%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LDA001-1 : 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 08:00:18 AM UTC 2026
% Result : Unsatisfiable 0.12s 5.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 15 ( 15 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 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_2,axiom,
n2 = f(n1,n1),
file('theBenchmark.p',clause_2) ).
cnf(c_3,plain,
n2 = f(n1,n1),
inference(clausify,[status(thm)],[clause_2]) ).
fof(clause_3,axiom,
n3 = f(n2,n1),
file('theBenchmark.p',clause_3) ).
cnf(c_4,plain,
n3 = f(n2,n1),
inference(clausify,[status(thm)],[clause_3]) ).
cnf(c_5,plain,
n3 = f(f(n1,n1),n1),
inference(paramod,[status(thm)],[c_3,c_4]) ).
fof(clause_4,axiom,
u = f(n2,n2),
file('theBenchmark.p',clause_4) ).
cnf(c_6,plain,
u = f(n2,n2),
inference(clausify,[status(thm)],[clause_4]) ).
cnf(c_31,plain,
u = f(f(n1,n1),n2),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_32,plain,
u = f(f(n1,n1),f(n1,n1)),
inference(paramod,[status(thm)],[c_3,c_31]) ).
cnf(c_7,plain,
u = f(n1,f(n1,n1)),
inference(paramod,[status(thm)],[c_2,c_32]) ).
fof(prove_equation,axiom,
f(f(n3,n2),u) != f(f(u,u),u),
file('theBenchmark.p',prove_equation) ).
cnf(c_8,plain,
f(f(n3,n2),u) != f(f(u,u),u),
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_33,plain,
f(f(f(f(n1,n1),n1),n2),u) != f(f(u,u),u),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_34,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),u) != f(f(u,u),u),
inference(paramod,[status(thm)],[c_3,c_33]) ).
cnf(c_35,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(n1,f(n1,n1))) != f(f(u,u),u),
inference(paramod,[status(thm)],[c_7,c_34]) ).
cnf(c_36,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(n1,f(n1,n1))) != f(f(f(n1,f(n1,n1)),u),u),
inference(paramod,[status(thm)],[c_7,c_35]) ).
cnf(c_37,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(n1,f(n1,n1))) != f(f(f(n1,f(n1,n1)),f(n1,f(n1,n1))),u),
inference(paramod,[status(thm)],[c_7,c_36]) ).
cnf(c_38,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(n1,f(n1,n1))) != f(f(n1,f(f(n1,n1),f(n1,n1))),u),
inference(paramod,[status(thm)],[c_2,c_37]) ).
cnf(c_39,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(n1,f(n1,n1))) != f(f(n1,f(n1,f(n1,n1))),u),
inference(paramod,[status(thm)],[c_2,c_38]) ).
cnf(c_40,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(n1,f(n1,n1))) != f(f(n1,f(n1,f(n1,n1))),f(n1,f(n1,n1))),
inference(paramod,[status(thm)],[c_7,c_39]) ).
cnf(c_41,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(n1,f(n1,n1))) != f(n1,f(f(n1,f(n1,n1)),f(n1,n1))),
inference(paramod,[status(thm)],[c_2,c_40]) ).
cnf(c_9,plain,
f(f(f(f(n1,n1),n1),f(n1,n1)),f(n1,f(n1,n1))) != f(n1,f(n1,f(f(n1,n1),n1))),
inference(paramod,[status(thm)],[c_2,c_41]) ).
cnf(c_11,plain,
f(f(f(A,B),C),f(A,f(B,D))) = f(f(A,B),f(C,f(A,D))),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_21,plain,
f(f(f(f(A,B),A),C),f(A,f(B,D))) = f(f(f(A,B),A),f(C,f(f(A,B),D))),
inference(paramod,[status(thm)],[c_2,c_11]) ).
cnf(c_42,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),f(f(n1,n1),n1))) != f(n1,f(n1,f(f(n1,n1),n1))),
inference(paramod,[status(thm)],[c_21,c_9]) ).
cnf(c_43,plain,
f(f(n1,n1),f(n1,f(f(n1,n1),n1))) != f(n1,f(n1,f(f(n1,n1),n1))),
inference(paramod,[status(thm)],[c_2,c_42]) ).
cnf(c_44,plain,
f(n1,f(n1,f(f(n1,n1),n1))) != f(n1,f(n1,f(f(n1,n1),n1))),
inference(paramod,[status(thm)],[c_2,c_43]) ).
cnf(c_30,plain,
$false,
inference(copy,[status(thm)],[c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.37 % Computer : n002.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Fri Sep 25 23:57:56 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.38 % Process 308618 was started by sandbox2 on n002,
% 0.12/5.38 % Fri Sep 25 23:57:56 2026
% 0.12/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/5.38
% 0.12/5.38 % From the command line: assign(max_seconds, 300).
% 0.12/5.39
% 0.12/5.39 % SZS status Unsatisfiable for theBenchmark
% 0.12/5.39
% 0.12/5.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/5.39 % Length of proof is 12.
% 0.12/5.39 % Level of proof is 4.
% 0.12/5.39 % Maximum clause weight is 27.000.
% 0.12/5.39 % Given clauses 7.
% 0.12/5.39
% 0.12/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------