%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL123-2 : 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 : n007.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 12:09:12 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL123-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 14:10:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.03/0.36 % Drodi V4.1.1
% 0.03/0.38 % Refutation found
% 0.03/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.03/0.38 fof(f1,axiom,(
% 0.03/0.38 (![V_p,V_r,T_a]: (( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ))),
% 0.03/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.38 fof(f2,axiom,(
% 0.03/0.38 (![V_b,V_c,T_a,V_r,V_a]: (( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ))),
% 0.03/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.38 fof(f3,negated_conjecture,(
% 0.03/0.38 c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
% 0.03/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.38 fof(f4,negated_conjecture,(
% 0.03/0.38 c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
% 0.03/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.38 fof(f5,negated_conjecture,(
% 0.03/0.38 (![V_U]: (( c_in(c_Pair(V_U,v_xaa(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))| ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ))),
% 0.03/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.38 fof(f6,negated_conjecture,(
% 0.03/0.38 (![V_U]: (( c_in(c_Pair(v_y,v_xaa(V_U),t_a,t_a),v_r,tc_prod(t_a,t_a))| ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ))),
% 0.03/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.38 fof(f7,negated_conjecture,(
% 0.03/0.38 (![V_U]: (( ~ c_in(c_Pair(v_z,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))| ~ c_in(c_Pair(v_xb,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ))),
% 0.03/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.38 fof(f8,negated_conjecture,(
% 0.03/0.38 (![V_V,V_U,V_W]: (( c_in(c_Pair(V_V,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a))| ~ c_in(c_Pair(V_U,V_W,t_a,t_a),v_r,tc_prod(t_a,t_a))| ~ c_in(c_Pair(V_U,V_V,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ))),
% 0.03/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.38 fof(f9,negated_conjecture,(
% 0.03/0.38 (![V_W,V_U,V_V]: (( c_in(c_Pair(V_W,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a))| ~ c_in(c_Pair(V_U,V_W,t_a,t_a),v_r,tc_prod(t_a,t_a))| ~ c_in(c_Pair(V_U,V_V,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ))),
% 0.03/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.38 fof(f10,plain,(
% 0.03/0.38 ![X0,X1,X2]: (~c_in(X0,X1,tc_prod(X2,X2))|c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)))),
% 0.03/0.38 inference(cnf_transformation,[status(thm)],[f1])).
% 0.03/0.38 fof(f11,plain,(
% 0.03/0.38 ![V_c,T_a,V_r,V_a]: ((![V_b]: (~c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))|~c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))))|c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)))),
% 0.03/0.38 inference(miniscoping,[status(thm)],[f2])).
% 0.03/0.38 fof(f12,plain,(
% 0.03/0.38 ![X0,X1,X2,X3,X4]: (~c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))|~c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))|c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)))),
% 0.03/0.38 inference(cnf_transformation,[status(thm)],[f11])).
% 0.03/0.38 fof(f13,plain,(
% 0.03/0.38 c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))),
% 0.03/0.38 inference(cnf_transformation,[status(thm)],[f3])).
% 0.03/0.38 fof(f14,plain,(
% 0.03/0.38 c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a))),
% 0.03/0.38 inference(cnf_transformation,[status(thm)],[f4])).
% 0.03/0.38 fof(f15,plain,(
% 0.03/0.38 ![X0]: (c_in(c_Pair(X0,v_xaa(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_Pair(v_x,X0,t_a,t_a),v_r,tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(cnf_transformation,[status(thm)],[f5])).
% 0.03/0.38 fof(f16,plain,(
% 0.03/0.38 ![X0]: (c_in(c_Pair(v_y,v_xaa(X0),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(v_x,X0,t_a,t_a),v_r,tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(cnf_transformation,[status(thm)],[f6])).
% 0.03/0.38 fof(f17,plain,(
% 0.03/0.38 ![X0]: (~c_in(c_Pair(v_z,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(v_xb,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.03/0.38 fof(f18,plain,(
% 0.03/0.38 ![V_V,V_U]: ((![V_W]: (c_in(c_Pair(V_V,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(V_U,V_W,t_a,t_a),v_r,tc_prod(t_a,t_a))))|~c_in(c_Pair(V_U,V_V,t_a,t_a),v_r,tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(miniscoping,[status(thm)],[f8])).
% 0.03/0.38 fof(f19,plain,(
% 0.03/0.38 ![X0,X1,X2]: (c_in(c_Pair(X0,v_xa(X1,X0,X2),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(X1,X0,t_a,t_a),v_r,tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(cnf_transformation,[status(thm)],[f18])).
% 0.03/0.38 fof(f20,plain,(
% 0.03/0.38 ![V_U,V_V]: ((![V_W]: (c_in(c_Pair(V_W,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(V_U,V_W,t_a,t_a),v_r,tc_prod(t_a,t_a))))|~c_in(c_Pair(V_U,V_V,t_a,t_a),v_r,tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(miniscoping,[status(thm)],[f9])).
% 0.03/0.38 fof(f21,plain,(
% 0.03/0.38 ![X0,X1,X2]: (c_in(c_Pair(X0,v_xa(X1,X2,X0),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(X1,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(cnf_transformation,[status(thm)],[f20])).
% 0.03/0.38 fof(f22,plain,(
% 0.03/0.38 ![X0,X1]: (~c_in(c_Pair(X0,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(X0,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(v_xb,v_xa(X0,v_z,X1),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(resolution,[status(thm)],[f19,f17])).
% 0.03/0.38 fof(f24,plain,(
% 0.03/0.38 ![X0]: (~c_in(c_Pair(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(v_xb,v_xa(v_y,v_z,X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(resolution,[status(thm)],[f22,f13])).
% 0.03/0.38 fof(f26,plain,(
% 0.03/0.38 ![X0,X1]: (~c_in(c_Pair(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(X1,v_xa(v_y,v_z,X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_Pair(v_xb,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(resolution,[status(thm)],[f24,f12])).
% 0.03/0.38 fof(f32,definition,(
% 0.03/0.38 sQ1_spl <=> (c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)))),
% 0.03/0.38 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.03/0.38 fof(f34,plain,(
% 0.03/0.38 ~c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))|sQ1_spl),
% 0.03/0.38 inference(component_clause,[status(thm)],[f32])).
% 0.03/0.38 fof(f39,plain,(
% 0.03/0.38 ![X0,X1]: (~c_in(c_Pair(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(v_xb,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_Pair(X1,v_xa(v_y,v_z,X0),t_a,t_a),v_r,tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(resolution,[status(thm)],[f26,f10])).
% 0.03/0.38 fof(f44,plain,(
% 0.03/0.38 ![X0]: (~c_in(c_Pair(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(v_xb,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_Pair(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)))),
% 0.03/0.38 inference(resolution,[status(thm)],[f39,f21])).
% 0.03/0.38 fof(f46,definition,(
% 0.03/0.38 ![X0]: (sQ2_spl <=> (~c_in(c_Pair(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(v_xb,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_Pair(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))))),
% 0.03/0.38 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.03/0.38 fof(f47,plain,(
% 0.03/0.38 ![X0]: (~c_in(c_Pair(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(v_xb,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~c_in(c_Pair(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))|~sQ2_spl)),
% 0.03/0.38 inference(component_clause,[status(thm)],[f46])).
% 0.03/0.38 fof(f49,plain,(
% 0.03/0.38 sQ2_spl|~sQ1_spl),
% 0.03/0.38 inference(split_clause,[status(thm)],[f44,f46,f32])).
% 0.03/0.38 fof(f57,plain,(
% 0.03/0.38 $false|sQ1_spl),
% 0.03/0.38 inference(forward_subsumption_resolution,[status(thm)],[f34,f13])).
% 0.03/0.38 fof(f58,plain,(
% 0.03/0.38 sQ1_spl),
% 0.03/0.38 inference(contradiction_clause,[status(thm)],[f57])).
% 0.03/0.38 fof(f59,plain,(
% 0.03/0.38 ![X0]: (~c_in(c_Pair(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(v_xb,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))|~sQ2_spl)),
% 0.03/0.38 inference(duplicate_literals_removal,[status(thm)],[f47])).
% 0.03/0.38 fof(f77,plain,(
% 0.03/0.38 ~c_in(c_Pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))|~c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a))|~sQ2_spl),
% 0.03/0.38 inference(resolution,[status(thm)],[f59,f15])).
% 0.03/0.38 fof(f80,definition,(
% 0.03/0.38 sQ5_spl <=> (c_in(c_Pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a)))),
% 0.03/0.38 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.03/0.38 fof(f82,plain,(
% 0.03/0.38 ~c_in(c_Pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))|sQ5_spl),
% 0.03/0.38 inference(component_clause,[status(thm)],[f80])).
% 0.03/0.38 fof(f83,definition,(
% 0.03/0.38 sQ6_spl <=> (c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)))),
% 0.03/0.38 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.03/0.38 fof(f85,plain,(
% 0.03/0.38 ~c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a))|sQ6_spl),
% 0.03/0.38 inference(component_clause,[status(thm)],[f83])).
% 0.03/0.38 fof(f86,plain,(
% 0.03/0.38 ~sQ5_spl|~sQ6_spl|~sQ2_spl),
% 0.03/0.38 inference(split_clause,[status(thm)],[f77,f80,f83,f46])).
% 0.03/0.38 fof(f91,plain,(
% 0.03/0.38 ~c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a))|sQ5_spl),
% 0.03/0.38 inference(resolution,[status(thm)],[f82,f16])).
% 0.03/0.38 fof(f92,plain,(
% 0.03/0.38 $false|sQ5_spl),
% 0.03/0.38 inference(forward_subsumption_resolution,[status(thm)],[f91,f14])).
% 0.03/0.38 fof(f93,plain,(
% 0.03/0.38 sQ5_spl),
% 0.03/0.38 inference(contradiction_clause,[status(thm)],[f92])).
% 0.03/0.38 fof(f94,plain,(
% 0.03/0.38 $false|sQ6_spl),
% 0.03/0.38 inference(forward_subsumption_resolution,[status(thm)],[f85,f14])).
% 0.03/0.38 fof(f95,plain,(
% 0.03/0.38 sQ6_spl),
% 0.03/0.38 inference(contradiction_clause,[status(thm)],[f94])).
% 0.03/0.38 fof(f96,plain,(
% 0.03/0.38 $false),
% 0.03/0.38 inference(sat_refutation,[status(thm)],[f49,f58,f86,f93,f95])).
% 0.03/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.03/0.42 % Elapsed time: 0.045847 seconds
% 0.03/0.42 % CPU time: 0.133691 seconds
% 0.03/0.42 % Total memory used: 56.731 MB
% 0.03/0.42 % Net memory used: 56.288 MB
%------------------------------------------------------------------------------