%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET857-1 : 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 : n026.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 02:15:37 PM UTC 2026
% Result : Unsatisfiable 145.30s 21.53s
% Output : CNFRefutation 145.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of clauses : 67 ( 24 unt; 29 nHn; 58 RR)
% Number of literals : 183 ( 11 equ; 80 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 117 ( 9 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/Axioms/MSC001-0.ax',cls_Set_OsubsetD_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_conjecture_3,negated_conjecture,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
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_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_6,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_6) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_n,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_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_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_SetInterval_OatLeast__iff__iff2_0,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oord(X1)
| c_in(X3,c_SetInterval_OatLeast(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_SetInterval_OatLeast__iff__iff2_0) ).
cnf(clsarity_set_1,axiom,
class_Orderings_Oord(tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsarity_set_1) ).
cnf(cls_SetInterval_OatLeast__subset__iff__iff2_0,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_SetInterval_OatLeast(X3,X1),c_SetInterval_OatLeast(X2,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
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(clsarity_set_2,axiom,
class_Orderings_Oorder(tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsarity_set_2) ).
cnf(cls_SetInterval_OatLeast__iff__iff1_0,axiom,
( ~ c_in(X2,c_SetInterval_OatLeast(X3,X1),X1)
| ~ class_Orderings_Oord(X1)
| c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_SetInterval_OatLeast__iff__iff1_0) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(X1,X1,tc_set(X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_Osubset__refl_0) ).
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_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_20,plain,
( ~ c_lessequals(X2,X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3) ),
c_0_18 ).
cnf(c_0_21,negated_conjecture,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
cls_conjecture_3 ).
cnf(c_0_22,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_23,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_24,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_6]) ).
cnf(c_0_25,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_19 ).
cnf(c_0_26,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_1 ).
cnf(c_0_27,negated_conjecture,
( ~ c_lessequals(v_Y,X1,tc_set(tc_set(tc_set(t_a))))
| c_in(v_x,X1,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,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_29,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_22 ).
cnf(c_0_30,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_23 ).
cnf(c_0_31,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_24 ).
cnf(c_0_32,negated_conjecture,
( ~ c_in(X1,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(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
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_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_35,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_36,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_37,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X1,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_x,tc_set(tc_set(t_a)))
| X1 = v_x ),
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_38,negated_conjecture,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_41,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_36 ).
cnf(c_0_42,negated_conjecture,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]) ).
cnf(c_0_43,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oord(X1)
| c_in(X3,c_SetInterval_OatLeast(X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_SetInterval_OatLeast__iff__iff2_0]) ).
cnf(c_0_44,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X1,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_33])]) ).
cnf(c_0_45,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oord(X1)
| c_in(X3,c_SetInterval_OatLeast(X2,X1),X1) ),
c_0_43 ).
cnf(c_0_46,negated_conjecture,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_44,c_0_26]) ).
cnf(c_0_47,axiom,
class_Orderings_Oord(tc_set(X1)),
clsarity_set_1 ).
cnf(c_0_48,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_SetInterval_OatLeast(X3,X1),c_SetInterval_OatLeast(X2,X1),tc_set(X1)) ),
inference(fof_simplification,[status(thm)],[cls_SetInterval_OatLeast__subset__iff__iff2_0]) ).
cnf(c_0_49,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
inference(fof_simplification,[status(thm)],[cls_conjecture_5]) ).
cnf(c_0_50,negated_conjecture,
( c_in(v_n,c_SetInterval_OatLeast(c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_51,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_SetInterval_OatLeast(X3,X1),c_SetInterval_OatLeast(X2,X1),tc_set(X1)) ),
c_0_48 ).
cnf(c_0_52,axiom,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
cls_Zorn_OAbrial__axiom1_0 ).
cnf(c_0_53,axiom,
class_Orderings_Oorder(tc_set(X1)),
clsarity_set_2 ).
cnf(c_0_54,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
c_0_49 ).
cnf(c_0_55,negated_conjecture,
( ~ c_lessequals(c_SetInterval_OatLeast(c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),X1,tc_set(tc_set(tc_set(t_a))))
| c_in(v_n,X1,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_20,c_0_50]) ).
cnf(c_0_56,plain,
c_lessequals(c_SetInterval_OatLeast(c_Zorn_Osucc(X1,X2,X3),tc_set(tc_set(X3))),c_SetInterval_OatLeast(X2,tc_set(tc_set(X3))),tc_set(tc_set(tc_set(X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
cnf(c_0_57,plain,
( ~ c_in(X2,c_SetInterval_OatLeast(X3,X1),X1)
| ~ class_Orderings_Oord(X1)
| c_lessequals(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_SetInterval_OatLeast__iff__iff1_0]) ).
cnf(c_0_58,negated_conjecture,
( ~ c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_26]),c_0_54]) ).
cnf(c_0_59,negated_conjecture,
( c_in(v_n,c_SetInterval_OatLeast(v_x,tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
inference(fof_simplification,[status(thm)],[cls_conjecture_4]) ).
cnf(c_0_61,plain,
( ~ c_in(X2,c_SetInterval_OatLeast(X3,X1),X1)
| ~ class_Orderings_Oord(X1)
| c_lessequals(X3,X2,X1) ),
c_0_57 ).
cnf(c_0_62,negated_conjecture,
( c_in(v_n,c_SetInterval_OatLeast(v_x,tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
c_0_60 ).
cnf(c_0_64,negated_conjecture,
v_n = v_x,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_47])]),c_0_63]) ).
cnf(c_0_65,axiom,
c_lessequals(X1,X1,tc_set(X2)),
cls_Set_Osubset__refl_0 ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_65])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET857-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:44:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 145.30/21.53 % Version: 3.5.1
% 145.30/21.53 % Preprocessing class: FMLMSMSMSSSNFFN.
% 145.30/21.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 145.30/21.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 145.30/21.53 % Starting new_bool_3 with 300s (1) cores
% 145.30/21.53 % Starting new_bool_1 with 300s (1) cores
% 145.30/21.53 % Starting sh5l with 300s (1) cores
% 145.30/21.53 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1486210 completed with status 0
% 145.30/21.53 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 145.30/21.53 % Preprocessing class: FMLMSMSMSSSNFFN.
% 145.30/21.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 145.30/21.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 145.30/21.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 145.30/21.53 % No SInE strategy applied
% 145.30/21.53 % Search class: FGHSM-SSLM33-MFFFFFNN
% 145.30/21.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 145.30/21.53 % Starting SubtermCWHack with 136s (1) cores
% 145.30/21.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 145.30/21.53 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S2k with 136s (1) cores
% 145.30/21.53 % Starting new_bool_3 with 136s (1) cores
% 145.30/21.53 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 145.30/21.53 % G-E--_200_B02_F1_AE_CS_SP_PI_S2k with pid 1486219 completed with status 0
% 145.30/21.53 % Result found by G-E--_200_B02_F1_AE_CS_SP_PI_S2k
% 145.30/21.53 % Preprocessing class: FMLMSMSMSSSNFFN.
% 145.30/21.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 145.30/21.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 145.30/21.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 145.30/21.53 % No SInE strategy applied
% 145.30/21.53 % Search class: FGHSM-SSLM33-MFFFFFNN
% 145.30/21.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 145.30/21.53 % Starting SubtermCWHack with 136s (1) cores
% 145.30/21.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 145.30/21.53 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S2k with 136s (1) cores
% 145.30/21.53 % Preprocessing time : 0.006 s
% 145.30/21.53
% 145.30/21.53 % Proof found!
% 145.30/21.53 % SZS status Unsatisfiable
% 145.30/21.53 % SZS output start CNFRefutation
% See solution above
% 145.30/21.53 % Parsed axioms : 1373
% 145.30/21.53 % Removed by relevancy pruning/SinE : 0
% 145.30/21.53 % Initial clauses : 1373
% 145.30/21.53 % Removed in clause preprocessing : 1
% 145.30/21.53 % Initial clauses in saturation : 1372
% 145.30/21.53 % Processed clauses : 45220
% 145.30/21.53 % ...of these trivial : 2576
% 145.30/21.53 % ...subsumed : 22496
% 145.30/21.53 % ...remaining for further processing : 20148
% 145.30/21.53 % Other redundant clauses eliminated : 32
% 145.30/21.53 % Clauses deleted for lack of memory : 0
% 145.30/21.53 % Backward-subsumed : 472
% 145.30/21.53 % Backward-rewritten : 2583
% 145.30/21.53 % Generated clauses : 1007713
% 145.30/21.53 % ...of the previous two non-redundant : 869661
% 145.30/21.53 % ...aggressively subsumed : 0
% 145.30/21.53 % Contextual simplify-reflections : 13
% 145.30/21.53 % Paramodulations : 1007628
% 145.30/21.53 % Factorizations : 10
% 145.30/21.53 % NegExts : 0
% 145.30/21.53 % Equation resolutions : 75
% 145.30/21.53 % Disequality decompositions : 0
% 145.30/21.53 % Total rewrite steps : 302323
% 145.30/21.53 % ...of those cached : 275348
% 145.30/21.53 % Propositional unsat checks : 0
% 145.30/21.53 % Propositional check models : 0
% 145.30/21.53 % Propositional check unsatisfiable : 0
% 145.30/21.53 % Propositional clauses : 0
% 145.30/21.53 % Propositional clauses after purity: 0
% 145.30/21.53 % Propositional unsat core size : 0
% 145.30/21.53 % Propositional preprocessing time : 0.000
% 145.30/21.53 % Propositional encoding time : 0.000
% 145.30/21.53 % Propositional solver time : 0.000
% 145.30/21.53 % Success case prop preproc time : 0.000
% 145.30/21.53 % Success case prop encoding time : 0.000
% 145.30/21.53 % Success case prop solver time : 0.000
% 145.30/21.53 % Current number of processed clauses : 17093
% 145.30/21.53 % Positive orientable unit clauses : 3015
% 145.30/21.53 % Positive unorientable unit clauses: 1
% 145.30/21.53 % Negative unit clauses : 3194
% 145.30/21.53 % Non-unit-clauses : 10883
% 145.30/21.53 % Current number of unprocessed clauses: 816792
% 145.30/21.53 % ...number of literals in the above : 1437233
% 145.30/21.53 % Current number of archived formulas : 0
% 145.30/21.53 % Current number of archived clauses : 3055
% 145.30/21.53 % Clause-clause subsumption calls (NU) : 9300249
% 145.30/21.53 % Rec. Clause-clause subsumption calls : 8654636
% 145.30/21.53 % Non-unit clause-clause subsumptions : 13945
% 145.30/21.53 % Unit Clause-clause subsumption calls : 1939312
% 145.30/21.53 % Rewrite failures with RHS unbound : 0
% 145.30/21.53 % BW rewrite match attempts : 12361
% 145.30/21.53 % BW rewrite match successes : 328
% 145.30/21.53 % Condensation attempts : 0
% 145.30/21.53 % Condensation successes : 0
% 145.30/21.53 % Termbank termtop insertions : 28382873
% 145.30/21.53 % Search garbage collected termcells : 1625
% 145.30/21.53
% 145.30/21.53 % -------------------------------------------------
% 145.30/21.53 % User time : 20.041 s
% 145.30/21.53 % System time : 0.629 s
% 145.30/21.53 % Total time : 20.670 s
% 145.30/21.53 % Maximum resident set size: 5644 pages
% 145.30/21.53
% 145.30/21.53 % -------------------------------------------------
% 145.30/21.53 % User time : 99.908 s
% 145.30/21.53 % System time : 3.283 s
% 145.30/21.53 % Total time : 103.191 s
% 145.30/21.53 % Maximum resident set size: 5376 pages
% 145.30/21.53 % E exiting
%------------------------------------------------------------------------------