%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV261-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 9.72s 3.07s
% Output : Proof 9.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 16 unt; 0 def)
% Number of atoms : 98 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 35 ~; 47 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 129 ( 6 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f7_nnf,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f6,axiom,
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f6_nnf,plain,
! [V_a,V_b,V_A,T_a] :
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [V_a,V_b,V_A,T_a] :
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X0 = X1
| c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p49,plain,
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2) = X0
| c_in(c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2),X1,X2)
| c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2)) ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(f8,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f8_nnf,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p173,plain,
( c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2))
| ~ c_in(X0,X3,X2)
| c_in(c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2),X1,X2)
| c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2)) ),
inference(superposition,[status(thm)],[p49,c8]) ).
cnf(p497,plain,
( ~ c_in(X0,X3,X2)
| c_in(c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2),X1,X2)
| c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2)) ),
inference(factoring,[status(thm)],[p173]) ).
cnf(f5,axiom,
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
fof(f5_nnf,plain,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_in(X0,c_union(X1,X3,X2),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f0,negated_conjecture,
c_in(v_X,v_G,tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
c_in(v_X,v_G,tc_Message_Omsg),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_in(v_X,v_G,tc_Message_Omsg),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p21,plain,
c_in(v_X,c_union(v_G,X0,tc_Message_Omsg),tc_Message_Omsg),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(p1803,plain,
( c_in(c_Main_OsubsetI__1(c_insert(v_X,X0,tc_Message_Omsg),c_union(v_G,X1,tc_Message_Omsg),tc_Message_Omsg),X0,tc_Message_Omsg)
| c_lessequals(c_insert(v_X,X0,tc_Message_Omsg),c_union(v_G,X1,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[p497,p21]) ).
cnf(f4,axiom,
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
fof(f4_nnf,plain,
! [V_c,V_B,T_a,V_A] :
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_c,V_B,T_a,V_A] :
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_in(X0,c_union(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p2534,plain,
( c_in(c_Main_OsubsetI__1(c_insert(v_X,X0,tc_Message_Omsg),c_union(v_G,X1,tc_Message_Omsg),tc_Message_Omsg),c_union(X2,X0,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,X0,tc_Message_Omsg),c_union(v_G,X1,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[p1803,c4]) ).
cnf(p2833,plain,
( c_lessequals(c_insert(v_X,X0,tc_Message_Omsg),c_union(v_G,X0,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,X0,tc_Message_Omsg),c_union(v_G,X0,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[p2534,c8]) ).
cnf(p2845,plain,
c_lessequals(c_insert(v_X,X0,tc_Message_Omsg),c_union(v_G,X0,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(factoring,[status(thm)],[p2833]) ).
cnf(f3,axiom,
( c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__mono_0) ).
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,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,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,X1,tc_set(tc_Message_Omsg)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p2846,plain,
c_lessequals(c_Message_Oparts(c_insert(v_X,X0,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,X0,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(resolution,[status(thm)],[p2845,c3]) ).
cnf(f9,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(f9_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)],[f9]) ).
fof(f9_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)],[f9_nnf]) ).
cnf(c9,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)],[f9_sk]) ).
cnf(f2,axiom,
c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__Un__subset2_0) ).
fof(f2_nnf,plain,
! [V_G,V_H] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_G,V_H] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
c_lessequals(c_Message_Oparts(c_union(X0,X1,tc_Message_Omsg)),c_union(c_Message_Oparts(X0),c_Message_Oparts(X1),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p67,plain,
( c_lessequals(X0,c_union(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_lessequals(X0,c_Message_Oparts(c_union(X1,X2,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[c9,c2]) ).
cnf(p2850,plain,
c_lessequals(c_Message_Oparts(c_insert(v_X,X0,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(X0),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(resolution,[status(thm)],[p2846,p67]) ).
cnf(f1,negated_conjecture,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/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_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),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_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),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_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p2854,plain,
$false,
inference(resolution,[status(thm)],[p2850,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV261-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n020.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 18:56:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.72/3.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.72/3.07 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------