%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET820-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 : Thu Sep 24 02:10:41 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 9 unt; 0 def)
% Number of atoms : 36 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 19 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
v_P(v_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [V_V,V_U] :
( c_in(v_x(V_U),V_U,tc_IntDef_Oint)
| ~ c_in(V_V,V_U,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [V_W,V_U] :
( ~ v_P(v_x(V_U))
| ~ c_in(V_W,V_U,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [V_a,V_b] :
( V_a = V_b
| ! [V_A,T_a] :
( c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
v_P(v_a),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [V_U] :
( c_in(v_x(V_U),V_U,tc_IntDef_Oint)
| ! [V_V] : ~ c_in(V_V,V_U,tc_IntDef_Oint) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0,X1] :
( c_in(v_x(X1),X1,tc_IntDef_Oint)
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [V_U] :
( ~ v_P(v_x(V_U))
| ! [V_W] : ~ c_in(V_W,V_U,tc_IntDef_Oint) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f15,plain,
! [X0,X1] :
( ~ v_P(v_x(X1))
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ c_in(X0,c_insert(X1,c_emptyset,X2),X2) ),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f18,plain,
! [X0,X1] :
( ~ c_in(X1,c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint)
| v_x(c_insert(X0,c_emptyset,tc_IntDef_Oint)) = X0 ),
inference(resolution,[status(thm)],[f17,f13]) ).
fof(f22,plain,
! [X0] : v_x(c_insert(X0,c_emptyset,tc_IntDef_Oint)) = X0,
inference(resolution,[status(thm)],[f18,f8]) ).
fof(f25,plain,
! [X0,X1] :
( ~ v_P(X1)
| ~ c_in(X0,c_insert(X1,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f22,f15]) ).
fof(f27,plain,
! [X0] : ~ c_in(X0,c_insert(v_a,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolution,[status(thm)],[f25,f11]) ).
fof(f29,plain,
$false,
inference(resolution,[status(thm)],[f27,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET820-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:40:25 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.037832 seconds
% 0.10/0.41 % CPU time: 0.105389 seconds
% 0.10/0.41 % Total memory used: 37.381 MB
% 0.10/0.41 % Net memory used: 37.179 MB
%------------------------------------------------------------------------------