%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 02:36:12 PM UTC 2026
% Result : Theorem 2.31s 6.30s
% Output : Proof 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 12
% Syntax : Number of formulae : 141 ( 136 unt; 0 def)
% Number of atoms : 150 ( 149 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 22 ~; 3 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 168 ( 2 sgn 57 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/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(t5,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t22,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
fof(f1,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/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(t24,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
fof(f10,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f10_nnf,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t13,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t449,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t13,t22]) ).
cnf(t35,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t449]) ).
fof(f9,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f9_nnf,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t8,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t56,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(orient,[status(thm)],[t8]) ).
fof(f7,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f7_nnf,plain,
! [X0] : converse(converse(X0)) = X0,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X0] : converse(converse(X0)) = X0,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
converse(converse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t1,plain,
converse(converse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t20,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t58,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t56,t20]) ).
cnf(t134,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t58]) ).
fof(f5,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
fof(f5_nnf,plain,
! [X0] : composition(X0,one) = X0,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X0] : composition(X0,one) = X0,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
composition(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t0,plain,
composition(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t19,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t135,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t134,t19]) ).
cnf(t456,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t135,t20]) ).
cnf(t149,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t456]) ).
cnf(t150,plain,
one = converse(one),
inference(cp,[status(thm)],[t149,t19]) ).
cnf(t156,plain,
converse(one) = one,
inference(orient,[status(thm)],[t150]) ).
cnf(t457,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t149,t156]) ).
cnf(t166,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t457]) ).
cnf(t167,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t166]) ).
cnf(t170,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t35,t167]) ).
cnf(t459,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t170,t156]) ).
cnf(t460,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t459,t167]) ).
cnf(t194,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t460]) ).
fof(f3,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f3_nnf,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t7,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t44,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t7]) ).
cnf(t204,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t44,t194]) ).
cnf(t211,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t204]) ).
fof(f2,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f2_nnf,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t14,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t16,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t14]) ).
cnf(t23,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t16]) ).
cnf(t469,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t23,t22]) ).
cnf(t470,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t469,t44]) ).
cnf(t471,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t470,t22]) ).
cnf(t284,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t471]) ).
fof(f12,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f12_nnf,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t3,plain,
meet(X1,complement(X1)) = zero,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t64,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t285,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t284,t64]) ).
cnf(t472,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t285,t44]) ).
cnf(t304,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t472]) ).
fof(f11,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f11_nnf,plain,
! [X0] : top = join(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X0] : top = join(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
top = join(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t2,plain,
join(X1,complement(X1)) = top,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t27,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t45,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t44,t27]) ).
cnf(t452,plain,
zero = complement(top),
inference(step,[status(thm)],[t45,t64]) ).
cnf(t66,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t452]) ).
cnf(t198,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t194,t66]) ).
cnf(t461,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t198,t66]) ).
cnf(t462,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t461,t66]) ).
cnf(t205,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t462]) ).
cnf(t206,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t24,t205]) ).
cnf(t221,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t206]) ).
cnf(t306,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t221,t304]) ).
cnf(t473,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t306,t304]) ).
cnf(t308,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t473]) ).
cnf(t474,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t304,t308]) ).
cnf(t315,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t474]) ).
cnf(t332,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t315]) ).
cnf(t481,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t211,t332]) ).
cnf(t335,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t481]) ).
cnf(t360,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t335]) ).
cnf(t362,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t194,t360]) ).
cnf(t492,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t362,t360]) ).
cnf(t493,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t492,t360]) ).
cnf(t374,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t493]) ).
cnf(t376,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t24,t374]) ).
cnf(t437,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t376]) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
=> ( join(X1,X2) = X2
& join(X0,X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
=> ( join(X1,X2) = X2
& join(X0,X2) = X2 ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0,X1,X2] :
( ( join(X1,X2) != X2
| join(X0,X2) != X2 )
& join(join(X0,X1),X2) = X2 ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( ( join(sk1,sk2) != sk2
| join(sk0,sk2) != sk2 )
& join(join(sk0,sk1),sk2) = sk2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f13_nnf]) ).
cnf(c13,plain,
join(join(sk0,sk1),sk2) = sk2,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t6,plain,
join(join(sk0,sk1),sk2) = sk2,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t447,plain,
join(sk0,join(sk1,sk2)) = sk2,
inference(step,[status(thm)],[t6,t24]) ).
cnf(t448,plain,
join(sk0,join(sk2,sk1)) = sk2,
inference(step,[status(thm)],[t447,t22]) ).
cnf(t30,plain,
join(sk0,join(sk2,sk1)) = sk2,
inference(orient,[status(thm)],[t448]) ).
cnf(t440,plain,
join(sk0,join(sk2,sk1)) = join(sk0,sk2),
inference(cp,[status(thm)],[t437,t30]) ).
cnf(t499,plain,
sk2 = join(sk0,sk2),
inference(step,[status(thm)],[t440,t30]) ).
cnf(t500,plain,
sk2 = join(sk2,sk0),
inference(step,[status(thm)],[t499,t22]) ).
cnf(t444,plain,
join(sk2,sk0) = sk2,
inference(orient,[status(thm)],[t500]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(c14,plain,
( join(sk1,sk2) != sk2
| join(sk0,sk2) != sk2 ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
true != ifeq(join(sk2,sk0),sk2,ifeq(join(sk2,sk1),sk2,false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(join(sk2,sk0),sk2,ifeq(join(sk1,sk2),sk2,false,true),true),
inference(rw,[status(thm)],[g0_0,t22]) ).
cnf(g0_2,plain,
true != ifeq(join(sk0,sk2),sk2,ifeq(join(sk1,sk2),sk2,false,true),true),
inference(rw,[status(thm)],[g0_1,t22]) ).
cnf(g0_3,plain,
true != ifeq(join(sk0,sk2),sk2,ifeq(join(sk1,join(sk2,sk0)),sk2,false,true),true),
inference(rw,[status(thm)],[g0_2,t444]) ).
cnf(g0_4,plain,
true != ifeq(join(sk0,sk2),sk2,ifeq(join(sk1,join(sk0,sk2)),sk2,false,true),true),
inference(rw,[status(thm)],[g0_3,t22]) ).
cnf(g0_5,plain,
true != ifeq(join(sk0,sk2),sk2,ifeq(join(join(sk0,sk2),sk1),sk2,false,true),true),
inference(rw,[status(thm)],[g0_4,t22]) ).
cnf(g0_6,plain,
true != ifeq(join(sk2,sk0),sk2,ifeq(join(join(sk0,sk2),sk1),sk2,false,true),true),
inference(rw,[status(thm)],[g0_5,t22]) ).
cnf(g0_7,plain,
true != ifeq(join(sk2,sk0),sk2,ifeq(join(sk0,join(sk2,sk1)),sk2,false,true),true),
inference(rw,[status(thm)],[g0_6,t24]) ).
cnf(g0_8,plain,
true != ifeq(join(sk2,sk0),sk2,ifeq(join(sk0,join(sk1,sk2)),sk2,false,true),true),
inference(rw,[status(thm)],[g0_7,t22]) ).
cnf(g0_9,plain,
true != ifeq(sk2,sk2,ifeq(join(sk0,join(sk1,sk2)),sk2,false,true),true),
inference(rw,[status(thm)],[g0_8,t444]) ).
cnf(g0_10,plain,
true != ifeq(join(sk0,join(sk1,sk2)),sk2,false,true),
inference(rw,[status(thm)],[g0_9,t21]) ).
cnf(g0_11,plain,
true != ifeq(join(sk0,join(sk2,sk1)),sk2,false,true),
inference(rw,[status(thm)],[g0_10,t22]) ).
cnf(g0_12,plain,
true != ifeq(sk2,sk2,false,true),
inference(rw,[status(thm)],[g0_11,t30]) ).
cnf(g0_13,plain,
true != false,
inference(rw,[status(thm)],[g0_12,t21]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/5.38 % Computer : n009.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Thu Sep 24 07:38:04 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.31/6.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.31/6.30 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------