%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET845-1 : 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 02:44:06 PM UTC 2026
% Result : Unsatisfiable 15.07s 2.32s
% Output : Proof 15.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 49
% Syntax : Number of formulae : 219 ( 183 unt; 0 def)
% Number of atoms : 259 ( 135 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 248 ( 208 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 43 ( 43 usr; 16 con; 0-4 aty)
% Number of variables : 492 ( 116 sgn 230 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f308,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(f308_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)],[f308]) ).
fof(f308_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)],[f308_nnf]) ).
cnf(c308,plain,
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f308_sk]) ).
cnf(t198,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)],[c308]) ).
cnf(t267,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)],[t198]) ).
cnf(f1359,axiom,
( c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a))
| ~ c_in(V_B,V_A,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).
fof(f1359_nnf,plain,
! [V_B,V_A,T_a] :
( c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a))
| ~ c_in(V_B,V_A,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f1359]) ).
fof(f1359_sk,plain,
! [V_B,V_A,T_a] :
( c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a))
| ~ c_in(V_B,V_A,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f1359_nnf]) ).
cnf(c1359,plain,
( c_lessequals(X0,c_Union(X1,X2),tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f1359_sk]) ).
cnf(t181,plain,
ifeq(c_in(X1,X2,tc_set(X3)),true,c_lessequals(X1,c_Union(X2,X3),tc_set(X3)),true) = true,
inference(equality_encoding,[status(esa)],[c1359]) ).
cnf(t1479,plain,
ifeq(c_in(X1,X2,tc_set(X3)),true,c_lessequals(X1,c_Union(X2,X3),tc_set(X3)),true) = true,
inference(orient,[status(thm)],[t181]) ).
cnf(f1361,axiom,
( c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ 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_Zorn_OTFin_OsuccI_0) ).
fof(f1361_nnf,plain,
! [V_x,V_S,T_a] :
( c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f1361]) ).
fof(f1361_sk,plain,
! [V_x,V_S,T_a] :
( c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f1361_nnf]) ).
cnf(c1361,plain,
( c_in(c_Zorn_Osucc(X1,X0,X2),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)],[f1361_sk]) ).
cnf(t230,plain,
ifeq(c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))),true,c_in(c_Zorn_Osucc(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))),true) = true,
inference(equality_encoding,[status(esa)],[c1361]) ).
cnf(t1963,plain,
ifeq(c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))),true,c_in(c_Zorn_Osucc(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))),true) = true,
inference(orient,[status(thm)],[t230]) ).
cnf(f1364,negated_conjecture,
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_conjecture_0) ).
fof(f1364_nnf,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f1364]) ).
cnf(c1364,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f1364_nnf]) ).
cnf(t48,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(equality_encoding,[status(esa)],[c1364]) ).
cnf(t379,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(orient,[status(thm)],[t48]) ).
cnf(t1964,plain,
true = ifeq(true,true,c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),true),
inference(cp,[status(thm)],[t1963,t379]) ).
cnf(t23,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t254,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t23]) ).
cnf(t2771,plain,
true = c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(step,[status(thm)],[t1964,t254]) ).
cnf(t2723,plain,
c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(orient,[status(thm)],[t2771]) ).
cnf(t2724,plain,
true = ifeq(true,true,c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),true),
inference(cp,[status(thm)],[t1479,t2723]) ).
cnf(t2772,plain,
true = c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(step,[status(thm)],[t2724,t254]) ).
cnf(f1365,negated_conjecture,
v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1365_nnf,plain,
v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(nnf_transformation,[status(thm)],[f1365]) ).
cnf(c1365,plain,
v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(cnf_transformation,[status(esa)],[f1365_nnf]) ).
cnf(t24,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m,
inference(equality_encoding,[status(esa)],[c1365]) ).
cnf(t2503,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m,
inference(orient,[status(thm)],[t24]) ).
cnf(t2773,plain,
true = c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
inference(step,[status(thm)],[t2772,t2503]) ).
cnf(t2739,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))) = true,
inference(orient,[status(thm)],[t2773]) ).
cnf(t2740,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = ifeq(true,true,ifeq(c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),true,v_m,c_Zorn_Osucc(v_S,v_m,t_a)),c_Zorn_Osucc(v_S,v_m,t_a)),
inference(cp,[status(thm)],[t267,t2739]) ).
cnf(t2774,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = ifeq(c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),true,v_m,c_Zorn_Osucc(v_S,v_m,t_a)),
inference(step,[status(thm)],[t2740,t254]) ).
cnf(f1360,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(f1360_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)],[f1360]) ).
fof(f1360_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)],[f1360_nnf]) ).
cnf(c1360,plain,
c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[status(esa)],[f1360_sk]) ).
cnf(t73,plain,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))) = true,
inference(equality_encoding,[status(esa)],[c1360]) ).
cnf(t2407,plain,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))) = true,
inference(orient,[status(thm)],[t73]) ).
cnf(t2775,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = ifeq(true,true,v_m,c_Zorn_Osucc(v_S,v_m,t_a)),
inference(step,[status(thm)],[t2774,t2407]) ).
cnf(t2776,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(step,[status(thm)],[t2775,t254]) ).
cnf(t2744,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(orient,[status(thm)],[t2776]) ).
cnf(t2,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t2432,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(f4,axiom,
c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(V_a_H,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1__iff1_0) ).
fof(f4_nnf,plain,
! [V_a_H,T_a] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(V_a_H,T_a),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_a_H,T_a] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(V_a_H,T_a),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X0,X1),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f5,axiom,
c_Datatype_Ooption_OSome(V_a_H,T_a) != c_Datatype_Ooption_ONone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__2__iff1_0) ).
fof(f5_nnf,plain,
! [V_a_H,T_a] : c_Datatype_Ooption_OSome(V_a_H,T_a) != c_Datatype_Ooption_ONone,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_a_H,T_a] : c_Datatype_Ooption_OSome(V_a_H,T_a) != c_Datatype_Ooption_ONone,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
c_Datatype_Ooption_OSome(X0,X1) != c_Datatype_Ooption_ONone,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f8,axiom,
c_Datatype__Universe_OAtom(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__not__Scons__iff1_0) ).
fof(f8_nnf,plain,
! [V_a,T_a,T_b,V_M,V_N] : c_Datatype__Universe_OAtom(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V_a,T_a,T_b,V_M,V_N] : c_Datatype__Universe_OAtom(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
c_Datatype__Universe_OAtom(X0,X1,X2) != c_Datatype__Universe_OScons(X3,X4,X1,X2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f10,axiom,
c_Datatype__Universe_OIn0(V_M,T_a,T_b) != c_Datatype__Universe_OIn1(V_N,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
fof(f10_nnf,plain,
! [V_M,T_a,T_b,V_N] : c_Datatype__Universe_OIn0(V_M,T_a,T_b) != c_Datatype__Universe_OIn1(V_N,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [V_M,T_a,T_b,V_N] : c_Datatype__Universe_OIn0(V_M,T_a,T_b) != c_Datatype__Universe_OIn1(V_N,T_a,T_b),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
c_Datatype__Universe_OIn0(X0,X1,X2) != c_Datatype__Universe_OIn1(X3,X1,X2),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f12,axiom,
c_Datatype__Universe_OIn1(V_N,T_a,T_b) != c_Datatype__Universe_OIn0(V_M,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
fof(f12_nnf,plain,
! [V_N,T_a,T_b,V_M] : c_Datatype__Universe_OIn1(V_N,T_a,T_b) != c_Datatype__Universe_OIn0(V_M,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [V_N,T_a,T_b,V_M] : c_Datatype__Universe_OIn1(V_N,T_a,T_b) != c_Datatype__Universe_OIn0(V_M,T_a,T_b),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
c_Datatype__Universe_OIn1(X0,X1,X2) != c_Datatype__Universe_OIn0(X3,X1,X2),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(f13,axiom,
c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb__iff1_0) ).
fof(f13_nnf,plain,
! [V_a,T_a,T_b,V_k] : c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [V_a,T_a,T_b,V_k] : c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(f14,axiom,
c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Scons__iff1_0) ).
fof(f14_nnf,plain,
! [V_a,T_a,T_b,V_M,V_N] : c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [V_a,T_a,T_b,V_M,V_N] : c_Datatype__Universe_OLeaf(V_a,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OScons(X3,X4,X1,X2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(f15,axiom,
c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Leaf__iff1_0) ).
fof(f15_nnf,plain,
! [V_k,T_a,T_b,V_a] : c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [V_k,T_a,T_b,V_a] : c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(f16,axiom,
c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Scons__iff1_0) ).
fof(f16_nnf,plain,
! [V_k,T_a,T_b,V_M,V_N] : c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [V_k,T_a,T_b,V_M,V_N] : c_Datatype__Universe_ONumb(V_k,T_a,T_b) != c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_OScons(X3,X4,X1,X2),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(f19,axiom,
c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OAtom(V_a,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom__iff1_0) ).
fof(f19_nnf,plain,
! [V_M,V_N,T_a,T_b,V_a] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OAtom(V_a,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [V_M,V_N,T_a,T_b,V_a] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OAtom(V_a,T_a,T_b),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
c_Datatype__Universe_OScons(X0,X1,X2,X3) != c_Datatype__Universe_OAtom(X4,X2,X3),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(f20,axiom,
c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Leaf__iff1_0) ).
fof(f20_nnf,plain,
! [V_M,V_N,T_a,T_b,V_a] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [V_M,V_N,T_a,T_b,V_a] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_OLeaf(V_a,T_a,T_b),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
c_Datatype__Universe_OScons(X0,X1,X2,X3) != c_Datatype__Universe_OLeaf(X4,X2,X3),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(f21,axiom,
c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb__iff1_0) ).
fof(f21_nnf,plain,
! [V_M,V_N,T_a,T_b,V_k] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [V_M,V_N,T_a,T_b,V_k] : c_Datatype__Universe_OScons(V_M,V_N,T_a,T_b) != c_Datatype__Universe_ONumb(V_k,T_a,T_b),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
c_Datatype__Universe_OScons(X0,X1,X2,X3) != c_Datatype__Universe_ONumb(X4,X2,X3),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(f28,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1__iff1_0) ).
fof(f28_nnf,plain,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(f29,axiom,
c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__2__iff1_0) ).
fof(f29_nnf,plain,
c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(f42,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
fof(f42_nnf,plain,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(f50,axiom,
~ c_in(c_Pair(V_xs,c_List_Olist_ONil,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
fof(f50_nnf,plain,
! [V_xs,T_a,V_r] : ~ c_in(c_Pair(V_xs,c_List_Olist_ONil,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
! [V_xs,T_a,V_r] : ~ c_in(c_Pair(V_xs,c_List_Olist_ONil,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
inference(skolemisation,[status(esa)],[f50_nnf]) ).
cnf(c50,plain,
~ c_in(c_Pair(X0,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X2,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(f56,axiom,
~ c_in(c_Pair(c_List_Olist_ONil,V_ys,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
fof(f56_nnf,plain,
! [V_ys,T_a,V_r] : ~ c_in(c_Pair(c_List_Olist_ONil,V_ys,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [V_ys,T_a,V_r] : ~ c_in(c_Pair(c_List_Olist_ONil,V_ys,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olex(V_r,T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
~ c_in(c_Pair(c_List_Olist_ONil,X0,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X2,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(f74,axiom,
~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(T_a)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).
fof(f74_nnf,plain,
! [T_a] : ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(T_a)),tc_nat),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
! [T_a] : ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(T_a)),tc_nat),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c74,plain,
~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X0)),tc_nat),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(f78,axiom,
c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
fof(f78_nnf,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
inference(nnf_transformation,[status(thm)],[f78]) ).
fof(f78_sk,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
inference(skolemisation,[status(esa)],[f78_nnf]) ).
cnf(c78,plain,
c_List_Olist_ONil != c_List_Olist_OCons(X0,X1,X2),
inference(cnf_transformation,[status(esa)],[f78_sk]) ).
cnf(f79,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
fof(f79_nnf,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil,
inference(nnf_transformation,[status(thm)],[f79]) ).
fof(f79_sk,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil,
inference(skolemisation,[status(esa)],[f79_nnf]) ).
cnf(c79,plain,
c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil,
inference(cnf_transformation,[status(esa)],[f79_sk]) ).
cnf(f101,axiom,
c_Suc(V_m) != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).
fof(f101_nnf,plain,
! [V_m] : c_Suc(V_m) != c_0,
inference(nnf_transformation,[status(thm)],[f101]) ).
fof(f101_sk,plain,
! [V_m] : c_Suc(V_m) != c_0,
inference(skolemisation,[status(esa)],[f101_nnf]) ).
cnf(c101,plain,
c_Suc(X0) != c_0,
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
cnf(f102,axiom,
c_0 != c_Suc(V_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
fof(f102_nnf,plain,
! [V_m] : c_0 != c_Suc(V_m),
inference(nnf_transformation,[status(thm)],[f102]) ).
fof(f102_sk,plain,
! [V_m] : c_0 != c_Suc(V_m),
inference(skolemisation,[status(esa)],[f102_nnf]) ).
cnf(c102,plain,
c_0 != c_Suc(X0),
inference(cnf_transformation,[status(esa)],[f102_sk]) ).
cnf(f116,axiom,
~ c_less(c_0,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
fof(f116_nnf,plain,
~ c_less(c_0,c_0,tc_nat),
inference(nnf_transformation,[status(thm)],[f116]) ).
fof(f116_sk,plain,
~ c_less(c_0,c_0,tc_nat),
inference(skolemisation,[status(esa)],[f116_nnf]) ).
cnf(c116,plain,
~ c_less(c_0,c_0,tc_nat),
inference(cnf_transformation,[status(esa)],[f116_sk]) ).
cnf(f117,axiom,
~ c_less(c_plus(V_i,V_j,tc_nat),V_i,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).
fof(f117_nnf,plain,
! [V_i,V_j] : ~ c_less(c_plus(V_i,V_j,tc_nat),V_i,tc_nat),
inference(nnf_transformation,[status(thm)],[f117]) ).
fof(f117_sk,plain,
! [V_i,V_j] : ~ c_less(c_plus(V_i,V_j,tc_nat),V_i,tc_nat),
inference(skolemisation,[status(esa)],[f117_nnf]) ).
cnf(c117,plain,
~ c_less(c_plus(X0,X1,tc_nat),X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f117_sk]) ).
cnf(f118,axiom,
~ c_less(c_plus(V_j,V_i,tc_nat),V_i,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).
fof(f118_nnf,plain,
! [V_j,V_i] : ~ c_less(c_plus(V_j,V_i,tc_nat),V_i,tc_nat),
inference(nnf_transformation,[status(thm)],[f118]) ).
fof(f118_sk,plain,
! [V_j,V_i] : ~ c_less(c_plus(V_j,V_i,tc_nat),V_i,tc_nat),
inference(skolemisation,[status(esa)],[f118_nnf]) ).
cnf(c118,plain,
~ c_less(c_plus(X0,X1,tc_nat),X1,tc_nat),
inference(cnf_transformation,[status(esa)],[f118_sk]) ).
cnf(f119,axiom,
~ c_less(V_n,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
fof(f119_nnf,plain,
! [V_n] : ~ c_less(V_n,c_0,tc_nat),
inference(nnf_transformation,[status(thm)],[f119]) ).
fof(f119_sk,plain,
! [V_n] : ~ c_less(V_n,c_0,tc_nat),
inference(skolemisation,[status(esa)],[f119_nnf]) ).
cnf(c119,plain,
~ c_less(X0,c_0,tc_nat),
inference(cnf_transformation,[status(esa)],[f119_sk]) ).
cnf(f120,axiom,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1__iff1_0) ).
fof(f120_nnf,plain,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
inference(nnf_transformation,[status(thm)],[f120]) ).
fof(f120_sk,plain,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
inference(skolemisation,[status(esa)],[f120_nnf]) ).
cnf(c120,plain,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
inference(cnf_transformation,[status(esa)],[f120_sk]) ).
cnf(f121,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2__iff1_0) ).
fof(f121_nnf,plain,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
inference(nnf_transformation,[status(thm)],[f121]) ).
fof(f121_sk,plain,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
inference(skolemisation,[status(esa)],[f121_nnf]) ).
cnf(c121,plain,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
inference(cnf_transformation,[status(esa)],[f121_sk]) ).
cnf(f122,axiom,
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
fof(f122_nnf,plain,
! [T_a,V_x] :
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f122]) ).
fof(f122_sk,plain,
! [T_a,V_x] :
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f122_nnf]) ).
cnf(c122,plain,
( ~ c_less(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f122_sk]) ).
cnf(f151,axiom,
( ~ c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
fof(f151_nnf,plain,
! [V_c,V_A,T_a] :
( ~ c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(nnf_transformation,[status(thm)],[f151]) ).
fof(f151_sk,plain,
! [V_c,V_A,T_a] :
( ~ c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(skolemisation,[status(esa)],[f151_nnf]) ).
cnf(c151,plain,
( ~ c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f151_sk]) ).
cnf(f156,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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
fof(f156_nnf,plain,
! [V_c,V_B,T_a,V_A] :
( ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f156]) ).
fof(f156_sk,plain,
! [V_c,V_B,T_a,V_A] :
( ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(skolemisation,[status(esa)],[f156_nnf]) ).
cnf(c156,plain,
( ~ c_in(X0,c_minus(X3,X1,tc_set(X2)),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f156_sk]) ).
cnf(f165,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
fof(f165_nnf,plain,
c_UNIV != c_emptyset,
inference(nnf_transformation,[status(thm)],[f165]) ).
fof(f165_sk,plain,
c_UNIV != c_emptyset,
inference(skolemisation,[status(esa)],[f165_nnf]) ).
cnf(c165,plain,
c_UNIV != c_emptyset,
inference(cnf_transformation,[status(esa)],[f165_sk]) ).
cnf(f173,axiom,
~ c_in(V_a,c_emptyset,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f173_nnf,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(nnf_transformation,[status(thm)],[f173]) ).
fof(f173_sk,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(skolemisation,[status(esa)],[f173_nnf]) ).
cnf(c173,plain,
~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(esa)],[f173_sk]) ).
cnf(f177,axiom,
~ c_less(V_A,c_emptyset,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
fof(f177_nnf,plain,
! [V_A,T_a] : ~ c_less(V_A,c_emptyset,tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f177]) ).
fof(f177_sk,plain,
! [V_A,T_a] : ~ c_less(V_A,c_emptyset,tc_set(T_a)),
inference(skolemisation,[status(esa)],[f177_nnf]) ).
cnf(c177,plain,
~ c_less(X0,c_emptyset,tc_set(X1)),
inference(cnf_transformation,[status(esa)],[f177_sk]) ).
cnf(f185,axiom,
c_Sum__Type_OInl(V_a,T_a,T_b) != c_Sum__Type_OInr(V_b,T_b,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
fof(f185_nnf,plain,
! [V_a,T_a,T_b,V_b] : c_Sum__Type_OInl(V_a,T_a,T_b) != c_Sum__Type_OInr(V_b,T_b,T_a),
inference(nnf_transformation,[status(thm)],[f185]) ).
fof(f185_sk,plain,
! [V_a,T_a,T_b,V_b] : c_Sum__Type_OInl(V_a,T_a,T_b) != c_Sum__Type_OInr(V_b,T_b,T_a),
inference(skolemisation,[status(esa)],[f185_nnf]) ).
cnf(c185,plain,
c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInr(X3,X2,X1),
inference(cnf_transformation,[status(esa)],[f185_sk]) ).
cnf(f187,axiom,
c_Sum__Type_OInr(V_b,T_b,T_a) != c_Sum__Type_OInl(V_a,T_a,T_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
fof(f187_nnf,plain,
! [V_b,T_b,T_a,V_a] : c_Sum__Type_OInr(V_b,T_b,T_a) != c_Sum__Type_OInl(V_a,T_a,T_b),
inference(nnf_transformation,[status(thm)],[f187]) ).
fof(f187_sk,plain,
! [V_b,T_b,T_a,V_a] : c_Sum__Type_OInr(V_b,T_b,T_a) != c_Sum__Type_OInl(V_a,T_a,T_b),
inference(skolemisation,[status(esa)],[f187_nnf]) ).
cnf(c187,plain,
c_Sum__Type_OInr(X0,X1,X2) != c_Sum__Type_OInl(X3,X2,X1),
inference(cnf_transformation,[status(esa)],[f187_sk]) ).
cnf(f191,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
fof(f191_nnf,plain,
! [V_y,V_x,T_a,V_r] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
inference(nnf_transformation,[status(thm)],[f191]) ).
fof(f191_sk,plain,
! [V_y,V_x,T_a,V_r] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
inference(skolemisation,[status(esa)],[f191_nnf]) ).
cnf(c191,plain,
( ~ c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)),X2) ),
inference(cnf_transformation,[status(esa)],[f191_sk]) ).
cnf(f194,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
fof(f194_nnf,plain,
! [V_y,V_x,T_a,V_r] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
inference(nnf_transformation,[status(thm)],[f194]) ).
fof(f194_sk,plain,
! [V_y,V_x,T_a,V_r] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)),T_a) ),
inference(skolemisation,[status(esa)],[f194_nnf]) ).
cnf(c194,plain,
( ~ c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)),X2) ),
inference(cnf_transformation,[status(esa)],[f194_sk]) ).
cnf(f263,axiom,
~ c_less(V_n,V_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f263_nnf,plain,
! [V_n] : ~ c_less(V_n,V_n,tc_nat),
inference(nnf_transformation,[status(thm)],[f263]) ).
fof(f263_sk,plain,
! [V_n] : ~ c_less(V_n,V_n,tc_nat),
inference(skolemisation,[status(esa)],[f263_nnf]) ).
cnf(c263,plain,
~ c_less(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f263_sk]) ).
cnf(f299,axiom,
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_less(V_A,V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f299_nnf,plain,
! [V_A,V_B,T_a] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_less(V_A,V_B,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f299]) ).
fof(f299_sk,plain,
! [V_A,V_B,T_a] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_less(V_A,V_B,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f299_nnf]) ).
cnf(c299,plain,
( ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_less(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f299_sk]) ).
cnf(f1366,negated_conjecture,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1366_nnf,plain,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
inference(nnf_transformation,[status(thm)],[f1366]) ).
fof(f1366_sk,plain,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
inference(skolemisation,[status(esa)],[f1366_nnf]) ).
cnf(c1366,plain,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
inference(cnf_transformation,[status(esa)],[f1366_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4,c5,c8,c10,c12,c13,c14,c15,c16,c19,c20,c21,c28,c29,c42,c50,c56,c74,c78,c79,c101,c102,c116,c117,c118,c119,c120,c121,c122,c151,c156,c165,c173,c177,c185,c187,c191,c194,c263,c299,c1366]) ).
cnf(g0_0,plain,
eq(v_m,c_Zorn_Osucc(v_S,v_m,t_a)) != false,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
eq(v_m,v_m) != false,
inference(rw,[status(thm)],[g0_0,t2744]) ).
cnf(g0_2,plain,
true != false,
inference(rw,[status(thm)],[g0_1,t2432]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET845-1 : 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 : n006.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 12:11:31 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 15.07/2.32 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.07/2.32 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------