%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET838-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 02:10:45 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 5 unt; 4 def)
% Number of atoms : 61 ( 29 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 61 ( 30 ~; 27 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 6 ( 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1358,negated_conjecture,
v_f(v_g(v_x)) = v_x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1359,negated_conjecture,
! [V_U] :
( v_f(v_g(V_U)) != V_U
| V_U = v_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1360,negated_conjecture,
! [V_U] :
( v_g(v_f(V_U)) != V_U
| v_g(v_f(v_xa(V_U))) = v_xa(V_U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1361,negated_conjecture,
! [V_U] :
( v_g(v_f(V_U)) != V_U
| v_xa(V_U) != V_U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2837,plain,
v_f(v_g(v_x)) = v_x,
inference(cnf_transformation,[status(thm)],[f1358]) ).
fof(f2838,plain,
! [X0] :
( v_f(v_g(X0)) != X0
| X0 = v_x ),
inference(cnf_transformation,[status(thm)],[f1359]) ).
fof(f2839,plain,
! [X0] :
( v_g(v_f(X0)) != X0
| v_g(v_f(v_xa(X0))) = v_xa(X0) ),
inference(cnf_transformation,[status(thm)],[f1360]) ).
fof(f2840,plain,
! [X0] :
( v_g(v_f(X0)) != X0
| v_xa(X0) != X0 ),
inference(cnf_transformation,[status(thm)],[f1361]) ).
fof(f2847,plain,
( v_g(v_x) != v_g(v_x)
| v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)) ),
inference(paramodulation,[status(thm)],[f2837,f2839]) ).
fof(f2848,definition,
( sQ1_spl
<=> v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f2849,plain,
( ~ sQ1_spl
| v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)) ),
inference(component_clause,[status(thm)],[f2848]) ).
fof(f2851,definition,
( sQ2_spl
<=> v_g(v_x) = v_g(v_x) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f2853,plain,
( sQ2_spl
| v_g(v_x) != v_g(v_x) ),
inference(component_clause,[status(thm)],[f2851]) ).
fof(f2854,plain,
( ~ sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f2847,f2848,f2851]) ).
fof(f2857,plain,
( ~ sQ1_spl
| v_f(v_xa(v_g(v_x))) != v_f(v_xa(v_g(v_x)))
| v_f(v_xa(v_g(v_x))) = v_x ),
inference(paramodulation,[status(thm)],[f2849,f2838]) ).
fof(f2865,definition,
( sQ5_spl
<=> v_f(v_xa(v_g(v_x))) = v_x ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f2866,plain,
( ~ sQ5_spl
| v_f(v_xa(v_g(v_x))) = v_x ),
inference(component_clause,[status(thm)],[f2865]) ).
fof(f2868,definition,
( sQ6_spl
<=> v_f(v_xa(v_g(v_x))) = v_f(v_xa(v_g(v_x))) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f2870,plain,
( sQ6_spl
| v_f(v_xa(v_g(v_x))) != v_f(v_xa(v_g(v_x))) ),
inference(component_clause,[status(thm)],[f2868]) ).
fof(f2871,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f2857,f2865,f2868,f2848]) ).
fof(f2872,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| v_g(v_x) = v_xa(v_g(v_x)) ),
inference(backward_demodulation,[status(thm)],[f2866,f2849]) ).
fof(f2878,plain,
( sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2870]) ).
fof(f2879,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f2878]) ).
fof(f2880,plain,
( sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2853]) ).
fof(f2881,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f2880]) ).
fof(f2882,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| v_g(v_f(v_g(v_x))) != v_g(v_x) ),
inference(resolution,[status(thm)],[f2872,f2840]) ).
fof(f2884,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| v_g(v_x) != v_g(v_x) ),
inference(forward_demodulation,[status(thm)],[f2837,f2882]) ).
fof(f2885,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2884]) ).
fof(f2886,plain,
( ~ sQ1_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f2885]) ).
fof(f2887,plain,
$false,
inference(sat_refutation,[status(thm)],[f2854,f2871,f2879,f2881,f2886]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET838-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 05:40:24 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.34 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.40 % Elapsed time: 0.092772 seconds
% 0.09/0.40 % CPU time: 0.227970 seconds
% 0.09/0.40 % Total memory used: 151.251 MB
% 0.09/0.40 % Net memory used: 150.816 MB
%------------------------------------------------------------------------------