%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET847-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 02:44:07 PM UTC 2026
% Result : Unsatisfiable 3.45s 0.81s
% Output : Proof 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 99 ( 71 unt; 0 def)
% Number of atoms : 135 ( 66 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-4 aty)
% Number of variables : 195 ( 31 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,axiom,
( c_Zorn_Osucc(V_S,V_c,T_a) != V_c
| ~ c_in(V_c,c_minus(c_Zorn_Ochain(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Osucc__not__equals_0) ).
fof(f9_nnf,plain,
! [V_c,V_S,T_a] :
( c_Zorn_Osucc(V_S,V_c,T_a) != V_c
| ~ c_in(V_c,c_minus(c_Zorn_Ochain(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_c,V_S,T_a] :
( c_Zorn_Osucc(V_S,V_c,T_a) != V_c
| ~ c_in(V_c,c_minus(c_Zorn_Ochain(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( c_Zorn_Osucc(X1,X0,X2) != X0
| ~ c_in(X0,c_minus(c_Zorn_Ochain(X1,X2),c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(tc_set(X2)))),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t26,plain,
or(not(c_in(X1,c_minus(c_Zorn_Ochain(X2,X3),c_Zorn_Omaxchain(X2,X3),tc_set(tc_set(tc_set(X3)))),tc_set(tc_set(X3)))),not(eq(c_Zorn_Osucc(X2,X1,X3),X1))) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t65,plain,
or(not(c_in(X1,c_minus(c_Zorn_Ochain(X2,X3),c_Zorn_Omaxchain(X2,X3),tc_set(tc_set(tc_set(X3)))),tc_set(tc_set(X3)))),not(eq(c_Zorn_Osucc(X2,X1,X3),X1))) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(f4,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,plain,
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t22,plain,
ifeq(c_lessequals(X1,X2,tc_set(X3)),true,ifeq(c_lessequals(X2,X1,tc_set(X3)),true,X2,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t34,plain,
ifeq(c_lessequals(X1,X2,tc_set(X3)),true,ifeq(c_lessequals(X2,X1,tc_set(X3)),true,X2,X1),X1) = X1,
inference(orient,[status(thm)],[t22]) ).
cnf(f2,axiom,
c_lessequals(c_emptyset,V_A,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f2_nnf,plain,
! [V_A,T_a] : c_lessequals(c_emptyset,V_A,tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_A,T_a] : c_lessequals(c_emptyset,V_A,tc_set(T_a)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
c_lessequals(c_emptyset,X0,tc_set(X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t9,plain,
c_lessequals(c_emptyset,X1,tc_set(X2)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t67,plain,
c_lessequals(c_emptyset,X1,tc_set(X2)) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t69,plain,
X1 = ifeq(c_lessequals(X1,c_emptyset,tc_set(X2)),true,ifeq(true,true,c_emptyset,X1),X1),
inference(cp,[status(thm)],[t34,t67]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t33,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t155,plain,
X1 = ifeq(c_lessequals(X1,c_emptyset,tc_set(X2)),true,c_emptyset,X1),
inference(step,[status(thm)],[t69,t33]) ).
cnf(t98,plain,
ifeq(c_lessequals(X1,c_emptyset,tc_set(X2)),true,c_emptyset,X1) = X1,
inference(orient,[status(thm)],[t155]) ).
cnf(f3,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c3,plain,
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t20,plain,
or(c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3),c_lessequals(X1,X2,tc_set(X3))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t64,plain,
or(c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3),c_lessequals(X1,X2,tc_set(X3))) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(f10,negated_conjecture,
~ c_in(V_U,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f10_nnf,plain,
! [V_U] : ~ c_in(V_U,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [V_U] : ~ c_in(V_U,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t13,plain,
c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) = false,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t80,plain,
c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) = false,
inference(orient,[status(thm)],[t13]) ).
cnf(t81,plain,
true = or(false,c_lessequals(c_Zorn_Omaxchain(v_S,t_a),X1,tc_set(tc_set(tc_set(t_a))))),
inference(cp,[status(thm)],[t64,t80]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t37,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t156,plain,
true = c_lessequals(c_Zorn_Omaxchain(v_S,t_a),X1,tc_set(tc_set(tc_set(t_a)))),
inference(step,[status(thm)],[t81,t37]) ).
cnf(t99,plain,
c_lessequals(c_Zorn_Omaxchain(v_S,t_a),X1,tc_set(tc_set(tc_set(t_a)))) = true,
inference(orient,[status(thm)],[t156]) ).
cnf(t100,plain,
c_Zorn_Omaxchain(v_S,t_a) = ifeq(true,true,c_emptyset,c_Zorn_Omaxchain(v_S,t_a)),
inference(cp,[status(thm)],[t98,t99]) ).
cnf(t157,plain,
c_Zorn_Omaxchain(v_S,t_a) = c_emptyset,
inference(step,[status(thm)],[t100,t33]) ).
cnf(t105,plain,
c_Zorn_Omaxchain(v_S,t_a) = c_emptyset,
inference(orient,[status(thm)],[t157]) ).
cnf(t107,plain,
true = or(not(c_in(X1,c_minus(c_Zorn_Ochain(v_S,t_a),c_emptyset,tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a)))),not(eq(c_Zorn_Osucc(v_S,X1,t_a),X1))),
inference(cp,[status(thm)],[t65,t105]) ).
cnf(t137,plain,
or(not(c_in(X1,c_minus(c_Zorn_Ochain(v_S,t_a),c_emptyset,tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a)))),not(eq(c_Zorn_Osucc(v_S,X1,t_a),X1))) = true,
inference(orient,[status(thm)],[t107]) ).
cnf(f6,axiom,
( c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
fof(f6_nnf,plain,
! [V_Y,V_S,T_a] :
( c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [V_Y,V_S,T_a] :
( c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2)))) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
ifeq(c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2)))),true,c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f5,axiom,
c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f5_nnf,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
c_lessequals(X0,X0,tc_set(X1)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h1,plain,
c_in(c_Union(c_Zorn_OTFin(V0,V1),tc_set(V1)),c_Zorn_OTFin(V0,V1),tc_set(tc_set(V1))) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi4]) ).
cnf(f7,axiom,
( c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__chain__lemma4_0) ).
fof(f7_nnf,plain,
! [V_c,V_S,T_a] :
( c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [V_c,V_S,T_a] :
( c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( c_in(X0,c_Zorn_Ochain(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(hi6,axiom,
ifeq(c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))),true,c_in(X0,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2))),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h5,plain,
c_in(c_Union(c_Zorn_OTFin(V0,V1),tc_set(V1)),c_Zorn_Ochain(V0,V1),tc_set(tc_set(V1))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h1]) ).
cnf(f0,axiom,
( c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
fof(f0_nnf,plain,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| c_in(V_c,V_B,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,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( c_in(X0,c_minus(X1,X3,tc_set(X2)),X2)
| c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(c_in(X0,X1,X2),true,or(c_in(X0,X3,X2),c_in(X0,c_minus(X1,X3,tc_set(X2)),X2)),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t31,plain,
or(c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),X3,tc_set(tc_set(X2))),c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),c_minus(c_Zorn_Ochain(X1,X2),X3,tc_set(tc_set(tc_set(X2)))),tc_set(tc_set(X2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5]) ).
cnf(t61,plain,
or(c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),X3,tc_set(tc_set(X2))),c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),c_minus(c_Zorn_Ochain(X1,X2),X3,tc_set(tc_set(tc_set(X2)))),tc_set(tc_set(X2)))) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(f1,axiom,
~ c_in(V_a,c_emptyset,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f1_nnf,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t7,plain,
c_in(X1,c_emptyset,X2) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t72,plain,
c_in(X1,c_emptyset,X2) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t77,plain,
true = or(false,c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),c_minus(c_Zorn_Ochain(X1,X2),c_emptyset,tc_set(tc_set(tc_set(X2)))),tc_set(tc_set(X2)))),
inference(cp,[status(thm)],[t61,t72]) ).
cnf(t163,plain,
true = c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),c_minus(c_Zorn_Ochain(X1,X2),c_emptyset,tc_set(tc_set(tc_set(X2)))),tc_set(tc_set(X2))),
inference(step,[status(thm)],[t77,t37]) ).
cnf(t129,plain,
c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),c_minus(c_Zorn_Ochain(X1,X2),c_emptyset,tc_set(tc_set(tc_set(X2)))),tc_set(tc_set(X2))) = true,
inference(orient,[status(thm)],[t163]) ).
cnf(t139,plain,
true = or(not(true),not(eq(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))))),
inference(cp,[status(thm)],[t137,t129]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t93,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t166,plain,
true = or(false,not(eq(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))))),
inference(step,[status(thm)],[t139,t93]) ).
cnf(t167,plain,
true = not(eq(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)))),
inference(step,[status(thm)],[t166,t37]) ).
cnf(f8,axiom,
( c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)) = c_Zorn_Osucc(V_S,c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),T_a)
| ~ c_in(c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Oequal__succ__Union_1) ).
fof(f8_nnf,plain,
! [V_S,T_a] :
( c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)) = c_Zorn_Osucc(V_S,c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),T_a)
| ~ c_in(c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V_S,T_a] :
( c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)) = c_Zorn_Osucc(V_S,c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),T_a)
| ~ c_in(c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)) = c_Zorn_Osucc(X0,c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),X1)
| ~ c_in(c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),c_Zorn_OTFin(X0,X1),tc_set(tc_set(X1))) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi7,axiom,
ifeq(c_in(c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),c_Zorn_OTFin(X0,X1),tc_set(tc_set(X1))),true,c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),c_Zorn_Osucc(X0,c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),X1)) = c_Zorn_Osucc(X0,c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),X1),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t21,plain,
c_Zorn_Osucc(X1,c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),X2) = c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),
inference(hyper_resolution,[status(thm)],[hi7,h1]) ).
cnf(t89,plain,
c_Zorn_Osucc(X1,c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),X2) = c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),
inference(orient,[status(thm)],[t21]) ).
cnf(t168,plain,
true = not(eq(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)))),
inference(step,[status(thm)],[t167,t89]) ).
cnf(t2,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t71,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t169,plain,
true = not(true),
inference(step,[status(thm)],[t168,t71]) ).
cnf(t170,plain,
true = false,
inference(step,[status(thm)],[t169,t93]) ).
cnf(t141,plain,
false = true,
inference(orient,[status(thm)],[t170]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c1,c9,c10]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t141]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET847-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Thu Sep 24 12:12:05 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.45/0.81 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.45/0.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------