%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LDA007-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 1.71s 0.69s
% Output : CNFRefutation 1.71s
% 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_12,plain,
tt = f(t,t),
inference(clausify,[status(thm)],[clause_1]) ).
cnf(c_13,plain,
f(t,t) = tt,
inference(copy,[status(thm)],[c_12]) ).
fof(clause_3,axiom,
ts = f(t,s),
file('theBenchmark.p',clause_3) ).
cnf(c_16,plain,
ts = f(t,s),
inference(clausify,[status(thm)],[clause_3]) ).
cnf(c_17,plain,
f(t,s) = ts,
inference(copy,[status(thm)],[c_16]) ).
fof(clause_4,axiom,
tt_ts = f(tt,ts),
file('theBenchmark.p',clause_4) ).
cnf(c_18,plain,
tt_ts = f(tt,ts),
inference(clausify,[status(thm)],[clause_4]) ).
cnf(c_19,plain,
f(tt,ts) = tt_ts,
inference(copy,[status(thm)],[c_18]) ).
fof(clause_7,axiom,
tk = f(t,k),
file('theBenchmark.p',clause_7) ).
cnf(c_24,plain,
tk = f(t,k),
inference(clausify,[status(thm)],[clause_7]) ).
cnf(c_25,plain,
f(t,k) = tk,
inference(copy,[status(thm)],[c_24]) ).
fof(clause_9,axiom,
tsk = f(ts,k),
file('theBenchmark.p',clause_9) ).
cnf(c_28,plain,
tsk = f(ts,k),
inference(clausify,[status(thm)],[clause_9]) ).
cnf(c_29,plain,
f(ts,k) = tsk,
inference(copy,[status(thm)],[c_28]) ).
fof(prove_equation,axiom,
f(t,tsk) != f(tt_ts,tk),
file('theBenchmark.p',prove_equation) ).
cnf(c_32,plain,
f(t,tsk) != f(tt_ts,tk),
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_33,plain,
f(tt_ts,tk) != f(t,tsk),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_58,plain,
f(tt,f(t,A)) = f(t,f(t,A)),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_81,plain,
f(f(t,A),tk) = f(t,f(A,k)),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_1290,plain,
f(tt,ts) = f(t,f(t,s)),
inference(paramod,[status(thm)],[c_17,c_58]) ).
cnf(c_1291,plain,
tt_ts = f(t,f(t,s)),
inference(paramod,[status(thm)],[c_19,c_1290]) ).
cnf(c_1292,plain,
tt_ts = f(t,ts),
inference(paramod,[status(thm)],[c_17,c_1291]) ).
cnf(c_525,plain,
f(t,ts) = tt_ts,
inference(copy,[status(thm)],[c_1292]) ).
cnf(c_1293,plain,
f(f(t,ts),tk) = f(t,tsk),
inference(paramod,[status(thm)],[c_29,c_81]) ).
cnf(c_1294,plain,
f(tt_ts,tk) = f(t,tsk),
inference(paramod,[status(thm)],[c_525,c_1293]) ).
cnf(c_1289,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_1294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA007-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 23:58:37 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3144867 was started by sandbox2 on n018,
% 0.09/0.37 % Fri Sep 25 23:58:37 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 1.71/0.69
% 1.71/0.69 % SZS status Unsatisfiable for theBenchmark
% 1.71/0.69
% 1.71/0.69 % Proof 1 at 0.20 (+ 0.07) seconds.
% 1.71/0.69 % Length of proof is 18.
% 1.71/0.69 % Level of proof is 4.
% 1.71/0.69 % Maximum clause weight is 13.000.
% 1.71/0.69 % Given clauses 185.
% 1.71/0.69
% 1.71/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------