%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET850-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 5.93s 1.29s
% Output : Proof 5.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 23 unt; 0 def)
% Number of atoms : 35 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 38 ( 6 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t7,axiom,
sFlat1 = tc_set(t_a),
introduced(definition) ).
cnf(t12,plain,
tc_set(t_a) = sFlat1,
inference(orient,[status(thm)],[t7]) ).
cnf(f0,axiom,
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
fof(f0_nnf,plain,
! [V_B,V_C,T_a,V_A] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_B,V_C,T_a,V_A] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( c_lessequals(X3,X1,tc_set(X2))
| ~ c_lessequals(X3,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(c_lessequals(X0,X1,tc_set(X2)),true,ifeq(c_lessequals(X3,X0,tc_set(X2)),true,c_lessequals(X3,X1,tc_set(X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f1,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(f1_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)],[f1]) ).
fof(f1_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)],[f1_nnf]) ).
cnf(c1,plain,
c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f2,negated_conjecture,
c_lessequals(v_x,v_y,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2_nnf,plain,
c_lessequals(v_x,v_y,tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
c_lessequals(v_x,v_y,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi2,negated_conjecture,
c_lessequals(v_x,v_y,tc_set(tc_set(t_a))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t3,plain,
c_lessequals(v_x,c_Zorn_Osucc(X1,v_y,t_a),tc_set(tc_set(t_a))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi2]) ).
cnf(t20,plain,
c_lessequals(v_x,c_Zorn_Osucc(X1,v_y,t_a),tc_set(sFlat1)) = true,
inference(step,[status(thm)],[t3,t12]) ).
cnf(t18,plain,
c_lessequals(v_x,c_Zorn_Osucc(X1,v_y,t_a),tc_set(sFlat1)) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(f3,negated_conjecture,
~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3_nnf,plain,
~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
c_lessequals(v_x,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a))) != true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
c_lessequals(v_x,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(sFlat1)) != true,
inference(rw,[status(thm)],[goal_0,t12]) ).
cnf(g0_1,plain,
true != true,
inference(rw,[status(thm)],[g0_0,t18]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET850-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:15:19 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.93/1.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.93/1.29 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------