%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LDA007-2 : TPTP v9.3.1. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 08:00:19 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.55s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1,axiom,
! [VAR_0,VAR_1,VAR_2] : f(VAR_0,f(VAR_1,VAR_2)) = f(f(VAR_0,VAR_1),f(VAR_0,VAR_2)),
file('theBenchmark.p',a1) ).
cnf(c_1,plain,
f(A,f(B,C)) = f(f(A,B),f(A,C)),
inference(clausify,[status(thm)],[a1]) ).
cnf(c_2,plain,
f(f(A,B),f(A,C)) = f(A,f(B,C)),
inference(copy,[status(thm)],[c_1]) ).
fof(clause_1,axiom,
tt = f(t,t),
file('theBenchmark.p',clause_1) ).
cnf(c_13,plain,
tt = f(t,t),
inference(clausify,[status(thm)],[clause_1]) ).
cnf(c_14,plain,
f(t,t) = tt,
inference(copy,[status(thm)],[c_13]) ).
fof(clause_3,axiom,
ts = f(t,s),
file('theBenchmark.p',clause_3) ).
cnf(c_17,plain,
ts = f(t,s),
inference(clausify,[status(thm)],[clause_3]) ).
cnf(c_18,plain,
f(t,s) = ts,
inference(copy,[status(thm)],[c_17]) ).
fof(clause_4,axiom,
tt_ts = f(tt,ts),
file('theBenchmark.p',clause_4) ).
cnf(c_19,plain,
tt_ts = f(tt,ts),
inference(clausify,[status(thm)],[clause_4]) ).
cnf(c_20,plain,
f(tt,ts) = tt_ts,
inference(copy,[status(thm)],[c_19]) ).
fof(clause_7,axiom,
tk = f(t,k),
file('theBenchmark.p',clause_7) ).
cnf(c_25,plain,
tk = f(t,k),
inference(clausify,[status(thm)],[clause_7]) ).
cnf(c_26,plain,
f(t,k) = tk,
inference(copy,[status(thm)],[c_25]) ).
fof(clause_9,axiom,
tsk = f(ts,k),
file('theBenchmark.p',clause_9) ).
cnf(c_29,plain,
tsk = f(ts,k),
inference(clausify,[status(thm)],[clause_9]) ).
cnf(c_30,plain,
f(ts,k) = tsk,
inference(copy,[status(thm)],[c_29]) ).
fof(prove_equation,axiom,
f(t,tsk) != f(tt_ts,tk),
file('theBenchmark.p',prove_equation) ).
cnf(c_33,plain,
f(t,tsk) != f(tt_ts,tk),
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_34,plain,
f(tt_ts,tk) != f(t,tsk),
inference(copy,[status(thm)],[c_33]) ).
cnf(c_48,plain,
f(tt,f(t,A)) = f(t,f(t,A)),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_71,plain,
f(f(t,A),tk) = f(t,f(A,k)),
inference(paramod,[status(thm)],[c_26,c_2]) ).
cnf(c_811,plain,
f(tt,ts) = f(t,f(t,s)),
inference(paramod,[status(thm)],[c_18,c_48]) ).
cnf(c_812,plain,
tt_ts = f(t,f(t,s)),
inference(paramod,[status(thm)],[c_20,c_811]) ).
cnf(c_813,plain,
tt_ts = f(t,ts),
inference(paramod,[status(thm)],[c_18,c_812]) ).
cnf(c_331,plain,
f(t,ts) = tt_ts,
inference(copy,[status(thm)],[c_813]) ).
cnf(c_814,plain,
f(f(t,ts),tk) = f(t,tsk),
inference(paramod,[status(thm)],[c_30,c_71]) ).
cnf(c_815,plain,
f(tt_ts,tk) = f(t,tsk),
inference(paramod,[status(thm)],[c_331,c_814]) ).
cnf(c_810,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_815]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LDA007-2 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n007.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Fri Sep 25 23:54:11 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 2220986 was started by sandbox on n007,
% 0.15/0.43 % Fri Sep 25 23:54:11 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.55
% 0.15/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.55
% 0.15/0.55 % Proof 1 at 0.09 (+ 0.02) seconds.
% 0.15/0.55 % Length of proof is 18.
% 0.15/0.55 % Level of proof is 4.
% 0.15/0.55 % Maximum clause weight is 13.000.
% 0.15/0.55 % Given clauses 104.
% 0.15/0.55
% 0.15/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------