%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL121-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 102 ( 56 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 71 ( 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_r,T_a,V_x,V_y_H,V_y] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),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_y,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_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_r,T_a,V_x,V_y_H,V_y] :
( c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,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_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
c_Comb_Odiamond(v_r,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
! [V_U] :
( ~ c_in(c_Pair(v_y,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_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [V_U] :
( ~ c_in(c_Pair(v_y,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_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
! [V_U] :
( ~ c_in(c_Pair(v_z,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_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [V_r,T_a,V_y_H,V_y] :
( c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ! [V_x] :
( ~ c_in(c_Pair(V_x,V_y,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_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1,X2,X3,X4] :
( c_in(c_Pair(X3,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Comb_Odiamond(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [V_r,T_a,V_y_H,V_y] :
( c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a))
| ! [V_x] :
( ~ c_in(c_Pair(V_x,V_y,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_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Comb_Odiamond(V_r,T_a) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f14,plain,
! [X0,X1,X2,X3,X4] :
( c_in(c_Pair(X4,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Comb_Odiamond(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,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)],[f3]) ).
fof(f16,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)],[f4]) ).
fof(f17,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)],[f16]) ).
fof(f18,plain,
c_Comb_Odiamond(v_r,t_a),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
! [X0] :
( ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
! [X0] :
( ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X0,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
! [X0] :
( ~ c_in(c_Pair(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_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)],[f10]) ).
fof(f29,plain,
! [X0,X1] :
( ~ c_in(c_Pair(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(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(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f17,f23]) ).
fof(f33,plain,
! [X0] :
( ~ c_in(c_Pair(v_y,v_xaa,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),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f29,f22]) ).
fof(f36,plain,
! [X0] :
( ~ c_in(c_Pair(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_x(v_xaa),X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f20]) ).
fof(f39,plain,
! [X0] :
( ~ c_in(c_Pair(v_x(v_xaa),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f36,f15]) ).
fof(f40,plain,
! [X0,X1,X2] :
( c_in(c_Pair(X2,c_Comb_Odiamond__strip__lemmaE__1(v_r,X2,X1,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),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)],[f14,f18]) ).
fof(f43,plain,
! [X0,X1,X2] :
( c_in(c_Pair(X1,c_Comb_Odiamond__strip__lemmaE__1(v_r,X2,X1,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),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)],[f12,f18]) ).
fof(f46,plain,
! [X0] :
( c_in(c_Pair(X0,c_Comb_Odiamond__strip__lemmaE__1(v_r,X0,v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f40,f19]) ).
fof(f47,plain,
! [X0] :
( ~ c_in(c_Pair(v_y,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),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(X0),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f46,f21]) ).
fof(f55,plain,
! [X0] :
( c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,X0,v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f43,f19]) ).
fof(f63,plain,
( ~ c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f47,f39]) ).
fof(f66,plain,
~ c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(forward_subsumption_resolution,[status(thm)],[f63,f20]) ).
fof(f67,plain,
~ c_in(c_Pair(v_ya,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[f66,f55]) ).
fof(f74,plain,
~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[f67,f21]) ).
fof(f77,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f74,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL121-2 : 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 : n018.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 14:14:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % 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
% 0.13/0.42 % Elapsed time: 0.047918 seconds
% 0.13/0.42 % CPU time: 0.156837 seconds
% 0.13/0.42 % Total memory used: 56.835 MB
% 0.13/0.42 % Net memory used: 56.347 MB
%------------------------------------------------------------------------------