%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LDA003-1 : 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 : n002.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 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 2 sgn 5 !; 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(a2,axiom,
! [VAR_0,VAR_1] : left(VAR_0,f(VAR_0,VAR_1)),
file('theBenchmark.p',a2) ).
cnf(c_3,plain,
left(A,f(A,B)),
inference(clausify,[status(thm)],[a2]) ).
fof(clause_4,axiom,
n2 = f(n1,n1),
file('theBenchmark.p',clause_4) ).
cnf(c_5,plain,
n2 = f(n1,n1),
inference(clausify,[status(thm)],[clause_4]) ).
cnf(c_6,plain,
f(n1,n1) = n2,
inference(copy,[status(thm)],[c_5]) ).
fof(clause_5,axiom,
n3 = f(n2,n1),
file('theBenchmark.p',clause_5) ).
cnf(c_7,plain,
n3 = f(n2,n1),
inference(clausify,[status(thm)],[clause_5]) ).
fof(clause_6,axiom,
u = f(n2,n2),
file('theBenchmark.p',clause_6) ).
cnf(c_8,plain,
u = f(n2,n2),
inference(clausify,[status(thm)],[clause_6]) ).
fof(prove_equation,axiom,
~ left(n3,u),
file('theBenchmark.p',prove_equation) ).
cnf(c_9,plain,
~ left(n3,u),
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_80,plain,
~ left(f(n2,n1),u),
inference(paramod,[status(thm)],[c_7,c_9]) ).
cnf(c_10,plain,
~ left(f(n2,n1),f(n2,n2)),
inference(paramod,[status(thm)],[c_8,c_80]) ).
cnf(c_13,plain,
left(f(A,B),f(A,f(B,C))),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_78,plain,
left(f(A,n1),f(A,n2)),
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_79,plain,
$false,
inference(resolve,[status(thm)],[c_78,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n002.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 23:57:42 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.39 % Process 308226 was started by sandbox2 on n002,
% 0.10/5.39 % Fri Sep 25 23:57:42 2026
% 0.10/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.40
% 0.15/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.40
% 0.15/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/5.40 % Length of proof is 12.
% 0.15/5.40 % Level of proof is 4.
% 0.15/5.40 % Maximum clause weight is 13.000.
% 0.15/5.40 % Given clauses 22.
% 0.15/5.40
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------