%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET854-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 : Thu Sep 24 02:15:36 PM UTC 2026
% Result : Unsatisfiable 19.23s 3.27s
% Output : CNFRefutation 19.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of clauses : 70 ( 18 unt; 41 nHn; 59 RR)
% Number of literals : 227 ( 23 equ; 99 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 170 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OsubsetD_0,axiom,
( ~ c_lessequals(X2,X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(cls_Zorn_OTFin__linear__lemma1_3,axiom,
( ~ c_lessequals(c_Zorn_Osucc(X2,c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X3),X1,tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
cnf(cls_conjecture_5,negated_conjecture,
( ~ c_in(X2,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X1,X2,tc_set(tc_set(t_a)))
| X1 = X2
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_Zorn_OTFin__linear__lemma1_1,axiom,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X1,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Zorn_OTFin__linear__lemma1_0,axiom,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
cnf(cls_Zorn_OTFin__linear__lemma1_2,axiom,
( c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3) != X1
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Zorn_OAbrial__axiom1_0,axiom,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
cnf(cls_Zorn_OUnion__lemma0_0,axiom,
( c_lessequals(c_Union(X3,X4),X1,tc_set(X4))
| c_lessequals(X2,c_Union(X3,X4),tc_set(X4))
| c_in(c_Zorn_OUnion__lemma0__1(X1,X2,X3,X4),X3,tc_set(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_0) ).
cnf(cls_Zorn_OUnion__lemma0_2,axiom,
( ~ c_lessequals(X1,c_Zorn_OUnion__lemma0__1(X2,X1,X3,X4),tc_set(X4))
| c_lessequals(c_Union(X3,X4),X2,tc_set(X4))
| c_lessequals(X1,c_Union(X3,X4),tc_set(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_2) ).
cnf(cls_Set_OsubsetI_1,axiom,
( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_conjecture_3,negated_conjecture,
v_x != c_Union(v_Y,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Zorn_OUnion__lemma0_1,axiom,
( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X2,X3,X4),X1,tc_set(X4))
| c_lessequals(c_Union(X3,X4),X1,tc_set(X4))
| c_lessequals(X2,c_Union(X3,X4),tc_set(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_1) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(v_x,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(c_0_18,plain,
( ~ c_lessequals(X2,X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3) ),
inference(fof_simplification,[status(thm)],[cls_Set_OsubsetD_0]) ).
cnf(c_0_19,plain,
( ~ c_lessequals(c_Zorn_Osucc(X2,c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X3),X1,tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OTFin__linear__lemma1_3]) ).
cnf(c_0_20,negated_conjecture,
( ~ c_in(X2,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X1,X2,tc_set(tc_set(t_a)))
| X1 = X2
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a))) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_5]) ).
cnf(c_0_21,plain,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X1,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OTFin__linear__lemma1_1]) ).
cnf(c_0_22,plain,
( ~ c_lessequals(X2,X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3) ),
c_0_18 ).
cnf(c_0_23,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
cls_conjecture_0 ).
cnf(c_0_24,plain,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OTFin__linear__lemma1_0]) ).
cnf(c_0_25,plain,
( c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3) != X1
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OTFin__linear__lemma1_2]) ).
cnf(c_0_26,plain,
( ~ c_lessequals(c_Zorn_Osucc(X2,c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X3),X1,tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
c_0_19 ).
cnf(c_0_27,negated_conjecture,
( ~ c_in(X2,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X1,X2,tc_set(tc_set(t_a)))
| X1 = X2
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a))) ),
c_0_20 ).
cnf(c_0_28,plain,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X1,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
c_0_21 ).
cnf(c_0_29,negated_conjecture,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
c_0_24 ).
cnf(c_0_31,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_1 ).
cnf(c_0_32,plain,
( c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3) != X1
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
c_0_25 ).
cnf(c_0_33,negated_conjecture,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X2,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_x,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_x,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( ~ c_in(X1,c_Zorn_Osucc(X5,X4,X3),tc_set(X3))
| ~ c_in(X4,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(X2,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3)))
| c_Zorn_OTFin__linear__lemma1__1(X5,X4,X3) != X4
| c_lessequals(X2,X4,tc_set(tc_set(X3)))
| c_in(X1,X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_22,c_0_32]) ).
cnf(c_0_36,axiom,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
cls_Zorn_OAbrial__axiom1_0 ).
cnf(c_0_37,negated_conjecture,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X2,X1,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]) ).
cnf(c_0_38,negated_conjecture,
( ~ c_in(X1,c_Zorn_Osucc(v_S,X2,t_a),tc_set(t_a))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X2,t_a) != X2
| c_lessequals(v_x,X2,tc_set(tc_set(t_a)))
| c_in(X1,v_x,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_39,plain,
( ~ c_in(X1,X3,tc_set(X4))
| c_in(X1,c_Zorn_Osucc(X2,X3,X4),tc_set(X4)) ),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) = X1 ),
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
cnf(c_0_41,negated_conjecture,
( ~ c_in(X1,X2,tc_set(t_a))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X2,t_a) != X2
| c_lessequals(v_x,X2,tc_set(tc_set(t_a)))
| c_in(X1,v_x,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_Osucc(v_S,X1,t_a),tc_set(t_a))
| c_lessequals(v_x,X1,tc_set(tc_set(t_a)))
| c_in(X2,v_x,tc_set(t_a))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) = X1 ),
inference(spm,[status(thm)],[c_0_22,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( ~ c_in(X1,X2,tc_set(t_a))
| ~ c_in(X2,v_Y,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X2,t_a) != X2
| c_lessequals(v_x,X2,tc_set(tc_set(t_a)))
| c_in(X1,v_x,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_41,c_0_29]) ).
cnf(c_0_44,negated_conjecture,
( ~ c_in(X1,X2,tc_set(t_a))
| ~ c_in(X2,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X2,tc_set(tc_set(t_a)))
| c_in(X1,v_x,tc_set(t_a)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_39]),c_0_43]) ).
cnf(c_0_45,axiom,
( c_lessequals(c_Union(X3,X4),X1,tc_set(X4))
| c_lessequals(X2,c_Union(X3,X4),tc_set(X4))
| c_in(c_Zorn_OUnion__lemma0__1(X1,X2,X3,X4),X3,tc_set(X4)) ),
cls_Zorn_OUnion__lemma0_0 ).
cnf(c_0_46,plain,
( ~ c_lessequals(X1,c_Zorn_OUnion__lemma0__1(X2,X1,X3,X4),tc_set(X4))
| c_lessequals(c_Union(X3,X4),X2,tc_set(X4))
| c_lessequals(X1,c_Union(X3,X4),tc_set(X4)) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OUnion__lemma0_2]) ).
cnf(c_0_47,plain,
( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
inference(fof_simplification,[status(thm)],[cls_Set_OsubsetI_1]) ).
cnf(c_0_48,negated_conjecture,
( ~ c_in(X1,c_Zorn_OUnion__lemma0__1(X2,X3,v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X2,tc_set(tc_set(t_a)))
| c_lessequals(X3,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(X2,X3,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_in(X1,v_x,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
cls_Set_OsubsetI_0 ).
cnf(c_0_50,plain,
( ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[cls_Set_Osubset__antisym_0]) ).
cnf(c_0_51,negated_conjecture,
v_x != c_Union(v_Y,tc_set(t_a)),
inference(fof_simplification,[status(thm)],[cls_conjecture_3]) ).
cnf(c_0_52,plain,
( ~ c_lessequals(X1,c_Zorn_OUnion__lemma0__1(X2,X1,X3,X4),tc_set(X4))
| c_lessequals(c_Union(X3,X4),X2,tc_set(X4))
| c_lessequals(X1,c_Union(X3,X4),tc_set(X4)) ),
c_0_46 ).
cnf(c_0_53,plain,
( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X2,X3,X4),X1,tc_set(X4))
| c_lessequals(c_Union(X3,X4),X1,tc_set(X4))
| c_lessequals(X2,c_Union(X3,X4),tc_set(X4)) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OUnion__lemma0_1]) ).
cnf(c_0_54,plain,
( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
c_0_47 ).
cnf(c_0_55,negated_conjecture,
( c_lessequals(X2,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),X3,tc_set(tc_set(t_a)))
| c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),X3,tc_set(t_a)),v_x,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,plain,
( ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| X2 = X1 ),
c_0_50 ).
cnf(c_0_57,negated_conjecture,
c_lessequals(v_x,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
cls_conjecture_2 ).
cnf(c_0_58,negated_conjecture,
v_x != c_Union(v_Y,tc_set(t_a)),
c_0_51 ).
cnf(c_0_59,negated_conjecture,
( ~ c_lessequals(X2,c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),X3,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),X3,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(X3,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X2,t_a),c_Union(X3,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),X3,tc_set(t_a)) = X2 ),
inference(spm,[status(thm)],[c_0_52,c_0_27]) ).
cnf(c_0_60,plain,
( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X2,X3,X4),X1,tc_set(X4))
| c_lessequals(c_Union(X3,X4),X1,tc_set(X4))
| c_lessequals(X2,c_Union(X3,X4),tc_set(X4)) ),
c_0_53 ).
cnf(c_0_61,negated_conjecture,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(X2,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_63,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(fof_simplification,[status(thm)],[cls_conjecture_4]) ).
cnf(c_0_64,negated_conjecture,
( ~ c_lessequals(X2,c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X2,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),v_Y,tc_set(t_a)) = X2 ),
inference(spm,[status(thm)],[c_0_59,c_0_45]) ).
cnf(c_0_65,negated_conjecture,
( c_lessequals(X1,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(v_x,X1,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_66,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
c_0_63 ).
cnf(c_0_67,negated_conjecture,
c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) = v_x,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_31])]),c_0_66]),c_0_62]) ).
cnf(c_0_68,plain,
c_lessequals(X1,X1,tc_set(X2)),
inference(spm,[status(thm)],[c_0_54,c_0_49]) ).
cnf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_67]),c_0_68])]),c_0_62]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET854-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:41:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.23/3.27 % Version: 3.5.1
% 19.23/3.27 % Preprocessing class: FSMSSMSSSSSNFFN.
% 19.23/3.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.23/3.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.23/3.27 % Starting new_bool_3 with 300s (1) cores
% 19.23/3.27 % Starting new_bool_1 with 300s (1) cores
% 19.23/3.27 % Starting sh5l with 300s (1) cores
% 19.23/3.27 % sh5l with pid 3253317 completed with status 0
% 19.23/3.27 % Result found by sh5l
% 19.23/3.27 % Preprocessing class: FSMSSMSSSSSNFFN.
% 19.23/3.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.23/3.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.23/3.27 % Starting new_bool_3 with 300s (1) cores
% 19.23/3.27 % Starting new_bool_1 with 300s (1) cores
% 19.23/3.27 % Starting sh5l with 300s (1) cores
% 19.23/3.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 19.23/3.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 19.23/3.27 % Search class: FGUSF-FFMS32-MFFFFFNN
% 19.23/3.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 19.23/3.27 % Starting SubtermCWHack with 31s (1) cores
% 19.23/3.27 % SubtermCWHack with pid 3253325 completed with status 0
% 19.23/3.27 % Result found by SubtermCWHack
% 19.23/3.27 % Preprocessing class: FSMSSMSSSSSNFFN.
% 19.23/3.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.23/3.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.23/3.27 % Starting new_bool_3 with 300s (1) cores
% 19.23/3.27 % Starting new_bool_1 with 300s (1) cores
% 19.23/3.27 % Starting sh5l with 300s (1) cores
% 19.23/3.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 19.23/3.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 19.23/3.27 % Search class: FGUSF-FFMS32-MFFFFFNN
% 19.23/3.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 19.23/3.27 % Starting SubtermCWHack with 31s (1) cores
% 19.23/3.27 % Preprocessing time : 0.001 s
% 19.23/3.27
% 19.23/3.27 % Proof found!
% 19.23/3.27 % SZS status Unsatisfiable
% 19.23/3.27 % SZS output start CNFRefutation
% See solution above
% 19.23/3.27 % Parsed axioms : 18
% 19.23/3.27 % Removed by relevancy pruning/SinE : 0
% 19.23/3.27 % Initial clauses : 18
% 19.23/3.27 % Removed in clause preprocessing : 0
% 19.23/3.27 % Initial clauses in saturation : 18
% 19.23/3.27 % Processed clauses : 4317
% 19.23/3.27 % ...of these trivial : 80
% 19.23/3.27 % ...subsumed : 1989
% 19.23/3.27 % ...remaining for further processing : 2248
% 19.23/3.27 % Other redundant clauses eliminated : 0
% 19.23/3.27 % Clauses deleted for lack of memory : 0
% 19.23/3.27 % Backward-subsumed : 143
% 19.23/3.27 % Backward-rewritten : 15
% 19.23/3.27 % Generated clauses : 149674
% 19.23/3.27 % ...of the previous two non-redundant : 91867
% 19.23/3.27 % ...aggressively subsumed : 0
% 19.23/3.27 % Contextual simplify-reflections : 59
% 19.23/3.27 % Paramodulations : 149674
% 19.23/3.27 % Factorizations : 0
% 19.23/3.27 % NegExts : 0
% 19.23/3.27 % Equation resolutions : 0
% 19.23/3.27 % Disequality decompositions : 0
% 19.23/3.27 % Total rewrite steps : 72221
% 19.23/3.27 % ...of those cached : 71241
% 19.23/3.27 % Propositional unsat checks : 0
% 19.23/3.27 % Propositional check models : 0
% 19.23/3.27 % Propositional check unsatisfiable : 0
% 19.23/3.27 % Propositional clauses : 0
% 19.23/3.27 % Propositional clauses after purity: 0
% 19.23/3.27 % Propositional unsat core size : 0
% 19.23/3.27 % Propositional preprocessing time : 0.000
% 19.23/3.27 % Propositional encoding time : 0.000
% 19.23/3.27 % Propositional solver time : 0.000
% 19.23/3.27 % Success case prop preproc time : 0.000
% 19.23/3.27 % Success case prop encoding time : 0.000
% 19.23/3.27 % Success case prop solver time : 0.000
% 19.23/3.27 % Current number of processed clauses : 2090
% 19.23/3.27 % Positive orientable unit clauses : 58
% 19.23/3.27 % Positive unorientable unit clauses: 0
% 19.23/3.27 % Negative unit clauses : 5
% 19.23/3.27 % Non-unit-clauses : 2027
% 19.23/3.27 % Current number of unprocessed clauses: 87251
% 19.23/3.27 % ...number of literals in the above : 737038
% 19.23/3.27 % Current number of archived formulas : 0
% 19.23/3.27 % Current number of archived clauses : 158
% 19.23/3.27 % Clause-clause subsumption calls (NU) : 338881
% 19.23/3.27 % Rec. Clause-clause subsumption calls : 61595
% 19.23/3.27 % Non-unit clause-clause subsumptions : 1961
% 19.23/3.27 % Unit Clause-clause subsumption calls : 1753
% 19.23/3.27 % Rewrite failures with RHS unbound : 0
% 19.23/3.27 % BW rewrite match attempts : 1189
% 19.23/3.27 % BW rewrite match successes : 5
% 19.23/3.27 % Condensation attempts : 0
% 19.23/3.27 % Condensation successes : 0
% 19.23/3.27 % Termbank termtop insertions : 10556443
% 19.23/3.27 % Search garbage collected termcells : 49
% 19.23/3.27
% 19.23/3.27 % -------------------------------------------------
% 19.23/3.27 % User time : 2.686 s
% 19.23/3.27 % System time : 0.064 s
% 19.23/3.27 % Total time : 2.750 s
% 19.23/3.27 % Maximum resident set size: 3648 pages
% 19.23/3.27
% 19.23/3.27 % -------------------------------------------------
% 19.23/3.27 % User time : 2.690 s
% 19.23/3.27 % System time : 0.067 s
% 19.23/3.27 % Total time : 2.756 s
% 19.23/3.27 % Maximum resident set size: 4608 pages
% 19.23/3.27 % E exiting
%------------------------------------------------------------------------------