%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 5.00s 1.18s
% Output : Proof 5.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 14
% Syntax : Number of formulae : 96 ( 26 unt; 0 def)
% Number of atoms : 291 ( 41 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 292 ( 97 ~; 195 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 148 ( 5 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f1_nnf,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f0,axiom,
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f0_nnf,plain,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p18,plain,
( c_in(c_Main_OsubsetI__1(X0,X1,X2),X3,X2)
| ~ c_lessequals(X0,X3,tc_set(X2))
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(f3,axiom,
c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
fof(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c3,plain,
c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p63,plain,
( c_in(c_Main_OsubsetI__1(X0,X1,tc_set(X2)),c_Zorn_Osucc(X3,X0,X2),tc_set(X2))
| c_lessequals(X0,X1,tc_set(tc_set(X2))) ),
inference(resolution,[status(thm)],[p18,c3]) ).
cnf(p185,plain,
( c_in(c_Main_OsubsetI__1(X0,X1,tc_set(X2)),X4,tc_set(X2))
| ~ c_lessequals(c_Zorn_Osucc(X3,X0,X2),X4,tc_set(tc_set(X2)))
| c_lessequals(X0,X1,tc_set(tc_set(X2))) ),
inference(resolution,[status(thm)],[p63,c0]) ).
cnf(f5,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(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c5,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)],[f5_sk]) ).
cnf(f10,negated_conjecture,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f10_nnf,plain,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(p14,plain,
( c_in(v_x,X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_Y,X0,tc_set(tc_set(tc_set(t_a)))) ),
inference(resolution,[status(thm)],[c0,c10]) ).
cnf(f8,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) ).
fof(f8_nnf,plain,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(p16,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[p14,c8]) ).
cnf(p40,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)],[c5,p16]) ).
cnf(f9,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) ).
fof(f9_nnf,plain,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(p136,plain,
( 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)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p40,c9]) ).
cnf(f13,negated_conjecture,
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(V_V,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_V,V_U,tc_set(tc_set(t_a)))
| V_V = V_U
| c_lessequals(c_Zorn_Osucc(v_S,V_V,t_a),V_U,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f13_nnf,plain,
! [V_V,V_U] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(V_V,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_V,V_U,tc_set(tc_set(t_a)))
| V_V = V_U
| c_lessequals(c_Zorn_Osucc(v_S,V_V,t_a),V_U,tc_set(tc_set(t_a))) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [V_V,V_U] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(V_V,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_V,V_U,tc_set(tc_set(t_a)))
| V_V = V_U
| c_lessequals(c_Zorn_Osucc(v_S,V_V,t_a),V_U,tc_set(tc_set(t_a))) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| X0 = X1
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p146,plain,
( ~ c_in(v_x,v_Y,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_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_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p136,c13]) ).
cnf(f4,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(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,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)],[f4_sk]) ).
cnf(p31,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)],[c4,p16]) ).
cnf(p98,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,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)],[p31,c9]) ).
cnf(p586,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| ~ c_in(v_x,v_Y,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_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p146,p98]) ).
cnf(p649,plain,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| ~ c_in(v_x,v_Y,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_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p586]) ).
cnf(p650,plain,
( ~ c_in(v_x,v_Y,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_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p649]) ).
cnf(p651,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_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p650,c10]) ).
cnf(f7,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(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(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)],[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(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)],[f7_nnf]) ).
cnf(c7,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)],[f7_sk]) ).
cnf(p56,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)],[c7,p16]) ).
cnf(p167,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,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,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)],[p56,c9]) ).
cnf(p654,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,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_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p651,p167]) ).
cnf(p659,plain,
( c_lessequals(v_n,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_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p654]) ).
cnf(p660,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_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p659]) ).
cnf(p732,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(v_x,X0,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(v_x,X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p185,p660]) ).
cnf(f2,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f2_nnf,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p738,plain,
( c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p732,c2]) ).
cnf(p739,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p738]) ).
cnf(f11,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f11_nnf,plain,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p740,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p739,c11]) ).
cnf(p741,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),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)],[p740,c13]) ).
cnf(p772,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),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)],[p741,c9]) ).
cnf(p773,plain,
( v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),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)],[p772,c10]) ).
cnf(f12,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) ).
fof(f12_nnf,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p774,plain,
( v_n = v_x
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
inference(resolution,[status(thm)],[p773,c12]) ).
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_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(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_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)],[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_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)],[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_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)],[f6_sk]) ).
cnf(p48,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)],[c6,p16]) ).
cnf(p83,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,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)],[p48,c9]) ).
cnf(p778,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(resolution,[status(thm)],[p774,p83]) ).
cnf(p785,plain,
( c_in(c_Main_OsubsetI__1(v_x,X0,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(v_x,X0,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(resolution,[status(thm)],[p778,p185]) ).
cnf(p787,plain,
( c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(resolution,[status(thm)],[p785,c2]) ).
cnf(p788,plain,
( c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(factoring,[status(thm)],[p787]) ).
cnf(p794,plain,
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(resolution,[status(thm)],[p788,c11]) ).
cnf(p795,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(resolution,[status(thm)],[p794,c13]) ).
cnf(p824,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(factoring,[status(thm)],[p795]) ).
cnf(p827,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(resolution,[status(thm)],[p824,c9]) ).
cnf(p828,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(resolution,[status(thm)],[p827,c10]) ).
cnf(p829,plain,
v_n = v_x,
inference(resolution,[status(thm)],[p828,c12]) ).
cnf(p830,plain,
~ c_lessequals(v_n,v_n,tc_set(tc_set(t_a))),
inference(superposition,[status(thm)],[p829,c11]) ).
cnf(p24,plain,
( c_lessequals(X0,X0,tc_set(X1))
| c_lessequals(X0,X0,tc_set(X1)) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(p78,plain,
c_lessequals(X0,X0,tc_set(X1)),
inference(factoring,[status(thm)],[p24]) ).
cnf(p926,plain,
$false,
inference(resolution,[status(thm)],[p830,p78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:15:17 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.00/1.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.00/1.18 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------