%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL049+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 : Fri Sep 25 02:36:13 PM UTC 2026
% Result : Theorem 2.85s 0.89s
% Output : Proof 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 26 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 39 ( 0 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f1_nnf,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t11,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t22,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( join(X2,X1) = X1
& join(X0,X1) = X1 )
=> join(join(X0,X2),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( join(X2,X1) = X1
& join(X0,X1) = X1 )
=> join(join(X0,X2),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0,X1,X2] :
( join(join(X0,X2),X1) != X1
& join(X2,X1) = X1
& join(X0,X1) = X1 ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( join(join(sk0,sk2),sk1) != sk1
& join(sk2,sk1) = sk1
& join(sk0,sk1) = sk1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f13_nnf]) ).
cnf(c14,plain,
join(sk2,sk1) = sk1,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t3,plain,
join(sk2,sk1) = sk1,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t42,plain,
join(sk2,sk1) = sk1,
inference(orient,[status(thm)],[t3]) ).
fof(f0,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f0_nnf,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t6,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t20,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(c13,plain,
join(sk0,sk1) = sk1,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t2,plain,
join(sk0,sk1) = sk1,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t45,plain,
join(sk1,sk0) = sk1,
inference(step,[status(thm)],[t2,t20]) ).
cnf(t40,plain,
join(sk1,sk0) = sk1,
inference(orient,[status(thm)],[t45]) ).
cnf(c15,plain,
join(join(sk0,sk2),sk1) != sk1,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
join(join(sk0,sk2),sk1) != sk1,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
join(sk0,join(sk2,sk1)) != sk1,
inference(rw,[status(thm)],[goal_0,t22]) ).
cnf(g0_1,plain,
join(sk0,sk1) != sk1,
inference(rw,[status(thm)],[g0_0,t42]) ).
cnf(g0_2,plain,
join(sk1,sk0) != sk1,
inference(rw,[status(thm)],[g0_1,t20]) ).
cnf(g0_3,plain,
sk1 != sk1,
inference(rw,[status(thm)],[g0_2,t40]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL049+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 07:35:53 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.85/0.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.85/0.89 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------