%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT394-2 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 07:50:31 AM UTC 2026
% Result : Unsatisfiable 0.95s 0.54s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 2
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 129 ( 32 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : f(f(f(f(VAR_0,VAR_1),f(VAR_1,VAR_2)),VAR_3),f(VAR_1,f(f(VAR_1,f(f(VAR_0,VAR_0),VAR_0)),VAR_2))) = VAR_1,
file('theBenchmark.p',sos) ).
cnf(c_1,plain,
f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C))) = B,
inference(clausify,[status(thm)],[sos]) ).
fof(goals,axiom,
f(x0,f(x0,x0)) != f(x1,f(x1,x1)),
file('theBenchmark.p',goals) ).
cnf(c_2,plain,
f(x0,f(x0,x0)) != f(x1,f(x1,x1)),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_3,plain,
f(x1,f(x1,x1)) != f(x0,f(x0,x0)),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_4,plain,
f(A,f(f(A,B),f(f(f(A,B),f(f(f(C,A),f(C,A)),f(C,A))),D))) = f(A,B),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
f(f(A,B),f(f(f(A,B),f(B,C)),B)) = f(f(A,B),f(B,C)),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_6,plain,
f(A,f(f(A,B),f(f(f(C,A),f(C,A)),f(C,A)))) = f(A,B),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_326,plain,
f(f(f(f(A,B),f(B,C)),B),f(B,B)) = f(f(f(f(A,B),f(B,C)),B),f(B,f(f(B,f(f(A,A),A)),C))),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_7,plain,
f(f(f(f(A,B),f(B,C)),B),f(B,B)) = B,
inference(paramod,[status(thm)],[c_1,c_326]) ).
cnf(c_8,plain,
f(f(A,A),f(A,A)) = A,
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_14,plain,
f(f(A,B),f(A,f(f(A,f(f(A,A),A)),A))) = A,
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_15,plain,
f(f(f(f(f(A,A),B),f(B,C)),D),f(B,f(f(B,f(A,f(A,A))),C))) = B,
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_327,plain,
f(f(f(f(A,f(B,B)),B),f(B,B)),f(f(B,B),f(B,B))) = f(B,B),
inference(paramod,[status(thm)],[c_8,c_7]) ).
cnf(c_19,plain,
f(f(f(f(A,f(B,B)),B),f(B,B)),B) = f(B,B),
inference(paramod,[status(thm)],[c_8,c_327]) ).
cnf(c_25,plain,
f(A,f(f(A,B),f(A,B))) = f(A,B),
inference(paramod,[status(thm)],[c_14,c_4]) ).
cnf(c_328,plain,
f(A,f(f(f(f(A,B),f(A,f(f(A,f(f(A,A),A)),A))),f(f(A,f(f(A,f(f(A,A),A)),A)),C)),f(A,f(f(A,f(f(A,A),A)),A)))) = f(f(f(A,B),f(A,f(f(A,f(f(A,A),A)),A))),f(f(A,f(f(A,f(f(A,A),A)),A)),C)),
inference(paramod,[status(thm)],[c_14,c_5]) ).
cnf(c_329,plain,
f(A,f(f(A,f(f(A,f(f(A,f(f(A,A),A)),A)),C)),f(A,f(f(A,f(f(A,A),A)),A)))) = f(f(f(A,B),f(A,f(f(A,f(f(A,A),A)),A))),f(f(A,f(f(A,f(f(A,A),A)),A)),C)),
inference(paramod,[status(thm)],[c_14,c_328]) ).
cnf(c_330,plain,
f(A,A) = f(f(f(A,B),f(A,f(f(A,f(f(A,A),A)),A))),f(f(A,f(f(A,f(f(A,A),A)),A)),C)),
inference(paramod,[status(thm)],[c_14,c_329]) ).
cnf(c_331,plain,
f(A,A) = f(A,f(f(A,f(f(A,f(f(A,A),A)),A)),C)),
inference(paramod,[status(thm)],[c_14,c_330]) ).
cnf(c_26,plain,
f(A,f(f(A,f(f(A,f(f(A,A),A)),A)),B)) = f(A,A),
inference(copy,[status(thm)],[c_331]) ).
cnf(c_332,plain,
f(f(f(A,f(f(A,f(f(A,f(f(A,A),A)),A)),B)),f(A,f(f(A,f(f(A,A),A)),A))),f(f(A,f(f(A,f(f(A,A),A)),A)),f(A,f(f(A,f(f(A,A),A)),A)))) = f(A,f(f(A,f(f(A,A),A)),A)),
inference(paramod,[status(thm)],[c_14,c_7]) ).
cnf(c_333,plain,
f(f(f(A,A),f(A,f(f(A,f(f(A,A),A)),A))),f(f(A,f(f(A,f(f(A,A),A)),A)),f(A,f(f(A,f(f(A,A),A)),A)))) = f(A,f(f(A,f(f(A,A),A)),A)),
inference(paramod,[status(thm)],[c_26,c_332]) ).
cnf(c_334,plain,
f(A,f(f(A,f(f(A,f(f(A,A),A)),A)),f(A,f(f(A,f(f(A,A),A)),A)))) = f(A,f(f(A,f(f(A,A),A)),A)),
inference(paramod,[status(thm)],[c_14,c_333]) ).
cnf(c_335,plain,
f(A,A) = f(A,f(f(A,f(f(A,A),A)),A)),
inference(paramod,[status(thm)],[c_14,c_334]) ).
cnf(c_28,plain,
f(A,f(f(A,f(f(A,A),A)),A)) = f(A,A),
inference(copy,[status(thm)],[c_335]) ).
cnf(c_32,plain,
f(A,f(f(A,A),B)) = f(A,A),
inference(paramod,[status(thm)],[c_28,c_26]) ).
cnf(c_336,plain,
f(f(A,B),f(A,f(f(A,A),A))) = A,
inference(paramod,[status(thm)],[c_32,c_14]) ).
cnf(c_34,plain,
f(f(A,B),f(A,A)) = A,
inference(paramod,[status(thm)],[c_32,c_336]) ).
cnf(c_337,plain,
f(A,f(f(A,B),f(f(f(A,A),f(f(f(f(C,f(A,A)),A),f(A,A)),A)),f(f(f(f(C,f(A,A)),A),f(A,A)),A)))) = f(A,B),
inference(paramod,[status(thm)],[c_19,c_6]) ).
cnf(c_338,plain,
f(A,f(f(A,B),f(f(f(A,A),f(A,A)),f(f(f(f(C,f(A,A)),A),f(A,A)),A)))) = f(A,B),
inference(paramod,[status(thm)],[c_19,c_337]) ).
cnf(c_339,plain,
f(A,f(f(A,B),f(A,f(f(f(f(C,f(A,A)),A),f(A,A)),A)))) = f(A,B),
inference(paramod,[status(thm)],[c_34,c_338]) ).
cnf(c_38,plain,
f(A,f(f(A,B),f(A,f(A,A)))) = f(A,B),
inference(paramod,[status(thm)],[c_19,c_339]) ).
cnf(c_340,plain,
f(f(A,A),f(A,B)) = f(f(A,A),f(A,A)),
inference(paramod,[status(thm)],[c_34,c_32]) ).
cnf(c_51,plain,
f(f(A,A),f(A,B)) = A,
inference(paramod,[status(thm)],[c_34,c_340]) ).
cnf(c_60,plain,
f(f(f(A,B),f(A,B)),A) = f(A,B),
inference(paramod,[status(thm)],[c_34,c_51]) ).
cnf(c_341,plain,
f(f(f(f(A,B),f(B,C)),D),f(B,f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C))))) = f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C))),
inference(paramod,[status(thm)],[c_1,c_25]) ).
cnf(c_342,plain,
f(f(f(f(A,B),f(B,C)),D),f(B,B)) = f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C))),
inference(paramod,[status(thm)],[c_1,c_341]) ).
cnf(c_69,plain,
f(f(f(f(A,B),f(B,C)),D),f(B,B)) = B,
inference(paramod,[status(thm)],[c_1,c_342]) ).
cnf(c_99,plain,
f(f(f(f(f(A,A),B),f(B,f(B,f(B,B)))),C),f(B,f(A,f(A,A)))) = B,
inference(paramod,[status(thm)],[c_38,c_15]) ).
cnf(c_102,plain,
f(f(A,B),f(B,B)) = B,
inference(paramod,[status(thm)],[c_34,c_69]) ).
cnf(c_122,plain,
f(A,f(f(B,A),f(B,A))) = f(B,A),
inference(paramod,[status(thm)],[c_102,c_34]) ).
cnf(c_343,plain,
f(f(A,f(f(B,A),f(A,A))),f(B,A)) = f(f(B,A),f(A,A)),
inference(paramod,[status(thm)],[c_102,c_60]) ).
cnf(c_344,plain,
f(f(A,A),f(B,A)) = f(f(B,A),f(A,A)),
inference(paramod,[status(thm)],[c_102,c_343]) ).
cnf(c_124,plain,
f(f(A,A),f(B,A)) = A,
inference(paramod,[status(thm)],[c_102,c_344]) ).
cnf(c_136,plain,
f(A,f(B,f(A,A))) = f(A,A),
inference(paramod,[status(thm)],[c_34,c_124]) ).
cnf(c_345,plain,
f(f(f(f(f(A,A),B),f(B,B)),C),f(B,f(A,f(A,A)))) = B,
inference(paramod,[status(thm)],[c_136,c_99]) ).
cnf(c_139,plain,
f(f(A,B),f(A,f(C,f(C,C)))) = A,
inference(paramod,[status(thm)],[c_102,c_345]) ).
cnf(c_346,plain,
f(A,A) = f(A,f(B,f(B,B))),
inference(paramod,[status(thm)],[c_139,c_25]) ).
cnf(c_171,plain,
f(A,f(B,f(B,B))) = f(A,A),
inference(copy,[status(thm)],[c_346]) ).
cnf(c_201,plain,
f(f(A,A),f(B,f(B,B))) = A,
inference(paramod,[status(thm)],[c_171,c_34]) ).
cnf(c_347,plain,
f(f(A,f(A,A)),f(f(B,f(A,f(A,A))),f(B,f(A,f(A,A))))) = f(B,B),
inference(paramod,[status(thm)],[c_171,c_122]) ).
cnf(c_208,plain,
f(f(A,f(A,A)),B) = f(B,B),
inference(paramod,[status(thm)],[c_139,c_347]) ).
cnf(c_265,plain,
f(f(f(A,f(A,A)),B),f(f(C,f(C,C)),f(C,f(C,C)))) = f(A,f(A,A)),
inference(paramod,[status(thm)],[c_208,c_139]) ).
cnf(c_313,plain,
f(A,f(f(B,f(B,B)),f(B,f(B,B)))) = f(B,f(B,B)),
inference(paramod,[status(thm)],[c_201,c_102]) ).
cnf(c_324,plain,
f(A,f(A,A)) = f(B,f(B,B)),
inference(paramod,[status(thm)],[c_313,c_265]) ).
cnf(c_325,plain,
$false,
inference(resolve,[status(thm)],[c_324,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT394-2 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 21:40:32 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 306225 was started by sandbox on n005,
% 0.08/0.36 % Fri Sep 25 21:40:32 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.95/0.54
% 0.95/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.95/0.54
% 0.95/0.54 % Proof 1 at 0.12 (+ 0.05) seconds.
% 0.95/0.54 % Length of proof is 33.
% 0.95/0.54 % Level of proof is 19.
% 0.95/0.54 % Maximum clause weight is 87.000.
% 0.95/0.54 % Given clauses 36.
% 0.95/0.54
% 0.95/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------