%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PUZ062-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 02:00:01 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 45 ( 27 unt; 0 def)
% Number of atoms : 68 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 27 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-4 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_A,T_a,V_x] :
( c_Finite__Set_Ocard(c_insert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a))
| c_in(V_x,V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_G,T_a,V_F] :
( c_in(c_inter(V_F,V_G,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_G,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_t] :
( c_in(V_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(V_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_c,V_B,T_a,V_A] :
( c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_x,V_A,T_a] : c_in(V_x,c_insert(V_x,V_A,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_c,T_a] : ~ c_in(V_c,c_emptyset,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1,X2] :
( c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(X0,X1))
| c_in(X2,X0,X1)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [V_G,T_a] :
( ! [V_F] : c_in(c_inter(V_F,V_G,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_G,c_Finite__Set_OFinites,tc_set(T_a)) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0,X1,X2] :
( c_in(c_inter(X2,X0,X1),c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0] :
( c_in(X0,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X0,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [V_c,V_B,T_a] :
( c_in(V_c,V_B,T_a)
| ! [V_A] : ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X2,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_inter(X3,X1,X2),X2)
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
! [X0] :
( c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat))
| ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat))
| ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat)) ),
inference(paramodulation,[status(thm)],[f25,f20]) ).
fof(f32,plain,
! [X0] :
( ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat))
| ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat)) ),
inference(forward_subsumption_resolution,[status(thm)],[f31,f22]) ).
fof(f34,plain,
! [X0,X1] :
( ~ c_in(X1,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))
| c_in(c_inter(X0,X1,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
inference(resolution,[status(thm)],[f16,f17]) ).
fof(f35,plain,
c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(paramodulation,[status(thm)],[f26,f21]) ).
fof(f36,plain,
c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
inference(resolution,[status(thm)],[f35,f19]) ).
fof(f37,plain,
c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(paramodulation,[status(thm)],[f27,f21]) ).
fof(f39,plain,
! [X0] : c_in(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
inference(resolution,[status(thm)],[f34,f23]) ).
fof(f41,plain,
! [X0,X1] :
( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
| c_in(X0,c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
inference(resolution,[status(thm)],[f39,f14]) ).
fof(f46,plain,
c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
inference(resolution,[status(thm)],[f37,f19]) ).
fof(f54,plain,
! [X0,X1] :
( c_in(X0,v_t,tc_prod(tc_nat,tc_nat))
| c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) ),
inference(resolution,[status(thm)],[f41,f19]) ).
fof(f72,plain,
! [X0,X1] :
( ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat))
| c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) ),
inference(resolution,[status(thm)],[f54,f32]) ).
fof(f84,plain,
! [X0] : c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))),
inference(resolution,[status(thm)],[f72,f46]) ).
fof(f85,plain,
! [X0] : c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))),
inference(resolution,[status(thm)],[f72,f36]) ).
fof(f86,plain,
c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))),
inference(backward_demodulation,[status(thm)],[f84,f28]) ).
fof(f88,plain,
c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))),
inference(forward_demodulation,[status(thm)],[f24,f86]) ).
fof(f92,plain,
c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))),
inference(forward_demodulation,[status(thm)],[f85,f88]) ).
fof(f93,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ062-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n001.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 03:54:13 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.050082 seconds
% 0.12/0.42 % CPU time: 0.155029 seconds
% 0.12/0.42 % Total memory used: 92.956 MB
% 0.12/0.42 % Net memory used: 92.568 MB
%------------------------------------------------------------------------------