%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET841-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 3.42s 0.91s
% Output : Proof 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 54 unt; 0 def)
% Number of atoms : 74 ( 40 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 39 ( 23 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 44 ( 6 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t18,axiom,
sFlat1 = tc_set(t_a),
introduced(definition) ).
cnf(t26,plain,
tc_set(t_a) = sFlat1,
inference(orient,[status(thm)],[t18]) ).
cnf(t17,axiom,
sFlat0 = c_Zorn_Osucc(v_S,v_x,t_a),
introduced(definition) ).
cnf(t56,plain,
c_Zorn_Osucc(v_S,v_x,t_a) = sFlat0,
inference(orient,[status(thm)],[t17]) ).
cnf(t9,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t24,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(f1,axiom,
( V_n = V_m
| c_lessequals(c_Zorn_Osucc(V_S,V_n,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_m,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))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__subsetD_0) ).
fof(f1_nnf,plain,
! [V_n,V_S,T_a,V_m] :
( V_n = V_m
| c_lessequals(c_Zorn_Osucc(V_S,V_n,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_m,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))) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_n,V_S,T_a,V_m] :
( V_n = V_m
| c_lessequals(c_Zorn_Osucc(V_S,V_n,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_m,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))) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,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)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))),true,ifeq(c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))),true,ifeq(c_lessequals(X0,X3,tc_set(tc_set(X2))),true,or(c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2))),eq(X0,X3)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f4,negated_conjecture,
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_conjecture_2) ).
fof(f4_nnf,plain,
c_in(v_x,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_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f2,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(f2_nnf,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi2,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f5,negated_conjecture,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5_nnf,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi5,negated_conjecture,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t14,plain,
or(c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),eq(v_x,v_m)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi4,hi2,hi5]) ).
cnf(t76,plain,
or(c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(sFlat1)),eq(v_x,v_m)) = true,
inference(step,[status(thm)],[t14,t26]) ).
cnf(t34,plain,
or(c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(sFlat1)),eq(v_x,v_m)) = true,
inference(orient,[status(thm)],[t76]) ).
cnf(f6,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f6_nnf,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t12,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) = false,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t80,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(sFlat1)) = false,
inference(step,[status(thm)],[t12,t26]) ).
cnf(t49,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(sFlat1)) = false,
inference(orient,[status(thm)],[t80]) ).
cnf(t81,plain,
or(false,eq(v_x,v_m)) = true,
inference(step,[status(thm)],[t34,t49]) ).
cnf(t3,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t22,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t82,plain,
eq(v_x,v_m) = true,
inference(step,[status(thm)],[t81,t22]) ).
cnf(t50,plain,
eq(v_x,v_m) = true,
inference(rw,[status(thm)],[t82]) ).
cnf(t68,plain,
eq(v_x,v_m) = true,
inference(orient,[status(thm)],[t50]) ).
cnf(t69,plain,
v_m = ifeq(true,true,v_x,v_m),
inference(cp,[status(thm)],[t24,t68]) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t23,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t7]) ).
cnf(t93,plain,
v_m = v_x,
inference(step,[status(thm)],[t69,t23]) ).
cnf(t71,plain,
v_m = v_x,
inference(orient,[status(thm)],[t93]) ).
cnf(f0,axiom,
c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f0_nnf,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t6,plain,
c_lessequals(X1,X1,tc_set(X2)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t28,plain,
c_lessequals(X1,X1,tc_set(X2)) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(goal_0,negated_conjecture,
c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) != true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(g0_0,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(sFlat1)) != true,
inference(rw,[status(thm)],[goal_0,t26]) ).
cnf(g0_1,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(sFlat1)) != true,
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
c_lessequals(sFlat0,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(sFlat1)) != true,
inference(rw,[status(thm)],[g0_1,t56]) ).
cnf(g0_3,plain,
c_lessequals(sFlat0,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(sFlat1)) != true,
inference(rw,[status(thm)],[g0_2,t71]) ).
cnf(g0_4,plain,
c_lessequals(sFlat0,sFlat0,tc_set(sFlat1)) != true,
inference(rw,[status(thm)],[g0_3,t56]) ).
cnf(g0_5,plain,
true != true,
inference(rw,[status(thm)],[g0_4,t28]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET841-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.37 % Computer : n017.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 12:05:32 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.42/0.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.42/0.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------