%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET851-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 22.03s 3.71s
% Output : Proof 22.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 19 unt; 0 def)
% Number of atoms : 58 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 22 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 5 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1360,axiom,
( c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
fof(f1360_nnf,plain,
! [V_x,V_y,T_a,V_S] :
( c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f1360]) ).
fof(f1360_sk,plain,
! [V_x,V_y,T_a,V_S] :
( c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f1360_nnf]) ).
cnf(c1360,plain,
( c_lessequals(X0,c_Zorn_Osucc(X3,X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(esa)],[f1360_sk]) ).
cnf(f1365,negated_conjecture,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1365_nnf,plain,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(nnf_transformation,[status(thm)],[f1365]) ).
fof(f1365_sk,plain,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(skolemisation,[status(esa)],[f1365_nnf]) ).
cnf(c1365,plain,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(esa)],[f1365_sk]) ).
cnf(p1482,plain,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(X0,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c1360,c1365]) ).
cnf(f1364,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1364_nnf,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f1364]) ).
fof(f1364_sk,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f1364_nnf]) ).
cnf(c1364,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f1364_sk]) ).
cnf(p1494,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[p1482,c1364]) ).
cnf(f1366,negated_conjecture,
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| V_U = v_m
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f1366_nnf,plain,
! [V_U] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| V_U = v_m
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(nnf_transformation,[status(thm)],[f1366]) ).
fof(f1366_sk,plain,
! [V_U] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| V_U = v_m
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(skolemisation,[status(esa)],[f1366_nnf]) ).
cnf(c1366,plain,
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| X0 = v_m
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(esa)],[f1366_sk]) ).
cnf(p1495,plain,
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x = v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p1494,c1366]) ).
cnf(f1362,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1362_nnf,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f1362]) ).
cnf(c1362,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f1362_nnf]) ).
cnf(p1563,plain,
( v_x = v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p1495,c1362]) ).
cnf(f1363,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1363_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)],[f1363]) ).
fof(f1363_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)],[f1363_nnf]) ).
cnf(c1363,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)],[f1363_sk]) ).
cnf(p1567,plain,
v_x = v_m,
inference(resolution,[status(thm)],[p1563,c1363]) ).
cnf(p1569,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(demodulation,[status(thm)],[p1567,c1364]) ).
cnf(f309,axiom,
c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f309_nnf,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f309]) ).
fof(f309_sk,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(skolemisation,[status(esa)],[f309_nnf]) ).
cnf(c309,plain,
c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(esa)],[f309_sk]) ).
cnf(p1611,plain,
$false,
inference(resolution,[status(thm)],[p1569,c309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET851-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:13:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.03/3.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.03/3.71 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------