%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET843-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 7.36s 6.61s
% Output : Proof 7.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 22 unt; 0 def)
% Number of atoms : 119 ( 48 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 111 ( 55 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 92 ( 4 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,negated_conjecture,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f9_nnf,plain,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f4,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(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,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)],[f4_sk]) ).
cnf(f7,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(f7_nnf,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p19,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))),
inference(resolution,[status(thm)],[c4,c7]) ).
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(p20,plain,
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(resolution,[status(thm)],[p19,c0]) ).
cnf(p22,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(superposition,[status(thm)],[c9,p20]) ).
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(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(p18,plain,
( c_Zorn_Osucc(X0,X1,X2) = X1
| ~ c_lessequals(c_Zorn_Osucc(X0,X1,X2),X1,tc_set(tc_set(X2))) ),
inference(resolution,[status(thm)],[c3,c1]) ).
cnf(p28,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) = v_m
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(resolution,[status(thm)],[p22,p18]) ).
cnf(p10,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(equality_factoring,[status(thm)],[c9]) ).
cnf(p13,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) != v_m
| v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(superposition,[status(thm)],[c9,p10]) ).
cnf(p14,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) != v_m
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(factoring,[status(thm)],[p13]) ).
cnf(p30,plain,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(resolution,[status(thm)],[p28,p14]) ).
cnf(p31,plain,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
inference(factoring,[status(thm)],[p30]) ).
cnf(p36,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) = v_m
| ~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm)],[p31,p18]) ).
cnf(f2,axiom,
c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f2_nnf,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p37,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(resolution,[status(thm)],[p36,c2]) ).
cnf(f6,axiom,
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| V_m != c_Zorn_Osucc(V_S,V_m,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_Oeq__succ__upper_0) ).
fof(f6_nnf,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| V_m != c_Zorn_Osucc(V_S,V_m,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)],[f6]) ).
fof(f6_sk,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| V_m != c_Zorn_Osucc(V_S,V_m,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)],[f6_nnf]) ).
cnf(c6,plain,
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| X0 != c_Zorn_Osucc(X1,X0,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)],[f6_sk]) ).
cnf(p32,plain,
( c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c6,c7]) ).
cnf(p42,plain,
( c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| v_m != v_m
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(demodulation,[status(thm)],[p37,p32]) ).
cnf(p47,plain,
( c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(equality_resolution,[status(thm)],[p42]) ).
cnf(f5,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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
fof(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c5,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)],[f5_sk]) ).
cnf(p24,plain,
c_in(c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),c_Zorn_OTFin(X0,X1),tc_set(tc_set(X1))),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(p48,plain,
c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[p47,p24]) ).
cnf(p12,plain,
c_lessequals(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[c0,c7]) ).
cnf(p15,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m
| ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c1,p12]) ).
cnf(p50,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m,
inference(resolution,[status(thm)],[p48,p15]) ).
cnf(f8,negated_conjecture,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| 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(f8_nnf,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p38,plain,
( v_m != v_m
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(demodulation,[status(thm)],[p37,c8]) ).
cnf(p46,plain,
v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(equality_resolution,[status(thm)],[p38]) ).
cnf(p52,plain,
v_m != v_m,
inference(demodulation,[status(thm)],[p50,p46]) ).
cnf(p53,plain,
$false,
inference(equality_resolution,[status(thm)],[p52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET843-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/5.45 % Computer : n011.cluster.edu
% 0.16/5.45 % Model : x86_64 x86_64
% 0.16/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.45 % Memory : 8046.5625MB
% 0.16/5.45 % OS : Linux 6.8.0-71-generic
% 0.16/5.45 % CPULimit : 300
% 0.16/5.45 % WCLimit : 300
% 0.16/5.45 % DateTime : Thu Sep 24 12:10:32 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.45 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.36/6.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.36/6.61 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------