%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV258-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 03:12:39 PM UTC 2026
% Result : Unsatisfiable 5.09s 6.36s
% Output : Proof 5.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 23 unt; 0 def)
% Number of atoms : 51 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 51 ( 3 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
( c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
fof(f2_nnf,plain,
! [V_G,V_H] :
( c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_G,V_H] :
( c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_lessequals(X0,c_Message_Oparts(X1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(X0),c_Message_Oparts(X1),tc_set(tc_Message_Omsg)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
ifeq(c_lessequals(c_Message_Oparts(X0),c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),true,c_lessequals(X0,c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f5,axiom,
c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f5_nnf,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
c_lessequals(X0,X0,tc_set(X1)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h2,plain,
c_lessequals(V0,c_Message_Oparts(V0),tc_set(tc_Message_Omsg)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi4]) ).
cnf(f4,axiom,
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
fof(f4_nnf,plain,
! [V_x,V_B,T_a,V_A] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_x,V_B,T_a,V_A] :
( c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_x,V_B,T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(c_insert(X0,X3,X2),X1,tc_set(X2))
| ~ c_lessequals(X3,X1,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(c_in(X0,X1,X2),true,ifeq(c_lessequals(X3,X1,tc_set(X2)),true,c_lessequals(c_insert(X0,X3,X2),X1,tc_set(X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f0,negated_conjecture,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,negated_conjecture,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h8,plain,
c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi0,h2]) ).
cnf(f3,axiom,
( c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
fof(f3_nnf,plain,
! [V_G,V_H] :
( c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_G,V_H] :
( c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_lessequals(c_Message_Oparts(X0),c_Message_Oparts(X1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(X0,c_Message_Oparts(X1),tc_set(tc_Message_Omsg)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,axiom,
ifeq(c_lessequals(X0,c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),true,c_lessequals(c_Message_Oparts(X0),c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t10,plain,
c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h8]) ).
cnf(t36,plain,
c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(f1,negated_conjecture,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) != true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t36]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV258-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.55 % Computer : n004.cluster.edu
% 0.09/5.55 % Model : x86_64 x86_64
% 0.09/5.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.55 % Memory : 8046.5625MB
% 0.09/5.55 % OS : Linux 6.8.0-71-generic
% 0.09/5.55 % CPULimit : 300
% 0.09/5.55 % WCLimit : 300
% 0.09/5.55 % DateTime : Thu Sep 24 18:54:42 UTC 2026
% 0.09/5.55 % CPUTime :
% 0.09/5.55 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.09/6.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.09/6.36 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------