%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL123-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 0.14s 5.49s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 41 ( 7 unt; 3 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 117 ( 61 ~; 53 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f317,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(f1366,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(f1368,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1369,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1370,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1371,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1372,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1373,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1374,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1806,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)],[f317]) ).
fof(f2860,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)],[f1366]) ).
fof(f2861,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)],[f2860]) ).
fof(f2863,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)],[f1368]) ).
fof(f2864,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)],[f1369]) ).
fof(f2865,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)],[f1370]) ).
fof(f2866,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)],[f1371]) ).
fof(f2867,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)],[f1372]) ).
fof(f2868,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)],[f1373]) ).
fof(f2869,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)],[f2868]) ).
fof(f2870,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)],[f1374]) ).
fof(f2871,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)],[f2870]) ).
fof(f2873,definition,
( sQ0_spl
<=> c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f2875,plain,
( sQ0_spl
| ~ c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f2873]) ).
fof(f2880,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2875,f2864]) ).
fof(f2881,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f2880]) ).
fof(f2900,plain,
! [X0,X1] :
( ~ c_in(c_Pair(v_x,X0,t_a,t_a),v_r,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))
| ~ c_in(c_Pair(v_xaa(X0),X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f2861,f2865]) ).
fof(f2963,plain,
! [X0,X1] :
( ~ c_in(c_Pair(v_xaa(X0),X1,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))
| 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)],[f2900,f1806]) ).
fof(f3206,plain,
! [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_xaa(v_xb),X0,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)) ),
inference(resolution,[status(thm)],[f2963,f2867]) ).
fof(f3216,definition,
! [X0] :
( sQ40_spl
<=> ( ~ c_in(c_Pair(v_z,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa(v_xb),X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f3217,plain,
! [X0] :
( ~ sQ40_spl
| ~ c_in(c_Pair(v_z,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa(v_xb),X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f3216]) ).
fof(f3219,plain,
( sQ40_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f3206,f2873,f3216]) ).
fof(f3224,plain,
! [X0,X1] :
( ~ sQ40_spl
| ~ c_in(c_Pair(X0,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,v_xa(X0,X1,v_xaa(v_xb)),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f3217,f2871]) ).
fof(f3645,plain,
! [X0] :
( ~ sQ40_spl
| ~ c_in(c_Pair(X0,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,v_xaa(v_xb),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(X0,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f3224,f2869]) ).
fof(f3646,plain,
! [X0] :
( ~ sQ40_spl
| ~ c_in(c_Pair(X0,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(duplicate_literals_removal,[status(thm)],[f3645]) ).
fof(f3647,plain,
( ~ sQ40_spl
| ~ 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_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f3646,f2866]) ).
fof(f3648,definition,
( sQ100_spl
<=> c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f3650,plain,
( sQ100_spl
| ~ c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f3648]) ).
fof(f3651,plain,
( ~ sQ40_spl
| ~ sQ0_spl
| ~ sQ100_spl ),
inference(split_clause,[status(thm)],[f3647,f3648,f2873,f3216]) ).
fof(f3652,plain,
( sQ100_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3650,f2863]) ).
fof(f3653,plain,
sQ100_spl,
inference(contradiction_clause,[status(thm)],[f3652]) ).
fof(f3654,plain,
$false,
inference(sat_refutation,[status(thm)],[f2881,f3219,f3651,f3653]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL123-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n010.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Mon Sep 21 14:12:48 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.14/5.41 % Drodi V4.1.1
% 0.14/5.49 % Refutation found
% 0.14/5.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.52 % Elapsed time: 0.144312 seconds
% 0.14/5.52 % CPU time: 0.638942 seconds
% 0.14/5.52 % Total memory used: 99.301 MB
% 0.14/5.52 % Net memory used: 98.820 MB
%------------------------------------------------------------------------------