%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET820-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 02:44:00 PM UTC 2026
% Result : Unsatisfiable 23.10s 3.49s
% Output : Proof 23.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 16 unt; 0 def)
% Number of atoms : 46 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 22 ~; 17 |; 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 : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 60 ( 13 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f176,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/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f176_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)],[f176]) ).
fof(f176_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)],[f176_nnf]) ).
cnf(c176,plain,
( X0 = X1
| c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(esa)],[f176_sk]) ).
cnf(f175,axiom,
c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f175_nnf,plain,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
inference(nnf_transformation,[status(thm)],[f175]) ).
fof(f175_sk,plain,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
inference(skolemisation,[status(esa)],[f175_nnf]) ).
cnf(c175,plain,
c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(esa)],[f175_sk]) ).
cnf(f1358,negated_conjecture,
( c_in(v_x(V_U),V_U,tc_IntDef_Oint)
| ~ c_in(V_V,V_U,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1358_nnf,plain,
! [V_V,V_U] :
( c_in(v_x(V_U),V_U,tc_IntDef_Oint)
| ~ c_in(V_V,V_U,tc_IntDef_Oint) ),
inference(nnf_transformation,[status(thm)],[f1358]) ).
fof(f1358_sk,plain,
! [V_V,V_U] :
( c_in(v_x(V_U),V_U,tc_IntDef_Oint)
| ~ c_in(V_V,V_U,tc_IntDef_Oint) ),
inference(skolemisation,[status(esa)],[f1358_nnf]) ).
cnf(c1358,plain,
( c_in(v_x(X1),X1,tc_IntDef_Oint)
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(esa)],[f1358_sk]) ).
cnf(p371,plain,
c_in(v_x(c_insert(X0,X1,tc_IntDef_Oint)),c_insert(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolution,[status(thm)],[c175,c1358]) ).
cnf(p664,plain,
( v_x(c_insert(X0,X1,tc_IntDef_Oint)) = X0
| c_in(v_x(c_insert(X0,X1,tc_IntDef_Oint)),X1,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[c176,p371]) ).
cnf(f173,axiom,
~ c_in(V_a,c_emptyset,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f173_nnf,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(nnf_transformation,[status(thm)],[f173]) ).
fof(f173_sk,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(skolemisation,[status(esa)],[f173_nnf]) ).
cnf(c173,plain,
~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(esa)],[f173_sk]) ).
cnf(p668,plain,
v_x(c_insert(X0,c_emptyset,tc_IntDef_Oint)) = X0,
inference(resolution,[status(thm)],[p664,c173]) ).
cnf(f1359,negated_conjecture,
( ~ v_P(v_x(V_U))
| ~ c_in(V_W,V_U,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1359_nnf,plain,
! [V_W,V_U] :
( ~ v_P(v_x(V_U))
| ~ c_in(V_W,V_U,tc_IntDef_Oint) ),
inference(nnf_transformation,[status(thm)],[f1359]) ).
fof(f1359_sk,plain,
! [V_W,V_U] :
( ~ v_P(v_x(V_U))
| ~ c_in(V_W,V_U,tc_IntDef_Oint) ),
inference(skolemisation,[status(esa)],[f1359_nnf]) ).
cnf(c1359,plain,
( ~ v_P(v_x(X1))
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(esa)],[f1359_sk]) ).
cnf(p370,plain,
~ v_P(v_x(c_insert(X0,X1,tc_IntDef_Oint))),
inference(resolution,[status(thm)],[c175,c1359]) ).
cnf(p681,plain,
~ v_P(X0),
inference(superposition,[status(thm)],[p668,p370]) ).
cnf(f1357,negated_conjecture,
v_P(v_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1357_nnf,plain,
v_P(v_a),
inference(nnf_transformation,[status(thm)],[f1357]) ).
cnf(c1357,plain,
v_P(v_a),
inference(cnf_transformation,[status(esa)],[f1357_nnf]) ).
cnf(p684,plain,
$false,
inference(resolution,[status(thm)],[p681,c1357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET820-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:03:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.10/3.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.10/3.49 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------