
c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(nnf_transformation,[status(thm)],[f1373]) ).
cnf(c1373,plain,
c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(esa)],[f1373_nnf]) ).
cnf(p1873,plain,
( v_pa = v_p
| c_in(v_pa,v_H,tc_PropLog_Opl(t_a)) ),
inference(resolution,[status(thm)],[c186,c1373]) ).
cnf(f9,axiom,
( c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
fof(f9_nnf,plain,
! [V_p,V_H,T_a] :
( c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_p,V_H,T_a] :
( c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,X1,tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p1874,plain,
( c_in(v_pa,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| v_pa = v_p ),
inference(resolution,[status(thm)],[p1873,c9]) ).
cnf(p4776,plain,
( v_pa = v_p
| c_in(X0,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pa,X0,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(resolution,[status(thm)],[c1369,p1874]) ).
cnf(f1368,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_p,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OK_0) ).
fof(f1368_nnf,plain,
! [V_p,V_q,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_p,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(nnf_transformation,[status(thm)],[f1368]) ).
fof(f1368_sk,plain,
! [V_p,V_q,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_p,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
inference(skolemisation,[status(esa)],[f1368_nnf]) ).
cnf(c1368,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Oop_A_N_62(X1,X0,X2),X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),
inference(cnf_transformation,[status(esa)],[f1368_sk]) ).
cnf(p4881,plain,
( v_pa = v_p
| c_in(c_PropLog_Opl_Oop_A_N_62(X0,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(resolution,[status(thm)],[p4776,c1368]) ).
cnf(f1374,negated_conjecture,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1374_nnf,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(nnf_transformation,[status(thm)],[f1374]) ).
fof(f1374_sk,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(skolemisation,[status(esa)],[f1374_nnf]) ).
cnf(c1374,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(esa)],[f1374_sk]) ).
cnf(p4884,plain,
v_pa = v_p,
inference(resolution,[status(thm)],[p4881,c1374]) ).
cnf(p4960,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pa,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(superposition,[status(thm)],[p4884,c1374]) ).
cnf(p5166,plain,
$false,
inference(resolution,[status(thm)],[c1371,p4960]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL434-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n004.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 23:21:29 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 83.78/16.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 83.78/16.34 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------