%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET845-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 6.15s 1.41s
% Output : Proof 6.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 49 unt; 0 def)
% Number of atoms : 77 ( 45 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 23 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 78 ( 6 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,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(f1_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)],[f1]) ).
fof(f1_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)],[f1_nnf]) ).
cnf(c1,plain,
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t5,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)],[c1]) ).
cnf(t9,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)],[t5]) ).
cnf(f0,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(f0_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)],[f0]) ).
fof(f0_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)],[f0_nnf]) ).
cnf(c0,plain,
( c_lessequals(X0,c_Union(X1,X2),tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,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)],[c0]) ).
cnf(t10,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)],[t4]) ).
cnf(f3,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(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c3,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)],[f3_sk]) ).
cnf(t6,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)],[c3]) ).
cnf(t11,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)],[t6]) ).
cnf(t7,axiom,
sFlat0 = c_Zorn_Osucc(v_S,v_m,t_a),
introduced(definition) ).
cnf(t20,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = sFlat0,
inference(orient,[status(thm)],[t7]) ).
cnf(t22,plain,
true = ifeq(c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),true,c_in(sFlat0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),true),
inference(cp,[status(thm)],[t11,t20]) ).
cnf(f4,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(f4_nnf,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(t2,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t12,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t38,plain,
true = ifeq(true,true,c_in(sFlat0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),true),
inference(step,[status(thm)],[t22,t12]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t39,plain,
true = c_in(sFlat0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(step,[status(thm)],[t38,t8]) ).
cnf(t26,plain,
c_in(sFlat0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(orient,[status(thm)],[t39]) ).
cnf(t27,plain,
true = ifeq(true,true,c_lessequals(sFlat0,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),true),
inference(cp,[status(thm)],[t10,t26]) ).
cnf(t40,plain,
true = c_lessequals(sFlat0,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(step,[status(thm)],[t27,t8]) ).
cnf(f5,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(f5_nnf,plain,
v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(t1,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t18,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m,
inference(orient,[status(thm)],[t1]) ).
cnf(t41,plain,
true = c_lessequals(sFlat0,v_m,tc_set(tc_set(t_a))),
inference(step,[status(thm)],[t40,t18]) ).
cnf(t29,plain,
c_lessequals(sFlat0,v_m,tc_set(tc_set(t_a))) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t30,plain,
sFlat0 = ifeq(true,true,ifeq(c_lessequals(v_m,sFlat0,tc_set(tc_set(t_a))),true,v_m,sFlat0),sFlat0),
inference(cp,[status(thm)],[t9,t29]) ).
cnf(t42,plain,
sFlat0 = ifeq(c_lessequals(v_m,sFlat0,tc_set(tc_set(t_a))),true,v_m,sFlat0),
inference(step,[status(thm)],[t30,t8]) ).
cnf(f2,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(f2_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)],[f2]) ).
fof(f2_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)],[f2_nnf]) ).
cnf(c2,plain,
c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t15,plain,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t21,plain,
true = c_lessequals(v_m,sFlat0,tc_set(tc_set(t_a))),
inference(cp,[status(thm)],[t15,t20]) ).
cnf(t23,plain,
c_lessequals(v_m,sFlat0,tc_set(tc_set(t_a))) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t43,plain,
sFlat0 = ifeq(true,true,v_m,sFlat0),
inference(step,[status(thm)],[t42,t23]) ).
cnf(t44,plain,
sFlat0 = v_m,
inference(step,[status(thm)],[t43,t8]) ).
cnf(t32,plain,
v_m = sFlat0,
inference(orient,[status(thm)],[t44]) ).
cnf(f6,negated_conjecture,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f6_nnf,plain,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
c_Zorn_Osucc(v_S,v_m,t_a) != v_m,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(g0_0,plain,
sFlat0 != v_m,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_0,t32]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET845-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.58 % Computer : n001.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.59 % CPULimit : 300
% 0.10/0.59 % WCLimit : 300
% 0.10/0.59 % DateTime : Thu Sep 24 12:17:09 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.59 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.15/1.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.15/1.41 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------