%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL049+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 08:25:07 AM UTC 2026
% Result : Theorem 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 15 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('theBenchmark.p',maddux2_join_associativity) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( ( join(X2,X1) = X1
& join(X0,X1) = X1 )
=> join(join(X0,X2),X1) = X1 ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( join(X2,X1) = X1
& join(X0,X1) = X1 )
=> join(join(X0,X2),X1) = X1 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_15,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_16,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
fof(nnf_14,plain,
? [X0,X1,X2] :
( join(join(X0,X2),X1) != X1
& join(X2,X1) = X1
& join(X0,X1) = X1 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( join(join(sK0,sK2),sK1) != sK1
& join(sK2,sK1) = sK1
& join(sK0,sK1) = sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
join(sK0,sK1) = sK1,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,negated_conjecture,
join(sK2,sK1) = sK1,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_33,negated_conjecture,
join(sK1,sK2) = sK1,
inference(paramod,[status(thm)],[c_15,c_32]) ).
cnf(c_34,negated_conjecture,
join(join(sK0,sK2),sK1) != sK1,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_35,negated_conjecture,
join(sK1,join(sK0,sK2)) != sK1,
inference(paramod,[status(thm)],[c_15,c_34]) ).
cnf(c_39,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_37,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_16,c_39]) ).
cnf(c_40,negated_conjecture,
join(sK0,join(sK1,sK2)) != sK1,
inference(paramod,[status(thm)],[c_37,c_35]) ).
cnf(c_41,negated_conjecture,
join(sK0,sK1) != sK1,
inference(paramod,[status(thm)],[c_33,c_40]) ).
cnf(c_42,negated_conjecture,
sK1 != sK1,
inference(paramod,[status(thm)],[c_31,c_41]) ).
cnf(c_38,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL049+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n005.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 05:42:16 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 1336076 was started by sandbox on n005,
% 0.16/0.42 % Sat Sep 26 05:42:16 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.44
% 0.16/0.44 % SZS status Theorem for theBenchmark
% 0.16/0.44
% 0.16/0.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.44 % Length of proof is 12.
% 0.16/0.44 % Level of proof is 3.
% 0.16/0.44 % Maximum clause weight is 11.000.
% 0.16/0.44 % Given clauses 2.
% 0.16/0.44
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------