%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LDA007-3 : 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 : 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 0.09s 0.42s
% Output : CNFRefutation 0.09s
% 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_3,plain,
tt = f(t,t),
inference(clausify,[status(thm)],[clause_1]) ).
cnf(c_4,plain,
f(t,t) = tt,
inference(copy,[status(thm)],[c_3]) ).
fof(clause_2,axiom,
ts = f(t,s),
file('theBenchmark.p',clause_2) ).
cnf(c_5,plain,
ts = f(t,s),
inference(clausify,[status(thm)],[clause_2]) ).
cnf(c_6,plain,
f(t,s) = ts,
inference(copy,[status(thm)],[c_5]) ).
fof(clause_3,axiom,
tt_ts = f(tt,ts),
file('theBenchmark.p',clause_3) ).
cnf(c_7,plain,
tt_ts = f(tt,ts),
inference(clausify,[status(thm)],[clause_3]) ).
cnf(c_8,plain,
f(tt,ts) = tt_ts,
inference(copy,[status(thm)],[c_7]) ).
fof(clause_4,axiom,
tk = f(t,k),
file('theBenchmark.p',clause_4) ).
cnf(c_9,plain,
tk = f(t,k),
inference(clausify,[status(thm)],[clause_4]) ).
cnf(c_10,plain,
f(t,k) = tk,
inference(copy,[status(thm)],[c_9]) ).
fof(clause_5,axiom,
tsk = f(ts,k),
file('theBenchmark.p',clause_5) ).
cnf(c_11,plain,
tsk = f(ts,k),
inference(clausify,[status(thm)],[clause_5]) ).
cnf(c_12,plain,
f(ts,k) = tsk,
inference(copy,[status(thm)],[c_11]) ).
fof(prove_equation,axiom,
f(t,tsk) != f(tt_ts,tk),
file('theBenchmark.p',prove_equation) ).
cnf(c_13,plain,
f(t,tsk) != f(tt_ts,tk),
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_14,plain,
f(tt_ts,tk) != f(t,tsk),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_17,plain,
f(tt,f(t,A)) = f(t,f(t,A)),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_24,plain,
f(f(t,A),tk) = f(t,f(A,k)),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_153,plain,
f(tt,ts) = f(t,f(t,s)),
inference(paramod,[status(thm)],[c_6,c_17]) ).
cnf(c_154,plain,
tt_ts = f(t,f(t,s)),
inference(paramod,[status(thm)],[c_8,c_153]) ).
cnf(c_155,plain,
tt_ts = f(t,ts),
inference(paramod,[status(thm)],[c_6,c_154]) ).
cnf(c_46,plain,
f(t,ts) = tt_ts,
inference(copy,[status(thm)],[c_155]) ).
cnf(c_156,plain,
f(f(t,ts),tk) = f(t,tsk),
inference(paramod,[status(thm)],[c_12,c_24]) ).
cnf(c_151,plain,
f(tt_ts,tk) = f(t,tsk),
inference(paramod,[status(thm)],[c_46,c_156]) ).
cnf(c_152,plain,
$false,
inference(resolve,[status(thm)],[c_151,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA007-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 23:58:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 3144454 was started by sandbox2 on n018,
% 0.09/0.38 % Fri Sep 25 23:58:22 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.42
% 0.09/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.42
% 0.09/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.09/0.42 % Length of proof is 19.
% 0.09/0.42 % Level of proof is 5.
% 0.09/0.42 % Maximum clause weight is 13.000.
% 0.09/0.42 % Given clauses 28.
% 0.09/0.42
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------