%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET853-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 02:44:09 PM UTC 2026
% Result : Unsatisfiable 5.67s 1.29s
% Output : Proof 5.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 24 unt; 0 def)
% Number of atoms : 251 ( 61 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 252 ( 83 ~; 169 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 110 ( 6 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,axiom,
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
fof(f9_nnf,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f0,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_0) ).
fof(f0_nnf,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p23,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,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)))
| c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(f1,negated_conjecture,
c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p28,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,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)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p23,c1]) ).
cnf(f5,negated_conjecture,
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_x,tc_set(tc_set(t_a)))
| V_U = v_x
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_x,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f5_nnf,plain,
! [V_U] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_x,tc_set(tc_set(t_a)))
| V_U = v_x
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_U] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_x,tc_set(tc_set(t_a)))
| V_U = v_x
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| X0 = v_x
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p30,plain,
( ~ 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_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| 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(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p28,c5]) ).
cnf(f8,axiom,
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
fof(f8_nnf,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p14,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| 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_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(p16,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| 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))) ),
inference(resolution,[status(thm)],[p14,c1]) ).
cnf(p124,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| 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(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p30,p16]) ).
cnf(p158,plain,
( c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| 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(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p124]) ).
cnf(p159,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| 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(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p158]) ).
cnf(f11,axiom,
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
fof(f11_nnf,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Osucc(X1,c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X2),X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p40,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| ~ 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_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c11,c0]) ).
cnf(p92,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| ~ 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))) ),
inference(resolution,[status(thm)],[p40,c1]) ).
cnf(p163,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p159,p92]) ).
cnf(p181,plain,
( c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p163]) ).
cnf(p182,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p181]) ).
cnf(f6,axiom,
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f6_nnf,plain,
! [V_B,V_A,T_a] :
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [V_B,V_A,T_a] :
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f2,negated_conjecture,
c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(p13,plain,
( c_Zorn_Osucc(v_S,v_x,t_a) = v_xa
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(p184,plain,
( c_Zorn_Osucc(v_S,v_x,t_a) = v_xa
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p182,p13]) ).
cnf(p199,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(resolution,[status(thm)],[p184,c5]) ).
cnf(p251,plain,
( v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(resolution,[status(thm)],[p199,c1]) ).
cnf(f12,axiom,
( c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
fof(f12_nnf,plain,
! [V_x,V_y,T_a,V_S] :
( c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [V_x,V_y,T_a,V_S] :
( c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( c_lessequals(X0,c_Zorn_Osucc(X3,X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p254,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(X0,v_x,t_a),tc_set(tc_set(t_a)))
| v_xa = v_x
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(resolution,[status(thm)],[p251,c12]) ).
cnf(f4,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f4_nnf,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p255,plain,
( v_xa = v_x
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(resolution,[status(thm)],[p254,c4]) ).
cnf(f10,axiom,
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a) != V_m
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
fof(f10_nnf,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a) != V_m
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a) != V_m
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) != X0
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p32,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c10,c0]) ).
cnf(p36,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x ),
inference(resolution,[status(thm)],[p32,c1]) ).
cnf(p271,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| v_xa = v_x
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa ),
inference(resolution,[status(thm)],[p255,p36]) ).
cnf(p274,plain,
( c_Zorn_Osucc(v_S,v_x,t_a) = v_xa
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| v_xa = v_x
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa ),
inference(resolution,[status(thm)],[p271,p13]) ).
cnf(p276,plain,
( c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| v_xa = v_x
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa ),
inference(factoring,[status(thm)],[p274]) ).
cnf(p277,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a)))
| v_xa = v_x
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa ),
inference(resolution,[status(thm)],[p276,c5]) ).
cnf(p292,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a)))
| v_xa = v_x
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa ),
inference(factoring,[status(thm)],[p277]) ).
cnf(p293,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a)))
| v_xa = v_x
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa ),
inference(resolution,[status(thm)],[p292,c1]) ).
cnf(p296,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(X0,v_x,t_a),tc_set(tc_set(t_a)))
| v_xa = v_x
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa ),
inference(resolution,[status(thm)],[p293,c12]) ).
cnf(p297,plain,
( v_xa = v_x
| c_Zorn_Osucc(v_S,v_x,t_a) = v_xa ),
inference(resolution,[status(thm)],[p296,c4]) ).
cnf(f3,negated_conjecture,
v_xa != c_Zorn_Osucc(v_S,v_x,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3_nnf,plain,
v_xa != c_Zorn_Osucc(v_S,v_x,t_a),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
v_xa != c_Zorn_Osucc(v_S,v_x,t_a),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
v_xa != c_Zorn_Osucc(v_S,v_x,t_a),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p298,plain,
( v_xa != v_xa
| v_xa = v_x ),
inference(superposition,[status(thm)],[p297,c3]) ).
cnf(p337,plain,
v_xa = v_x,
inference(equality_resolution,[status(thm)],[p298]) ).
cnf(p339,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(demodulation,[status(thm)],[p337,c4]) ).
cnf(f7,axiom,
c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f7_nnf,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p384,plain,
$false,
inference(resolution,[status(thm)],[p339,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET853-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n006.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 : Thu Sep 24 12:14:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.67/1.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/1.29 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------