%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT394-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /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 : Sun Sep 27 07:50:31 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 3
% Syntax : Number of formulae : 62 ( 62 unt; 0 def)
% Number of atoms : 62 ( 61 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 139 ( 32 sgn 6 !; 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(sos_001,axiom,
! [VAR_0,VAR_1] : or(VAR_0,VAR_1) = f(f(VAR_0,VAR_0),f(VAR_1,VAR_1)),
file('theBenchmark.p',sos_001) ).
cnf(c_2,plain,
or(A,B) = f(f(A,A),f(B,B)),
inference(clausify,[status(thm)],[sos_001]) ).
fof(goals,axiom,
f(x0,f(x0,x0)) != f(x1,f(x1,x1)),
file('theBenchmark.p',goals) ).
cnf(c_5,plain,
f(x0,f(x0,x0)) != f(x1,f(x1,x1)),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_6,plain,
f(x1,f(x1,x1)) != f(x0,f(x0,x0)),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_7,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_8,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_7]) ).
cnf(c_9,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_7,c_7]) ).
cnf(c_339,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_8]) ).
cnf(c_10,plain,
f(f(f(f(A,B),f(B,C)),B),f(B,B)) = B,
inference(paramod,[status(thm)],[c_1,c_339]) ).
cnf(c_11,plain,
f(f(A,A),f(A,A)) = A,
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_17,plain,
f(f(A,B),f(A,f(f(A,f(f(A,A),A)),A))) = A,
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_18,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_11,c_1]) ).
cnf(c_340,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_11,c_10]) ).
cnf(c_22,plain,
f(f(f(f(A,f(B,B)),B),f(B,B)),B) = f(B,B),
inference(paramod,[status(thm)],[c_11,c_340]) ).
cnf(c_28,plain,
f(A,f(f(A,B),f(A,B))) = f(A,B),
inference(paramod,[status(thm)],[c_17,c_7]) ).
cnf(c_341,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_17,c_8]) ).
cnf(c_342,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_17,c_341]) ).
cnf(c_343,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_17,c_342]) ).
cnf(c_344,plain,
f(A,A) = f(A,f(f(A,f(f(A,f(f(A,A),A)),A)),C)),
inference(paramod,[status(thm)],[c_17,c_343]) ).
cnf(c_29,plain,
f(A,f(f(A,f(f(A,f(f(A,A),A)),A)),B)) = f(A,A),
inference(copy,[status(thm)],[c_344]) ).
cnf(c_345,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_17,c_10]) ).
cnf(c_346,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_29,c_345]) ).
cnf(c_347,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_17,c_346]) ).
cnf(c_348,plain,
f(A,A) = f(A,f(f(A,f(f(A,A),A)),A)),
inference(paramod,[status(thm)],[c_17,c_347]) ).
cnf(c_31,plain,
f(A,f(f(A,f(f(A,A),A)),A)) = f(A,A),
inference(copy,[status(thm)],[c_348]) ).
cnf(c_35,plain,
f(A,f(f(A,A),B)) = f(A,A),
inference(paramod,[status(thm)],[c_31,c_29]) ).
cnf(c_349,plain,
f(f(A,B),f(A,f(f(A,A),A))) = A,
inference(paramod,[status(thm)],[c_35,c_17]) ).
cnf(c_37,plain,
f(f(A,B),f(A,A)) = A,
inference(paramod,[status(thm)],[c_35,c_349]) ).
cnf(c_350,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_22,c_9]) ).
cnf(c_351,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_22,c_350]) ).
cnf(c_352,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_37,c_351]) ).
cnf(c_41,plain,
f(A,f(f(A,B),f(A,f(A,A)))) = f(A,B),
inference(paramod,[status(thm)],[c_22,c_352]) ).
cnf(c_353,plain,
f(f(A,A),f(A,B)) = f(f(A,A),f(A,A)),
inference(paramod,[status(thm)],[c_37,c_35]) ).
cnf(c_54,plain,
f(f(A,A),f(A,B)) = A,
inference(paramod,[status(thm)],[c_37,c_353]) ).
cnf(c_63,plain,
f(f(f(A,B),f(A,B)),A) = f(A,B),
inference(paramod,[status(thm)],[c_37,c_54]) ).
cnf(c_354,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_28]) ).
cnf(c_355,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_354]) ).
cnf(c_72,plain,
f(f(f(f(A,B),f(B,C)),D),f(B,B)) = B,
inference(paramod,[status(thm)],[c_1,c_355]) ).
cnf(c_102,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_41,c_18]) ).
cnf(c_105,plain,
f(f(A,B),f(B,B)) = B,
inference(paramod,[status(thm)],[c_37,c_72]) ).
cnf(c_125,plain,
f(A,f(f(B,A),f(B,A))) = f(B,A),
inference(paramod,[status(thm)],[c_105,c_37]) ).
cnf(c_356,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_105,c_63]) ).
cnf(c_357,plain,
f(f(A,A),f(B,A)) = f(f(B,A),f(A,A)),
inference(paramod,[status(thm)],[c_105,c_356]) ).
cnf(c_127,plain,
f(f(A,A),f(B,A)) = A,
inference(paramod,[status(thm)],[c_105,c_357]) ).
cnf(c_139,plain,
f(A,f(B,f(A,A))) = f(A,A),
inference(paramod,[status(thm)],[c_37,c_127]) ).
cnf(c_358,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_139,c_102]) ).
cnf(c_142,plain,
f(f(A,B),f(A,f(C,f(C,C)))) = A,
inference(paramod,[status(thm)],[c_105,c_358]) ).
cnf(c_359,plain,
f(A,A) = f(A,f(B,f(B,B))),
inference(paramod,[status(thm)],[c_142,c_28]) ).
cnf(c_174,plain,
f(A,f(B,f(B,B))) = f(A,A),
inference(copy,[status(thm)],[c_359]) ).
cnf(c_360,plain,
or(A,A) = f(f(A,A),f(B,f(B,B))),
inference(paramod,[status(thm)],[c_174,c_2]) ).
cnf(c_361,plain,
f(f(A,A),f(A,A)) = f(f(A,A),f(B,f(B,B))),
inference(paramod,[status(thm)],[c_2,c_360]) ).
cnf(c_362,plain,
A = f(f(A,A),f(B,f(B,B))),
inference(paramod,[status(thm)],[c_54,c_361]) ).
cnf(c_202,plain,
f(f(A,A),f(B,f(B,B))) = A,
inference(copy,[status(thm)],[c_362]) ).
cnf(c_363,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_174,c_125]) ).
cnf(c_213,plain,
f(f(A,f(A,A)),B) = f(B,B),
inference(paramod,[status(thm)],[c_142,c_363]) ).
cnf(c_275,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_213,c_142]) ).
cnf(c_326,plain,
f(A,f(f(B,f(B,B)),f(B,f(B,B)))) = f(B,f(B,B)),
inference(paramod,[status(thm)],[c_202,c_105]) ).
cnf(c_337,plain,
f(A,f(A,A)) = f(B,f(B,B)),
inference(paramod,[status(thm)],[c_326,c_275]) ).
cnf(c_338,plain,
$false,
inference(resolve,[status(thm)],[c_337,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT394-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 21:40:06 UTC 2026
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3109682 was started by sandbox2 on n012,
% 0.13/0.36 % Fri Sep 25 21:40:06 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.47
% 0.13/0.47 % Assigning unary symbol neg kb_weight 0 and highest precedence (7).
% 0.13/0.47
% 0.13/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.47
% 0.13/0.47 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.13/0.47 % Length of proof is 34.
% 0.13/0.47 % Level of proof is 19.
% 0.13/0.47 % Maximum clause weight is 87.000.
% 0.13/0.47 % Given clauses 39.
% 0.13/0.47
% 0.13/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------