%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET852-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:44:08 PM UTC 2026
% Result : Unsatisfiable 3.78s 1.08s
% Output : Proof 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 70 ( 20 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 57 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(V_B,c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_2) ).
fof(f5_nnf,plain,
! [V_B,V_A,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(V_B,c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_B,V_A,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(V_B,c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_lessequals(c_Union(X2,X3),X1,tc_set(X3))
| c_lessequals(X0,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(X1,X0,X2,X3),tc_set(X3)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f3,axiom,
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| c_in(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_0) ).
fof(f3_nnf,plain,
! [V_A,V_B,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| c_in(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_C,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_A,V_B,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| c_in(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_C,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| c_in(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X2,tc_set(X3)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f2,negated_conjecture,
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f2_nnf,plain,
! [V_U] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_U] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p7,plain,
( c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X0,v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X1,X0,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(X0,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(p11,plain,
( c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c5,p7]) ).
cnf(p12,plain,
( c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p11]) ).
cnf(p14,plain,
( c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p12]) ).
cnf(f4,axiom,
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_A,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_1) ).
fof(f4_nnf,plain,
! [V_A,V_B,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_A,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_A,V_B,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_A,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X0,tc_set(X3)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p15,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p14,c4]) ).
cnf(p16,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p15]) ).
cnf(p18,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p16]) ).
cnf(f1,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1_nnf,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p19,plain,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[p18,c1]) ).
cnf(f0,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f0_nnf,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p20,plain,
$false,
inference(resolution,[status(thm)],[p19,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET852-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:16:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.78/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.78/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------