%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL123-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 12:08:51 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 91 ( 51 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_p,V_r,T_a] :
( c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(V_p,V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_b,V_c,T_a,V_r,V_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))
| ~ 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_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [V_U] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| 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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [V_U] :
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_xaa(V_U),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [V_U] :
( ~ 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))
| ~ c_in(c_Pair(v_z,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
! [V_V,V_U,V_W] :
( ~ c_in(c_Pair(V_U,V_V,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_V,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [V_W,V_U,V_V] :
( ~ c_in(c_Pair(V_U,V_V,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_W,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1,X2] :
( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(X0,X1,tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [V_c,T_a,V_r,V_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))
| ! [V_b] :
( ~ 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_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1,X2,X3,X4] :
( c_in(c_Pair(X4,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(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0] :
( ~ c_in(c_Pair(v_x,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| 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)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0] :
( ~ c_in(c_Pair(v_x,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_xaa(X0),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0] :
( ~ 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_z,X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
! [V_V,V_U] :
( ~ c_in(c_Pair(V_U,V_V,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ! [V_W] :
( ~ 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_V,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ 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))
| c_in(c_Pair(X0,v_xa(X1,X0,X2),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [V_U,V_V] :
( ~ c_in(c_Pair(V_U,V_V,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ! [V_W] :
( ~ 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_W,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ 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))
| c_in(c_Pair(X0,v_xa(X1,X2,X0),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ~ 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))
| ~ c_in(c_Pair(X0,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X1,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f19,f17]) ).
fof(f24,plain,
! [X0] :
( ~ 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))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f22,f13]) ).
fof(f26,plain,
! [X0,X1] :
( ~ 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),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)) ),
inference(resolution,[status(thm)],[f24,f12]) ).
fof(f36,plain,
! [X0,X1] :
( ~ c_in(c_Pair(X1,v_xa(v_y,v_z,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(v_y,X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f26,f10]) ).
fof(f39,plain,
! [X0] :
( ~ c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,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_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)) ),
inference(resolution,[status(thm)],[f36,f21]) ).
fof(f41,plain,
! [X0] :
( ~ c_in(c_Pair(v_y,v_z,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)) ),
inference(duplicate_literals_removal,[status(thm)],[f39]) ).
fof(f42,plain,
! [X0] :
( ~ 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)) ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f13]) ).
fof(f45,plain,
( ~ c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f42,f15]) ).
fof(f48,plain,
~ c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(forward_subsumption_resolution,[status(thm)],[f45,f16]) ).
fof(f49,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f48,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL123-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.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 14:12:22 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.052027 seconds
% 0.12/0.42 % CPU time: 0.157047 seconds
% 0.12/0.42 % Total memory used: 56.658 MB
% 0.12/0.42 % Net memory used: 56.223 MB
%------------------------------------------------------------------------------