↑ Up

iProver---3.9.4.UNS-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : LCL118-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n014.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 : Fri Sep 25 02:05:43 PM UTC 2026

% Result   : Unsatisfiable 7.22s 11.79s
% Output   : CNFRefutation 7.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   50
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   73 (  18 unt;   0 def)
%            Number of atoms       :  159 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  222 ( 136   ~;  86   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  156 (   0 sgn 156   !;   0   ?; 151   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).

fof(f2,axiom,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,equivalent(X1,X0)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wo) ).

fof(f3,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_yqm) ).

tcf(c_52,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,X1)) ),
    inference(cnf_transformation,[],[f1]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,equivalent(X1,X0)))),
    inference(cnf_transformation,[],[f2]) ).

tcf(c_54,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))),
    inference(cnf_transformation,[],[f3]) ).

tcf(c_71,plain,
    ! [X0: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a))))) ),
    inference(resolution,[status(thm)],[c_52,c_54]) ).

tcf(c_77,plain,
    ~ is_a_theorem(equivalent(equivalent(c,a),equivalent(equivalent(c,b),equivalent(a,b)))),
    inference(resolution,[status(thm)],[c_71,c_53]) ).

tcf(c_85,plain,
    ! [X0: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(equivalent(c,a),equivalent(equivalent(c,b),equivalent(a,b))))) ),
    inference(resolution,[status(thm)],[c_77,c_52]) ).

tcf(c_89,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(c,a),equivalent(equivalent(c,b),equivalent(a,b)))))) ),
    inference(resolution,[status(thm)],[c_85,c_52]) ).

tcf(c_92,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(equivalent(X2,equivalent(X1,X0)))
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
    inference(superposition,[status(thm)],[c_53,c_52]) ).

tcf(c_93,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,equivalent(X1,equivalent(X0,X2))))),
    inference(superposition,[status(thm)],[c_53,c_92]) ).

tcf(c_110,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(equivalent(X2,equivalent(X1,equivalent(X0,X2))))
      | ~ is_a_theorem(equivalent(X0,X1)) ),
    inference(superposition,[status(thm)],[c_93,c_52]) ).

tcf(c_122,plain,
    ! [X0: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,b)),equivalent(equivalent(c,a),X0))) ),
    inference(resolution,[status(thm)],[c_89,c_53]) ).

tcf(c_125,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(equivalent(equivalent(X0,X2),equivalent(X1,X2)))
      | ~ is_a_theorem(equivalent(X0,X1)) ),
    inference(superposition,[status(thm)],[c_110,c_92]) ).

tcf(c_137,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(c,b),equivalent(a,b)),equivalent(equivalent(c,a),X1)))) ),
    inference(resolution,[status(thm)],[c_122,c_52]) ).

tcf(c_148,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ is_a_theorem(X2)
      | ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(equivalent(c,b),equivalent(a,b)),equivalent(equivalent(c,a),X2))))) ),
    inference(resolution,[status(thm)],[c_137,c_52]) ).

tcf(c_159,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(equivalent(X2,equivalent(X1,X0)))
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
    inference(superposition,[status(thm)],[c_53,c_52]) ).

tcf(c_160,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(equivalent(X1,X2))
      | ~ is_a_theorem(equivalent(X0,X2))
      | ~ is_a_theorem(equivalent(X0,X1)) ),
    inference(superposition,[status(thm)],[c_125,c_52]) ).

tcf(c_162,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(equivalent(X2,equivalent(X1,equivalent(X0,X2))))
      | ~ is_a_theorem(equivalent(X0,X1)) ),
    inference(superposition,[status(thm)],[c_125,c_159]) ).

tcf(c_211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( is_a_theorem(equivalent(equivalent(X2,equivalent(X1,X0)),X3))
      | ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),X3)) ),
    inference(superposition,[status(thm)],[c_53,c_160]) ).

tcf(c_213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( is_a_theorem(equivalent(equivalent(X1,equivalent(X0,X2)),X3))
      | ~ is_a_theorem(equivalent(X2,X3))
      | ~ is_a_theorem(equivalent(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162,c_160]) ).

tcf(c_217,plain,
    ( is_a_theorem(equivalent(equivalent(a,equivalent(a,a)),a))
    | ~ is_a_theorem(equivalent(a,a)) ),
    inference(instantiation,[status(thm)],[c_213]) ).

tcf(c_504,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(c,a),X0),equivalent(equivalent(equivalent(c,b),equivalent(a,b)),X1))) ),
    inference(resolution,[status(thm)],[c_148,c_53]) ).

tcf(c_520,plain,
    ! [X0: $i] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(c,a)))
      | ~ is_a_theorem(equivalent(X0,equivalent(equivalent(c,b),equivalent(a,b)))) ),
    inference(resolution,[status(thm)],[c_504,c_53]) ).

tcf(c_526,plain,
    ~ is_a_theorem(equivalent(equivalent(b,equivalent(a,equivalent(c,b))),equivalent(c,a))),
    inference(resolution,[status(thm)],[c_520,c_53]) ).

tcf(c_528,plain,
    ! [X0: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(equivalent(b,equivalent(a,equivalent(c,b))),equivalent(c,a)))) ),
    inference(resolution,[status(thm)],[c_526,c_52]) ).

tcf(c_532,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(b,equivalent(a,equivalent(c,b))),equivalent(c,a))))) ),
    inference(resolution,[status(thm)],[c_528,c_52]) ).

tcf(c_581,plain,
    ! [X0: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(equivalent(c,a),equivalent(equivalent(b,equivalent(a,equivalent(c,b))),X0))) ),
    inference(resolution,[status(thm)],[c_532,c_53]) ).

tcf(c_585,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(equivalent(c,a),equivalent(equivalent(b,equivalent(a,equivalent(c,b))),X1)))) ),
    inference(resolution,[status(thm)],[c_581,c_52]) ).

tcf(c_635,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ is_a_theorem(X2)
      | ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(c,a),equivalent(equivalent(b,equivalent(a,equivalent(c,b))),X2))))) ),
    inference(resolution,[status(thm)],[c_585,c_52]) ).

tcf(c_1604,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(equivalent(X2,equivalent(X1,X0)))
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
    inference(superposition,[status(thm)],[c_53,c_52]) ).

tcf(c_1625,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,equivalent(X1,X2)))),
    inference(superposition,[status(thm)],[c_53,c_211]) ).

tcf(c_1653,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,equivalent(X2,equivalent(X0,X1))))),
    inference(superposition,[status(thm)],[c_1625,c_1604]) ).

tcf(c_1657,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(equivalent(X2,equivalent(X2,equivalent(X0,X1))))
      | ~ is_a_theorem(equivalent(X0,X1)) ),
    inference(superposition,[status(thm)],[c_1653,c_52]) ).

tcf(c_1663,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,X2)))
      | ~ is_a_theorem(equivalent(X0,X1)) ),
    inference(superposition,[status(thm)],[c_1657,c_1604]) ).

tcf(c_1667,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(equivalent(X2,X2))
      | ~ is_a_theorem(equivalent(X0,X1)) ),
    inference(superposition,[status(thm)],[c_1663,c_52]) ).

tcf(c_1680,plain,
    ! [X0: $i] : is_a_theorem(equivalent(X0,X0)),
    inference(superposition,[status(thm)],[c_1653,c_1667]) ).

tcf(c_1683,plain,
    is_a_theorem(equivalent(a,a)),
    inference(instantiation,[status(thm)],[c_1680]) ).

tcf(c_2033,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(b,equivalent(a,equivalent(c,b))),X0),equivalent(equivalent(c,a),X1))) ),
    inference(resolution,[status(thm)],[c_635,c_53]) ).

tcf(c_2040,plain,
    ! [X0: $i] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(c,a)))
      | ~ is_a_theorem(equivalent(X0,equivalent(b,equivalent(a,equivalent(c,b))))) ),
    inference(resolution,[status(thm)],[c_2033,c_53]) ).

tcf(c_2044,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X1,equivalent(c,a)))
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(b,equivalent(a,equivalent(c,b)))))) ),
    inference(resolution,[status(thm)],[c_2040,c_52]) ).

tcf(c_2098,plain,
    ! [X0: $i] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(c,a)))
      | ~ is_a_theorem(equivalent(equivalent(a,equivalent(c,b)),equivalent(b,X0))) ),
    inference(resolution,[status(thm)],[c_2044,c_53]) ).

tcf(c_2103,plain,
    ~ is_a_theorem(equivalent(equivalent(c,a),equivalent(c,a))),
    inference(resolution,[status(thm)],[c_2098,c_53]) ).

tcf(c_2105,plain,
    ! [X0: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(equivalent(c,a),equivalent(c,a)))) ),
    inference(resolution,[status(thm)],[c_2103,c_52]) ).

tcf(c_2109,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(c,a),equivalent(c,a))))) ),
    inference(resolution,[status(thm)],[c_2105,c_52]) ).

tcf(c_2208,plain,
    ! [X0: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(equivalent(c,a),equivalent(equivalent(c,a),X0))) ),
    inference(resolution,[status(thm)],[c_2109,c_53]) ).

tcf(c_2212,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(equivalent(c,a),equivalent(equivalent(c,a),X1)))) ),
    inference(resolution,[status(thm)],[c_2208,c_52]) ).

tcf(c_2290,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ is_a_theorem(X2)
      | ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(c,a),equivalent(equivalent(c,a),X2))))) ),
    inference(resolution,[status(thm)],[c_2212,c_52]) ).

tcf(c_4700,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(c,a),X0),equivalent(equivalent(c,a),X1))) ),
    inference(resolution,[status(thm)],[c_2290,c_53]) ).

tcf(c_4707,plain,
    ! [X0: $i] : ~ is_a_theorem(equivalent(X0,equivalent(c,a))),
    inference(resolution,[status(thm)],[c_4700,c_53]) ).

tcf(c_4717,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(c,a)))) ),
    inference(resolution,[status(thm)],[c_4707,c_52]) ).

tcf(c_4721,plain,
    ! [X0: $i] : ~ is_a_theorem(equivalent(a,equivalent(c,X0))),
    inference(resolution,[status(thm)],[c_4717,c_53]) ).

tcf(c_4723,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(a,equivalent(c,X1)))) ),
    inference(resolution,[status(thm)],[c_4721,c_52]) ).

tcf(c_4726,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(a,equivalent(c,X2))))) ),
    inference(resolution,[status(thm)],[c_4723,c_52]) ).

tcf(c_4740,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(equivalent(equivalent(c,X0),equivalent(a,X1))) ),
    inference(resolution,[status(thm)],[c_4726,c_53]) ).

tcf(c_4743,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ is_a_theorem(X2)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(equivalent(c,X1),equivalent(a,X2)))) ),
    inference(resolution,[status(thm)],[c_4740,c_52]) ).

tcf(c_4753,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ is_a_theorem(X3)
      | ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(c,X2),equivalent(a,X3))))) ),
    inference(resolution,[status(thm)],[c_4743,c_52]) ).

tcf(c_6197,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ is_a_theorem(X2)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(equivalent(a,X0),equivalent(equivalent(c,X1),X2))) ),
    inference(resolution,[status(thm)],[c_4753,c_53]) ).

tcf(c_6202,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(equivalent(X0,a))
      | ~ is_a_theorem(equivalent(X0,equivalent(c,X1))) ),
    inference(resolution,[status(thm)],[c_6197,c_53]) ).

tcf(c_6205,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X1,a))
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(c,X2)))) ),
    inference(resolution,[status(thm)],[c_6202,c_52]) ).

tcf(c_6217,plain,
    ! [X0: $i,X1: $i] :
      ( ~ is_a_theorem(equivalent(X1,a))
      | ~ is_a_theorem(equivalent(X0,equivalent(c,X1))) ),
    inference(resolution,[status(thm)],[c_6205,c_53]) ).

tcf(c_6221,plain,
    ! [X0: $i,X1: $i] : ~ is_a_theorem(equivalent(equivalent(X0,X1),a)),
    inference(resolution,[status(thm)],[c_6217,c_53]) ).

tcf(c_6224,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),a))) ),
    inference(resolution,[status(thm)],[c_6221,c_52]) ).

tcf(c_6227,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X3),a)))) ),
    inference(resolution,[status(thm)],[c_6224,c_52]) ).

tcf(c_6245,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ is_a_theorem(X2)
      | ~ is_a_theorem(equivalent(a,equivalent(equivalent(X0,X1),X2))) ),
    inference(resolution,[status(thm)],[c_6227,c_53]) ).

tcf(c_6248,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ is_a_theorem(X3)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(a,equivalent(equivalent(X1,X2),X3)))) ),
    inference(resolution,[status(thm)],[c_6245,c_52]) ).

tcf(c_6257,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ is_a_theorem(X4)
      | ~ is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(a,equivalent(equivalent(X2,X3),X4))))) ),
    inference(resolution,[status(thm)],[c_6248,c_52]) ).

tcf(c_6857,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ is_a_theorem(X3)
      | ~ is_a_theorem(X2)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(a,X3))) ),
    inference(resolution,[status(thm)],[c_6257,c_53]) ).

tcf(c_6863,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ is_a_theorem(equivalent(X0,a))
      | ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
    inference(resolution,[status(thm)],[c_6857,c_53]) ).

tcf(c_6868,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),a)),
    inference(resolution,[status(thm)],[c_6863,c_53]) ).

tcf(c_6869,plain,
    ~ is_a_theorem(equivalent(equivalent(a,equivalent(a,a)),a)),
    inference(instantiation,[status(thm)],[c_6868]) ).

tcf(c_6870,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_6869,c_1683,c_217]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL118-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/10.39  % Computer : n014.cluster.edu
% 0.11/10.39  % Model    : x86_64 x86_64
% 0.11/10.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39  % Memory   : 8046.5625MB
% 0.11/10.39  % OS       : Linux 6.8.0-71-generic
% 0.11/10.40  % CPULimit : 300
% 0.11/10.40  % WCLimit  : 300
% 0.11/10.40  % DateTime : Wed Sep 23 21:59:58 UTC 2026
% 0.15/10.40  % CPUTime  : 
% 0.15/10.40  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.44  Running first-order theorem proving
% 0.15/10.44  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/10.45  
% 0.15/10.45  % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.45  
% 0.15/10.45  % Detected problem language: tptp
% 0.15/10.46  % Proving...
% 7.22/11.79  % SZS status Started for theBenchmark.p
% 7.22/11.79  % SZS status Unsatisfiable for theBenchmark.p
% 7.22/11.79  
% 7.22/11.79  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.22/11.79  
% 7.22/11.79  % ------  iProver source info
% 7.22/11.79  
% 7.22/11.79  % git: date: 2026-07-19 20:42:38 +0200
% 7.22/11.79  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.22/11.79  % git: non_committed_changes: false
% 7.22/11.79  
% 7.22/11.79  % ------ Parsing...% successful
% 7.22/11.79  
% 7.22/11.79  
% 7.22/11.79  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 7.22/11.79  
% 7.22/11.79  % ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe_e % 
% 7.22/11.79  
% 7.22/11.79  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.22/11.79  % ------ Proving...
% 7.22/11.79  % ------ Problem Properties 
% 7.22/11.79  
% 7.22/11.79  % 
% 7.22/11.79  % clauses                               3
% 7.22/11.79  % conjectures                           1
% 7.22/11.79  % EPR                                   0
% 7.22/11.79  % Horn                                  3
% 7.22/11.79  % unary                                 2
% 7.22/11.79  % binary                                0
% 7.22/11.79  % lits                                  5
% 7.22/11.79  % lits eq                               0
% 7.22/11.79  % fd_pure                               0
% 7.22/11.79  % fd_pseudo                             0
% 7.22/11.79  % fd_cond                               0
% 7.22/11.79  % fd_pseudo_cond                        0
% 7.22/11.79  % AC symbols                            0
% 7.22/11.79  
% 7.22/11.79  % ------ Input Options Time Limit: Unbounded
% 7.22/11.79  
% 7.22/11.79  
% 7.22/11.79  % ------ 
% 7.22/11.79  % Current options:
% 7.22/11.79  % ------ 
% 7.22/11.79  
% 7.22/11.79  
% 7.22/11.79  % 
% 7.22/11.79  
% 7.22/11.79  % ------ Proving...
% 7.22/11.79  % 
% 7.22/11.79  
% 7.22/11.79  % SZS status Unsatisfiable for theBenchmark.p
% 7.22/11.79  
% 7.22/11.79  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.22/11.79  
% 7.22/11.79  
%------------------------------------------------------------------------------