%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 02:44:10 PM UTC 2026
% Result : Unsatisfiable 6.80s 1.48s
% Output : Proof 6.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 21 unt; 0 def)
% Number of atoms : 218 ( 23 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 232 ( 82 ~; 150 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 2 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 : 115 ( 2 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,axiom,
( V_U = V_m
| c_lessequals(c_Zorn_Osucc(V_S,V_U,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_U,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_U,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma2_0) ).
fof(f10_nnf,plain,
! [V_U,V_S,T_a,V_m] :
( V_U = V_m
| c_lessequals(c_Zorn_Osucc(V_S,V_U,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_U,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_U,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [V_U,V_S,T_a,V_m] :
( V_U = V_m
| c_lessequals(c_Zorn_Osucc(V_S,V_U,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_U,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_U,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( X0 = X3
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| ~ c_lessequals(X0,X3,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)],[f10_sk]) ).
cnf(f6,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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
fof(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c6,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)],[f6_sk]) ).
cnf(f0,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
c_in(v_m,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_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p18,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,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(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(f1,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
c_in(v_n,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_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p21,plain,
( 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))) ),
inference(resolution,[status(thm)],[p18,c1]) ).
cnf(p78,plain,
( 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) = X0
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),t_a),X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),X0,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)],[c10,p21]) ).
cnf(p615,plain,
( 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_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_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p78,c0]) ).
cnf(f7,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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
fof(f7_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)],[f7]) ).
fof(f7_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)],[f7_nnf]) ).
cnf(c7,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)],[f7_sk]) ).
cnf(p30,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,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(X0,v_m,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)],[c7,c0]) ).
cnf(p42,plain,
( 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))) ),
inference(resolution,[status(thm)],[p30,c1]) ).
cnf(p671,plain,
( 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,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_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))) ),
inference(resolution,[status(thm)],[p615,p42]) ).
cnf(p680,plain,
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| 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_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))) ),
inference(factoring,[status(thm)],[p671]) ).
cnf(p681,plain,
( 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_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))) ),
inference(factoring,[status(thm)],[p680]) ).
cnf(f9,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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
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(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)],[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(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)],[f9_nnf]) ).
cnf(c9,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)],[f9_sk]) ).
cnf(p65,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,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(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(p163,plain,
( 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))) ),
inference(resolution,[status(thm)],[p65,c1]) ).
cnf(p686,plain,
( 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,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 ),
inference(resolution,[status(thm)],[p681,p163]) ).
cnf(p706,plain,
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| 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 ),
inference(factoring,[status(thm)],[p686]) ).
cnf(p707,plain,
( 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 ),
inference(factoring,[status(thm)],[p706]) ).
cnf(f4,axiom,
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
fof(f4_nnf,plain,
! [V_B,V_C,T_a,V_A] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_B,V_C,T_a,V_A] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(X3,X1,tc_set(X2))
| ~ c_lessequals(X3,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p708,plain,
( c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,c_Zorn_Osucc(v_S,v_m,t_a),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 ),
inference(resolution,[status(thm)],[p707,c4]) ).
cnf(f5,axiom,
c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
fof(f5_nnf,plain,
! [V_x,V_S,T_a] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_x,V_S,T_a] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p719,plain,
( c_lessequals(v_m,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 ),
inference(resolution,[status(thm)],[p708,c5]) ).
cnf(f2,negated_conjecture,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p720,plain,
( c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m ),
inference(resolution,[status(thm)],[p719,c2]) ).
cnf(f3,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3_nnf,plain,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p721,plain,
c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m,
inference(resolution,[status(thm)],[p720,c3]) ).
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_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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
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_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)],[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_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)],[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_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)],[f8_sk]) ).
cnf(p48,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) != v_m
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(p61,plain,
( 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 ),
inference(resolution,[status(thm)],[p48,c1]) ).
cnf(p732,plain,
( 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)))
| v_m != v_m ),
inference(demodulation,[status(thm)],[p721,p61]) ).
cnf(p922,plain,
( 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))) ),
inference(equality_resolution,[status(thm)],[p732]) ).
cnf(p923,plain,
( c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p922,c4]) ).
cnf(p968,plain,
( c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p923,c5]) ).
cnf(p969,plain,
c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[p968,c2]) ).
cnf(p970,plain,
$false,
inference(resolution,[status(thm)],[p969,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:18:04 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.80/1.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.80/1.48 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------