%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : PUZ062-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 02:00:25 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ062-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 03:48:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % 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
% 0.12/0.38 fof(f1,axiom,(
% 0.12/0.38 (![V_A,T_a,V_x]: (( ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))| c_in(V_x,V_A,T_a)| c_Finite__Set_Ocard(c_insert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f2,axiom,(
% 0.12/0.38 (![V_G,T_a,V_F]: (( ~ c_in(V_G,c_Finite__Set_OFinites,tc_set(T_a))| c_in(c_inter(V_F,V_G,T_a),c_Finite__Set_OFinites,tc_set(T_a)) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f3,axiom,(
% 0.12/0.38 (![V_t]: (( ~ c_in(V_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))| c_in(V_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f4,axiom,(
% 0.12/0.38 (![V_c,V_A,V_B,T_a]: (( ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a)| c_in(V_c,V_B,T_a) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f5,axiom,(
% 0.12/0.38 (![V_c,V_B,T_a,V_A]: (( ~ c_in(V_c,V_B,T_a)| ~ c_in(V_c,V_A,T_a)| c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f6,axiom,(
% 0.12/0.38 (![V_x,V_A,T_a]: (c_in(V_x,c_insert(V_x,V_A,T_a),T_a) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f7,axiom,(
% 0.12/0.38 (![V_c,T_a]: (~ c_in(V_c,c_emptyset,T_a) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f8,negated_conjecture,(
% 0.12/0.38 c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f9,negated_conjecture,(
% 0.12/0.38 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)) ),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f10,negated_conjecture,(
% 0.12/0.38 c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset ),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f11,negated_conjecture,(
% 0.12/0.38 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)) ),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f12,negated_conjecture,(
% 0.12/0.38 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)) ),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f13,negated_conjecture,(
% 0.12/0.38 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)) ),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f14,plain,(
% 0.12/0.38 ![X0,X1,X2]: (~c_in(X0,c_Finite__Set_OFinites,tc_set(X1))|c_in(X2,X0,X1)|c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1)=c_Suc(c_Finite__Set_Ocard(X0,X1)))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.38 fof(f15,plain,(
% 0.12/0.38 ![V_G,T_a]: (~c_in(V_G,c_Finite__Set_OFinites,tc_set(T_a))|(![V_F]: c_in(c_inter(V_F,V_G,T_a),c_Finite__Set_OFinites,tc_set(T_a))))),
% 0.12/0.38 inference(miniscoping,[status(thm)],[f2])).
% 0.12/0.38 fof(f16,plain,(
% 0.12/0.38 ![X0,X1,X2]: (~c_in(X0,c_Finite__Set_OFinites,tc_set(X1))|c_in(c_inter(X2,X0,X1),c_Finite__Set_OFinites,tc_set(X1)))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f15])).
% 0.12/0.38 fof(f17,plain,(
% 0.12/0.38 ![X0]: (~c_in(X0,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))|c_in(X0,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.38 fof(f18,plain,(
% 0.12/0.38 ![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_B,T_a))),
% 0.12/0.38 inference(miniscoping,[status(thm)],[f4])).
% 0.12/0.38 fof(f19,plain,(
% 0.12/0.38 ![X0,X1,X2,X3]: (~c_in(X0,c_inter(X1,X2,X3),X3)|c_in(X0,X2,X3))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f18])).
% 0.12/0.39 fof(f20,plain,(
% 0.12/0.39 ![X0,X1,X2,X3]: (~c_in(X0,X1,X2)|~c_in(X0,X3,X2)|c_in(X0,c_inter(X3,X1,X2),X2))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.39 fof(f21,plain,(
% 0.12/0.39 ![X0,X1,X2]: (c_in(X0,c_insert(X0,X1,X2),X2))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.39 fof(f22,plain,(
% 0.12/0.39 ![X0,X1]: (~c_in(X0,c_emptyset,X1))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.12/0.39 fof(f23,plain,(
% 0.12/0.39 c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.12/0.39 fof(f24,plain,(
% 0.12/0.39 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))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.12/0.39 fof(f25,plain,(
% 0.12/0.39 c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat))=c_emptyset),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.12/0.39 fof(f26,plain,(
% 0.12/0.39 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))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.12/0.39 fof(f27,plain,(
% 0.12/0.39 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))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.12/0.39 fof(f28,plain,(
% 0.12/0.39 ~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))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f13])).
% 0.12/0.39 fof(f31,plain,(
% 0.12/0.39 ![X0]: (~c_in(X0,v_t,tc_prod(tc_nat,tc_nat))|~c_in(X0,v_a,tc_prod(tc_nat,tc_nat))|c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat)))),
% 0.12/0.39 inference(paramodulation,[status(thm)],[f25,f20])).
% 0.12/0.39 fof(f32,plain,(
% 0.12/0.39 ![X0]: (~c_in(X0,v_t,tc_prod(tc_nat,tc_nat))|~c_in(X0,v_a,tc_prod(tc_nat,tc_nat)))),
% 0.12/0.39 inference(forward_subsumption_resolution,[status(thm)],[f31,f22])).
% 0.12/0.39 fof(f33,plain,(
% 0.12/0.39 c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))),
% 0.12/0.39 inference(resolution,[status(thm)],[f17,f23])).
% 0.12/0.39 fof(f35,plain,(
% 0.12/0.39 ![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))))),
% 0.12/0.39 inference(resolution,[status(thm)],[f16,f33])).
% 0.12/0.39 fof(f37,plain,(
% 0.12/0.39 ![X0,X1]: (c_in(X0,c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),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))))),
% 0.12/0.39 inference(resolution,[status(thm)],[f35,f14])).
% 0.12/0.39 fof(f44,plain,(
% 0.12/0.39 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))),
% 0.12/0.39 inference(paramodulation,[status(thm)],[f26,f21])).
% 0.12/0.39 fof(f45,plain,(
% 0.12/0.39 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))),
% 0.12/0.39 inference(paramodulation,[status(thm)],[f27,f21])).
% 0.12/0.39 fof(f51,plain,(
% 0.12/0.39 c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat))),
% 0.12/0.39 inference(resolution,[status(thm)],[f44,f19])).
% 0.12/0.39 fof(f52,plain,(
% 0.12/0.39 ~c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat))),
% 0.12/0.39 inference(resolution,[status(thm)],[f51,f32])).
% 0.12/0.39 fof(f55,plain,(
% 0.12/0.39 c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat))),
% 0.12/0.39 inference(resolution,[status(thm)],[f45,f19])).
% 0.12/0.39 fof(f57,plain,(
% 0.12/0.39 ~c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat))),
% 0.12/0.39 inference(resolution,[status(thm)],[f55,f32])).
% 0.12/0.39 fof(f62,plain,(
% 0.12/0.39 ![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,v_t,tc_prod(tc_nat,tc_nat)))),
% 0.12/0.39 inference(resolution,[status(thm)],[f37,f19])).
% 0.12/0.39 fof(f70,plain,(
% 0.12/0.39 ![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))))),
% 0.12/0.39 inference(resolution,[status(thm)],[f62,f57])).
% 0.12/0.39 fof(f71,plain,(
% 0.12/0.39 ![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))))),
% 0.12/0.39 inference(resolution,[status(thm)],[f62,f52])).
% 0.12/0.39 fof(f72,plain,(
% 0.12/0.39 ~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)))),
% 0.12/0.39 inference(backward_demodulation,[status(thm)],[f70,f28])).
% 0.12/0.39 fof(f73,plain,(
% 0.12/0.39 ~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_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f71,f72])).
% 0.12/0.39 fof(f74,plain,(
% 0.12/0.39 ~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)))),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f24,f73])).
% 0.12/0.39 fof(f75,plain,(
% 0.12/0.39 $false),
% 0.12/0.39 inference(trivial_equality_resolution,[status(thm)],[f74])).
% 0.12/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.41 % Elapsed time: 0.053215 seconds
% 0.12/0.41 % CPU time: 0.135650 seconds
% 0.12/0.41 % Total memory used: 103.016 MB
% 0.12/0.41 % Net memory used: 102.569 MB
%------------------------------------------------------------------------------