%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN069-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 03:15:07 PM UTC 2026
% Result : Unsatisfiable 0.08s 5.59s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 51 ( 6 unt; 5 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 198 ( 98 ~; 95 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_h(X,f(X))
| ~ big_f(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_j(X,f(X))
| ~ big_f(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ big_k(X)
| ~ big_l(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
big_f(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( big_l(X)
| ~ big_h(a,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( big_j(a,X)
| ~ big_h(a,X)
| ~ big_g(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
! [X] :
( big_g(g(X))
| ~ big_f(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [X] :
( big_h(X,g(X))
| ~ big_f(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [Y] :
( big_k(Y)
| ! [X] :
( ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] :
( big_k(X1)
| ~ big_h(X0,X1)
| ~ big_g(X1)
| big_g(f(X0))
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [Y] :
( big_k(Y)
| ! [X] :
( ~ big_h(X,Y)
| ~ big_g(Y)
| big_h(X,f(X))
| ~ big_f(X) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( big_k(X1)
| ~ big_h(X0,X1)
| ~ big_g(X1)
| big_h(X0,f(X0))
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [Y] :
( big_k(Y)
| ! [X] :
( ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_j(X,f(X))
| ~ big_f(X) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( big_k(X1)
| ~ big_h(X0,X1)
| ~ big_g(X1)
| ~ big_j(X0,f(X0))
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0] :
( ~ big_k(X0)
| ~ big_l(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
big_f(a),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [X0] :
( big_l(X0)
| ~ big_h(a,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f19,plain,
! [X0] :
( big_j(a,X0)
| ~ big_h(a,X0)
| ~ big_g(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f20,plain,
! [X0] :
( big_g(g(X0))
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f21,plain,
! [X0] :
( big_h(X0,g(X0))
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
big_h(a,g(a)),
inference(resolution,[status(thm)],[f17,f21]) ).
fof(f23,plain,
! [X0] :
( ~ big_k(X0)
| ~ big_h(a,X0) ),
inference(resolution,[status(thm)],[f18,f16]) ).
fof(f24,plain,
! [X0] :
( big_k(X0)
| ~ big_h(a,X0)
| ~ big_g(X0)
| ~ big_f(a)
| ~ big_h(a,f(a))
| ~ big_g(f(a)) ),
inference(resolution,[status(thm)],[f19,f15]) ).
fof(f25,definition,
( sQ0_spl
<=> big_g(f(a)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( sQ0_spl
| ~ big_g(f(a)) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,definition,
( sQ1_spl
<=> big_h(a,f(a)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f31,definition,
( sQ2_spl
<=> big_f(a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( sQ2_spl
| ~ big_f(a) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,definition,
! [X0] :
( sQ3_spl
<=> ( big_k(X0)
| ~ big_h(a,X0)
| ~ big_g(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f35,plain,
! [X0] :
( ~ sQ3_spl
| big_k(X0)
| ~ big_h(a,X0)
| ~ big_g(X0) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f24,f25,f28,f31,f34]) ).
fof(f38,plain,
! [X0] :
( ~ sQ3_spl
| ~ big_h(a,X0)
| ~ big_g(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f35,f23]) ).
fof(f39,plain,
! [X0] :
( ~ sQ3_spl
| ~ big_f(X0)
| ~ big_h(a,g(X0)) ),
inference(resolution,[status(thm)],[f38,f20]) ).
fof(f40,plain,
( ~ sQ3_spl
| ~ big_f(a) ),
inference(resolution,[status(thm)],[f39,f22]) ).
fof(f41,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f40,f17]) ).
fof(f42,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f41]) ).
fof(f43,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f17]) ).
fof(f44,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f43]) ).
fof(f47,plain,
! [X0] :
( sQ0_spl
| big_k(X0)
| ~ big_h(a,X0)
| ~ big_g(X0)
| ~ big_f(a) ),
inference(resolution,[status(thm)],[f11,f27]) ).
fof(f48,plain,
( sQ0_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f47,f31,f34,f25]) ).
fof(f49,plain,
! [X0,X1] :
( ~ big_h(a,X1)
| ~ big_h(X0,X1)
| ~ big_g(X1)
| big_h(X0,f(X0))
| ~ big_f(X0) ),
inference(resolution,[status(thm)],[f13,f23]) ).
fof(f50,plain,
! [X0] :
( ~ big_h(a,X0)
| ~ big_h(a,X0)
| ~ big_g(X0)
| big_h(a,f(a)) ),
inference(resolution,[status(thm)],[f49,f17]) ).
fof(f51,definition,
! [X0] :
( sQ4_spl
<=> ( ~ big_h(a,X0)
| ~ big_h(a,X0)
| ~ big_g(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f52,plain,
! [X0] :
( ~ sQ4_spl
| ~ big_h(a,X0)
| ~ big_h(a,X0)
| ~ big_g(X0) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,plain,
( sQ4_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f50,f28,f51]) ).
fof(f55,plain,
! [X0] :
( ~ sQ4_spl
| ~ big_h(a,X0)
| ~ big_g(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f52]) ).
fof(f56,plain,
( ~ sQ4_spl
| ~ big_g(g(a)) ),
inference(resolution,[status(thm)],[f55,f22]) ).
fof(f57,plain,
( ~ sQ4_spl
| ~ big_f(a) ),
inference(resolution,[status(thm)],[f56,f20]) ).
fof(f58,plain,
( ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f57,f31,f51]) ).
fof(f59,plain,
$false,
inference(sat_refutation,[status(thm)],[f37,f42,f44,f48,f54,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN069-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.57 % Computer : n017.cluster.edu
% 0.08/5.57 % Model : x86_64 x86_64
% 0.08/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.57 % Memory : 8046.5625MB
% 0.08/5.57 % OS : Linux 6.8.0-71-generic
% 0.08/5.57 % CPULimit : 300
% 0.08/5.57 % WCLimit : 300
% 0.08/5.57 % DateTime : Mon Sep 21 10:37:03 UTC 2026
% 0.08/5.57 % CPUTime :
% 0.08/5.58 % Drodi V4.1.1
% 0.08/5.59 % Refutation found
% 0.08/5.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/5.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.61 % Elapsed time: 0.034449 seconds
% 0.13/5.61 % CPU time: 0.082443 seconds
% 0.13/5.61 % Total memory used: 9.876 MB
% 0.13/5.61 % Net memory used: 9.587 MB
%------------------------------------------------------------------------------