%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : LCL429-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:13:47 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named cls_conjecture_3ERROR: Could not build tree for root finalERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(6,plain,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X0,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(cnf,[status(esa)],[cls_conjecture_3]) ).
cnf(l0,plain,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(instantiation,[status(thm)],[6]) ).
cnf(5,plain,
( ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_lessequals(X1,X3,tc_set(tc_PropLog_Opl(X2)))
| c_in(X0,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)) ),
inference(cnf,[status(esa)],[cls_PropLog_Oweaken__left_0]) ).
cnf(l1,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
| ~ c_lessequals(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a)))
| c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(2,plain,
c_lessequals(c_minus(X0,X1,tc_set(X2)),c_insert(X3,c_minus(X0,c_insert(X3,X1,X2),tc_set(X2)),X2),tc_set(X2)),
inference(cnf,[status(esa)],[cls_PropLog_Oinsert__Diff__same_0]) ).
cnf(l2,plain,
c_lessequals(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),
inference(instantiation,[status(thm)],[2]) ).
cnf(4,plain,
( ~ c_in(X0,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3))
| ~ c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Ofalse,X3),X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3))
| c_in(X0,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) ),
inference(cnf,[status(esa)],[cls_PropLog_Othms__excluded__middle__rule_0]) ).
cnf(l3,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l4,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
| ~ c_lessequals(c_minus(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),v_F,tc_set(tc_PropLog_Opl(t_a))),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a)))
| c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(7,plain,
~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(cnf,[status(esa)],[cls_conjecture_5]) ).
cnf(l6,plain,
~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(instantiation,[status(thm)],[7]) ).
cnf(3,plain,
c_lessequals(c_minus(c_insert(X0,c_minus(X1,c_insert(X2,c_emptyset,X3),tc_set(X3)),X3),X4,tc_set(X3)),c_insert(X0,c_minus(X1,c_insert(X2,X4,X3),tc_set(X3)),X3),tc_set(X3)),
inference(cnf,[status(esa)],[cls_PropLog_Oinsert__Diff__subset2_0]) ).
cnf(l18,plain,
c_lessequals(c_minus(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),v_F,tc_set(tc_PropLog_Opl(t_a))),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),
inference(instantiation,[status(thm)],[3]) ).
cnf(0,plain,
( ~ c_in(X0,c_PropLog_Othms(c_minus(X1,X2,tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3))
| ~ c_lessequals(X1,X4,tc_set(tc_PropLog_Opl(X3)))
| c_in(X0,c_PropLog_Othms(c_minus(X4,X2,tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3)) ),
inference(cnf,[status(esa)],[cls_PropLog_ODiff__weaken__left_0]) ).
cnf(l19,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,c_minus(v_t,c_insert(v_v,c_emptyset,t_a),tc_set(t_a)),t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
| ~ c_lessequals(c_PropLog_Ohyps(v_p,c_minus(v_t,c_insert(v_v,c_emptyset,t_a),tc_set(t_a)),t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a)))
| c_in(v_p,c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(1,plain,
c_lessequals(c_PropLog_Ohyps(X0,c_minus(X1,c_insert(X2,c_emptyset,X3),tc_set(X3)),X3),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X2,X3),c_PropLog_Opl_Ofalse,X3),c_minus(c_PropLog_Ohyps(X0,X1,X3),c_insert(c_PropLog_Opl_Ovar(X2,X3),c_emptyset,tc_PropLog_Opl(X3)),tc_set(tc_PropLog_Opl(X3))),tc_PropLog_Opl(X3)),tc_set(tc_PropLog_Opl(X3))),
inference(cnf,[status(esa)],[cls_PropLog_Ohyps__Diff_0]) ).
cnf(l20,plain,
c_lessequals(c_PropLog_Ohyps(v_p,c_minus(v_t,c_insert(v_v,c_emptyset,t_a),tc_set(t_a)),t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l21,plain,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,c_minus(v_t,c_insert(v_v,c_emptyset,t_a),tc_set(t_a)),t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(instantiation,[status(thm)],[6]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l4,l6,l18,l19,l20,l21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL429-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 19:09:06 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % launching worker at depth: 1
% 0.10/0.37 % launching worker at depth: 2
% 0.10/0.37 % launching worker at depth: 3
% 0.10/0.37 % launching worker at depth: 4
% 0.10/0.37 % launching worker at depth: 5
% 0.10/0.37 % launching worker at depth: 6
% 0.10/0.37 % launching worker at depth: 7
% 0.10/0.37 % launching worker at depth: 8
% 0.10/0.37 % launching worker at depth: 9
% 0.10/0.37 % launching worker at depth: 10
% 0.10/0.37 % launching worker at depth: 11
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------