%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL012-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 : Sun Sep 27 07:57:45 AM UTC 2026
% Result : Unsatisfiable 273.94s 50.50s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 73 ( 38 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 39 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% 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 : 213 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [VAR_0,VAR_1] :
( is_a_theorem(VAR_1)
| ~ is_a_theorem(VAR_0)
| ~ is_a_theorem(equivalent(VAR_0,VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(um,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(equivalent(VAR_0,VAR_1),VAR_2),equivalent(VAR_1,equivalent(VAR_2,VAR_0)))),
file('theBenchmark.p',um) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(B,equivalent(C,A)))),
inference(clausify,[status(thm)],[um]) ).
fof(prove_yqj,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(b,c)))),
file('theBenchmark.p',prove_yqj) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(b,c)))),
inference(clausify,[status(thm)],[prove_yqj]) ).
cnf(c_33020,plain,
( is_a_theorem(equivalent(B,equivalent(C,A)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B)))),
inference(resolve,[status(thm)],[c_33020,c_2]) ).
cnf(c_33021,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(equivalent(C,equivalent(B,D)),equivalent(D,C))),E)),equivalent(E,A))),
inference(resolve,[status(thm)],[c_33021,c_4]) ).
cnf(c_33022,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),D),equivalent(C,equivalent(D,B))),E)),equivalent(E,A))),
inference(resolve,[status(thm)],[c_33022,c_2]) ).
cnf(c_33023,plain,
( is_a_theorem(equivalent(B,equivalent(C,A)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_16,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B))),D),equivalent(equivalent(D,E),E))),
inference(resolve,[status(thm)],[c_33023,c_5]) ).
cnf(c_33024,plain,
( is_a_theorem(equivalent(E,A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),D),equivalent(C,equivalent(D,B))),E))) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_24,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,C),A)),C)),
inference(resolve,[status(thm)],[c_33024,c_4]) ).
cnf(c_33025,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_29,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),equivalent(equivalent(C,D),B)),D),E)),equivalent(E,A))),
inference(resolve,[status(thm)],[c_33025,c_24]) ).
cnf(c_33026,plain,
( is_a_theorem(C)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(B,C),A))) ),
inference(resolve,[status(thm)],[c_1,c_24]) ).
cnf(c_30,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),B),A)),
inference(resolve,[status(thm)],[c_33026,c_4]) ).
cnf(c_33027,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(equivalent(A,B),B)) ),
inference(resolve,[status(thm)],[c_1,c_30]) ).
cnf(c_36,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_33027,c_30]) ).
cnf(c_33028,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_40,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),C),B),D)),equivalent(D,A))),
inference(resolve,[status(thm)],[c_33028,c_30]) ).
cnf(c_33029,plain,
( is_a_theorem(equivalent(B,equivalent(C,A)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_41,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(B,A)))),
inference(resolve,[status(thm)],[c_33029,c_30]) ).
cnf(c_33030,plain,
( is_a_theorem(equivalent(B,equivalent(C,A)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_47,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,A),B))),
inference(resolve,[status(thm)],[c_33030,c_36]) ).
cnf(c_33031,plain,
( is_a_theorem(equivalent(B,equivalent(B,A)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_41]) ).
cnf(c_54,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(B,B)))),
inference(resolve,[status(thm)],[c_33031,c_36]) ).
cnf(c_33032,plain,
( is_a_theorem(equivalent(equivalent(B,A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_47]) ).
cnf(c_70,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,C),C),B)),A)),
inference(resolve,[status(thm)],[c_33032,c_30]) ).
cnf(c_33033,plain,
( is_a_theorem(equivalent(equivalent(B,A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_47]) ).
cnf(c_77,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,C),D),equivalent(C,equivalent(D,B)))),A)),
inference(resolve,[status(thm)],[c_33033,c_2]) ).
cnf(c_33034,plain,
( is_a_theorem(equivalent(A,equivalent(B,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_54]) ).
cnf(c_105,plain,
is_a_theorem(equivalent(equivalent(A,A),equivalent(B,B))),
inference(resolve,[status(thm)],[c_33034,c_36]) ).
cnf(c_33035,plain,
( is_a_theorem(equivalent(B,equivalent(C,A)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_132,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,B),A))),
inference(resolve,[status(thm)],[c_33035,c_105]) ).
cnf(c_33036,plain,
( is_a_theorem(equivalent(equivalent(B,A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_47]) ).
cnf(c_175,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(C,C),B))),A)),
inference(resolve,[status(thm)],[c_33036,c_132]) ).
cnf(c_33037,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),C),B))) ),
inference(resolve,[status(thm)],[c_1,c_70]) ).
cnf(c_502,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,A),C),C)),B)),
inference(resolve,[status(thm)],[c_33037,c_2]) ).
cnf(c_33038,plain,
( is_a_theorem(equivalent(equivalent(D,E),E))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B))),D)) ),
inference(resolve,[status(thm)],[c_1,c_16]) ).
cnf(c_1073,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,C),A)),C),D),D)),
inference(resolve,[status(thm)],[c_33038,c_7]) ).
cnf(c_33039,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(equivalent(C,C),B)))) ),
inference(resolve,[status(thm)],[c_1,c_175]) ).
cnf(c_3859,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(C,C),B)),A),D),D))),
inference(resolve,[status(thm)],[c_33039,c_502]) ).
cnf(c_33040,plain,
( is_a_theorem(equivalent(E,A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),equivalent(equivalent(C,D),B)),D),E))) ),
inference(resolve,[status(thm)],[c_1,c_29]) ).
cnf(c_20503,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,B),C),A),C))),
inference(resolve,[status(thm)],[c_33040,c_3859]) ).
cnf(c_33041,plain,
( is_a_theorem(equivalent(E,A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),D),equivalent(C,equivalent(D,B))),E))) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_20577,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(A,B)))),
inference(resolve,[status(thm)],[c_33041,c_20503]) ).
cnf(c_33042,plain,
( is_a_theorem(equivalent(B,equivalent(C,A)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_20992,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(equivalent(C,A),B)),C))),
inference(resolve,[status(thm)],[c_33042,c_20577]) ).
cnf(c_33043,plain,
( is_a_theorem(C)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(B,C),A))) ),
inference(resolve,[status(thm)],[c_1,c_24]) ).
cnf(c_21558,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(A,B)),B)),
inference(resolve,[status(thm)],[c_33043,c_20992]) ).
cnf(c_33044,plain,
( is_a_theorem(equivalent(B,equivalent(C,A)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_21636,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
inference(resolve,[status(thm)],[c_33044,c_21558]) ).
cnf(c_33045,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,C),A)),C),D)) ),
inference(resolve,[status(thm)],[c_1,c_1073]) ).
cnf(c_21670,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,A),B)))),
inference(resolve,[status(thm)],[c_33045,c_21636]) ).
cnf(c_33046,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),D),equivalent(C,equivalent(D,B))))) ),
inference(resolve,[status(thm)],[c_1,c_77]) ).
cnf(c_21704,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(C,A),B))),
inference(resolve,[status(thm)],[c_33046,c_21636]) ).
cnf(c_33047,plain,
( is_a_theorem(equivalent(D,A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),C),B),D))) ),
inference(resolve,[status(thm)],[c_1,c_40]) ).
cnf(c_22411,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(A,C),C)),B)),
inference(resolve,[status(thm)],[c_33047,c_21670]) ).
cnf(c_33048,plain,
( is_a_theorem(equivalent(B,equivalent(C,A)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_22544,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(B,C),A),C))),
inference(resolve,[status(thm)],[c_33048,c_21704]) ).
cnf(c_33049,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_21636]) ).
cnf(c_23586,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,A),equivalent(equivalent(B,C),C)))),
inference(resolve,[status(thm)],[c_33049,c_22411]) ).
cnf(c_33050,plain,
( is_a_theorem(equivalent(equivalent(C,A),B))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_21704]) ).
cnf(c_24937,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),B),C),equivalent(A,C))),
inference(resolve,[status(thm)],[c_33050,c_23586]) ).
cnf(c_33051,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_24937]) ).
cnf(c_27209,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(A,B)),C))),
inference(resolve,[status(thm)],[c_33051,c_22544]) ).
cnf(c_33052,plain,
( is_a_theorem(equivalent(equivalent(C,A),B))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_21704]) ).
cnf(c_33018,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(B,C)))),
inference(resolve,[status(thm)],[c_33052,c_27209]) ).
cnf(c_33019,plain,
$false,
inference(resolve,[status(thm)],[c_33018,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/15.40 % Computer : n004.cluster.edu
% 0.10/15.40 % Model : x86_64 x86_64
% 0.10/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.40 % Memory : 8046.5625MB
% 0.10/15.40 % OS : Linux 6.8.0-71-generic
% 0.01/15.40 % CPULimit : 300
% 0.01/15.40 % WCLimit : 300
% 0.01/15.40 % DateTime : Fri Sep 25 21:43:39 UTC 2026
% 0.01/15.40 % CPUTime :
% 0.01/15.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.01/15.40 % Process 29423 was started by sandbox2 on n004,
% 0.01/15.40 % Fri Sep 25 21:43:39 2026
% 0.01/15.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.01/15.41
% 0.01/15.41 % From the command line: assign(max_seconds, 300).
% 273.94/50.50
% 273.94/50.50 % given #500 (T,wt=16): 1374 is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(C,B)),C)),A),equivalent(D,D))). [hyper(1,a,54,a,b,165,a)].
% 273.94/50.50
% 273.94/50.50 % given #1000 (T,wt=12): 24082 is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(C,B)),A)),C)). [hyper(1,a,2636,a,b,22548,a)].
% 273.94/50.50
% 273.94/50.50 % SZS status Unsatisfiable for theBenchmark
% 273.94/50.50
% 273.94/50.50 % Proof 1 at 23.05 (+ 11.87) seconds.
% 273.94/50.50 % Length of proof is 37.
% 273.94/50.50 % Level of proof is 22.
% 273.94/50.50 % Maximum clause weight is 20.000.
% 273.94/50.50 % Given clauses 1138.
% 273.94/50.50
% 273.94/50.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------